815-820, 1997 July Stellar Coronagraph with Phase Mask

Publications of the Astronomical Society of the Pacific 109: 815-820, 1997 July

Stellar Coronagraph with Phase Mask

François Rodder and Claude Roddier Institute for Astronomy, 2680 Woodlawn Drive, Honolulu, Hawaii 96822 Electronic mail: roddier or croddier® uhifa.ifa.hawaii.edu Received 1996 December 12; accepted 1997 April 7

ABSTRACT. The detection of faint light sources very close to a bright star is primarily limited by light scattered by the Earth's atmosphere. This source of scattered light can now be reduced by means of adaptive optics, or totally eliminated by using a telescope in space. Then diffraction by the telescope aperture becomes the primary source of scattered light. Whereas a classical Lyot coronagraph can reduce the amount of light diffracted away from the star, it becomes inefficient very close to the star. Instead of forming the stellar image on an opaque mask, here it is proposed to use a small phase plate which produces a 180° phase shift on the core of the stellar image. Light diffracted outside the core is then eliminated by destructive interference. Applied to the Hubble Space Telescope, the technique would easily allow detection of a stellar companion 0"3 away from a star and at least 8 mag fainter.

1. INTRODUCTION 2. THE LYOT CORONAGRAPH Astronomers are increasingly interested in detecting faint The coronagraph was invented by Lyot (1939) as a light sources in the close stellar environment. Some observe means to reduce the amount of light diffracted by the light scattered by dust either ejected from evolved stars, or telescope aperture. It was used to observe the solar corona condensing around young stars and forming proto-planetary a few arcmin away from the solar limb. At this distance, disks. Others are looking for faint stellar companions or light scattered by the telescope dominates and must be first "brown dwarfs." In addition, indirect evidence recently reduced by using super-smooth refractive optics often re- found for extra-solar planets has boosted interest in their ferred to as "coronagraphic optics." During the last decade, direct detection. "stellar coronagraphs" have been built and used with some Such observations are hampered by light scattered from success on ground-based telescopes (Vilas and Smith 1987; the central star. There are essentially three sources of scat- Paresce et al. 1988). By masking the star image, they avoid tered light: atmospheric turbulence, diffraction by the tele- blooming, a detrimental effect observed on most CCD de- scope aperture, and surface roughness of optical elements. tectors. In addition, the Lyot stop in the pupil plane reduces Figure 1 shows a typical example of intensity distribution as light diffracted by the telescope spider arms. However, the a function of distance to the central star. Calculation was reduction of light diffracted by the telescope aperture ap- made for a 3.6-m telescope operating at a wavelength of pears to be of little use as long as the two other sources of 1.65 /xm. The full line is for light scattered by the atmo- scattered light dominate. According to Fig. 1, a stellar coro- sphere. Fried's seeing parameter was taken equal to 18 cm nagraph is most effective at a distance of a few arcsec from at 0.5 μιη, a median value at the Mauna Kea Observatory. the central star where the two other sources have a similar At large distances the amount of scattered light decreases as contribution, but the gain is small. the - 11/3 power of the distance (Roddier 1981). The dot- Light scattered by the atmosphere can now be reduced ted line is for light diffracted by the telescope circular by adaptive optics and is totally absent in the Hubble Space aperture. At large distances it decreases as the cube of the Telescope (HST). It is clear from Fig. 1 that under these distance (Bom and Wolf 1980). Light diffracted by struts conditions the use of a stellar coronagraph will be much supporting the telescope secondary mirror (spider arms) is more effective, particularly when one wants to observe very not plotted here. Although it decreases as the square of the close to a star. Golimowski et al. (1992) were the first to distance and rapidly dominates all other sources of scattered associate real-time atmospheric tip-tilt compensation with a light, it usually does so only along two orthogonal direc- stellar coronagraph. A similar system was later operated by tions, and is negligible anywhere else. The dashed line is Walker et al. (1994) using a modification of the CFHT for light scattered by the surface roughness of optical ele- tip-tilt compensated camera (HR Cam). More recently Mal- ments. Values are typical for a telescope mirror. They are bet (1996) described results obtained with a stellar corona- wavelength independent and approximately decrease as the graph operating with the ESO "COME-ON" adaptive optics square of the distance (de Vaucouleurs 1958; KenKnight system. As shown in Fig. 1, these coronagraphs are ex- 1977). Figure 1 shows that all three sources of scattered pected to be particularly effective at a distance of less than light have a similar contribution at a distance of about 2 2" from the occulted star, with a small stellar mask. Un- arcsec from the star. Beyond this distance, light scattered by fortunately, a small mask diffracts light which blurs the telescope optics dominates whereas at shorter distances pupil edge. The smaller the mask, the wider the blur, and scattering is mostly due to the Earth's atmosphere. the more one has to stop the pupil down to eliminate light

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distance (arc-second) B{F) Fig. 1—Distribution of scattered light as a function of distance to a mag 0 Mñ star. Full line: atmospheric turbulence. Dotted line: diffraction by telescope aperture. Dashed line: optical surface roughness. Calculations are for a Fig. 2—Top row: sketches of the amplitude in the image plane. A(a): 3.6-m telescope at wavelength of 1.65 μιη. outside the mask. Β (a): inside the mask. Bottom row: sketches of the amplitude in the pupil plane. A(r): diffracted outside the mask. 5(r) : diffracted inside the mask. diffracted by the edge. Typically a Lyot mask will cover the central core and the first three or four rings in the Airy light from a faint companion outside the phase mask will be diffraction pattern. However, this is the region where adap- little affected and almost totally transmitted. Figure 2 shows tive optics is the most effective in reducing light scattered by the atmosphere and therefore where a coronagraph a sketch of the four functions A (a), 5(a), A(r), and would be the most effective. Here we propose a new type of 5(r). stellar coronagraph which avoids this problem. Obviously, a very small phase mask will produce ampli- tudes A(r) and B{y) which are fairly uniform all over the 3. THE PROPOSED CORONAGRAPH telescope aperture but 5(r) will be smaller than A(r). To balance the two illuminations one must absorb light outside The proposed coronagraph is essentially identical to the of the phase mask with a density filter. Theoretically, light Lyot coronagraph apart from the stellar occulting mask rejection can be as good as one wants, but at the cost of an which is replaced with a phase mask. The phase mask is ever increasing exposure time. On the other hand, one can much smaller than the occulting mask. It covers only a balance the illuminations by using a phase mask which fraction of the core of the Airy pattern. It is totally trans- covers exactly 50% of the energy in the Airy pattern. Then, parent, but introduces a 180° phase shift on the incoming a density filter is no longer needed but the two interfering wave. After transmission through the mask, the complex beams are no longer uniform over the aperture plane, and amplitude can be expressed as a sum of two terms A (a) imperfectly cancel each other. Computer simulations de- + B{a), where A (a) is the complex amplitude of the Airy scribed below show that the level of light rejection is still pattern in which the central part has been set to zero over better than that of a conventional Lyot coronagraph, com- the phase mask area, and Β (a) is a function equal to zero parable to that of an apodized Lyot mask (OUver 1975; everywhere except over the small mask are where it is Ftaclas et al. 1988; Ftaclas 1995). In addition it allows negative (180° phase shift). The position vector a is con- observations to be made much closer to the central star. sidered here as angular coordinates on the sky (Fig. 2). The It is interesting to note that the phase mask technique complex amphtude in the following pupil plane is the Fou- could also be used to detect a faint object within the side rier transform A(r) + 5(r) of A{a) + B{a), where the po- lobes of a stellar image produced by a telescope array. In sition vector r is expressed in wavelength units in the tele- this case, a Lyot mask covering only the core of the stellar scope aperture plane. Since the Airy pattern A{a) has been image would diffract light over the whole aperture array, set to zero at the origin, its Fourier transform A(r) re- and would be useless. A phase mask of the same size would sembles the telescope aperture transmission function but it also diffract light over the whole aperture array, but by is zero mean, that is, A(r) is positive inside the telescope interfering with the direct beam, the 180° phase shifted aperture, but negative outside. If Β (a) is much narrower beam would cancel stellar light inside each aperture. Unfor- than the Airy pattern, its Fourier transform Β (τ) is much tunately, a density filter would be needed to balance the wider than the telescope aperture and negative everywhere. fluxes. This may still be acceptable with a sufficiently com- If its modulus can be made equal to that of A ( r) inside the pact array. aperture, both terms will cancel out by destructive interfer- A drawback of the technique is that the phase mask is ence sending all the light outside the telescope aperture wavelength dependent. Means to produce achromatic phase where it is intercepted by the Lyot stop. On the other hand, masks will be discussed in Sec. 5. We describe here com-

© Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System STELLAR CORONAGRAPH 817 puter simulations which have been made to assess the sys- with a phase mask as it is with an occulting mask (see Sec. tem performance on single telescopes. 6). No attempt was made to use an apodized Lyot stop. A conventional Lyot coronagraph was first simulated with a 4. COMPUTER SIMULATIONS 074 radius occulting mask covering the first three diffraction rings. Figure 3(a) shows a plot of the log intensity in All simulations were made at a wavelength of X = 1.65 yLtm. The diameter of the telescope aperture was the final image plane. The full line is without a coronagraph first assumed to be D = 3.6 m, and reduced down to 3.1 m (no occulting mask, no Lyot stop). The dashed line is with by a Lyot stop, although such a stop is not as necessary the coronagraph. Although the attenuation of the envelope

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Fig. 3—Distribution of light diffracted by the telescope aperture as a function of distance to star. Full lines: without coronagraph. Dashed lines: (a) with a conventional Lyot coronagraph, (b) with a large phase mask, (c) with a small phase mask surrounded with a density 1.8 filter. Dotted lines: with hybrid masks. All calculations are at a wavelength of 1.65 /xm for a 3.6-m telescope (Lyot stop size: 3.1 m).

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(line of maximums) is larger further away, at the edge of the result of simulations made with a phase mask radius the mask it is only by a factor of 40. Moreover, part of the Po = 0.24 λ/D, that is 0.20 times the radius of the first attenuation is due to the Lyot stop and will also affect a dark ring in the Airy pattern. To balance the fluxes, the stellar companion. After correction for this effect the back- illumination outside the mask had to be reduced by a factor ground rejection is by a factor of 30. of about 38, which may still be acceptable on bright objects. The occulting mask was then replaced by a pure phase The dashed line in Fig. 3(c) has been corrected for the mask producing a 180° phase shift inside a small circle of increased exposure time. At a distance of 0'.'4, the attenu- 3 radius po · The value of the radius p0 was adjusted by trial ation of the envelope is now by a factor of 10 , and the and error to minimize the total flux inside the Lyot stop. background rejection is by a factor of 750. Moreover, at the The optimum size was found to be 0.43 times the radius of distance of the first bright ring (0r.r15), the rejection is the first dark ring in the Airy pattern, that is p0 approximately as high. = 0.53 \/D. This radius indeed encircles 50% of the en- One can also envisage the use of a hybrid mask that will ergy of the Airy pattern (Bom and Wolf 1980), and there- change both the phase and the amplitude of the incoming fore exactly balances fluxes with opposite phases which wave front within a given radius pi. To determine the cancel each other on the telescope pupil. Figure 3(b) is a optimum amplitude change, we use the following algorithm. plot of the log intensity. Again, the full line is without a We first start with a pure phase mask of radius p0 either coronagraph (no occulting mask, no Lyot stop) whereas the large with no density filter or small but surrounded with a dashed line is with the phase mask and the Lyot stop. At density filter, and we compute the complex amplitude in the the same distance of 074 that was considered above, the pupil plane. The resulting modulus is set to zero inside the attenuation of the envelope is now by a factor of 210. pupil and the inverse Fourier transform is taken producing a Taking into account the loss through the Lyot stop the new complex amplitude in the image plane. We replace it background rejection is by a factor of 156, that is seven with the original complex amplitude except for the modulus times larger than with a conventional coronagraph but still which is replaced by the new modulus inside the radius comparable to that of an apodized coronagraph (Olivier Pi(pi '> Po)· After several iterations the algorithm con- 1975; Patelas et al. 1988; Patelas 1995). However, observa- verges toward an optimized amplitude in the image plane. tions can now be made much closer to the central star. At The ratio of the modulus of the optimized amplitude over the distance of the first bright ring (0'.'15), background the modulus of the original amplitude is taken as the am- rejection is still by a factor of 74, a performance impossible plitude transmission of the optimized mask. Since this ratio to achieve with an occulting mask. may exceed unity, it is renormalized to a new maximum As shown in Sec. 3, a smaller phase mask should be equal to unity. even more effective as long as the fluxes can be properly Results of simulations made with hybrid masks are balanced, that is as long as the surrounding field can be shown by the dotted lines in Figs. 3(b) and 3(c). For each attenuated with a proper density filter. Pigure 3(c) shows figure the dashed line and the dotted line were obtained

Fig. 4—Image profile along two points sources 0'.'3 apart with a magnitude difference Am = 8. (a) Without coronagraph; (b) dashed line; with a pure phase mask; dotted line: with a hybrid mask. Calculations are for a 2.4-m telescope (HST) at λ = 1.65 μτη. They include the effects of HST residual aberrations and finite optical bandwidth (Δλ = 0.1 /¿m). with the same phase transmission. The dotted lines show mize the mask depending upon the application. At this the effect of also modifying the amplitude up to a radius point, factors such as residual optical aberrations or the p1 equal to that of the first Airy dark ring (Fig. 3(b)) or the finite optical bandwidth become important limitations. We second dark ring (Fig. 3(c)). The dotted line has been cor- now examine such limitations and discuss how they can be rected for the exposure time increase due to the mask. Note, overcome. the gain in rejection brought by the amplitude change, es- 5. OPTICAL BANDWIDTH LIMITATION pecially close to the mask. In Fig. 3(c), at the distance of the first bright ring (0"15), the rejection is now by a factor A phase retardation of 180° can be obtained with a phase of 1.5 X 105. It is clear that there are many ways to opti- plate. A phase plate of thickness e made of material of

© Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System 820 RODDIER AND RODDIER index η will introduce a phase retardation φ — Ιπηβ/λ, μιη intervals and co-added. The object consists of two point which varies as the inverse of the wavelength λ. This varia- sources 0".3 apart with a magnitude difference Am = 8. In tion will obviously limit the bandwidth. If the phase φ the Η band this magnitude difference is that of a brown differs from 180° by an angle Αφ, light no longer cancels dwarf such as Gliese 229B near an Ml star (Nakajima et al. out. A fraction Δ φ2 of the total intensity remains. If we 1995) but much closer (073 instead of 7"6). want this fraction to be less than 0.01, then Δφ must be less Figure 4 shows photometric profiles of the images taken than 0.1. Since |Δφ/φ| = ΐΔλ/λ|, taking ψ = π,Δφ along the two sources, and reproduced with the same inten- = 0.1, and λ = 1.65 μπι gives Δλ = ±0.05 μιη, that sity scale. Figure 4(a) shows the profile of the image ob- is about one third of the standard infrared Η band. Another tained without a coronagraph. Its central intensity was nor- limitation comes from the wavelength dependence of the malized to unity. Depending on the signal-to-noise ratio width of the Airy disk. The same requirement that the (SNR), it would clearly be difficult to detect the faint com- residual intensity must be less than 0.01 implies that the panion source among the bright diffraction rings. Figure intensities must be balanced within 10%. From the profile 4(b) shows profiles of the image obtained with the corona- of the encircled energy in the Airy pattern (Bom and Wolf graphic masks. The dashed line is for a pure phase mask 1980), it implies a maximum variation of 7% on the size of with no density filter. The dotted line is for a hybrid mask the Airy disk. At λ = 1.65 μτη, this corresponds to a more extending up to the first Airy dark ring. In both cases the relaxed tolerance of Δ λ = ±0.11 μτη. companion is clearly seen. Depending again on the SNR, a There are ways to overcome these limitations. The phase much fainter companion could easily be detected by sub- plate can be surrounded by another material with refractive tracting an appropriate reference profile. For instance a index nf. Then the relative phase retardation becomes φ brown dwarf 10-100 times fainter could possibly be de- = 2π(η — n')e/k. By appropriate choice of material one tected by comparing images taken inside the methane band can attempt to make η —η ' approximately proportional to λ (1.65 μιη) with images taken outside (1.55 μιη). A detailed within the wavelength range of interest so that φ becomes study of the ultimate performance that could be achieved wavelength independent. If necessary, one can also keep the with the proposed coronagraph is beyond the scope of this fluxes balanced by using glass material with an appropriate paper. color dependent transmission. In the following section we assume that no such refine- This research is supported under NSF Grant AST- ment is made and shows the results of simulations which 9618852 take both into account chromatic effects and telescope aberrations. REFERENCES 6. APPLICATION TO THE HUBBLE SPACE Bom, M., and Wolf, E. 1980, in Principles of Optics (London, TELESCOPE Pergamon), 6th ed., p. 395 As discussed in Sec. 2, a stellar coronagraph is particu- de Vaucouleurs, G., 1958, ApJ, 128, 487 larly useful under conditions where diffraction by the tele- Ftaclas, C., Siebert, E. T., and Ternie, R. J. 1988, in Space Optics scope aperture is the primary source of scattered light. This for Astrophysics and Earth and Planetary Remote Sensing, OSA Tech. Dig., 10, 62 is the case for observations made with the HST very close Ftaclas, C. 1995, Proceedings of the 15th NSO/Sac Peak Summer to a star. Not only is the atmospheric contribution absent, Workshop, ed. J. R. Kuhn and M. J. Perm (Singapore, World but the telescope optical quality is also particularly good. Scientific), p. 181 Moreover, HST will soon be equipped with an infrared Golimowski, D. Α., Clampin, M., Durrance, S. T., and Bark- camera operating in a wavelength region (1-2.5 μνη) where houser, R. H. 1992, Appl. Opt., 31, 4405 telescope aberrations are less detrimental than in the visible. KenKnight, C. E. 1977, Icarus, 30, 422 We have simulated HST images taken inside a bandwidth Lyot, B. 1939, MNRAS, 99, 580 extending from 1.60 to 1.70 /mi, both without a corona- Malbet, F. 1996, A&AS, 115, 161 graph and with a coronagraph equipped with a pure phase Nakajima, T., Oppenheimer, Β. R., Kulkami, S. R., Gollimowski, mask covering 50% of the Airy disk energy with no density D. Α., Matthews, Κ., and Durrance, S. T. 1995, Nat, 378, 463 filter, that is the simplest to implement. For these simula- Oliver, Β. D. 1975, in Imaging in Astronomy (OSA Meeting, Cambridge, MA, 18-21 June 1975) OSA Tech. Dig. tions the Lyot stop was open to the full pupil size. The Paresce, F., Burrows, C., and Home, K. 1988, ApJ, 329, 318 diameter of the phase plate was optimized for the central Roddier, F. 1981, Prog. Opt. , 19, 281 bandwidth of λ = 1.65 μιη. The telescope aberrations Roddier, C., and Roddier, F. 1993, Appl. Opt., 32, 2992 were taken from a phase map published by Roddier and Vilas, F., and Smith, B. A. 1987, Appl. Opt., 26, 664 Roddier (1993), which assumes no residual spherical aber- Walker, G. A. H., Walker, A. R., Racine, R., Murray Fletcher, J., ration. Images were computed at eleven wavelengths at 0.01 and McClure, R. D. 1994, PASP, 106, 356