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Si (NASA-CR-170758) FEASI73ILIIY ETUC'Y CF AN N8=-25!45 OPTICALLI CCHERENT T:EL,ESCOFE AfFl y I'N SPACE Final Report, 19 May 1960 - 31 rec. 1982 (Sni"63,sonilz u Astrophysical Cbsetvatcry) Unclds 235 p HC A 1 1/ME A01 CSCL '2OF G3/74 1176C FEASIBILITY STUDY OF AN OPTICALLY COHERENT

TELESCOPE ARRAY IN SPACE

CONTRACT NAS8-33893

r Final Report and Technical Report No. 2 For the period 19 May 1980 to 31 December 1982

Dr. Wesley A, Traub Principal Investigator

February 1983

r Prepared f6r1^Z+-°`'^^^ National Aeronautics and Space Administra T Marshall Space Flight Center n MAY 1 983 Alabama 35812 RECEIVED SILFACIUR awn Smithsonian Institution Astrophysical Observatory Cambridge, Massachusetts 02138

The Smithsonian Astrophysical Observatory and the Harvard College Observatory are members of the Center for Astrophysics

,- The NASA Technical. Officer for this contract is Mr. Max Nein, Deputy Director, Advanced Systems Office, Marshall Space Flight Center, Alabama

^.. 35812.

9 a ry

C3RtGiNA1- PAW-' OF pooR QUALITY

FEASIBILITY STUDY OF AN OPTICALLY COHERENT

TELESCOPE ARRAY IN SPACE

CONTRACT, NAS8-33893

Final Report and Technical Report Flo, 2 For the period 19 May 1980 to 31 December 1982

Princiaal Investigator Associate Director for Dr. Wesley A. Traub Optical and Infrared Astronomy Smithsonian Astrophysical Observatory Dr. David W. Latham 60 Garden Street Cambridge, MA 02138 (617) 495-7406; (FTS: 830-7406)

Coinvestigators Dr. Nathaniel P. Carleton, SAO (617) 495-7405 (FTS: 830-7405) s^ Dr. Giuseppe Colombo, SAO (617)495-7261

Dr. Herbert Gursky Space Science Division Naval Research Laboratory Code 4100 Washington, DC 20375

Smithsonian Institution Astrophysical Observatory Cambridge, Massachusetts 02138 {

Director: Dr. Irwin I. Shapiro Deputy Director: Mr. John G. Gregory

. The Smithsonian Astrophysical Observatory and the Harvard College Observatory are members of the Center for Astrophysics

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ORIGINAL OF POOR QUAL!?Y Y TABLE OF CONTENTS

1. Introduction...... 0 ...... 1

2.1. Publications A. Coherent optical system of modular imaging collectors (COSMIC) telescope array: astronomical goals and preliminary image reconstruction results (Traub and Davis) ...... Al B. Conceptual design of a coherent system of modular imaging collectors (COSMIC) (Nein and Davis) ...... Bl C. Concepts for large interferometers in space (Morgan, Nein, Davis, Hamilton, Roberts, and Traub)...... Cl

2.2. Internal Working Papers D. First results from a crude image reconstruction computer prot,,~am (Traub) ...... D1 E. Computer demonstration of the initial coherent alignment of COSMIC (Traub)...... E7. F. Lab demonstration of image reconstruction (Traub) ...... Fl G. Scientific prospects with the COSMIC telescope array (ed., Traub) ...... G1 H. Notes on image reconstruction for COSMIC, Part II, pp. 60•-155 (Davis) ...... H1 I. Summary of COSMIC image reconstruction as of Oct. 15, 1982 (Davis). •...... Il J. Appendix A: Relationship to radio interferometry (Davis) ..... J1

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1. Introduction

F This report summarizes the second stage of work done at the Smithsonian Astrophysical Observatory on a feasibility study of a coherent optical system of modular imaging collectors, or COSMIC. This report; is also submitted as the Final Report, Considerable progress was wade since the submission of Technical Report #1 in November 1981, We believe that the work done to date will form a solid base on which to build for subsequent progress,

The 3 publications that appeared during this period are reprinted in sections A, B, and C. Supportive details as well as developments on a number of as-yet unpublished topics are included directly as 7 internal working papers. One of these, the notes by W. F. Davis, is a continuation of the series which appeared in the preceding Technical Report No. 1. These latter notes contain suggestions for a number of image reconstruction techniques which should be tested in future programs.

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Coherent optical system of modular imaging collectors , (COS MIC) telescope array: .n, astronomical goals and preliminary image reconstruction results Wesley A. Taub, Warren F. Davis Harvard-Smithsonian Center for Astrophysics 60 Gordon Street, Cambridge, Met,ieschusetts 02138

Abstract

We are developing numerical methods of image reconstruction which can be used to produce very high angular resolution images at optical wavelengths of astronomical objects from an orbiting array of telescopes. The engineering design concept for COSMIC (coherent optical system of nodular imaging collectors) is currently being developed at Marshall S.F.C., and includes four to six telescope modules arranged in a linear array. Each telescope has a 1.8 meter aperture, and the total length of the array is about 14 meters. This configuration, when controlled to fractional wavelength tolerances, will yield a diffraction pattern with an elongated central lobe about 4 milli-arc-sec wide and 34 milli-arc- sec long, at a wavelength of 0.3 microns, and correspondingly larger at longer wavelengths. The goal of image reconstruction is to combine many images taken at various aspect angles in such a way as to reconstruct the field of view with 4 milli-arc-sec angular resolution in all directions. We are developing a Fourier transform method for extracting from each individual image the maximum amount of information, and then combining these results in an appropriately weighted fashion to yield an optimum estimate of the original scene. The mathematical model is discussed, and the results of preliminary numerical simulations of data are presented. Introduction We have recently developed a method of image reconstruction which makes efficient use of the individual images received by an orbiting linear array of telescopes, and allows the reconstruction of a conventional image of the scene which is equivalent to that which would be recorded by a large circular apejtt2re3 of diameter equal to the longest dimension of the linear array. Our previous papers on the concept of a coherent, linear array of telescopes in space alluded to the likelihood that such a reconstruction scheme should be possible, but at that time we were not able to suggest an appropriate procedure, Now, however, we are able to present: first, an optimized algorithm for image combination; second, a suggestion of the direction in which we are currently moving to develop &.n optimum noise filtering technique; and third, a series of numerical examples of image reconstruction using hueristic .noise filters which demonstrate the effects of noise and optical imperfections, and also demonstrate the initial coherent alignment procedure. 1 i Astronomical goals The preceding paper in this volume 4 discusses a first-stage COSMIC with an effective length of about 14 m, and a second-stage of about 35 m, corresponding to angular resolution limits at 0.3 micron of about 4 and 1.6 milli-arc-sec, respectively. This unprecedented capability means that we will be exploring a new domain, so our scientific expectations must necessarily be relatively general and open-ended. However, by analogy with the spectacular results from the VLA and VLBI radio instruments as well as the x-ray images from Einstein, we should anticipate a dramatic increase in our ability to understand the visible universe. COSMIC in fact should have an angular resolution in the optical region which will match VLA and VLBI images. A sampling of projects which have recommended themselves on the basis of a simple extrapolation from present knowledge includes the following: investigate the nature of ° the diffuse emission seen around certain quasars, to see if it represents an underlying galaxy, and if so, what type; probe the structure of the region surrounding the nuclei of Seyfert galaxies, down to the equivalent of about a light-year in size, i.e. the scale on which broad-line spectral variations are seen; study the nuclei of ordinary galaxies with suspected massive black hole centers to see if the gravitational potential is truly point-like; make detailed comparisons of the several ima g es produced by a k gravitational lens, to probe more fully the gravity field of the lens; examine the as-yet E unresolvable central regions of globular clusters for Evidence of mass distributions indicative of either black holes or simply self-gravitation; image the actual motion and excitation of material around-a recent nova; measure diameters, limb and polar darkening, f, and spots of nearby stars; directly image reflected light from circumstellar shells or discs; image stellar surfaces in very narrow spectral bands, as is done for hydrogen or ' calcium on the sun; directly image nearby asteroids to measure rotation and search for

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companions; resolve cometary nuclei and follow the evolution of the coma and jet-like activity; search for Jupiter-like planets around nearby stars by detecting position variations using localized astrometric techniques. Telescope concept The basic idea of the rotating linear array is indicated schematically in Figure 1 where we see a plan view of 7 telescope primaries with a beam-combiner telescope (BCT) at one end. To fit into the Shuttle bay, the length of the collecting area is limited to about 14 m. Although it is, of course, extremely desirable to have available all 7 mirrors, in principle one can still achieve the same resolution if a minimum redundency array is used, i.e., only mirrors 1, 2, 5, and 7; the discussion in this paper is applicable in either case. As the array rotates about the line of sight, it sweeps out an area of diameter Dl , as shown. We will show in the following sections that the final image, which can be reconstructed while the array is rotating through 180 0 and simultaneously recording instantaneous images, is equivalent in angular resolution to that obtained with a single large mirror D The power of the array is further increased by adding a second colinear stage, and poshbly two perpendicular stages, as indicated by t,e dotted elements and the final equivalent diameter D2. i L_J

^E] C] 73 I ] Cf C] 0; 8CT rL_J L_J-

1 Dp

Figure 1. Linear array of 7 telescopes, plus beam combiner telescope. Motivation The image produced by a linear coherent array will exhibit non-uniform resolution as a function of direction in the image plane. Specifically, the diffraction-limited resolution in the direction colinear with the array will exceed that normal to the array in the same ratio as the aperture aspect ratio L/W. If the array width is decreased to zero, resolution in the normal direction will also become zero (normal diffraction limit becomes infinite). The situation is analogous to the CAT scan in medical imaging in which the ability to resolve along the beam path is zero. in the latter technique views are taken from a number of directions around the subject and the results combined in such a way that the favorable resolution capability across the beam path is exhibited in all directions i in the final image. This suggests that a similar echnxque might be possible in the case of the linear coherent array. The array would be rotated slowly about the optical axis and the intermediate images combiner3 in such a way that the more favorable colinear resolution would obtain in all directions in the image, , plane. i In fact such a technique is possible as we will sh,^w. An important distinction is that, due to the finite array or aperture width, the normal resolution of the coherent array is not zero as it is along the CAT beam path. Consequently, the appropriate reconstruction algorithm differs somewhat from the SCAT but, not surprisingly, goes over to the CAT algorithm in the limit as the aperture width goes to zero. This will be ^. demonstrated. The image reconstruction algorithm appropriate to the rotating linear coherent array is, then, a generalization of the CAT algorithm familiar from medical applicationspp . As is th! clise in CAT analysis,y Fourier techniquesq yield an exact

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reconstruction algorithm and provide a deep insight into the nature of the process, Fourier techniques are used in the derivation which follows. Concepts The starting point of the derivation of the reconstruction algorithm is the integral representation of the effect of the telescope aperture on the incident wave field. See Figure 2.

ey ex f Figure 2. Diffraction by an aperture a(x,z). k and V are the incident and outgoing wave vectors. k = kxev + kyey + kzee^:

k Iki = w1c = 27T/X The aperture a(x,z) which is, in general, a complex f gnr4tion is assumes x,z-plane. To simplify the notation, vectors confined to the x , z-plans by a subscript zero. Thus, for example,

a(X,Z) = affo)

To = Xex + Zez

we assume that u (k) represelts the amplitude of the incoming E-field a direction. By formally representing the outgoing field as a superposi- (Fraunhofer diffract: n), we are led to the result that5

k I(kp) .^» 0dkxdkx I u( )I2 IAL(kx-kx),(kz-k=)

where !; ( k^) is the time- averaged intensity of the outgoing component in and A ( k) is the Fouri^sr transform of the aperture defined by r _ a-&-ft A(k) -(jp) f d2ro a(ro)

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in words, (3) says that the outgoing intensity distribution is given by the convolution of the squared magnitude of the Fourier transform of the aperture with the incoming ,•.., ^ ,,,. ,.,•. ,. intensity function. .•...... , ,. —

Consider now the Fourier transform of the intensity I(k). z, acv.1" 9(v) = L" f +adkxdkz I(k) a ► (5) v vxex + vie.

We find from evaluation of (5) using ( 3) that

where a z,^*^ dkX U(v) - f. J_. dk: lu(k)^2 (7)

a z,rix^ .^4(v) = ff dk.dk. JA(k)12 (e)

Result (6) is just the familiar Borel convolution theorem applied to,(3). UM given by (7) is the Fourier transform of the incoming intensity function. ,!(v) given by (8) can be related to the aperture function by substituting (4) into (8) and evaluating to get o .^1(V) =f'f' a(2^rro) a'[2zr(ro+V)] (9)

= fdr'o a*(2,rrr0) a[21r(r0-V)]

Result (9) is the generalized autocorrelation of the aperture function and represents a second application of Borel's convolution theorem to the product A(k)A*(k). The resalts derived so far state that the Fourier transform of the image intensity is equal to the product of the Fourier transform of the incoming, unmodified intensity distribution and the generalized aperture autocorrelation function in suitable coordinates. It is useful to think of the aperture autocorrelation as providing a "window" onto the true ( unmodified by the instrument aperture) image Fourier plane. As the aperture rotates, eo does the aperture autocorrelation. At each orientation only a portion of the Fourier plane can be "seen" through the window. By piecing together glimpses of the Fourier plane provided by a set if distinct aperture orientations, a measure of U(v) can be built up over a region corresponding to the union of the areas covered by the individual autocorrelations. From ( 9) it is seen that

so that after one-half revolution of the aperture it is possible to map out a circular region of the v-plane whose radius L/2n is given by the largest value of ;VJ for which d(v) is non-zero. Depending on the geometry, there may be annular regions within this ' radius which can not be mapped because d(v) = 0 there. ' Such a circular region corresponds to the autocorrelation of a circular aperture of _ diameter L. In this way we see the possibility of synthesizing from the rotating linear aperture of length L an image equivalent in resolution to that obtainable from a full circular aperture of diameter L. In particular, the resolution in all directions in the synthesized image plane will be equivalent to that attainable from the greatest dimensio across the aperture, L.

SHE Vol. 332 Advanced Technology Dprieal Telescopes (1982) .k 4 ORIGINAL PAGV' @° OF yPOQR QUALITY .• Relationship to CAT algorithm

f^ imagine now that the aperture width •W ,isreduced , to zero. o in ^^this case , the aperture autocorrelation too reduces to a line of width zero, and length L /it. The corresponding image resolution normal to the array also goes to zero.. For each angular orientation of the aperture, the autocorrelation "window" permits determination of the image Fourier transform only along a line through the origin of v-space at the orientation angle. This process matches precisely the Fourier description of the computer-assisted tomography (CAT) algorithm in which the one-dimensional Fourier transforms of the individual 6 ray projection functions are mapped onto U-space at angles equal to the projection angles. The inverse transform yields the reconstructed image. Just as the instantaneous image resolution of the telescope is zero normal to the aperture, so too is the resolution of the CAT scanner along the beam and, hence, normal to the projection. Thus our present algorithm contains the CAT algorithm as a special case.

i mage combination Each orientation of the aperture "exposes" part of U(v) in the Fourier domain, weighted by the aperture autocorrelation according to (6). A given point in the v-plane may be exposed, with a different weight, by each of several aperture orientations. The question is how to combine optimally the information about the value of U( g ) implicit in each exposure. In particular, a real instrument will produce images contaminated by noise F: so that the true value of U(v) can only be estimated. Let us assume that a set of images, N in number, has been formed corresponding to various aperture orientations. We use a subscript to denote a specific member of the set. r Let us also assume that signal-independent noise has been added to the spatial domain t images. Because of the linearity of the transform, the noise will be additive also in the Fourier domain. Thus, we write for the measured signal at a specific point v in the n-th image transform,

1 { yn = W n "L En (11)

f where en represents the noise. Explicit reference to v has been dropped to ease the a e notation. ' iet us assume that the e n are statistically independent, have zero mean, and variance °en }! R fc = avg(cn) = 0 (12a) '( ) Ekn^ w = 0 (nom) ( 12b)

2 /n = 12)c{ c=va1'(En) Q ^i: l m ) (

In this formulation the variance of the noise at a given v is a function. (if the image] member index. 'ibis might be the case, for-example, if unequal times are spent observing at the various aperture orientations. To estimate U let us form a weighted sum of the measurements yn over • the set of images. f i! gnyn = Ug n^ n +gnL F h (13) owl a^i ^}

' where gn are weights to be determined. The Estimated value of U is, from ( 13), .i n ^^vv {14) °J U = gnYn ^LBrrd n = U + BnEn gn n E awl n^1 awl famt

where U is defined only where /( v) ¢ 0. If the noise goes to zero, the estimate U goes 3) over to the true value U.

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The proper value for the weights gn is found by demanding that the variance of U - U be minimum. . .. .^•. . m. .. a . ra• a',. ... r, ., . •y-P 7M , ;1M ,.t ,r ►7 r•n...,,^.. ••

A straightforward calculation leads to the conclusion that • Z n 'i11 ^n ^J^.^ (16)

so that ]^ [ _ L fin, n ^ = U f t L 2 t [ --=n (17) 0-1 gA -1 a •-1 til114-1 cren

It is easy to show that the variance of 0 about the true value U will be

^aZ —t2; o (1e) EAU Lam,C^^-' The aperture autocorrelation a n can be determined from the geometry or, using (6), from a test image with good signal-to-noise ratio whose transform U(v) is known. Assuming white noise, the variance a 2 is probably best estimated by considering those parts of the n-th v-plane which are n$t "exposed" by the autocorrelation window. There, i.n the absence of noise, the image transform should be zero. Any non-zero contribution can be assumed to be due to noise or other image contaminant. In this way, using (16), the weights which minimize the variance of the estimate of U (17) can be determined. Equation (17) represents the optimum combination, in the sense of minimum variance of U, of information from the Fourier transforms of the individual images formed with the aperture at different orientations. Discounting the need to deal with the effects of noise, the desired spatial image is, by (7), the inverse Fourier transform of (17). Equation (16) shows that in general the variance of the estimate of U will not be constant over the v-plane. In particular, the variance will increase in those regions in whicn the magnitude of the aperture autocorrelation decreases. Thus, the noise associated with the weighted combination of the individual image transforms will be non-stationary over v. Equation (14) expresses the estimate of U which is to be optimized in the weighted combination of images. Direct implementation of (14), or (17), in a practical image reconstruction application would suffer from the effective amplification of noise, attributable to the second term, in regions where the magnitude of the aperture autocorrelation is small. We have already described this effect in terms of the non- stationarity of the noise in the v-plane. To recover satisfactory images in the presence of noise, a filtering operation, to be discussed in the next section, must generally follow the image-combining step. Image combination according to the criterion of least variance of U and the subsequent filtering operation are separate and distinct steps in the overall processing. Noise filterin

A frequently applied method for dealing with noise is Wiener filtering 7 ' 8 in this tecnnique the noisy function is filtered (weighted) by another function which is inversely proportional to the noise variance. To be effective it is important that regions in which most of the signal information is contained do not coincide with regions in which the noise variance is greatest. The noisy function is, thereby, attenuated most where the + noise is greatest, and least where the signal is greatest. r In the case at hand the variance of the noise associated with the estimate of U may be -^ greatest, due to the geometry of the aperture, in regions where U is also most significant. Intuitively, it is undesirable to apply a filtering function which simply attenuates i (biases downward) the estimate of U in such regions. Rather, it would be preferable to adopt a strategy which utilizes information from adjacent areas where the noise variance is less, as well as averaging within the relatively noisy areas, to provide a filtered T estimate of U which is everywhere unbiased.

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We are currently investigating a technique, which irmy k;* described as weighted multiple regression, which yields such an unbiased filtered estirAte. The results of this work ..... " ekA . 1k?I two- , , V n..o4. . 4 will be presented-elaewhere.. ..., ,.....,..,..4a r... ,',. ..*.. ;w 0. Resolution The limiting resolution, in the absence of noise, inherent in the image combination scheme described above is twice that of an aperture of comparable dimensions according to the usual laws of passive optics. That is, without Fourier-domain processing, This is most easily seen by considering a one-dimensional example. Assume that a point source is observed in the absence of noise. The magnitude of its Fourier transform U(v) will be constant over S. Let the cftArture be unity over a span of length h # and zero elsewhere. The one-dimensional aperture autocorrelation will be a "tent" function centered on v - 0 which spans an interval L/n.

-L/x. o +L/.I. r

Figure 3.ja) Image transform .tO for a point source. ( b) Effective point-source image transform frow eqn. (17) with no noise.

Since the transform of the source is a constant, the ;image transform (6) given by the product with the aperture autocorrelation will also have the form of a "tent" function in v of width L/n. The inverse Fourier transform of this tent is, within a scale factor, sin(kL 2)^^- L[LL kL 2 which has its first zeros at k ° f2n/L (19)

For small angles 0 the normal component of k is (2rr/a)e so that ( 19) is equivalent to 8 = th/L (20)

which is the result familiar from elementary optics.

i Result ( 17), which divides -out the magnitudeof the autocorrelation, recovers the underlying uniform source transform in the interval -L/2n < v < + L/2n. The inverse 'i transform of the resulting pedestal of width L / n is, within a scale factor, .f L sin W1 (21) J which has its first zeros at

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E; k =. in/L -- 6, tX12L . ., .. ... (22) Thus the zesolltion of gnu proposed image combination scheme is, in the absence of noise, twice that expected from elementary optics. In the presence of noise resolution will I necessarily be degraded ,from this ideal because of the requirement to suppress noise amplification in regions whore the aperture autocorrelation is small.

4 Sampling The results derived so far have been in terms of integral representations. Digital implementation recessarily involves manipulation of sampled functions. The relevant expressions can be converted to discrete sununatio .is amenable to computer processing by introducing a series of Dirac delta functions under the integral signs.

(23) `•6(x-znX) 4► 2n'N[2'Tr(v-n1X)]

Ill relation ( 23), which is applicable to one dimension, — indicates that the two sides are Fourier transform pairs. x and v represent the two domains] X, the sampling interval in the x-domain, is a constant to be determined, 1/X is the corresponding sampling interval in the v-domain. r Sampling of the aperture at intervals X will, by (9), cause the aperture autocorrelation, and hence .f(v), to be sampled at intervals X/2n in v. From the convolution theorem and (23) the corresponding image domain representation will be given by the convolution of the continuous reconstructed image with a series of Dirac delta functions at intervals 2n/X. That is, the continuous image will be replicated at intervals 27r /X in f, Suppose that the field of view (FOV) is ko . Suppose also that we demand that the point-source image response given by (21) be attenuated by a factor a at the point at which such a source at the lower (upper) FOV edge enters the upper (lower) FOV edge due 1 to the sampling -induced image replication. That is, wa require from ( 21) that the separation of the upper and lower edges of the FOv in the replicated images be K k ? cx/L

Allowing also for the FOV k , the image domain periodicity must be at least k o + a/L. Therefore, the required aperture sampling interval is

(24) — k X ko+ a L 80 +Xa 27TL

where 9 0 is the FOV in radians. The reconstruction simulations which follow employ discrete Fourier techniques (FFTs) with sampling intervals over the aperture lased on the above considerations. Numerical imaqe reconstruction: examples We imaginetthe detector ( CCD or equivalent) to be fixed in inertial space, while the ` telescope array is rotated, so the center of each star image will not move with respect to the detector, but the diffraction pattern will rotate about each bright point source. To display the various stages in a calculation, we will first discuss what happens when a conventional circular telescope aperture . is used to image a point source. In tha following figures we will display the apertures, functions, or images as points on a 64 by 64 grid, with contour levels at either 5 or 9 equispaced intervals between the maximum and minimum values. Above each contour diagram there is a plot displaying a slice through the same data, from left to right; the slice is positioned to include the peak data point.

C..:.i In Figure 4a we show a single large telescope mirror which i s circular to within the i discrete limits of our grid, and has unity transmission and no phase delay within this k. circle. The mirror diameter is 31 units. From eqn. ( 8) we find the autocorrelation of ^t the aperture, /(v), as a function of spacial frequency v across the detector, and E ^ display this in Fiqure 4b. The corresponding conventional, diffraction - limited image I(k) is obtained from the real part of the inverse transform of eqn. 5, and is shown in

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1 f (t'"+^1;+"nazi' 3 1

. .b...._.^._._.^., Figure 4.(a) Telescope aperture a(x,z), dim i9 ter w 31 units. (b) Autocorrelation of :,^erture t("v). (c) Image of point source T(k). Figure 4c for the case of a single, point-like star centered in the FOV. For contrast, We show in Figure 5 the same sequence for a mirror with diameter 7 units; as expected, the smaller mirror samples fewer of the spatial high frequencies, and therefore produces a broader star image. ,

O en 1

II Figure 5.(a) Telescope aperture a(x,z), diameter = 7 units. ( b) Autocorrelation of aperture dO ). (c) Image point source

The imaging properties of a coherent linear array of telescopes will now be sketched in a way that attempts to clarify the relationship between a circular aperture and a rotating linear aperture. This discussion also applies to rectangular single mirror segments, since it is the overall shape of the aperture, not the details of construction, that matters here. In Figure 6a we show an aperture which is 3 by 15 units; the autocorrelation of the aperture in Figure 6b extends to high frequencies in the direction parallel to the long axis of the aperture. Figure 6c shows the effect of this aperture on a star field which consists of 3 stars of equal intensity; 2 of the stars are completely unresolved with this viewing angle. In Figure 7 we show the case where the aperture has rotated by 45 degrees. From eqn. (17) we see that an appropriately weighted sum over all angles of Fourier transforms of snapshot images will yield a reconstructed image. However, as was pointed out above, eqn. (17) also tends to produce highly amplified noise, and appropriate filtering must be applied to control this effect. We have done numerical experiments with various types of filters, and have found that, although we do not yet have in hand an optimally derived filter, it isrelatively easy to generate filters which perform quite well. One such ad hoc filter we have tried is to multiply eqn. (17) by LW.12/f.d n (25)

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{ or equivalently, simply to replace Jd njl in the denominator of (17) by d 1 in All our cases we assume equal noise variance and equal exposure time at,each angle snapshot, $o the , 0 V.%. WV l..h'A. We., YY. -ko' e.. terms drop out. r4.0 K'~F44-.01

o b e

Figure 6. ( a) Linear aperture at 0 degrees, 3 b- 5 units. (b) Autocorrelation. ( c) Snapshot

c b t

Figure 7. ( a) Linear aperture at 45 degrees, 3 by 15 units. ( b) Autocorrelation. (c) Snapshot image.

(S0 11 \Y1.

'; I From left to right: Figure 8. Three point - like•: stars. Figure 9. Image reconstruction, using 16 angle views and a 3 by 15 telescope. Figure 10, Snapshot image using a 3 by 3 telescope. Figure 11. Snapshot image using a 15 unit circular aperture. For reference we show in Figure 8 the inrut star field which was used to generate Figures 6c and 7c. Ca rrying out the reconstruction for 16 angle views between 0 and 180 degrees, in the noise - free case, we find the result shown in Figure 9; note the clean separation of the wide - spaced components and the clear elongation of the c`ose-spaced stars. Fox comparison gyre show what the star field would look like if we used a small telescope with a 3 by 3 aperture (Figure 10), and a large telescope with a round aperture 15 units in diameter ( Figure 11). Note that Figure 9 is quite similar to Figure 11, but l VIE Vol. 332 Advanced Technology Optical Telescopes (1982 / 173 J j A

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with slightly stronger sidelobes. in comparing these figures, note that the diffraction FWHM of a 15 pixel circular mirror is 4.4 pixels, and the star separati wis shown are 3 e > • and 10 pixels center-to-center, • •r ea the.•close• pair-is +expected, too be Auntresa`I'vesd u +•^"+ ^" Effects of noise and misalignment To test the robustness of the algorithm to noise, we have added to each pixel in each snapshot random noise values with relative peak-to-peak levels of 0.1 and 1.0, with the results shown in Figures 12 and 13. The algorithm clearly is stable.

I .• ^ Qu o 9 • ^ ^ p'^ ^ .o s ,

From left to right: Figure 12. Image reconstruction with relative noise = oil. Figure 13. Image reconstruction with relative noise = 1.0. Figure 14. Image reconstruction with phase error = 1/4 peak-to-peak. Figure 15. Image reconstruction with phase error = 1/2 peak-to-peak.. The mirror train between the incident wavefront and the detector will undoubtedly include various types of imperfections. Here we model random small-scale piston errors distributed over the pixels which represent the mirrors, with peak-to-peak phase shifts uniformly distributed over-the range of 90 and 180 degrees (i.e. 1/4 and 1/2), in Figures n, 14 and 15, respectively. If we take 1/4 as an upper limit on the phase variation, and we have 7 Tt3, 5rrors in the optical path, the surface quality on each mirror must be roughly (1/2)/7 / times better, or 1/20, which is well within the limits of conventional optical polishing technology. We conclude the numerical results with a brief description of tip-tilt and (large scale) piston errors as applied to individual telescope primaries and their optical trains. This is essentially an exercise in initial alignment of the array, from a non-coherent to a coherent state. We start by blocking the beams from all but two of the telescopes. Taking these two to be adjacent, we will initially see two sets of star images in the focal plane. The telescopes can now be focussed to that each one produces images which are as small in diameter as is possible. If we look at a portion of this field of view, we will have a situation similar to that shown in Figure 16a, where a single star appears double because the mirrors are tilted with respect to one another. Here the wavefront tilt in each of two directions is 1/D, where D is the width of each primary, and for convenience we have scaled each mirror to be 7 by 7 units in size. Removing the tilt on one axis gives us the situation in Figure 16b, where we see significant interference developing in the overlap region. A final tip brings us to Figure 16c, perfect alignment. Intermediate tilts (not shown) demonstrate that 0.125 1/D is virtually indistinguishable from perfect alignment, and that even 0.25 1/D-is quite good; these may be taken as preliminary upper limits on tip-tilt. Monochromatic piston errors between two adjacent telescopes are illustrated in Figure 17a, where one of the two 7 by 7 unit primaries is displaced by 0.5 1 toward the star; the image bifurcation is an artifact produced by the exact cancellation of amplitudes at the position where the star should ideally have been imaged. Reducing the piston error to 0.25 1 yields Figure 17b, where one of the images grows at the expense of the other, and the peak intensity shifts toward the expected star position. Zero error simply returns us to Figure 16c. Polychromatic piston correction requires the leverage of several different wavelength'bands, and is an extension of the technique just discussed. Conclusion The preliminary results presented here have demonstrated that image reconstruction fur a rotating linear array of coherent telescopes in space is both theoretically and " practically a tractable problem. Nevertheless it is clear that there are many avenues yet

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♦ i ^ f ^ i'^ + n., .7 .,• 1, . . o' ,•.• .! .^f • ^ .. r ., + 1I+ • a i r ^ j ^^ ^ f ` tl f

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0 a b Figure 17. Snapshot images of a Figure 16. Snapshot images of , a single star, using I two adjacent 7 by 7 telescopes, with tip-tilt single star, using two adjacent 7 by + errors. ( a) Wavefront tip = X / D, tilt = X /D. 7 telescopes, with piston errors. (b) Wavefront tip = 0, tilt = X / D. (c) Wavefront ( a) Wavefront piston error = 0.5 X. tip = 0, tilt = 0. (b) Wavefron t piston error = 0.25 X. to be explored, including for example the definition of an optimum falter function, the question of limiting magnitude, the effect of signal -dependent noise, the effect of varying pointing of the spacecraft, the handling of a rotating detector instead of an inertially fixed detector, the sensitivity of the image to optical imperfections, and many other points. We are continuing active study of these problems, meanwhile also addressing the related question of maintaining optical alignment of the array. r^ As a result of these efforts, it is becoming increasingly clear that it would be extremely helpful to build in the next few years a balloon -borne version of COSMIC, perhaps at half scale. A balloon -borne COSMIC would be especially valuable because it would allow key engineering questions to be addressed at an early stage. Such an instrument would be capable of investigating a small but significant number of scientifically i' rewarding questions, much t,n the spirit of the pioneering Stratoscope flights of two decades ago. f x Acknowledgements This work was supported by NASA, through MSFC contract NAS 8-33893. We are grateful to M. Nein and his colleagues at MSFC for thekr preliminary engineering studies which have F encouraged our recent image reconstruction wo.A. We gratefully acknowledge many fruitful conversations with our collaborators H. Gursky and N. P. Carleton. References 1. Gursky, H. and Traub, W. A., "Use of coherent arrays for optical astronomy in space," in Space Optics, SPIE vol. 183, pp. 188-197, 1979. 2. Traub, W. A. and Gursky, H., "Coherent arrays for optical astronomy in space," in Otical9§ and Infrared Telescopes for the 1990 ' s, vol. I, ed. A. Hewitt, KPNO, pp. 250-262, 0. 3. Traub, W. A. and Gursky, H., "Coherent optical arrays for space astronomy," in Active Optical Devices and Applications, SPIE vol. 228, pp. 136 - 140, 1980. 4. Nein, M ,. E. and Davis, B., "Conceptual design of coherent optical system of multiple imaging collectors ( COSMIC)", this vol., 1982. 5. Born, M. and Wolf, E., Principles of Optics, section 9 . 5.2, Pergamon Press, 1965. 6. Brooks, R. A. and Di Chiro, G., "Princ i ples of Computer Assisted Tomography (CAT) in Radiographic and Radioisotopic Imaging," Phys. Med. Biol., Vol. 21 (5), pp. 689-732, 1976. 7. Pratt, W. K., Digital Image Processing, section 15.1, John Wiley and Sons, 1978. 8. Brault, +7. W. and White, 0, R., "The Analysis and Restoration of Astronomical Data via the Fast Fourier Transform," Astron. and Astrophys., Vol. 13 ( 2), pp. 169-189, 1971.

j SPIE Vol. 332 Advanced Technology Optical Telescopes (1982) / 175 Lr

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Bi OF POOR QUALIV

Conceptual design of a coherent optical system of modular imaging collectors (COSMIC) - Max E. Noin, Billy G. Davis NASA/Marshall Space Flight Center, Alabama 35812

Abstract A concept is presented for a phase-coherent optical telescope array Which may be deployed in orbit by the Space Shuttle in the 1990°s. The system would start out as a four-element linear array with a 12 m baseline. The initial module is a minimum redundant array with a photon ocollecting area three times larger than Space Telescope and a one-dimenaioi)al resolution of better than 0.01 arc seconds in the visible range. Thermal structural requirements for the optical bench are assessed, and major subsystem concepts are identified.

Introduction A vigorous and comprehensive astronDmical program in the-1990's and beyond must provide for the increased spatial resolution and large apertures which will be required to address the questions raised but not answered by the Space Telescope. These needs derive, on the one hand, from the fact that the large cosmological distances over which light must travel reduce the number of photons available to be recorded by Space Tele- scope (ST) to fewer than 1/sec for many objects of interest. On the other hand, understanding the details of the fundamental interaction of matter and energy in the most energetic objects in the universe depends on recording the spectral characteristics of photons over small physical volumes, a fact which dictates high angular resolution for the large distances involved. Scientific investigations that will'be pursued in the 1990's and beyond will require imaging resolutions of 10 -3 arc-sec. To meet these requirements, a comprehensive program must be formulated that makes use of the Space Transportation System, the advanced technology inherent in the Space Telescope Program, and new technology as it can be foreseen and developed in order to produce a phased, cost-effective set of astrophysics payloads with a wide spectrum of capabilities. One such program which is currently being studied is a phase-coherent optical telescope array for launch on the Space Shuttle in the 1990's. The scientific goals for such an instrument and the initial results of image reconstruction analyses are discussed in a companion paper during this conference by W. A. Traub and W. F. Davis of the Harvard-Smithsonian C nter for Astrophysics.

Coherent Optical System of Modular Imaging Collectors (COSMIC) The COSMIC Program will meet the needs of increased resolution and aperture by the development of phase-coherent arrays which will be progressively combined to form a large equivalent aperture imaging complex capable of achieving 90- 3 arc-sec imaging resolution.

f The study objective for COSMIC is to investigate the feasibility of developing a modular phase-coherent array which may achieve at least an order-of-magnitude increase in capability over the Space Telescope, through a single Shuttle launch. Later addi- tions to the linear array module would then further build up the capability of the F F telescope facility. Figure 1 shows an artist's concept of COSMIC and the envisioned 4 evolutionary construction of a large cruciform array. The initial linear array contains four Afocal Interferometric Telescopes (AIT) with a Beam Combining Telescope (BCT) at one end. The COSMIC spacecraft module pivots from its launch position at the end of the BCT to its deployed position below the BCT. The solar arrays deploy from stowed positions alongside the telescope module. The scientific instruments are placed

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in the focal plane of the BCT, and sunshades are extended above the telescope apertures. Telemetry antennas will pivot into position for communicarlon and data C .j tCanRmlaalOn.

Figure 1. Initial COSMIC Module and Evolutionary Buildup

COSMIC Configuration

Optics

The key to high angular resolution is that light remains coherent over large distances. Diffraction-limited performance of an array of telescopes requires coherence i of all participating wave fronts. Such a method has been used successfully to study radio sources at high resolution (0.001 arc-sec) by using data from simultaneously observing radiotelescopes on baselines stretching over the diameter of the Earth. Theoretically, the same resolution can be achieved at optical wavelengths by devices one hundred thousand times smaller in scale. Since the spatial coherence of widely s separated beams of visible light is nearly destroyed by passing through the atmosphere, investigations of interesting faint sources of small angular size must be performed in space.

The concept of a minimum redundancy array of telescopes is borrowed from radio astronomy and has been applied by the Smithsonian Astrophysical Observatory to optical systems, as illustrated by the linear four-element array shown in Figure 2. The AIT's are iden:-ical and all feed through fold flats, which compensate for the staggered spacings, to the BCT. The four AIT's are located at positions (0, 1, 4, 6), giving the effect of simultaneously having mirror separations of 0, 1, 2, 3, 4, S, and 6 units.

It is required that the array be rotated about its target axis so that two-dimensional images can be constructed that have the full resolution of a single large mirror with a diameter equal to the lenith of the array. The requirement for maintaining all i the optical path lengths equal ti within 1/4 wavelength peak to valley is the traditional Rayleigh criterion for nfar-diffraction imagery. It is an overly simplistic criterion in this case, but it a'equately scopes the required dimensional stability at

t SPIE Vol 332 Advanced Technology Optical Telescopes /19821 / 157 .^...... : .-_°^' yew". r.« q. ^.. J+•.-.wr.,. ...-•-.+••n^r*.IDU4sMf i

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this conceptual stage. To minimize the complexity of an already beyond-the-state- r of-the-art adaptive optics control problem, the primary mirrors were restricted to a size that would retain their, figure quality passively and be packaged within the Shuttle payload bay constraints.

PRIMARY MIRROR OPTICAL JICMSKATIC OP ONE MODULE 0101 LENGTH 1.1 m THICKNESS I' M P I 1•T RADIUS Of C, • O.TO m / OUTPUT * WEIGHT E00 SIAM KP ScT OICONDARY MIRROR 1101 LENGTH • 0.101• WEIGHTTHICKNESS • E.Itm ^ Sl 0 OUTPUT SIAM 1 ,Y AP ROK,1,10 111 1GUAR9 C^ M^. •^ ► AI)- I AI AO E^ 0,7 1MUTTll EAT

i.t m ^^ISOUAR I Figure 2. Linear Four Element Array Optical Schematic and AIT Mirror Definition

The 1.8 m square mirrors selected for COSMIC are lightweight mirrors of the Space Telescope class. Figure 2 shows the AIT optical schematic and mirror definition. Active alignment of all secondary mirrors is essential, but probably will only require occasional intermittent adjustment as in the case of Space Telescope. Conversely, it is almost certain that one or more beam-steering fold mirrors and some j sort of active path length adjustment will be required in each leg. The beam from AIT 1 is directed into the BCT in a direct path. The beam from AIT 2, however, must be folded in an indirect 'manner (optical delay line) so that the total path length is the same as for AIT 1. AIT 3 and AIT 4, which are even closer to the BCT, must have proportionately longer folded paths so that all, wave fronts from the four AIT's arrive in phase at the BCT entrance aperture. The large number of reflec- tions, a minimum of seven for AIT 1, ' from entrance aperture to focus is rn inherent drawback to the COSMIC concept. At visible and infrared wavelengths where very low- loss reflective coatings are achievable, the drawback is minimal, but the uv through- put will be significantly attenuated. With about 3 sq m of collecting area per AIT for a total of 12 sq m, COSMIC has ti three times the collecting area of the Space Telescope. This, coupled with the factor iI of ten increase in angular resolution, means that COSMIC will have a faint-object- detectivity advantage over Space Telescope comparable to the advantage Space Telescope has over ground-based observatories.

Although it is an objective of this study to develop a system which can provide meaningful science with one Shuttle flight, the design concepts which wire considered are based on the eventual coupling of several linear arrays to form a cross configuration. For this reason, the beam combiner telescope was placed at the end of the linear array to accommodate additional modules (Figure 1).

Thermal Structural Concept t Two .major factors were design drivers for COSMIC: (1) The structural members and structural/thermal approach must produce an optical system with dimensional stability in all directions. In most telescopes, the structure holding the mirrors in relative alignment must be designed to focus the beam on a specified point with very little 4 deviation caused by disturbances which act on thesystem. But in COSMIC, both relative j alignment between individual telescope mirrors and between AIT's and the BCT must be maintained. Although the coherent beam combination requirement will be met by an 1 active control system, the structural/thermal design for COSMIC must still meet more 1 stringent criteria than previously designed optical systems such as Space Telescope. }

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(2) The beams from individual telescopes must be combined to form a coherent wave front to approximatey one-tenth wavelength RMS. Thus, dimensional stability of the structure and/or active path-length contrl..; must be better than 0.1 micrometer RMS. COSMIC has an overall line-of-sight aspect determination goal of 0.0005 arc -sec RMS. Figures 3 and 1 show the strpcture of COSMIC. The telescopes and instruments are mounted in or on the optical bench, which is mounted inside an aluminum structure. Since active path-length control of the optical components has been ground- ruled, the overall dimensional stability does not depend entirely on the metering structure. d A tradeoff exists between the stability of the metering structure and the range over which the active control system must compensate. However, since the structural stability has not been budgeted, the approach was to determine the best metering structure ( using Space Telescope technology. Ideally, the metering structure material should have a coefficient of thermal expan- 'sion (CTE) of zero. However, to postulate a zero CTE would not be practical. Based on results of very precise measurements of Space Telescope metering truss members, a CTE value of about 4x10-8 in/in * F was chosen for the structural members of the graphite epoxy truss.

COsmlc (Ditmom 150MeTeIC view)

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Figure 3. COSMIC Isometric View Figure 4. Exterior Shell Structure of Interior Structure

A relatively high natural frequency is desirable to have adequate separation between the structure and attitude control bandwidth during on -orbit operations. For the launch or return phase, the observatory should be designed to prevent coupling with the Shuttle's 16 Hz critical frequency. Since the truss weight increases rapidly with increasing frequencies, a lower frequency of 15 Hz was selected as a basis for the truss design. The metering structure is supported at many redundant points along the outside shell structure during launch. The redundant attach points are subsequently released for on- orbit operations so that thermal deflections are not transmitted from the outside shell to the metering structure. The mirrors are attached directly to the metering structure by flexure joints similar to the ST mirror supports. Launch loads are taken directly to the outside shell.

SP/E Vol 332 Advanced Technology Optical Telescopes (1982) / 159 r a

r ii OiRIGINAL PAM'. OF, poop QUAL", To obtain a truss structure with minimum elongation and .bore -sighting deflections resulting from temperature gradients in the metering truss, a thermally stable optical bench structure was designed to support the mirrors. The truss is thermally isolated by an outer shell covered with a Multiple Layer Insulation (MLI) having a low a /e ratio. This thermal configuration results in a temperature bias, causing energy to be continuously lost from the bench,. Thermal conditions are maintained by replacing the lost energy with energy supplied by electric heaters which are controlled by a micro- processor, This power is estimated to be 200 wat er ;. Other thermal control requirements are estimated to be approximately four times that of Space Telescope, as shown in Figure 6.

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?WERMAL CONTROL. BUDGET IWI SUN SIDE, 41 _^oF MLI

COMPONENT COSMIC U 70oF PIMA 35 175 SMA 13 SS 11 MRA 43 -2001 FPS Jos 105 1N i15 • ,12 -1000F TRUSS IMRAJ f .SS PMA - PRIMARY MIRROR ASSEMBLY DARK SIDE SMA - SECONDARYMIRRORASSEMBLY 12 MRA - METERING REFERENCE0"EMBLY TRUSS HEATER POWER- FPS - FOCALPLANESTRUCTURE POR CONTROL OF I L G L-41 M2 MLI - MULTILAYER INSULATION 4 - NEAT LOSS

Figure 6. Thermal Control Budget and ' Truss Thermal Control Approach

Application of classical beam bending equations for an unconstrained configuration led to expressions for bore sighting and elongation. Truss elongation and boresighting values as functions of temperature changes are shown in Figure 7 and 8 for various CTE values.

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Based on ST performance obtained in extensive thermal vacuum testing of the ST metering structure, COSMIC requirements for elongation control to 0.1 µm can be met with a CTE of x10- 8 in/in'F. The bore-sighting error, however, exceeds the allowable requirement by a factor of two. The results imply that the active optical correction mechanism must be capable to span this range.

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Figure 7. Influence of Bulk Temperature Figure 8. Bore-sighting Error as Change on Truss Elongation a Function of Radial Temperature Difference

Avionics The avionics subsystems consisting of the Attitude Control System (ACS), Fine Guid- ance System (FGS), Communications and Data Management System (CDMS), Electrical Power System (EPS), and the Propulsion Systems (PS) were analyzed. This paper concentrates on the Attitude Control and Fine Guidance Systems because of their role in establishing feasibility. It was assumed that COSMIC should permit viewing any source on the celestial sphere at any time, subject to constraints such as the sun, moon, and the Earth's limb viewing interference.

Since COSMIC will view a target for periods up to hours and then maneuver to another selected target, the maneuver rate should be rapid to optimize total viewin g time. In addition, COSMIC must, be rotated about its line-of-sight (LOS) to build'up a total high resolution image with the data being digitally reconstructed on the gound. While attitude-holding against environmental forces, the ACS must point the COSMIC LOS within 0.2 arc-sec of the target and be stable to 0.001 arc-sec per sec while data is being taken. These requirements are similar to those of the Space Telescope. How- ever, COSMIC uses photon-counting science detectors with continuous readout; therefore, long-term stability (slow drift) has little meaning in contrast with Space Telescope. However, in reconstructing the data on the ground, the location of the source viewed must be determined relative to the guide stars used for inertial reference to an accuracy of 0.001 arc-sec or better (0.0005 arc -sec goal).

The ACS actuators must be sized to provide control authority during all mission phases from Shuttle deployment to Shuttle revisit for repair or retrieval.

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} CDIt1 PPAGE M OF POOR QUALITY b Since COSMIC is unbalanced bath in mass distribution and surface areas, large gravity gradient, 0.46 It-lb, and aerodynamic torques, 0.17 ft-1b, will result at the operational orbit altitude of 500 km. As a minimum sizing criterion, the Reaction Wheel Assembly (RWA) or Control Moment Gyron (CMG's) must be sized to counteract the cyclic momentum and have some reserve capacity for failure modes and to prevent saturation during the peaks of each cycle. With 50 percent contingency, approximately 18 of the Space Telescope's 200 ft-1b -s RWA's would be needed. Obviously, new and larger torque devices must be provided. It appears that four single gimbal control moment gyros of an existing design (Sperry 1200) can provide sufficient control authority. To prevent the momentum exchange system from saturating, the secular momentum buildup iw continuously reacted against the Earth's magnetic field by utilizing three Space Telescope magnetic torquer bars per control axis. ' Several design approaches for the Fine Guidance system were investigated (see Figure 9). Option I was selected for COSMIC. In this approach, the FGS uses part of the field from one AIT that has its total field enlarged to obtain the required probability of guide star acquisition. Fixed solid-state detectors are positioned around the perimeter of the square field of the AI•T. Several Charge Transfer Devices (CTD's) are needed to cover the field required for a high star acquisition probability. Option 1 appears viable for the 0.001 arc-sec resolution requirement. Thermal control of the detector is critical. Currently we assume an operational temperature of -20'C.

OPTION 1: USE AIT FIELD - APPROACH; SEVERAL FIXED CTD IN FGS FIELD THE FGS FIELD - ASSESSMENT: VIABLE FOR 0.001 ARC-SEC REQUIREMENT SI FIELD

OPTION 2; TELESCOPE WITH FIXED FIELD t 4 - APPROACH: FOV FOR STAR ACQUISITION WITH FGS FIELD FIXED CTD' TO COVER THE FIELD - ASSESSMENT: VIABLE FOR 0.001 , ARC-SEC REQUIREMENT - PROBLEM OF ALIGNMENT WITH AIT FIXED CTD

OPTION 3; SCAN MECHANISMS TO COVER FIELD 'Y - APPROACH: DEDICATED TELESCOPE WITH CTD AND SCAN MECHANISMS X-- --Q MOVABLE - ASSESSMENT; OPTICAL GAIN MUST BE BETTER THAN ST FIELD VIABLE FOR 0.0005 ARC -SEC GOAL

Figure 9. Fine Guidance System Options

Adv anced Technology

Several areas for advanced technology were examined that should increase the probability that COSMIC can meet its mission objectives,'especially for the full cross configuration. The structural members for the metering structure must be designed using very low Coefficient of Thermal Expansion (CTE) materials to meet the one-tenth wavelength criterion over the long length of COSMIC. Materials, manufacturing techniques, and ways of joining members should be examined in detail.

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The :large and difficult - to-cantrol 4cosmic configuration will require new attitude 0 control actuators that have the precision of Space Telescope, but are several times larger than Space Telescope actuators. At the shorter wavelengths and for the cruciform, the expected resolution will require that the subsystems and structure be designed for the 0 . 0005 arc - sec stability goal. Improvements in sensing for the fine guidance and aspect determinatio n will require development of more accurate rates gyros and star trackers with less noise than those currently available. While devices for measuring and correcting the optical path distances from each collecting telescope to the science instruments were not addressed during this study, emphasis should be placed in this general technology area. Optical devices for correcting both the path length and focal point must be examined in more depth to determine the operational range requited. COSMIC uses photon-counting detectors on the science instruments whose output is telemetered to Earth for image reconstruction. The COSMIC subsystems selection and permissible performance ranges must be related to image quality and/or complexity of data reconstruction, currently under investigation. A greater understanding of those relationships could lead to a relaxation of spacecraft pointing and structural stability requirements.

Conclusions

Overall system concepts for COSMIC were developed, and the primary subsystems, such as thermall control, attitude control, fine guidance, communication and data management, and electrical power, were analyzed. The initial engineering work concentrated primarily on achieving a very stable optical bench structure by selectively utilizing low thermal expansion materials in conjunction with structural heaters. The design approach results in a structure which is sufficiently stable to allow fine tuning of the optical train via active beam steering devices. Although current technology should suffice in development of many of the systems, advanced technology will be required in areas where COSMIC systems exhibit specific sensitivity to technological advances, such as in the active optical path length control and alignment, and fine pointing and control of the spacecraft.

Acknowledgert'ents

We gratefully acknowledge the advice and engineering analyses provided by the members of the COSMIC Study Team at the Marshall Space Flight Center and the invaluable veview comments by the Smithsonian Astrophysical Observatory. The encouragement and support of Dr. George Newton, Manager, Advanced Programs and Technology, Office of Space Science and Applications, NASA Headquauters, is also greatly appreciated.

Bibliogr,t^ 1. Gursky, H., Traub, W. A., and Colombr., G., Proposal for a Feasibility Study of an Optically Coherent Telescope Array in :pace, Smithsonian Institution Astrophysical Observatory, Cambridge, Massachusetts, May 1979. 2. Astrophysics Long Term Program, Project Concept Summary: COSMIC, NASA, October, 1980,

3. Rosendhal, J. D., Space Astronomy to the Year 2000: A Preview of the Possibilities Society of Photo Optical Instrumentation Engineers, Proceedings, Volume 228, 1980. 4. A Conceptual Definition Study of "Coherent Optical System of Modular Imaging Collectors" ( COSMIC), Program Development Directorate, NASA/George C. Marshall Space Flight Center, Alabama, December 1981.

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Reprinted from a Round Collection of Technical Papers

AIAA 82-1851-CP Concepts for Large Interferometers in Space S.H. MORGAN, M.E. NEIN, B.G. DAVIS E. C. ' HAMILTON, D.H. ROB,ERTS and W.A. TRAU B

AIAA/SPIE/OSA TECHNOLOGY FOR SPACE ASTROPHYSICS CONFEREN The Next 30 Years , October 4-6, 1982/Danbury, Connecticut

For permission to copy or republish, contact the American Institute of Aeronautics and Astrona 1290 Avenue of the Americas, New York, N,Y, 10104 821851

CONCEPTS FOR LARfe INTERFEROMETERS IN SPACE

S. H, Morgan ORIGINAL PAQ1 IS M. E. Nein OF POOR QUALITY B. G. Davis E. C. Hamilton Program Development George 1:, Marshall Space Flight Center National Aeronautics and Space Administration Huntsville, Alabama

D. H. Roberts Brandeis University Waltham, Massachusetts

W, A. Traub Smithsonian Astrophysical Observatory Cambridge, Massachusetts

Abstract Frontier problems in astrophysics during the next 30 years will requ re angular resolution approaching 10- Very high angular resolution car p be arcaeconds in the UV/visible spectral achieved in optical and radio astronomy region. This high resolving power coupled through interferometers in space. Evolu- with large flux collectors will lead to tionary approaches and required techno- great advances in our understanding of logical advances are presenter]. In the objects within our solar system, stars, optical region a phase-coherent array galactic nuclei and other objects as well (COSMIC) starting as a four-element linear as offering new avenues to cosmological array is discussed. Combining several studies. modules results in greatly improved resolution with a goal of combining images At the longer (radio) wave^engths to obtain a single field of view with milliaresecond resolution has already been 0,004 aresecond resolution. The angular surpassed with intercontinental VLSI. resolution, detail and temporal coverage However, in most objects, there remains of radio maps obtained by ground-based spatial structure that is unresolved. For Very Long Interferometry (VLSI) can be example, virtually every active galactic greatly improved by placing one of the nucleus has angular structure that cannot stations in Earth orbit. An evolutionary be resolved, even with the best VLSI net- program leading to a large aperture VLSI work currently available (offering a observatory in space is discussed. resolution of 10- 4 aresec). VLBI measurements have reached the limits Introduction imposed by the size of the Earth. During the 1980's Space Astronomy The capaWlity to assemble large will, without doubt, make discoveries and structures in .pace and the existence of raise questions that require the use of advanced technology fQr'maintaining more powerful astronomical instruments in precise baselines and accurate pointing of order for us to understand the diverse large systems will make possible inter- astrophysical phenomena that will be ferometers in space. Two such concepts unveiled. Detailed structural studies of currently under study by the Marshall objects ranging from nearby planets and Space Flight Centex (MSFC) are the small bodies to distant quasars will be orbiting VLBI and a phase-coherent required during the final decades of this UV/visible telescope array. Each concept century and into the next. To meet these is.considered to be evolutionary in needs, large astronomical facilities with nature, progressing from simpler to more greatly improved angular resonation and complex configurations. The concepts, larger collecting areas will be placed in program approach and technological readi- space above the absorbing and distorting ness of the required systems are discussed interference of the Earth's atmosphere. in the following sections.

This paper Is declared a work of eke U.S. Govenmaeuf and tkerefon Is in Ike public domain, 78 ORIOINAII Fpier pq OF P Extending VLSI To Space OOR QUALITY 3C273 HSTM Radio interfeuometry observations of ad celeotial sources are routinely performed OVHI on Earth by using atomic frequency stand- ®ONP ards to synchronize radio telescopes that may be separated by as much as intercon - tinental distances, Angular resolution .better than a milliaresecond, four ordes of magnitude superior to that of Earth- based optical telescopes, has been achieved. By placing one or more of the observing elements in Earth orbit and making observations in concert with those ^^) H on the ground, significant advantages over purely ground-based systems may be obtained. Among these advantages are z improved angular resolution, improved coverage of the celestial sphere, more 30273 accurate radio maps, and more rapid HSTK am S mapping-(1) ov"o SHUTT Scientific Advances with S pace VLBI With orbiting VLBI we will be able to study in detail the structure of many v astrophysical objects. For example, we will be able to investigate the super- x luminal phenomenon in quasars (expansion

of different portions of quasars that Iba N apparently exceed the velocity of light), the structure of the interstellar masers Figure 1. Comparison of Synthesized Beams that are often associated with the star- from VLBI Observatories formation processo active binary systems, radio stars and other objects. Figure 2 shows the Fourier (u-v) coverage for the two cases shown in Figure The famous quasar 3C273 provides an 1. The u-v plane is normal to the vector interesting example of the dramatic to the source being studied; u and v are improvements that we will achieve with the east-West and North-South components orbiting VLBI. It has become evident that of the baseline joining a pair of highly unusual phy5icsal processes are antennas, as seen from the source. As the occurring within quasars and galactic elements of the VLBI network move in space nuclei. Very large amounts of energy are due to the Earth's rotation or the orbital being produced within compact structures. motion, the apparent baselines joining the The map resolution and quality required to stations change. When the entire set of study these compact sources surpasses the baselines from all network stations are capabilities of our current ground-based plotted in the u-v plane, the result is instruments. In particular, for a low equivalent to the synthesized telescope declination source such as 3C273, the aperture. The extent and completeness of North-South resolution is poor. This u-v coverage determines the resolution and limitation is caused by the location of quality of the radio image constructed present radio telescopes in the temperate from the data. Note from Figure 2(b) both zone of the Northern Hemisphere. the density and extent of the Fourier coverage is greatly improved by adding a Figures 1 and 2 are computer terminal in space. simulations illustrating the advantages of a VLBI terminal in space. Observations are 03 of 30273 at 18 cm. Figure 1(a) shows the Ib) synthesized beam from a conventional X ground-based network consisting of stations at Haystack (Mass.), NRAO Green Z 2 0 Bank (W.Va.), Owens Valley (Calif.) and Bonn (W. Germany). Figure 1(b) adds a space-based terminal in low-Earth orbit to a three-station ground-based network. By -0,2 0 0.2 comparing Figures 1(a) and 1(b), one notes the dramatic ,,improvement in resolution U )/UMAX) U UUMAX) obtained by adding a single space-based station. Figure 2. Comparison of Fourier Coverage from VLBI Observatories

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ORIGINAL' PAGE BLACK AND WHITE PHOTOGRAPH

A Spa VLBI Pro Cam

The Astronomy Survey Committee of the National Academy of Sciences has recommended that a space VLRi ant•tnna be launched in 1 7w Earth orbit during this .jecade. (2) To achieve a perm4nent VLBI system in space, three nature: phasee, can he identified (see Figure 3). Each phase utilizes the expected evolution in the capabilities of space syntems.

.gure 4. SO Meter Deployable Antenna

Figure 3. An Evolutionary Space VLbI antenna is desirable, an important set of Program bright sources could be observed with a space antenna as small as 5 to 10 meters An initial step would be to utilize in diameter. the capability of the Space Shuttle to demonstrate orbiting VLBI by deploying a large retrievable antenna attached to the r •- ) ~~— ~, Shuttle. This mission could be part of r--n the Large Deployable Antenna Flight Exper-- — - _ ••.•_•j Me .w NN• IY.1• iment that has been under active study by " --••-- ...... ~~...... MSFC and aerospace conr1tractors during the past several years. (3,4) This flight would provide an on-orbit test of a large ^% N1. (•.50 meter) antenna system (which also ^^^^ ^^ __ has potential applications in detense, ~ communications and Earth observations .^ i ^•''' •^ ~ `— J amon g others). An artist's concept of one possible antenna is shown in Figure 4. During the mission about three days wo.,:d ^.....I be devoted to VLBI observations. Figure 5 ...... _._._._ is a block diagram of the system with ^, ••N^• probable locations of the various """"' J •"^• " " i subsystems indicated in Figure 6. 4n alternative system now under study aL MSFC I ...... •••••• --- - is a 15 meter antenna aboard the Shuttle that cou14 later be used on the Space Platform or perhaps on an Explorer class -^ mission. Although a larger aperture Figure 5. Block uiagtam of a Space VLBI - System

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s +tea..- -^,

ORIGINAL PAGE 17 OF POOR QUALITY ORIGINAL' PAGE BLACK AND WHITE PHOTOGRAPH SUnREFLICTOR

FEEDS AND LOw— NOISE AMPLIFIERS ASTROMAST Technology Requirements 150 METER REFLECTOR 1//i The technology readiness for orbiting VLRI depends upon the availability of RECORDERS EXPERIMENT space versions of the same systems that CONTROL are used for ground observations. These major systems include antenna, receiver, frequency standards, IF to digital electronics and data handiing systems. Each of these will be discussed briefly below. 7 The mission and system parameters for the Shuttle mission are shown in Table 1.

Antennas 1' 10 '`^^'^• VC\ Two major parameters determine the antenna contribution to the signal-to- FREOUENCVST noise ratio of the received signal: RD I-FCONVERTERS FORMATTER diameter and efficiency. The first is the Figure 6. Shuttle VLRI Flight System more important of the two. The largest civilian space antenna was the 9 meter The Space Platform could be available ATS-6 reflector that was flown in 1974. by the end of this decade. A V:HI termi- During the past decade antenna technology nal aboard a Space Platform (or Space has progressed significantly, however a 50 Station) could carry out observations for meter antenna operating up to about 8 GHz extended periods using essentially the will probably require demonstration in same science package previously demon- space. strated or the Shuttle. Figure 7 illustrates the Platform concept with a 15 The antenna efficiency depends on the meter VLB1 antenna attached to one of the mesh size and surface irregularities with ports. A Platform mission woulA yield a the latter the more difficult to control. high-resolution survey of the entire sky Predicted values of the ratio of antenna and temporal studies of the most important diameter to rms surface irregularity for sources. the 50 meter Shuttle antenna is estimated to be about 2x10 4 which should allow During this time frame an alternative good performance up to about 10 GHz. or perhaps concurrent flight confivuration might be a 15 meter free flyer n the A final important consideration is Explorer class but placed at a higher the antenna pointing. It. is essential (5000 kn.) altitude. Ultimately a large that the antenna be pointed to within the aperture antenna aboard a high altitude half power beamwidth (i.e., approximately free flyer would be desirable. X /D where X is the observing wavelength and D the antenna dameter). For A - 3.6 cm Both Platform and free flyer VLRI and 7 - 50 m the pointing requirement is observations are naturally implementary about 0.04 degrees. The pointing can be to a dedicated ground-based VLBI array. A achieved using several steps. single space VLRI terminal improves both the resolution and density of u-v coverage For the Shuttle mission the following by large factors and significantly three steps could be used: increases the sky coverage available. (1) the Shuttle points the antenna to within 0.5 degrees of the celestial target. (2) An optical or RF sensor is used to drive a movable subreflector to place the target within the 3 dB beamwidth of the antenna. (3) Knowledge of pointing is recorded from the above sensor to later correct for any residual mispointing of the antenna. This knowledge will permit aosteriori corrections for amplitude loss uring mispointing.

As part of the Shuttle VLBI mission study the C. S. Draper Laboratory performed a brief study of the dynamics and control of the Shuttle attached antenna. (5) Initial finite elements simulations have indicated that the antenna structure that was considered is Orbiting VLBI quite stable during various Shuttle Conf iguration motions.

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RECEIVER SYSTEM SURFACE ACCURACY FRED, (ONO BEAM POLARIZATION BANDWIDTH NOISE TYPE TEMPERATURE ANTENNA SYSTEM X 0 1.4 GH: 1.66 SINGLE ONE SENSE - 100 MHz 1600K 30 2,3 CIRC, POL. Q 814 TO BE DETECTED FEEDPOiNT

ANT, TRACKING/ KNOWLEDGE SLEW INTEG. ELECTRICAL AXIS POINTING SUBSYS. OF POINTING RATE TIME POINTING POINTED TO WITHIN i 0,0250 t 0.01 0 30 /MIN 60 SEC IREOUIRED REQUIRE- 1/2 BEAMWIDTH OF TO TRACK SOURCE MENTS OF TARGET FOR 60 SEC WITHOUT ANTENNA ------VRCSFIRING) SYSTEM• 1.66 GHZ - 0.250 2.3 - 0,180 8.4 y- 0.060

ORBIT ALTITUDE INCLINATION POSITION KNOWLEDGE VELOCITY KNOWLEDGE REQUIRE- MENTS MINIMUM: 350 km 40° C i r; 570 i iOkm i 1 m/SEC

• ANTENNA SYSTEM POINTING INCLUDES: ORBITER, ANTENNA STRUCTURE, MOVABLE FEED/SUHREFLECTOR AND BEAM STEERING TO REACH REOUIRED ACCURACIES,

Table 1 VLSI Demonstration Exper iment Parameters

Receivers

Gallium arsenide field effect transis- The data recording equipment for a tor (GaAs FET) receivers are very suitable space mission will depend upon the data for orbiting VLSI. Through radiative storage and transmission capability of the cooling, system temperatures of 70 • K at 2 particular mission. For the Shuttle GHz and 160°K at 8 GHz are probably possi- mission one could use several cassette ble. The long cooldown time of radiative tape recorders each of which would record cooling systems rr.ay preclude their use for one 4 Mbits /s channel. The tapes would the Shuttle mission. However, Peltier then be returned to the central correlator devices may be used. Performance can be site to be combined with the recorded data considerably improved by cryogenic cool- from the ground -based radio telescopes. ing. VLSI systems aboard a platform, space Freauencv Standards station-or free flyer would periodically return data via the TDRSS system. High The local oscillator frequency altitude free flyers having long term standard must be stable over the data communication with the Deep Space Network integration periods to a small fraction of could send data directly to the ground for a cycle of RF phase. A hydrogen maser recording. flown in 1976 as part of the sub-orbital Gravity Probe-A (Redshif.t) rocket flight Summary of VLSI Technolo q v Readiness achieved a level of stabil ;^,ty of df/f 3x10 !14 This is sufficient for a 100 In general, the subsystems required second coherent integration at frequencies to support orbiting VLSI missions are as high as 22 GHz. technologically ready. Antennas as large as 50 meters appear to be technologically IF to Di q ital Electronics and Data feasible; however testing in space is Handling probably required.

The signal from the receiver is mixed The program for orbiting VLSI dis- with the local oscillator and converted to cussed in this paper is driven'by the an IF signal. It is then converted to a availability of the space systems describ - video signal and digitized (See Figure 3). ed and the continued interest in extend- The standard for ground-based observations ing the capability tcs utilize space. The is the Mark III system. The electronic technology is available. Only the oppor- modules of this system could be repackaged tunity remains for us to enter into the and qualified for-space. exciting era of space VLSI.

82 's Ok(GINAL PAGE BLACK AND WHITE PHOTOGRAPH

sp ace Based Coherent Optical ;Systempf stage COSMIC ( 14m in length) and finally Mo u ar Imaging o ectors (uOSMI^) T second stage COSMIC (35m In length). 9 At microwave wavelengths large COSMIC will be able to resolve the Y ground-based interferometers are routinely central regions of active galactic nuclei employed for high resolution astronomical to help us understand what powers these observations. However, the difficulties very bright and condensed regions. of dealing with wavelengths 5 orders of magnitude smaller than microwave have made Because such a telescope will be able this a less attractive technique for to solve outstanding astrophysical achieving similar advances with ground- problems such as these, the Astronomy based observations at UV/visible wave- Survey Committee of the National Academy lengths. In addition, ground-based of Sc.ences has recommended "the study and problems of atmospheric absorption and development of the technology rejuired to seeing fundamentally limit the possible place a very large telescope in space advances. Space will overcome these early in the next century."(2) barriers as well as providing the necessary undisturbed environment. The capabiity to construct large systems in space and the development of advanced optical control technology to maintain accurate baselines and alignment, will allow the development of an array of coherent optical telescopes - the optical analog of radio VLBI. This program, calleu COSMIC, will meet the needs of increased resolution and larger aperture through the development of phase-coherent arrays which are progressively combined to form a large equivalent aperture imaging complex. Images with angular resolution in the mil'iaresecond range can be achieved. W8) Figure S. Advances in Telescope Scientific Prospect! with COSMIC kesolutlon

There are a large number of unique The COSMIC Configuration astronomical observations which would be possible with an orbitinc telescope having Figure 9 shows an artist's concept of both a large collecting area and an COSMIC and the evolutionary construction angular resolution in the milliaresecond of a large cruciform array. The initial range. COSMIC will bye able to resolve the nucleus of many comets, to detect the splitting of a nucleus, and to study the activity of the inner core. At Jupiter, COSMIC will be able to obtain images down to 5 km resolution, comparable to some of the best images obtained by Voyager 2. Detailed studies of the large scale features of nearby main sequence stars will also be made. Correletions with VLBI measurements of the H 2O and SiO maser emissions in the atmospheres of super giant stars will be possible.

COSMIC will be unique in being able to resolve the highly condensed cores of globular clusters. As an illustration we show in Figure 8 a series of images of the globular cluster M3 as it would appear if it were removed from our own galaxy to a much more remote distance, in the galaxy M87. The first panel in Figure 1 is a long-exposure photograph of M87 which shows the many globular clusters surrounding this galaxy. The next three A^ 2 3 4 panels show respectively the appearance 1 0< X )^$ of M3 (taken from a CCD image) as it would

' D appear at the distance of M87 from the Figure 9. Coherent Optical System of Space Telescope, then from a first Modular Imaging Collectors

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!i CjjlettNA.L PAGE 19 OF POOR QUALITY f linear array contains four Afocal Inter-$ Optical Schematic of One Module ferometric Telescopes ( AIT) with a Beam Combining Telesc,Dpe (BCT) at one end. The COSMIC spacecraft module pivots from its launch position at the end of the BCT to An its deployed position below the OCT. The ^...... OI OCT solar arrays deploy from stowed positions alongside the telescope module: The scientific instruments are placed in the focal plane of the BCT, and sunshades are Iw ^O extended above the telescope apertures. All All All Alit O Telemetry antennas will pivot into posi- IV tion for communication and data transmission. Optics The concept of a minimum redundancy array of telescopes is borrowed from radio astronomy and applied to optical systems, as illustrated by the linear four-element Opti.cal Schematic of Afocal array shown in Figure 10. The AIT's ave Interferometric Telescope identical and all feed through fold flaw, which compensate for the variations in the optical path lengths to the BCT. The four AIT's are located at positions (0,1,4,6), giving the effect of simultaneously having mirror separations of 0,1,2,3,4 , 5, and 6 units. PRIMARY MIRROR MELENGTH 1,210 T"ICKIIE SE • IL 5. The instantaneous diffraction -limited IT 0 • 1.7 image of a point source is narrow along RAOIUSOfIt 11.711- NQGHT • SW KI the array ' s major axis only, but by using OUTPI SEAM an already demonstrated image reconstruc- SECONDARY MIRROR tion technique it will be easy to build up SIDE LENGTH 0. 16 In fully resolved images after a 180 degree THICKNEU Um rotation of the array, even in the pre- IMEIGNT. 416• KI sence of noise and optical imperfections. OUTPUT SEAM WROIC S.IS IA SQUARE The requirement for maintaining all the optical path lengths equal to within 1/4 wavelength peak to valley is the I.S rn traditional Rayleigh criterion for near- IEQIIAR 1 diffraction imagery. It is an overly simplistic criterion in this case, but it adequately scopes the required dimensional stability at this conceptual stage. To minimize the complexity of an adaptive Figure 10. Linear Four Element Array optics control problem that is already optical Schematic and AIT beyond-the -state -of-the-art, the primary Mirror Definition mirrors were restricted to a size that would retain their figure quality passively and be packaged within the constraints The beam from AIT 1 is directed into of the Shuttle payload bay. the BCT in a direct path. The beam from AIT 2, however, must be folded in an in- Active alignment of all secondary direct manner ( optical delay line) so that mirrors is essential, but probably will the total path length is the same as for only require occasional adjustment as in AIT 1. AIT 3 and AIT 4, which are even the case of the Space Telescope. closer to the BCT, must have proportion- Conversely, it is almost certain that one ately longer folded paths so that all wave or more beam - steering fold mirrors and an fronts from the four AIT's arrive in phase active path length adjustment will be at the BCT entrance aperture. required in each leg.

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ORIGINAL PAGE 111; OF POOR QUALITY

A collecting area of about 3m* per Structural Concept AIT gives the initial COSMIC configuration three times the collecting area of the Two major factors were design drivers Space Telescope. This, coupled with a for COSMIC: (1) The structural members and factor of six increase in angular structural/thermal approach must produce resolution, means that COSMIC will have a an optical system with dimensional stabil- faint-object-detectivity advantage over ity in all directions. In most tele- Space Telescope comparable to the scopes, the structure holding the mirrors advantage Space Telescope has over in relative alignment must be designed to ground-based observatories. focus the beam on a specified point with very little deviation caused by disturb- Image Reconstruction ances. But in COSMIC, both relative alignment between individual telescope The image produced by a linear mirrors and between AIT's and the BCT must coherent array will exhibit non-uniform be maintained. Although the coherent beam resolution as a function of direction in combination requirement will be met by an the image plane. Specifically, the active control system, the structural/ diffraction-limited resolution in the thermal design for COSMIC must still meet direction colinear with the array will more stringent criteria than previous exceed that normal to the array in the optical systems such as Space Telescope; same ratio as the aperture aspect ratio. (2) The beams from individual telescopes The image formed in the focal plane is the must be combined to form a coherent wave convolution of the aperture autocorrela- front to approximately one-tenth wave- tion function and the "ideal" sky which length rms. Thus, dimensional stability falls in the several telescopes' common of the structure coupled with active path field of view. If we consider the focal length control must be better than 0.03 plane two-dimensional detector (such an as micrometer rms. COSMIC has an overall intensified CCD) to be fixed in inertial Line-of-sight aspect determination goal of space, while the linear telescope rotates 0.0005 aresec rms. about the line of sight, then it is useful to think of the aperture autocorrelation Figures 11 and 12 illustrate the as providing a "window" onto the true structure of COSMIC. The telescopes and (unmodified by the instrument aperture) instruments are mounted in or on the opti- image Fourier plane. As the aperture cal bench, which is mounted inside an rotates, so does the aperture autocorrela- aluminum structure. tion. At each orientation only a portion of the Fourier plane can be "seen" through Since active path length control of the window. By piecing together glimpses the optical components has been assumed of the Fourier plane provided by a set of the overall dimensional stability does not distinct aperture orientations, a measure depend entirely on the metering structure. of the Fourier transform of the sky can be A tradeoff exists between the stability of built yp over a region corresponding to the metering structure and the range over the union of the areas covered by the which the active control system must individual autocorrelations. compensate. However, since the structural stability has not been budgeted, the We have begun computer simulations of apz^oach used was to determine the best the image reconstruction process and have metering structure using Space Telescope been able to investigate the effects of technology. additive noisear well as optical system imperfections. (9 Noise is strongly . Ideally, the metering structure rejected in this technique, since in the material should have a zero coefficient of Fourier-plane summing operation, we are thermal expansion (CTS). However, to able to exploit natural opportunity to postulate a zero CTE would not be suppress noise from non-information practical. Based on results of very bearing frequencies. The images are also precise measurements of Space Telescope very stable against optical imperfections metering truss members, a CTE value of up to about one-quarter wavelength, peak- about 4x10- 8 in/in'F was chosen for to-peak, Finally, no artifacts have been the structural members of the graphite found to be generated; this should not be epoxy truss. This will allow elongation at all surprising because the reconstruc- control to 0.1,pm. The boresighting error tion process is in fact very close to which exceeds the allowable requirements being a "selective addition" process by a factor of two must be corrected with wherein we simply save and then add an active optical compensation mechan- together the "good" parts of each image; ism. there is no amplification whatsoever of a weak signals, so artifacts and instabilities are completely avoided.

F m C

85 ^I OF*6Ggh AL PAG9 TV OF POOR QUALITY,

calm IC N wIC VIS r1 While attitude-holding against envi- Tr►IW ► o . 11o ►T ronmental forces, the ACS must point the COSMIC line-of-sight within 0.2 aresec of the target and be stableTto 0.001 aresec per sec while data is being taken. These requirements are less restrictive than w those of the space Telescope. Since COSMIC will use photon -counting detectors with continuous readout, long-term . stability (slow drift) has lil: tle meaning in contrast with Space Telescope. How- ever, id reconstructing the data on the ground, the location of the source viewed must be determined relative to the guide stars used for inertial reference to an accuracy of 0.001 aresec or better (0.0005 aresec goal).

Since COSMIC is unbalanced both in mass distribution and surface areas, large gravity gradient and aerodynamic torques will be present at the operational orbit Figure 11. COSMIC - Isometric View of altitude of 500 km. Approximately 18 of Intcrior Structure the Space Telescope's 200 ft-lb • s Reaction Wheels would be needed to counteract these torques.

r w Obviously, new and larger torque devices must be provided. It appears that four single gimbal control• moment gyros of an existing design can provide sufficient control authority. To prevent the momentum exchange system from saturating, the secular momentum buildup is continuously ATTACIMINI reacted against the Earth's magnetic field 1111111 by utilizing three magnetic torquer bars per cont:;ol axis. ^^• )IOOwIb IANl ►1 1 • .11 IN IA►1WIMU»I ^ ^--- vAw ►oAOloN► r Several design approaches for the 1111»AIIG YA1/011lICilor • ,I IN FGS were investigated. selected an FGS 1al»nno ur »ool lTAruAA ► relo•nNl which uses part of the field from one AIT rvAwmetcnoN^ that has its total field enlarged to .» A.IIiNau •.« INI obtain the required probability of guide +•Inw^unw star acquisition. This system is capable of meeting the 0.001 aresec resolution requirements. Figure 12. Exterior Shell Structure Summary of COSMIC Technology Readine ss The metering structure is supported at many redundant points along the outside Several areas of advanced technology shell structure during launch. The were examined that should increase the redundant attach points are subsequently probability that COSMIC can meet its released for on-orbit operations so that mission objectives, especially for the thermal deflections are not transmitted full cross configuration. The structural from the outside shell to the metering members for the metering structure must be structure. The mirrors are attached designed using very low Coefficient of directly to the metering structure by Thermal Expansion materials to meet the flexure joints similar to the Space one-tenth wavelength criterion over the Telescope mirror supports. long length of COSMIC. Materials, manufacturing techniques, and methoJs of joining members should be examined in detail. Avio nics The large COSMIC configuration will The avionics subsystems consisting of require new attitude control actuators the Attitude Control System (ACS), Fine that have the precision of Space Tele- Guidance System (FGS), Communications and scope, but are several times larger than Data Management System, Electrical Power Space Telescope actuators. At the shorter System, and the Propulsion Systems were wavelengths and for the cruciform configu- analyzed. ration the expected resolution will require that the subsystems and structure be

T 86 ORIGINAL PA?2 ; ^4 OF POUR QUALITY

designed for the 0.0005 aresec stab dity Acknowledgement goal. Improvements in sensing for the fine guidance and aspect determination The authors wish to thank Professor will require development of more accurate Bernard Burke (MIT), Dr. Frank Dordan rate gyros and star trackers with less (JPL), Dr. Robert Preston (JPL), and noise than those currently available. Lester Sackett (Draper Lab), members of a NASA-sponsored VLBI working group. The While devices for measuring and VLBI concepts discussed in this paper are correcting the optical path distances based on studies conducted by this working from each collecting telescope to the group. We would also like to thank Dr. science instruments were not addressed, Herbert Gursky (NRL), Dr. Nathaniel emphasis should be placed in this general Carleton (SAO), and Dr. Warren Davis (SAO) technology area. who have made significant contributions to the COSMIC studies. COSMIC uses photon-counting detectors on the science instruments with outputs References telemetered to Earth for image reconstruction. The COSMIC subsystems selection and 1. Shuttle VLBI Experiment: Technical permissible performance ranges must be Working Group Summary Report, NASA related to image quality and/or complexity TM-82491 (Samuel H. Morgan and D. H. of data reconstruction, currently under Roberts, eds.), NASA, G. C. Marshall Space investigation. A greater, understanding of Flight Center, July 1982. those relationships could lead to a relaxation of spacecraft pointing and 2. Field, G. et al., Astronomy and structural stability requirements. Astrophysics for the 1980's, Report by the Astronomy Survey Committee, National Conclusion Academy of Sciences, National Academy Press, Washington, DC, 1982. Results from preliminary studies of two large interferometers in space have 3. Deployable Antenna Flight Experiment been presented that would lead to major Definition Study, Final Report, Grumman advances in capabilities for astrophysics Aerospace Corp., Bethpage, NY, March during the next 30 years. 1962, At radio wavelengths the technology 4. Deployable Antenna Flight Experiment is generally available to place a VLBI Definition Study, Final Report, Harris station in Earth orbit. However, large Government Electronics Systems Division, (..+50 m) aperture deployable antennas will Melbourne, FL, March 1982. probably require demonstration in space. 5. L. L. Sackett and C. B. Kirchwey, For UV/visible spectral coverage Dynamic Interaction of the Shuttle COSMIC is a very attractive approach that On-Orbit Flight Control System with is both theoretically and practically Deployable Flexible Payloads, AIAA feasible. -Although major technology Symposium on Guidance and Control, Paper barriers have not been identified in our No. 82-1535-CP, San Diego, CA, August studies thus far, one must recognize that 1982. the development of the large systems presented here poses formidable tasks in 6. W. A. Traub and H. Gursky, "Coherent orbital aaesembly and servicing, mainten- Arrays for Optical Astronomy in Space," in ance of optical coherency, pointing and Optical and Infrared Telesco pes for the stability of the spacecraft and thermal 4990's, Vol. 1, ed. A. Hewitt, Kitt Peak control. —Na t Tonal Observatory, pp. 250-262, 1980.

For current systems the accepted 7. M. E. Nein and B. G. Davis, approach is to verify performance through "Conceptual Design of a Coherent Optical extensive ground testing. However, the System cf Modular Imaging Collectors new generation of large aperture instru- (COSMIC)," in Advanced Technology Optical ments which have structural frequencies as Telescopes, SPIE Vol. to appear in 1982. low as a few Hertz can only be adequately tested as functional systems in space. It 8. W. A. Traub, N. P. Carleton and G. is thus imperative that considerable space Colombo, Feasibility Study of an Optically demonstration work precede any commitment Coherent Telescope Array in Space, to a specific design of a long duration Technical Report No. 1, Smithsonian space system. Since the space demonstra- Institution Astrophysical Observatory, tion capability would lead the design of Cambridge, MA, November 1981. the final system by sever al years, it A would actually establish many of the 9. W. A. Traub and W. F. Davis, "The 3 technology requirementso COSMIC Telescope Array: Astronomical Goals and Preliminary Image Reconstruction Results," Advanced Technology Optical Telescopes, SPIE Vol. to appear in 1982.

87 t t ,.

k ORIGINAL ['A# I OF POOR QUALITY D,L Center for Astrophysics Harvard College Observatory Smithsonian Astrophysical Observatory

MEMORANDUM

To: Distribution December 16, 1981 ^f"^ From: W. A. Traub I'a / Subject: First results from a crude image reconstruction cbmpul",er program.

The theoretical work that Warren Davis has been e,oing during the past three months has led to a better understanding of the image reconstruction problem for COSMIC (OCTAS), and has suggested a simple computer technique which will be illustrated in this memo:, Part of the motivation for writing this computer program was to gain some experience with the practical aspects of generating an image, doing fast Fourier transforms with the array processor, and displaying the results in a meaningful way. The program also provides a simple reconstruction technique as a baseline against which more refined methods can be compared later. The name of this program, CRUDE, is intended to convey a sense of its current state of sophistication. In fact, only a very few of the theoretical constructs which appear in Davis' notes on this subject have been used in the current computer program; many as yet untouched areas must be explored before we can claim to be able to extract the full amount of information from the individual images produced by a linear array of coherent telescopes.

Consider a single image of a small region of the sky as formed by an ideal, diffraction-limited telescope having an aperture which is essentially a long, narrow slit. The diffraction pattern in the focal plane which corresponds to a point source in the sky will also be elongated, but at a right angle to the aperture slit. This image clearly contains the maximum available amount of high-resolution information ii, one spatial direction, but little information in the orthogonal direction. W6 can demonstrate this by taking the two-dimensional Fourier transform of the image: we will find many more Fourier coefficients going out in the high-resolution direction than we will in the low-resolution direction. Suppose we save these coefficients.

Now we imagine the detector to be fixed in inertial space, while the telescope array is rotated, so the center of each star image will { not move with respect to the detector, but the diffraction pattern will rotate about each bright point source. An image with such a rotated aperture will have high-resolution information in a different direction, so Fourier-transforming the new image and combining this result with the original will start to fill in the frequency plane. Clearly some low-frequency points will, be represented in both views and they will be disproportionally represented unless we allow for this multiple counting, a weight function of some sort can easily be used which essentially will keep track of the degree to which each frequency point has been sampled by the various rotated slit apertures. After all views have been added, this weight can be used to normalize each frequency

# ORIGINAL CLAM ig 2 , OF POOR QUALITY

point. The inverse Fourier transform will then be a representation of the star field which contains essentially all measured high-spatial- frequency components in all directions. This reconstructed star field should be essentially the same as could have been obtained with a single large mirror having a diameter equal to the length of the slit-aperture telescope, and this is indeed true, as we shall show below. 1. Conventional telescope apertures. To illustrate these concepts and to show how program CRUDE can be used to display the various stages in a calculation, we will first discuss what happens when a conventional circular telescope aperture is used to image a point source. In the following figures we will display various 2-dimensional objects, functions, or images as points on a 64 by 64 grid, with contour levels drawn at either 9 intervals (ie, 10, 20, ..., 90 percent) or at 5 intervals (ie, 16, 33, 50, 67, 83 percent). Above each contour diagram there is plot displaying a slice through the same data, from left to right; the slice is positioned to include the peak data point. In Fig. la we show a single large telescope mirror which is circular to within the discrete limits of our grid, and has unity transmission within this circle. The mirror diameter is 31 units.

For photons of a given wavelength, the diffraction pattern of a telescope is conveniently given by the Fourier transform of the autocorrelation of the aperture transmission, as described in Davis' notes (eqn. 26). The autocorrelation can be calculated either by stepping the aperture across itself and multiplying a total of 64 x 64 times, or more conveniently by calculating the Fourier transform, taking the square magnitude, and again Fourier transforming (eqns. 24 and 25). Using the latter technique, we calculate the autocorrelation shown in Fig. lb, where the lower left-hand corner point is the origin, ie., the point which corresponds to zero relative displacement.between the multiplied apertures. This figure and all others are periodic modulo 64 points, so the plane should be considered to be tiled with such figures, making it clear that the four filled corners of Fig. lb can be looked upon as offset segments of circles centered on the origin. The total extent of these circles is just one point less than twice the telescope diameter, as expected (Davis' eqn. 197). Again, viewing Fig. lb as the Fourier transform of the diffraction pattern of the aperture, we see that the origin corresponds to the zero-frequency or DC point, and that higher spatial frequencies correspond to points farther from the origin. Those points beyond 64/2 , 32 points in either direction are aliased, and the values in these 3 quadrants should be considered to be translated to the left by 64 points so as to surround the origin.

--d The image of a single point-like star, as seen by the telescope in Fig. la, is shown in Fig. lc. This image was calculated by first setting up a single (1 pixel) star, then calculating the Fourier transform-of the star (in this case a complex vector with unity .aagnitude everywhere in the frequency plane), multiplying by Fig. lb, inverse Fourier transforming, and displaying the real part as seen in Fig. lc. k, 2t t

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Continuing the illustration, we show in Figs. 2 and 3 the corresponding apertures, autocorrelations, and star images from circular t rrors with diameters of 15 and 7 pixels respectively. As expected, smaller mirrors sample fewer of the spatial high frequencies, and therefore produce broader star images.

With these three images before us, it is of interest to attach an absolute scale to the figures and make A comparison with standard measures of resolution. Interpolating between the discrete data points shown in the upper parts of Figs, lc, 2c and 3c, we find values for the full-width at half-maximum (FWHM) of 2.18, 4.43, and 9.67 pixels, respectively. Referring to Davis' eqn. 172, we find that the field-of view, ie. the width of Fig:. lc, 2c, or 3c, is given by ^/AX where X is the wavelength and Ax is the sample interval across the mirror, ie. the pixel size in Fig. la, 2a, or 3a. If we choose a visible wavelength ^ = 0.5 micron, and a telescope scale factor of AX = 1 meter per pixel, we find a field-of-view of 0.103 arc-sec, which for 64 pixels gives a scale factor of 1.61 milli-arc-sec per pixel. The mirrors in Figs la, 2a, and 3a are then 31, 15, and 7 meters in diameter, and the stars have FWHM = 3.5, 7.1, and 15.6 milli-arc-sec, respectively.

To compare this with the classical equation for the intensity distribution given by [2 J 1 (z) I , where z is a distance scaled by na/D and D is the telescope diameter, we find that this function has a FWHM of 1.03 X/D and a distance to the first zero of 1.22 a/D. This predicts values of FWHM = 3.4, 7.1, and 15.2, all of which are close enough to the hand-measured values that the differences can be attributed to uncertainties in the linear interpolation process, and the discrete approximation to a circular mirror (which biases the perimeter to be less than or equal to a specified diameter, so the diffraction pattern is always wider than predicted by the classical formula).

2. Linear apertures. The imaging properties of a coherent linear array of telescopes will now be sketched in a way that attempts to clarify the relationship between a circular aperture and a rotating linear aperture. This discussion also applies to rectangular single mirror segments, since it is the overall shape of the aperture, not the details of construction, that matters here, In Fig. 4a we show an aperture which is 3 by 15 pixels, or 3 by 15 meters using our previous scaling for the sake of concreteness. The autocorrelation of the aperture appears in Fig. 4b, where the lower left-hand corner is the zero spatial-frequency point. Note that the orientation of the aperture is important, since the higher spatial frequencies are sampled in a direction parallel to the long axis of the aperture. In Fig. 4c we show the effect of this aperture on a star field which consists of 3 stars of equal intensity; 2 of the stars are completely unresolved with this viewing angle. ( In this and the following, only 5 contour levels appear in the figures.)

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If we now imagine the detector to stay fixed with respect to inertial space, while the aperture is rotated by 45 degrees, we have the situation shown in Fig. 5. Note that the rather simple technique which IS employed to rotate the discrete 3 by 15 aperture sometimes produces edge distortions and even gaps in the rotated array, bc,th of which are seen in the aperture drawn in Fig. 5a. The effects of these edge distortions and gaps on the final image are relatively minor however, since the overall shape of the aperture is not strongly affected. The frequency plane coverage is shown in Fig. 5b, and the star field image appears in Fig. 5c.

To complete the present example we show in Fig. 6 the case where the rotation has reached 90 degrees. Here the 3 stars have been completely smeared into one feature. In the next section we show how these snapshots can be combined and an image reconstructed.

3. Image reconstruction. The key idea behind our present image reconstruction scheme is given by Davis' eqn. 35, namely that we consider a stack of frequency planes and that we simply add these planes together, with a suitable filtering function if desired. This sum should be properly normalized to account for the greater number of low frequency measurements with respect to samples at tho rotating high frequency end of the autocorrelation function. The real part of the inverse Fourier transform then is the desired image. This method is very general, as can be seen from the fact that in the limit of very long and narrow apertures, the calculation yields just the computer-assisted-tomographic (CAT) scan reconstruction (see Davis, pp. 9-11).

The entire simulation procedure which was used can be outlined as ( follows: A. Set up real stars within the basic 64 by 64 pixel field-of-view. x B. Calculate FT of stars and nave. C. Set up an "ideal"aperture shape by assigning real 1's to the 3 by 15 aperture and 0's elsewhere. x D. Rotate the aperture to the nearest discrete grid points available for a specified rotation angle. E. Set up a "noisy" aperture by following C and D, except that the l's are replaced by exp (ix) where x is a real random number between +X/2 and -X/2 and X is the peak-to-peak phase error assigned to each mirror, element. F. For the "ideal" aperture, calculate the FT, find the magnitude squared at each point, and calculate a second FT; this is the autocorrelation function. G. `..I For the "noisy" aperture, follow step F. .. H. Set up background noise, by filling the 64 by 64 field-of-view with real random numbers y, where y is between +Y/2 and -Y/2 and Y is the peak-to-peak background noise assigned to each pixel in the field of view, from CCD read-out noise, cosmic rays, etc. ORIGINAL ' ter 1 OF POOR QUALITY

1. Calculate the FT of the background noise. J. Calculate the effect of image smearing and added noise by forming (B x G) + I. K. Calculate a filter function according to whether filter number 0, 1, or 2 ie desired: Filter 0 - real 1's filling 64 by 6441 Filter 1 - real 1's where the magnitude of P is essentially non-zero;

Filter 2 R magnitude of F. L. Filter the image FT by forming J x K, and add this to previously formed stack, if any. M. Calculate the current contribution to the normalizing function by adding K into a separate stack. N. If there are more angles to contribute to the final image, return to step C, and repeat this until the desired number of images has been added, typically 1, 8, or 16. i } P. For the summed data now, calculate the normalized, weighted image FT by forming L/M. Q. Find the final ,image by calculating the inverse FT of P and keeping the real part. 1 The above reconstruction procedure differs from that discussed by Davis (eqn. 56) in that Davis' normalizing factor includes an extra multiplicative aperture term: in the noise-free case this term will H K enhance the angular resolt?;tion substantially, but when noise is included ;{ the algorithm becomes ur'ntable. The present method of reconstruction has not yet been theoretically analyzed to optimize the filtering (K) j or the normalization (M), and shculd be regarded as being purely exploratory. . r For reference we show in Fig. 7 the input star field (step A above) which was used to generate Figs. 4, 5, and 6. Carrying out the full i reconstruction as outlined above, in the noise-free case and using filter type 2, we have tried both 8 and 16 angle views (between 0 and 180 degrees) with the results shown in Fig. 8 and 9a, respectively. Except for an improved baseline, the two reconstructions are quite similar. Both show a clean separation of the wide-spaced components, and a clear elongation of the close-spaced stars. For comparison, we show what this '4 star field would look like if we used a small telescope with a 3 by 3 1( aperture (Fig. 9b), and a large telescope with around aperture 15 pixels in diameter (Fig. 9c). Note that Fig. 9a is quite similar to Fig. 9c, but with slightly stronger sidelobes (see also Fig. 4c). In comparing these figures, note that the diffraction FWHM of a 15 pixel circular mirror is 4.4 pixels, and the star separations shown are 3 and 10 pixels, so the close pair is expected to be unresolved.

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4. Background noise and filters. We now present a catalog of images showing the effects of adding background noise as described in section 3H. At present the noise level is not clearly related to the amplitudes of the stars; this will have to be clarified in later versions of the program. For now, amounts of noise with peak-to-peak parameters of 0.0, 0.1, and 1.0 have been tried, and the effects of the 3 filter schemes have been examined. In Fig. 10 we show the results of using filter types 0, 1, and 2 with no noise. Figs. 11 and 12 are similar, but with noise levels of 0.1 and 1.0 respectively. Several points can be made from these figures. First, filter type 0 gives large, extended wings and relatively poor noise rejection, as could be expected from adding unweighted and unfiltered data. Second, filter types 1 and 2 are roughly comparable in their effects, with type 1 apparently giving somewhat better smoothing of the noise; this is surprising because by design filter type 2 smoothly rolls off the higher frequencies within the passband, whereas type I keeps all frequency components right out to the edge of the passband and then cuts off sharply. Future work will be needed to better define useful filters which will deliver optimum resolution at a given noise level.

5. optical phase fluctuations. The mirror train which lies between the incident wavefront and the detector will undoubtedly include various types of imperfections. We assume here that there are no gross tip-tilt errors in the alignment of the combining wavefronts, but that there is a residual, random piston error distributed over the pixels which represent the mirrors. In Fig. 13 we show the effect of introducing piston errors with peak-to-pear phase shifts uniformly distributed over the ranges of 36, 90, 180, and 360 degrees, corresponding to amplitudes of a/10, X/4, A/2, and X. The rms values are about 4 times smaller than the peak-to-peak values. We see from Fig. 13b in particular that an acceptable upper limit on the phase variation is probably somewhat greater than X/4, assuming that we require a signal-to-noise of about 100 in the image. If there are 7 mirrors in the optical path, the surface quality on each mirror must be roughly 7 1/2 times better, or X/10. This is certainly within the limits of conventional optical polishing technology and should not be too expensive to achieve. This value should be only tentatively entertained however until further computer simulations have been completed, using more pixels across each mirror, and including some tip-tilt errors as well.

WAT:iv

Distribution: N. P. Carleton W. F. Davis : H. Gursky, NRL M. Nein, MSFC R. Taylor

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Fig. la Mirror, Fig. lb Autocorrelation. Fig. lc Image diameter = 31 units k

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r Fig. 3a Mirror, Fig. 3b Autocorrelation Fig. diameter 7 units r F

ORIGINAL VAC.4. OF POOR QUALITY

Fig. 4a Linear aperture Fig. 4b Autocorrelation Fig. 4c Snapshot image at 0 degrees

Fig. 5a Linear aperture Fig. 5b Autocorrelation Fig. 5c Snapshot image at 45 degrees

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Fig. 6a Linear aperture Fig. 6b Autocorrelation Fig. 6c Snapshot image at 90 degrees

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Fig. 7 Three point-like stars Fig. 9a Reconstruction Fig. 8 Reconstruction using 16 angle views, using 8 angle views and a 3 x 15 telescope and a 3 x 15 array

10RIGINAL PA^L fl OF p0OR QUALITY,

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Fig. 9b Single image using Fig. 9c Single image using one 3 x 3 telescope aperture one round 15 pixel aperture

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Fig. 10a Filter 0 Fig. 10b Filter 1 Fig. 10C Filter 2 Noise level = 0.0 in each case.

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Fig. 13a Phase errors = X/10 Fig. 13b Phase error p-p peak-to-peak

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OF POOR QUALITY. Ei f Center for Astrophysics Harvard College Observatory Smithsonian Astrophysical Observatory

MEMORANDUM January 1982 To, Distribution (revised version) From; W. A. Traub 1 J f'' 1 Sub)ect; :;omputer demonstration of the initial coherent alignment of COSMIC

1. Introduction. This memo is an illustrated demonstration of the technique by which the COSMIC telescope array can be easily aligned using a small or distant star. To start;, we assume that each independent telescope module is essentially optically ideal, and that the recombinat.ton optics and detector are likewise ideal. Initially, however, these ideal telescopes are assumed to be mutually non-coherent, so that each one is pointing in a slightly different direction and each is slightly ahead or behind its proper position with respect to l the incoming wavefront. j r 'i The presentation of results here follows that in the previous memo, "first results from a crude image reconstruction computer program." Modifications to that program (CRUDE) now allow each telescope module to be tipped, tilted, and piston displaced. For ! ea.zh case, we show 'a contour diagram of the intensity in the focal plane, along with a cross-section through the focal-plane which t ( includes the point of maximum intensity.

F ^ ! 2. Tip-tilt correction. We start by blocking the beams from ? all but two of the telescopes. Taking these two to be adjacent, , and square, we will initially see two sets of star images in the focal plane. The telescope, can now be focussed so that each one produces images which are as small in diameter as is possible. If we look at a portion of

E this field of view, we will have a situation similar to that shown in ^ Fig. la, where a single star appears double because the mirrors are tilted with respect to one another. We have offset the second wavefront* by one wavelength across its width for an angular tilt of a/D, and f also by the same angular amount in the perpendicular direction, for a net shift of r X/D, where D is the mirror dimension. iA ;s

M To combine the images, it is easy to see that a telescope t operator can reduce the error to essentially zero along one axis 'F ` without much difficulty, bringing us to the state shown in Fig. lb. Here we see interference patterns developing in the overlap region. ?; Successive tilts in the remaining direction produce the images shown in Figs. lc, d, e, and f, going -to tilts of (0.5, 0.25, 0.125, and 0.0)a/D respectively. f#

^- *Throughout, we will refer to the state of the wavefront, rather than the state of the mirrors or other optical compontnts. Thus a wavefront tilt of 1/D will be produced when the primary mirror is tilted by 0.5 X/D, and 3 `., likewise for piston errors.

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3. Monochromatic piston correction. The telescopes in F'ig. 1 had no piston displacement, i.e. we assumed coincident arrival of wavefronts in the focal plane. If there had been, say piston error of 0.5X, then Fig. la would still fairly accurately describe the images since they do not yet overlap, but bringing the tip-tilt errors to zero will produce the result in Fig. 2a, rather than that in Fig. lf. The "double image" in Fig. 2a is an artifact produced by the exact cancellation of amplitudes at the position where the star should ideally have been imaged. As we reduce the piston error to ( 0.25, 0.125, and O.0)X we find that one of the images grows at the expense of the other, and that the peak intensity shifts toward the expected star position.

4. Combined tip-tilt and piston correction. The first two mirrors ( or telescope modules) are now perfectly aligned. In general, of course, both tip-tilt and piston errors will be present together. However it is not necessary to demonstrate the simultaneous correction of both conditions because it is clear from Fig. la that we can immediately determine the tip - tilt error simply by measuring the offset between images and doing a one step correction, which takes us immediately to Fig. 2a.

5. Polychromatic piston correction. In monochromatic light the piston correction can only be made modulo one wavelength; but it is also reasonable to expect that if we use a wide spectral band we can reduce the error to at most a very few wavelengths, since we then have the combined leverage of the longest and shortest wavelengths to produce the sharpest possible image. As an example, suppose that the mechanical integrity and structural stability of the COSMIC array is such that we can assume each wavefront to be within a piston displacement p >> a of the ideal position.

Then using a filter to generate monochromatic light, and following the correction steps shown in Figs. 1 and 2, we adjust the piston position of the second wavefront by an amount < 1.Oa. If we define n = p/a, there are approximately n >> 1 different positions where we will get about the same image quality, and these positions are spaced by X. Suppose that the accuracy of positioning is e^, where e << 1.0; comparison of Fig. 2c with 2d suggests that e ti 0.1 is appropriate. This argument can also be used to show that the spectral purity of the nominally monochromatic beam does not have to be any better than AX= ea, which is easy to produce with an interference filter or a circular variable filter.

We now use a different filter to select a second wavelength X , where differs from the first wavelength X by a fractional amount given by the quantity e, so that a 2 N X(1.0 + e). In general this will require a slightly different piston correction, again < 1.0 a . Now the number of possible positions where both k and give good images X2 is reduced to approximately en, spaced by X2/e ti a/e.

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If we repeat this process with a third wavelength.^ 3 ti X (1.0 + 2e), we will again increase the spacing between acceptable piston displacements to approximately X/e 2 , i.e., another factor of 1/e. If we carry out this process a total of m times, we will tncxease the spacing between acceptable piston spacings to about X/e m ; we can stop when this quantity grows las large as the original positional uncertainty p, so we have = p.

If we use the above estimate that e = 0.1, and take X = 0.5 micron and p = 5 mm (say), then we require .m = 5. Thus we need 5 different filters centered at wavelengths 0.50, 0.55, 0.60, 0.65, 0.70 microns. Equivalently, it is likely to be true that we could simply use a single wide band ranging from 0.50 to 0.70 microns and sweep the mirror through the full adjustment range of 5 mm, searchin47 for the minimum image width or brightest central peak.

6. Multi-mirror corrections. The procedures described above will bring two adjacent mirrors into essentially perfect a]',gnment; remaining imperfections are clearly below the level of measurement, and are therefore unimportant. The other telescope mirrors can be aligned in succession. For example, the first mirror could be shuttered, and mirrors number two and three co-aligned, then three and four, etc. Uncovering all mirrors together should yield a well-aligned telescope array, with further minor adjustments needed only to eliminate any accumulated errors.

It may also be possible to devise even more automatic schemes whereby we perturb each mirror control element by a fixed amount, measure the image, and then calculate the complete correction needed, using a matrix inversion (for the linearized case) or an inverted image formation program (for the more general case). In the ideal case, of course, a single image measurement should suffice in order to generate the full correction needed, but this is not likely to be stable in the presence of noise. Nevertheless, these cases all deserve further investigation.

WAT:jv

Distr ibution N. P. Carleton W. F. Davis H. Gursky, MRL M. stein, MSFC R. Taylor :.E t> ORMINAL PAGE : p OF POOR QUAWY

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a. b. c.

Fig. 1. Images from a single star, as formed by two adjacent telescope mirrors, each 7 by 7 elements in size, with second wavefront tipped and tilted with respect to the first mirror. (a.) Tilt-tip from edge-to-edge of second wavefront is one wavelength (1.0X) on each axis, so image splits in two parts, such that the first (reference) mirror's image remains centered. (b.) Up-down tip on one axis restored to zero (0.0X), with other axis tilt remaining at one wavelength (1.0X). (c.) Tilt reduced to 0.5X.

_J _LL IF a^ o i 0 (d.) Tilt reduced to 0.25X, (e.) Tilt reduced to 0.125X. (f.) Tilt reduced to zero (0.0X); note that, as may be expected, Figs. 1(e) and (f) are very similar. .i ^^ k

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a. b.

Fig. 2. Images from a single star, as formed by two adjacent telescope mirrors, each 7 by 7 elements in size, with second mirror displaced toward the star (i.e. a piston error) with respect to the first mirror. (a.) Piston error of one-half wavelength (0.5X) in the wavefront. (b.) Piston error reduced to 0.251.

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(c.)Piston error reduced to 0.125x.' (d.)Piston error reduced to zero (O.OA).

i ORIGINAL f AO el OF pOOR QUALI.1"1f'

Memo

To: Distribution 'J'anuary 25, 1983

From: W. A. Traub

Subjects Lab demonstration of image reconstruction

This is a brief account of the first laboratory simulation of COSMIC, with computer reconstruction of the image. The work was done in August and September 1982, with Drs. J.Geary and N. P. Carleton in the lab and John Lavagnino at the computer. Optics, The optical set-up is shown in Fig. 1. The light box, aperture slit, lens and CCD camera were clamped to a simplb triangular-cross-section optical bench. The wood light box contains a low-wattage incandescent frosted bulb, run at 110 volts. The object mask is a 6 by 12 mm T-shaped slot milled in a thin sheet of brass, and backed by a piece of diffusing glass. The object mask and lens are separated by about 1067 mm. The aperture slit is from a lab monochrom►ator, formed by evaporated metal jaws on glass; the width is 102 f 2 um and length is 534 t 12 um. The aperture slit mount can be rotated about the optical axis, and set by reference to an azimuth grid of polar coordinate paper taped to the mount. A blue-transmitting filter follows. The camera uses a multi-element f/5.6, 135 mm Componan Schneider-Kreuznach lens. The CCD is a thinned, back-illuminated RCA 320-by-512-element device, with 30 pm pixels, and essentially no dead space. The chip is located behind a window in an evacuated space, and is cooled by connection to an LN 2 reservoir to about 150 K.

Xposure. With the slit removed, the lens is first focussed at full aperture. With the slit inserted, the image is only slightly blurred in the 534 um direction, but strongly blurred in the 102 um direction. Eighteen frames are exposed at slit rotation increments of 10 degrees. Each frame consists of a short bias exposure and a long object exposure, in any order, summed on the CCD chip. The bias exposure is 1/30 sec, with the slit assembly removed, the object blocked, and the camera illuminated by dim room light scattered from a white surface; the bias level amounts to about 100 counts/pixel, and is needed because there is a loss of almost this amount in the camera readout. With the slit in place, the object exposure is 120 sec, giving a peak intensity of about 8000 counts/pixel. A flat field exposure is also made, like the bias exposure, but with a higher light level; the average intensity is 12000 counts/pixel. The conversion factor is 1 count _ 30 electrons.

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The 18 frames are spread over 2 days, since 5 of the original frames are contaminated by a ghost. A 15 degree tilt of the filter throws the ghost out of the field. The 18 useable frames are flat-fielded with standard Nova software. Readout defects affecting several columns outside the mailn image are removed by local averaging.

The centering is slightly different on the 2 days. From direct images without the slit, the first group appears to be centered at (row, column) a (208.5 1 205(+)), and the second group is centered at (218(+), 204.5). A 256 by 256 pixel array is selected from each frame, centered at (208, 205) for the first group, and (218, 204) for the second group. There is th-us some residual centering difference between the groups. The Nova images are recorded on tape for subsequent processing.

Reconstruction. The resulting clean, centered images are manipulated and displayed on the T S/VAX system. All images are first reduced to 128 by 128 pixels, by binning groups of 2 by 2; this is done to accommodate the finite storage space in the Array Processor.

The reconstruction algorithm needs to know the aperture shape; size, and orientation for each exposure * In our discrete Fourier transform approximation, with 128 points in each dimension, a rectangular function of width W pixels has

a DFT which is a sinc 4 function having zeroes spaced at multiples of p = 128/W pixels. Thus the recorded image is (ideally) the convolution of this sinc function with the geometric-optics image.

4 We determine W by measuring the relative positions of the lst and 2nd secondary maxima in a selected image, where c the object axes are conveniently aligned with the pixel axes. As sketched in Fig. 2 1 the diffraction pattern is

(sin Tr p/po ) 2 / (up/po ) 2 . (1) The first zero occurs at pixel

Po ( X/d) f (2) where f is the distance from the lens to the image:

Cl + (1067) -1 = (135) -1 , or f = 155 mm. (3) From 7 measurements of various secondary maxima at positions

p(max) _ (integer + 1/2)p o (4)

we find . ` 23.90 t 0.76 pixel. (5) ) Y Po M YP ' 1 Ol t r

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Using equation (1) we calculate an effective wavelength

A = 0.472 * 0.015 um. (6) The discrete equivalent aperture width is W - 128/po = 5.36 * 0.17 pixel. (7) Given the measured length to width ratio of the slit 535/102 5.24 f 0.16 (8) we calculate the discrete equivalent aperture length as

L = 5.24 x 5.36 = 28.09 * 1.24 pixel. (9)

The reconstruction algorithm requires the autocorrelation function, which we usually generate from the DFT of the aperture transmission function. However since (L,W) are not whole integers, some approximation is needed. A modification to the program now allows non-integer aperture sizes, by adding a one-pixel fringe around the aperture with a fractional transmissi qn instead of unity or zero transmission. The algorithm is also improved by a new aperture rotation scheme which searches out and eliminates gaps which occur as the aperture is numerically rotated on a discrete grid of points. However there still remains the effect that a numerically rotated aperture does not turn smoothly, but in discrete steps, generally producing a staircase profile where it should be smooth. Numerical simulations verified that the above modifications did indeed improve the quality of the reconstruction. Further simulations with a numerical point source also verified the two-dimensional analog of equation (1), as well as the fringe-pixel approximation which leads to

poW ! const. = 122 to - 129 (10)

in the examples tested.

The mathematical procedure is described in Traub and Davis (1982), SPIE =1 164-175. In Fig. 3 and 4 we show individual images at 0, 40, 90 degrees, and the final reconstructed image. ,Several variations of parameters were tried, none of which had any strong effect on the reconstructed image. First we tried 19 frames instead of 18, with only slight improvement. Next we tried filter 1 instead of filter 2, and it was worse, as expected. We

tried various values of the cutoff parameter (E) which prevents very small numbers from being divideg by other, even smaller numbers; we foung e = 0 and 10 to be r essentially identical, but 19 to be large enough to degrade the image noticeably. We tried changing the F numerical aperture dimensions, finding +10 percent to give a slightly sharper image, and -10 percent to give a slightly

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ORIGINAL PA(" [rj OF POOR QUALITY Page 4

poorer image. Finally we tried changing the initial offset angle of the aperture with respect to the pixel axes, and found -5 degrees to be a bit worse, +5 degrees to be a bit better, in agreement with independent estimates that +3 degrees M or so would be most appropriate. conclusion. Our first laboratory demonstration of image reconstruction was remarkably successful. Many non-ideal factors entered into the process, amply demonstrating that the algorithm is immune to small perturbations. In the future, with an improved optical system, we can expect to do even better.

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I , f- ' , ^~ ' ' !, I ^ /_". Tit ^ • I I / f/ ' ^ i ! i I i t ! ^^ ^^ Y Figure 1. Optical arrangement. Starting from the back-illuminated object at the left, the light passes through the defining aperture slit, the blue filter, an imaging lens, a vacuum window, and finally falls on the CCD chip. Note that the aperture slit is not being used in strictly parallel light as would be required to simulate an astronomical telescope aperture. Also neither is the aperture coincident with the imaging lens, although it is as close as possible. Numerous glass-air surfaces in this system can contribute to ghosts, although the (untilted) filter-reflection ghost was the only major one noted.

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Figure 2. The slit, and its digital approximation (see text) are shown on the left. A schematic diffraction C___ pattern with zero positions marked is shown on the right. ORIGINAL PAGE IS ORIGINAL PAGE OF POOR QUALITY BLACK AND WHITE PHOTOGRAPH

`, A • ReconstructionnO! 18 CCD Images, to Demonstrate COSMIC Imaqe Reconstruction Method.

Figure 3. Images generated in the I 2 6, originally rendered in false color on a transparency. The 0, 40, and 90 degree images are shown, along with the relative orientation of the aperture slit. The reconstructed image is shown at the lower right, along with the equivalent diameter circular aperture. i W' n 1 ORIGINAL MV i OF POOR QUALIT "o

(b) %

(c) LI (d)

Figure 4. Contour diagrams of meaSL'red intensity are shown in (a)-(c) for the 0, 40, and 90 degree images. All contours are drawn at the 10, 20, 30,...80, 90 percent levels after subtraction of a weak background. The reconstructed image is (d), showing a small ghost feature at the 10 percent level near the inner edge of the arms.

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r. ORIGINAL PAGE M OF 'POOR QUALITY G1

r DRAFT NOT FOR CIRCULATION ^x k

SCIENTIFIC PROSPECTS WITH THE COSMIC TELESCOPE ARRAY

June 1982

s t r

Center for , Harvard College Observatory and Si

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ORIGINAL K4;4 f, OF POOL QUA'LI'TY f I

SCIENTIFIC PROSPECTS WITH THE COSMIC TELESCOPE ARRAY

Contributing Authors N. P. Carleton S. S. Murray F. A. Franklin R. W. Noyes M. Geller M. J. Reid J. E. Grindlay R. Stachnik J. P. Huchra L. P. van Speybroeck R. E. McCrosky M. V. Zombeck Edited by W. A. Traub

Contents Introduction 2 Comets 4 Asteroids 4 Jupiter 5 Saturn 6 Pluto 6 Main Sequence Stars 6 Supergiants 7 Circumstellar Emission 8 Binary Stars 8 Globular Clusters 8 Active Galactic Nuclei 10 Supernova Remnants 11 Jets in Galactic Nuclei 11 Supermassive Galactic Cores 12 Identification of Faint X-ray Sources 12 Extragalactic Distance Scale 13 Deceleration Parameter 13 References and Acknowledgments 14

( t Cover: General view of the full cruciform configuration of COSMIC, developed during the Marshall Space Fli-1ht Center engineering conceptual definition study (1981). Each of the four main arms is a telescope module which has been brought into orbit by the Space Shuttle. The fully-extended sunshades distributed along the upper surface of each telescope module are collapsed during launch. Also the downward projecting spacecraft and articulated solar panels are folded for launch. Each telescope module is sized to nearly fill the Shuttle bay (4.6 m diameter, 18.3 m length). ` The first telescope module to be placed in orbit will have an optical baseline of 14 m, and will be fully operational. The second telescope module will increase the optical baseline to 35 m. Third and fourth modules may be added to forma cruciform shape, although recent image reconstruction developments suggest that the cross arms may not be needed. Each telescope module is capable of supporting 7 collecting mirrors, each 1.8 m across : •— I (square as shown, or round); only 4 of the 7 possible telescopes in each `'j module are shown, and these are arranged in a minimum redundancy configuration, although ideally of course all available positions will be utilized. A `t diffraction limited image of the sky is formed in a centrally located focal plane, which is instrumented with cameras and spectrometers analogous to those in Space Telescope.

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ORtONAL RAOR 19 OF POOR QUALITY

SCIENTIFIC PROSPECTS WITH THE COSMIC TELESCOPE ARRAY

INTRODUCTION

In this paper we discuss for the first time a selected number of unique astronomical observations which would be possible with an orbiting telescope having both a large collecting area and an angular resolution in the milli-are-second range. Most of these observations will allow us to study at- firsthand. phenomena for which we currently have little or no direct evidence. In many cases we will finally be able to resolve objects on an angular scale such that significant new features and new events can be seen, vastly enhancing the opportunity for discovery. In other cases we will be extending to a much greater distance our present capabilities for both isolating individual objects and making morphological measurements, so we will be able to study a significantly increased fraction of the universe at the same level that we can now with relatively nearby objects.

The COSMIC telescope array has been specifically designed to investigate the class of problems described in this paper. COSMIC stands for Coherent optical system of modular imaging collectors. In particular we envision a linear array of orbiting telescopes held in a rigid framework which rotates about its line of sight, sweeping out an equivalent diameter circular aperture. All telescopes feed a common focal plane where a diffraction-limited image is formed when the optical path-lengths are rin adjusted to be within a quarter wavelength. For resolvable stellar surfaces a narrow band filter or attenuator will be used to avoid detector saturation; otherwise broad-band imaging will be the normal mode of operation. The t instantaneous diffraction-limited image of a point source is narrow along a, the array's major axis only, but by using an already demonstrated image ffl reconstruction technique it will be easy to build up fully resolved images f, _ after a 180 degreeg rotation of the array,y, even in the presence of noise and optical imperfections. A 1981 conceptual definition study of COSMIC by engineering personnel at Marshall Space Flight Center established that the f overall concept was viable using currently available or anticipated technology. Focal plane instrumentation could be similar to that now being built for f Space Telescope in that both cameras, and spectrometers can be provided, the

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3 ORIGINAL PACE W OF MOOR QUAUTY

latter taking advantage of the slit-like nature of the imaging point response function. Rapid read-out of the focal plane will ease spacecraft pointing requirements, now expected to be less stringent than for Space Telescope.

For concreteness, this report considers a COSMIC telescope array which is 35 m in length, brought up in two shorter sections by two Space Shuttle flights, although useful science can be done with only the first section in place. There are up to 14 collecting mirrors, each 1.8 m in diameter, feeding a central focal plane. The wavelength range is roughly 0.3 um to 1.1 ums,at the short wavelength end this corresponds to an angular resolution a/D = 1.8 milli-arc -sec, and in the visible the resolution is 3 milli-arc-sec. The array is a natural follow-on for Space Telescope, since it has about 28 times better angular resolution and 8 times greater collecting area. We expect that the limiting magnitude for COSMIC will be in the neighborhood of m y = 29, for .about 100 counts in a one hour observation.

The observing programs in this report were selected by the contributing authors from the perspective of their current research activities. Each of these programs has requirements in angular resolution and collecting area which go beyond the capabilities of Space Telescope. The only fundamental limitation is one which is common to all high angular resolution telescopes, including ST and VLSI, viz., the minimum detectable surface brightness increases as the angular resolution element decreases.. Fortunately in the visible, as in the radio, there are a large number of classes of objects with intrinsically high surface brightness in the milli-arc-sec size range. The enhanced angular resolution of COSMIC will finally allow us to cross that boundary which separates our present status, where mist astrophysical objects appear either as point sources or as hopelessly smeared images, from our potential future status, where a vast number of objects will become well enough resolved that we can begin to understand their true nature.

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4 ORIGINAL PACF. L9 OF POOR QUALITY

COMETS

Comet nuclei are thought to have diameters of from 1-10 km. Because of this small size and because of the difficulty in distinguishing between. the solid nucleus and the bright, inner coma, there has not been a definitive, unambiguous measurement of a nucleus. Radar observation can give useful limits on the radar cross-section. Full scale COSMIC resolution capabilities should be adequate to resolve the nucleus of a comet passing within about 0.2 A.U. of Earth if the contrast between the nucleus and the coma - which will be fully developed at that heliocentric distance - is sufficiently high. COSMIC will also be able to detect and measure the velocities of comet nuclei which have split during perihelion passage.

COSMIC will permit detailed studies of the growth and activity of the inner coma. This includes: the formation, velocity and, possibly, the "hot spot" location of jets;;, the velocity field in the coma as displayed by any bright feature; and the evolution of the molecular species from the time gas is emitted from the /iwzface until an equilibrium is reached.

ASTEROIDS

Radii of asteroids are normally obtained by a combination of visual and far-infrared photometry. Confirmation and/or calibration of these somewhat indirect results by direct measurement is important.

The COSMIC telescope will permit us to examine those asteroids for which there is some evidence of'a bound companion.

Earth-bound observations of asteroids are limited to whole-disk measurements. Petrological or mineralogical differences between asteroids are apparent from narrow-band spectrophotometric measures. The periodic light variations seen in broad-band photoelectric photometry are probably due to irregular shapes rather than inhomogeneities in the surface composition but the-two effects can not be separated in most asteroids by currently available observing procedures.

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5 ORIGNAL PAL *_. E3 OF POOR QUALITY

Assuming a mean perihelion distance of 2.5 A.U. for main belt asteroids and an albedo of 0.2 (measured albedus range from 0.05 to 0.4), the resolution element in the visible would be 3.2 km with a brightness of my ti 19 per resolution element. Significant observations could be made on most of the numbered asteroids as displayed in the following table.

No. of resolution Perihelion magnitude No. of cases elements per diameter

15- 16 672 25 14- 15 666 60 13- 14 364 160 <13 397 >270

Twelve of the asteroids included in the table are Amors with perihelion approaches to the earth of 0.2 A.U. or less and, in addition. there are 19 Apollos with still smaller approach distances. For these bodies, the resolution element will be in the range 100-400 meters. Apollos and Amors hold a special significance in that they, or still smaller bodies in similar orbits, are the source of meteorites. The question of their ultimate origin - asteroids, comets, or both - is unresolved. If, as believed by soma, the Apollos include extinct cometary nuclei, the best hope for studying these lies in high resolution observations by COSMIC.

JUPITER

It would be possible with COSMIC to measure the shapes and rotation rates of the larger of the outer satellites J6 - J12. Time-dependent observations of lo and studies of Jupiter's atmosphere could also be carried a out, since 1.8 milli-arc-sec at Jupiter corresponds to about 5 km resolution, which is comparable to some of the highest resolution images obtained by voyager 2; for reference, the volcanic plumes on Io are about 100 km high.

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SATURN

Two particular dynamical problems in the Saturnian system require high resolution astrometry. (a)Positions of the two "co-orbital" satellites, 1980 S1 and 1980 S3. These two can be observed from the earth only at the time of ring plane passage (every 15 years). Accurate relative positions will provide the sum of the masses of the two bodies thanks to their unique "co-orbital" motion. (b)Hyperion, S8, is a very irregular body whose long axis, apparently, points toward Saturn. This satellite moves in an orbit with an eccentricity of ti 0.11 so that a libratron should occur. Measurement of this libratron provides a knowledge of the moment of inertia ratio of the body.

PLUTO

A detailed survey of the Pluto system would provide us with the planet's radius, rotation rate and axial orientation; it would also allow.' us to improve the orbit o£, and possibly measure the radius of, its recentlyy iscovered satellite. Reliable values for these quantities are unobtainable by other means - i.e. although Voyager flights may provide such material for Uranus and Neptune, no encounters with Pluto are fl scheduled.

MAIN SEQUENCE STARS

A prototypical main sequence star, a Cen, has an angular diameter of about 10 milli-arc-sec, so one should be able to detect (using a narrow- band filter in the K-line, for instance) its rotation axis. It may be possible to obtain rough information on surface distribution of activity 'j (whether, for example, emission is concentrated near the poles or the equator) and, over several years, follow crudely the "butterfly diagram" of

i ^^ z

? PAWS N OF POOR QUALITY

latitude of activity versus phase in the activity cycle -- an experiment of importance for stellar dynamo theory. One might detect differential rotation (another parameter of great interest'for dynamo theory) with precision sufficient to be extremely important. One could obtain information on size and shape of active regions or activity complexes. In a "magneto graph" mode, one could begin to map large-scale surface structure of magnetic fields. All of these would be extremely useful, when compared with solar behavior.

SUPERGIANTS

a Orionis has an angular diameter of 40 milli-arc s-sec and reported diameters for o Cet range up to 100 milli-arc-sec. For o Cet, this implies as many as 30 resolution elements across the disk, in the visible. These µw M-type red giants possess very interesting and complex atmuspheric structure. COSMIC may be able to answer some fundamental questions, such as whether the variability of these stars is primarily due to pulsation or temperature changes. Spectral-line VLSI observations of H2O and SiO maser emission allow one to probe the extended photospheres of these stars in great detail. Very complex motions involving both expansion, contraction, and shocks are suggested by the data. The ability of COSMIC to obtain spectral information as a function of position on the stellar surface would greatly :aid in the understanding of this class of objects. There are a wealth of features that should be searched for, including: a) Brightness inhomogeneities on the disk due to large convective cells, predicted (Schwarzschild) to have sizes ti 0.1 of the radius. b) Velocity asymmetries on the disk due to the above convective motions. c) Overall shape changes due to photospheric motions; these are already inferred from polarization studies by Daniel Hayes. d) Chromospheric emission structure above the limb in strong lines like Ca II 8542, Ha, or others; already detections of this by speckle techniques are being reported (not yet in print). ^i

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OF POOR QUALITY,

e) Variable velocity outflow in expanding shell could be mapped using doppler-resolved imaging. f) Radial and nonradial large-scale pulsation.

CIRCUMSTELLAR EMISSION

Emission from circumstellar material surrounding and enveloping interacting binaries is potentially a very rich field for investigation with narrow-band interferometry isolating excited lines like Ha, Ca II, O IV, etc. Much X-ray radio, UV and visual data suggest complex structure and motions. It would be extremely exciting to map this, for comparison with higher-energy data, including time development.

BINARY STARS

Although high resolution observations of binary stars may lack a certain glamour, they provide fundamental information on stellar masses. At the cost of a relatively small amount of observing time, a vast amount of fundamental information could be gathered.

GLOBULAR CLUSTERS

The milli-arc-sec angular resolution capability of COSMIC would be of

special importance for studies of the highly condensed stellar cores of - ,lo globular clusters. Centrally condensed globular clusters have central densities in the range 104 - 10 5 starsjpc 3 . Thus the typical stellar

separations are only ti 0.01 parsec and would subtend an angle of 0.2 aresec at typical cluster distances of 10 kpe. Star counts and stellar population studies can than be carried out in cluster cores with COSMIC. This could only be partially accomplished with ST bebause of both the more limited angular resolution and sensitivity. The extra factor of ;, 10 in angular resolution achieved with COSMIC will allow direct searches for visual

binaries in,cluster cores, since N 2 AU separations are resolveable at

a-, r 9 ORIGINAL PAM E9 b OF POOR QUALITY

N 1 kpc. This permits direct study of the frequency of binary systems in cluster cores. Compact binary systems are now known to exist in cluster cores since recent Einstein X-ray results have determined the mass of globular cluster X-ray sources to be ti 2 IM0 , or consistent (only) with the sources being compact binary systems and not massive black holes. These binary systems have presumably evolved from a significant population of wider-separation binary ;systems formed by tidal capture, and it is these systems which COSMIC could study directly.

In addition to studying the binary problem in globular cluster cores with direct images, spatially resolved spectra (with long slits across the core) could extend the search greatly by allowing velocity 'variations to be measured for a large number of stars simultaneously. This is also of fundamental importance for measuring the velocity dispersions in the centers of globulars. Central velocity dispersions are now very poorly known (they are inferred from line profiles in the integrated cluster spectrum) and yet they are the most fundamental quantity of interest in describing the stellar dynamics of dense stellar systems. Again, the great improvements.in both resolution and sensitivity over the ST capabilities allow much more detailed studies to be carried out, e.g., measurements of the degree of isotropy in the velocity dispersion vs. radius and velocity dispersions vs. stellar mass (i.e., spectral type) to explore the central potential.

Finally, the "classic" problem of searching for central cusps in the stellar density profile such as would arise from either a central black hole or a subcore of heavier; evolved stellar remnants (black holes, neutron stars or white dwarfs) can be carried out with COSMIC better than with any other instrument in the forseeable future. Present upper limits on the mass of central black holes in globulars (which are not, and need not, be X-ray sources).are ti 3000 M . COSMIC could measure the r-7/4 E) density profile cusp expected around a central black hole for masses as small as N 50-100 ME), or significantly below the limits possible with ST. The existence of subcores in clusters, already suggested for the X-ray clusters M15 and NGC 6624, could similarly be explored and important constraints on stellar evolution and the initial; mass functions of globulars derived.

10 ^t ORIGINAL 'Pi A..4- '- OF POOR QUALITV

ACTIVE GALACTIC NUCLEI

COSMIC in ,oll suited for imaging of galactic nuclei. (Seyferts, quasars, BL Lac objects), The structure of the central regions of AGN's - existence and possible variability of compact sources, accretion disk structure, etc. - is a topic of great current interest. Present descriptions of the source morphology are based primarily on radiative transfer modeling of spectroscopic emission line data, variability timescale arguments and poor resolution ( 1 arc -sec) imaging. very few AGN are bright enough radio sources to be studied with VLSI, especially the closest objects (eg. NGC 4151 or NGC 1068) where the smallest spatial scales would be visible, so optical imaging may provide the key to understanding these objects.

Stratoscope observations ( 0.2 arc - sec resolution) coupled with lower resolution ground-based spectroscopy have placed some constraints on dynamical models of M31. However, models with M/L's from 0 to 50 can still be made to

fit the data! Higher resolution observations (ti 0.05 arc-sec) can distinguish between the photometric profiles of the high and low M /L models. COSMIC can also be used to make high resolution observations of the nuclei of other nearby galaxies with a variety of morphologies.

To illustrate with a particular example, there would be great interest in studying the terminal results of emission flows onto active galactic nuclei. X-ray measurements on M87 and NGC 1275, which go down to a level of about 1 aresecond, permit accretion. flow studies down to distances of 100 to several hundred parsecs from the galactic nucleus.' In this regime, r there is considerable X-ray emission with temperatures falling dowrt. to a few million degrees. At closer distances, temperatures should continue to fall to the point where most of the emission is in the optical. Accreting gas would form bright filaments. It would be interesting to observe this k structure on the scale of a few tenths of -a parsec. Thus, the milli-

rareser.'.^;, aid optical observations would provide a means of continuing the r accretion flaw studies that begins with X - rays at much larger distances.

. 3 1 i 11 f= 4 ORIGINAL P, G--" 113 OF POOR QUALITY

SUPERNOVA REMNANTS

X-ray observations of galactic SNR :Indicate that several contain t,,,nusually bright knots that are not obviously associated with ri ,utron stars or pulsars. The Vela SNR and MSH 15-52 are two examples containing brilInt knots (in addition to pulsars). It would be interesting to examine these bright knots to search for point-like components or for very fine filamentary structure that might show up in the optical.

JETS IN GALACTIC NUCLEI

Radio astronomers are now constructing images with an angular resolution from 0.0003 to 0.1 =sec with VLBI techn,:,ques. These images have proven to be exciting and revolutionary and VLBI has become an - unparalleled tool for studying the structure and origins of the great variety of bright sources in the Universe. At present, however, inter- pretation of VLBI images has been limited in part because high quality op ical images with angular resolution better than 0.1 aresec do not exist.

There are several cases where high resolution optical images would clearly show significant xtructure and greatly aid in the astrophysical understanding of the nature of the emitting objects. For example, radio jets are seen on scales from smaller than 0.001 to 10 a •cseconds in objects such as QSO's, galaxies with active nuclei, and from the galactic "star" SS433. The mechanism for the radio emission is thought to be incoherent synchrotron emission. Extrapolating the synchrotron brightness to optical wavelengths suggests that many of these objects could be imaged with COSMIC. One of the most interesting extra-galactic sources, M87, appears to emit synchrotron radiation over nearly the entire electro-magnetic spectrum. It exhibits a striking radio/optical/X-ray jet emanating from the nucleus of the galaxy. VLSI images of the nucleus suggest that intensities of r > 20 ergs/sec/cm**2/ sterad would be seen at optical wavelengths from a jet less than 0.01 wide and 0.2 areseconds long; this intensity is nearly 104 times greater than the detection threshold for COSMIC, and should therefore be very easily detected.

s x -, r 12 r^,W #^q OF MOOR QUALrrf,

SUPERMASSIVE GALACTIC CORES

Most of the problems outlined above for globular clusters can be carried out as well for the stellar clusters which are likely in galactic nuclei. A prime object for study, of course, is the nucleus of M31. Stars could be resolved if the density is as high as ti 4 x 107 pe 3 which is larger than required to fit the central surface brightness. In M87 stars could be resolved and counted into the nucleus at densities of ti 104 pc-3 . This would allow measurements of the isotropy of the velocity dispersion to be made in regions where it should be anisotiropic if the apparent central cusps in both density and velocity dispersion are not due to a supermassive black hole. Thus COSMIC can directly probe the dynamical questions'necessary to test whether active galactic nuclei and quasars are powered by supermassive (ti 10 8 - 109 MO) black holes.

IDENTIFICATION OF FAINT X-RAY SOURCES

The most obvious use of the high optical resolution in conjunction with X-ray measurements is to find optical counterparts for X-ray sources which appear in deep surveys. For many X-ray sources, counterparts are too dim to be identified by present means. Very high resolution images, including color measurements (and high resolution spectroscopy, which should also be possible with COSMIC) might help us to find the counterpart or possibly to set very high lower limits on X-ray to optical luminosity and determine if the X-ray to optical ratio is evolving in the early universe. It is quite possible that the early universe contains X-ray sources with no optical counterparts. In general, the X-ray positions would be very well known from AXAF or LAMAR measurements so that the small field of view of COSMIC should not be a problem. A limiting magnitude of 29 will be suitable and necessary,for these observations. (Space Telescope is already needed for the Einstein de^) surveys.) 13 ORIGINAL 6U OF POOR QUALITY

EXTRAGALACTIC DISTANCE SCALE

The extension of galaxy distance measurements using Cepheids depends critically not only on light gathering power because the or-- ncts are faint (MV -6), but also on resolution because the objects are <,'ets.Aed in the parent galaxy. This is also true for the identification and photometry of globular pluster systems (MV = -10) around othergalaxies. COSMIC can be used to measure Cepheids in nearby galaxies and in galaxies as far as the Virgo and Pegasus clusters (distance modulii of 31 and 33 magnitudes respectively). It can also be used to identify and measure the globular cluster systems around galaxies as far away as the Coma cluster and possibly the Hercules cluster (100 Megaparsecs or a distance modulus of 35). Such measurements are important for studies of the large-scale dynamics of clusters of galaxies as well as for determination of the Hubble constant. Large-scale dynamical studies are a fundamental probe of the local mean mass density. Complete positional coordinates for galaxies in the flattened Local Supercluster are necessary for discrimination between the pancake and gravitational instability pictures for cluster formation.

DECELERATION PARAMETER

The morphology of the central regions of the brightest elliptical galaxies in clusters is interesting not only for the study of the dynamical evolution of such systems but also for the possible application of the angular size-redshift test to the determination of the cosmic deceleration parameter, qo . If scale lengths in gal,saies or clusters of galaxies can be used as "standard measuring rods," the determination of change in scale as a function of redshift relativ- to the expected Euclidean 1/r relation is a very powerful first order test of cosmological models. Brightest cluster galaxies have core-radii (Hubble profile) on the order cf 1 kpc which is already smaller than 1 arc-sec at a redshift of only z 0.1. To study galaxies at redshifts of 0.5, resolution well in excess of 0.05 arc-sec is required, so COSMIC is ideally matched to this type of observation. 3 `

14 $ ORIGINAL OF POOR QPupaLt"^' ,

ACKNOWLEDGEMENTS

We gratefully acknowledge the contribution of ideas and review comments by a number of individuals, including J. M. Moran, H. D. Tananbaum, W. H. Press, and G. B. Field. This work has been partially supported by NASA contract NAS8-33893 through Marshall Space Flight Center.

DL.LAG?DL•ATMVC

The astronomical advantages of operating a large (but conventional) telescope in space have been presented in some detail in: Longair, M. S., and Warner, J. W. 1979, editors, Scientific Research with the Space Telescope, IAU Colloquium No. 54, NASA publication CP-2111, 327 pp.

A discussion of the COSMIC telescope array may be found in: Traub, W. A. and Gursky, H. 1980, "Coherent arrays for optical astronomy in space," in Optical and Infrared Telescopes for the 19901s, vol. I, ed. A. Hewitt, KPNO, pp. 250-262.

The mathematic basis of the image reconstruction algorithm, along with numerical demonstrations, is presented in; Traub, W. A. and Davis, W. F. 1982, "The COSMIC telescope array: astronomical goals and preliminary image. reconstruntion results," in Advanced Technology Optical Telescopes, SPIE vol. to appear.

The engineering conceptual design study mentioned in the Introduction is found in: Nein, M. E. and Davis, B. G. 1982, "Conceptual design of a coherent optical system of modular imaging collectors (COSMIC)," in Advanced Technology Optical Telescopes, SPIE vol. to appear. _ 1 i ^ e i^

ORIGINAL PAGE 199 OF POOR QUALIV H1

1 Notes on Image Reconstruction for COSMIC l

Part II (pp, 60-155)

Warren F. Davis

15 October 1982

Contents

page

Rotation and autocorrelation of the aperture 60

Aperture synthesis 75

Fourier shift theorem 75

Poisson photon statistics 85

Review of Poisson statistics 86

Post-aperture statistics 89

Fourier domain statistics 89

Other sources of noise 94

Noise filter with Poisson statistics 96

Some moments in the Fourier plane 108

Optimization in the Fourier plane 110

Combined images 132

Iterative solution 141

Hill-climbing solution 142 I

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