A Photoelectric­ Photographic Study of the Normal Albedo of the Moon

By HOWARD A. PORN and ROBERT L. WILDEY Accompanied by an ALBEDO MAP OF THE MOON

By HOWARD A. PORN, ROBERT L. WILDEY, and GAIL E. SUTTON CONTRIBUTIONS TO ASTROGEOLOGY

GEOLOGICAL SURVEY PROFESSIONAL PAPER 599-E

Prepared on behalf of the National Aeronautics and Space Administration

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON 1970

CONTRIBUTIONS TO ASTROGEOLOGY

A PHOTOELECTRIC-PHOTOGRAPHIC STUDY OF THE NORMAL ALBEDO OF THE MOON

By HowARD A. PoHN and RoBERT L. WILDEY

ABSTRACT urement of this brightness V1ariation and its delineation A map of the normal albedo of the moon has been prepared are the subjects of this study. by automatically measuring and raster-recording the optical Differences in reflected brightness of the lunar sur­ density of a photoelectrically calibrated full-moon photographic face are obvious to the naked eye. Even without a tele­ plate. Calibration permits direct transfer of normal albedo (after scope, the eye can distinguish between large mare areas reduction from the photoelectric signal recorded by the photom­ eter) to the isodensity contours of the photographic image. On (dark) and highland or other mountainous areas of the night that the photog·raphic and photoelectric Observations large extent (bright). The significance of these bright­ were made, the lunar phase angle was 1.5°. Photoelectric obser­ ness variations, especially under full-moon illumination, vations of 182 points scattered across the lunar surface were has been an intriguing problem to astronomers for more correlated with the density of corresponding points on the photo­ than four centuries. gravhic plate. Plate exposure coincided in time with the photo­ electric photometry. The photographic emulsion-filter combina­ During the past 6-7 years, geologists have under­ tion used provided a poorer approximation of the spectral taken lunar albedo studies as a tool in mapping the bandpass of the Johnson photoelectric V magnitude than the lunar surface. Several relationships between reflected emulsion-filter combination normally used for stellar photo­ brightness and geology have been investigated in the graphic V; however, the spectroscopic emulsion used for stars is lunar mapping program of the U.S. Geological Sur­ unnecessarily grainy and too fast for a photometric exposure. The moon's color is much more uniform than that of a field of vey. Wilhelms (1966) noted that the brightness of startS; hence, the errors due to color effects that were introduced some mare materials varies inversely with their age: during calibration are insignificant. The photographic plate was the older-and more densely cratered-the mare, the transcribed as a density map at a scale of 1: 5,000,000, using a higher its albedo. Before this relationship had been Joyce-Loebl-Beckman-Whitley combination densitometer and stated, however, differences in albedo had been used code tracer. Steps were taken to reduce random error by insur­ ing uniformity of the photographic process. This random error to divide the mare area and to establish superposition was measured to be about 1 percent. The range Olf normal albedo relationships in maTe areas (Shoemaker and Hackman, was divided into 20 contour intervals, with extremes of 7 and 23 1962). The bright ray materials, whose radial pat­ percent nt the 3" of arc resolution employed. Reliability of the terns are so strikingly displayed under full-moon illu­ map is assured because, for the first time, simultaneous photo­ mination, 'vere notable examples of candidates for such elec-tric calibration was utilized and the plate parameters~ were analysis. Relative ages of crater ray patterns as well demonstrably uniform. The map has already proven to 1be of as other albedo patterns of mare units were thus de­ great utility in the fields of lunar geologic mapping and astro­ nautical engineering. lineated. As a result of photoelectric studies, Wildey and Pohn ( 1964) noted a general correlation between INTRODUCTION brightness of probable impact craters and their age : the younger the crater, the brighter its appearance. The primary principles of superposition, intersection, This inverse relationship (in comparison with the and topographic expression are fundamental to both maria) may depend in part on the fact that larger terrestrial and lunar geologic mapping. Rock color, a areas of relatively light shock-metamorphosed material secondary property useful on earth, cannot be used in will be exposed in younger craters than in older de­ mapping the moon because of the moon's lack of color graded ones~·· Much more work is needed to determine diversity. The lunar surface does, however, exhibit a hmv and to what extent geology correlates with albedo wide range of reflected surface brightness. Precise meas- on a 1noon-wide scale. E1 E2 CONTRIBUTIONS TO ASTROGEOLOGY

While variation in reflective brightness is an impor­ direction. (For more details see section on "The theory tant characteristic of the appearance of surficial ma­ of Lambert scattering and the absolute calibration of terials during all phases of the moon, it is inseparable normal albedo.") Because the reflectivity of the moon from topographic expression except when the phase appears to be independent of the incident and emergent angle is close to zero (during the full moon) . The ge­ angles at zero phase angle (at least for terrestrial ob­ ometry of the general case is shown in figure 1. At full servations), the measured geometric albedo 1 at zero moon, when no shadows are visible from earth, the phase angle can be equated with the normal albedo, distribution of reflectivity appears to express actual even though, as formally defined, they do not coincide variations in the composition or surface characteristics at the subearth point. of the lunar surface materials. The diffuse reflectivity of NOTE.-In other words, the brightness exhibited by the lunar the full moon is commonly expressed as normal al­ surface when sun, earth, and moon are alined (idealistically bedo-the brightness of the lunar surface divided by :a voiding eclipse) is the same whether the lunar surface is the brightness of a Lambert surface when observer and oriented perpendicular to the line of sight or oriented in any light source are along the same normal vector. A Lam­ 1 Geometric albedo is defined in association with a Lambert surface, as bert surface is an ideal diffuse reflecting surface ; it is is normal albedo; however, the geometry is flexible and must be specified together with the numerical value of the geometric albedo to avoid nonabsorbing and uniformly bright from any viewing ambiguity.

local normal vector Local normal vector

lunar tangent ~--e-J-----;r----J~~~j)

Earth

lunar tangent

FIGURE 1.-Geometry of the generalized illumination and ob­ at o=O; g:=phase angle; a::=brightness longitude. A third servation of the moon. An altazimuth coordinate system coordinate seems to be unnecessary for specifying lunar .possessing no singularities is shown at left: i:=angle of brightness to present observational precision. That the di­ incidence (of the sun), e:::::angle of emergence (of the earth rections to the sun (and the earth) are nearly parallel •or wherever observation might be taken), and u:=azimuth whether taken from the moon's center (shown as point 0) between sun and earth. (Note that i and e are the comple­ or from any point on its ·surface is what characterizes a: ws ments of the local altitudes of the sun and the earth respee­ a "longitude," ·assuming that the topography is fiat. Full tively.) On the right is a coordinate system having special moon implies o=O. significance for lunar reflectivity, which has :a singularity PHOTOELECTRIC-PHOTOGRAPIDC STUDY OF THE NORMAL ALBEDO OF THE MOON E3 other arbitrary way. Of course, the abrupt tralllSition to zero curve is obtained from the imprint of a wedge or a brightness at an observing angle of ooo, beyond which forward spot photometer, one will obtain relative brightnesses scattering into an opaque medium would be indicated, must be smooth to avoid a physical discontinuity. However, the transi­ devoid of systematic errors only if ( 1) the exposure tion region occupies too small an ·angular range to be of con­ times used in the lunar and calibration photography cern here. The map resulting from the present study shows no are the same to within approximately 50 percent and obvious limb darkening with the possible exception of the ex­ ( 2) the radiative energy distributions of the moon and treme proximity of the limb. This c>olliStitutes one of the observa­ the calibration source agree to within a few tens of tional bases for the assumption that the photometric function of the moon has a value, at zero phase angle, which is independ­ percent. The imprinting process must also be known ent of ·all other geometric degrees of freedom. The test iJs partly to be devoid of errors. vitiated by the fact that the moon is not a body of uniform Second, absolute calibration by purely photographic absorptivity. means requires an rubsolutely standard comparison There is a second observational basis for ·assuming that source whose image is processed in a rigorously equiva­ normal albedo and zero-phase a1bedo are equal. It is a fact, lent maimer. If errors due to atmospheric transmission previously observed photoelectrically by the authors, that the brightness versus phase curves of a collection of 25 lunar fea­ fluctuation are avoided, the standard should be extrater­ tures of various types and locations possess waxing and waning restrial, preferably near the moon. In general, if the branches which coincide assymptotically near zero .phase spectral energy distributions of moon and standard are angle, regardless of location on the moon. Thus, for two small not exactly the same, the spectral responsivity of the and equiV'alent phase angles (up to about 5°) taken before and emulsion must be known. Thus to relate photographic after full moon, the value of the photometric function is the same even though changes in the values of the angle of inci­ density to normal albedo, it is helpful to make true dence and the angle of observation may be as much as several radiative power measurements external to the plate. degrees. '..Vllis is, of course, a direct test of the assumption that Even calibration in this manner is not possible, how­ the moon's zero-phase albedo is equivalent to its normal albedo. ever, unless care is taken to insure uniformity of ex­ Unfortunately, the geometric limitations imposed by the moon's posure, emulsion sensitivity, and development. synchronous rotation and the earth-based nature of the observa­ tions do not permit ·a test in which the changes in dbserving Most early lunar photometric observations were and incident angles are a large fraction of their possible range. purely photographic (Minnaert, 1961). The advantage A thi·rd basis is derived from the fact that previous studies of a photographic plate is that all image elements 2 in have shown that the moon's photometric :function depends pre­ the brightness distribution of a celestial body can be dominantly, if not wholly, upon phase angle and brightness observed simultaneously. On the other hand, the photo­ longitude, over the general range of variables. From the geome­ electric technique, although it can only record one image trical definition of brightness longitude, it can be easily shown that it is mathematically indeterminate at zero phase angle, element at a time, produces a recorded signal which is hence the implication that it must approach zero influence in linear in specific intensity (equivalent to surface bright­ this neighborhood. ness), extremely precise, highly stable, and easily cali­ It thus appears that the assumption of the equivalence of brated to absolute units. Unfortunately, individual normal albedo and zero-phase albedo rests upon a great deal resolution elements of the picture must be recorded con­ of evidence. It is not fair to say, however, that the precision (over all the ranges of the variables involved) with which secutively by some form of spatial scanning. This is time the assumption has been tested has been equal to the funda­ consuming and can lead, under certain conditions, to mental precision of the observational photometry, for the test spurious brightness variations in ·the image because of of such an assumption appears to be fundamentally limited by 3 the techniques of ground-based astronomy. Should practical the fluctuations with time in atmospheric transmission. consequences of the fact ever become significant, the authors Clearly, one way to obtain reliable photometric measure­ wish to point out that the present study has produced a map ments of the entire full-moon disk is to use a photoeloo­ of zero-phase geometric albedo whose approximation to a map trically calibrated photograph. of normal albedo is better than for which we can now test. Obtaining reliable photoelectric and photographic Photographic density can be measured on a full-moon data on the full moon presents several pr

FIGURE 2.-The 61-inch flO astrometric reflecting telescope with piece. The side-mounted eyepiece near the top of the black direct photographic camera used to collect the photographic module immediately behind the primary mirror cell is for plate data for the albedo map obtained in the present study. manual telescope guiding. The rest of this section contains Folded-prime focus is behind primary mirror as in Cassegrain the automatic photoelectric guiding. Auxiliary telescope fa­ systems. A swing-out position-finding eyepiece is shown at bot­ cilitates position finding. (Photograph by U.S. Geological tom. The plateholder fits into slot immediately behind this eye- Survey through the courtesy of U.S. Naval Observatory.)

373-263 0-70-- 2 E6 CONTRIBUTIONS TO ASTROGEOLOGY

FIGURE 3.-U.S. Geological Survey 30-inch fl5 Cassegrain tele­ tion, containing filter wheel, focal-plane-diaphragm wheeil, scope with photoelectric photometer attached to tailpiece; this and knife-edge focus viewer. The box on the immediate left equipment was used to obtain the photoelectdc observations side contains a periscope for viewing the focal plane image. for the albedo map of the present study. The electronics bay From top to bottom in the electronics hay to the right of cen­ on the left houses the power supply, oscillator, and amplifier ter, is seen a Mosely Autograf strip chart recorder, a Frigi­ for the variable hour angle drive of the telescope. A variable tronics thermoelectric current generator, and a General Radio declination drive is not shown. The photometer is displayed Direct-Current Amplifier and Electrometer. Farther down and with three prominent sections. Lowermost is the Frigitronics out of the picture is a OaUbration Standards high voltage colld-box housing the 1P21. Thermoelectric cooling is used, power supply that is set at 900 volts; it supplies the photo­ with styrofoam insulation. Heat is carried away from the multiplier bias. A •Sorenson voltage regulator is the main cooling fins by an electric f.an. In the middle is the optics sec- power source for the bay. PHOTOELECTRIC-PHOTOGRAPffiC STUDY OF THE NORMAL ALBEDO OF THE MOON E7

FIGURE 4.-Photoelectric photometer with periscope viewer filters. Behind this wheel is a partition with a filter-size removed to reveal the internal workings. The light from aperture for reduction of the admission of scattered light into the telescope enters from the lower right-hand corner. The to cold-box. A .rotating polarimeter which can be inserted wheel angled at 45° to the optical axis has selectable into the light path via a plunger-operated slide was not used ·aluminized diaphragms with variable sized apertures. The in this study and is shown at the far side (upper right) of focal plane is formed at the center of the aperture. A large the section behind the partition. On the upper left wall of aperture is used for stellar measurement, and the smallest this section may be seen the Fabry lens (quartz) which for lunar measurements. The periscope thus views the lunar focuses an image 0.25 centimeters in diameter of the prima.ry image with a dark spot signifying the portion of light ad­ mirror on to the photocathode of the 1P21. The toggle switch mitted to the photomultiplier. Immediately behind this wheel •at the side of the cold-box enables the selection of either is a plunger-operated periscope which, when "in," provides the standard 10 dynodes of multiplication or, through short a view of that part of the focal plane within the aperture. circuiting the last stage, nine dynodes and a double anode. Since one of the positions on the wheel is a knife edge, the In this way the linear range of the photomultiplier is ex­ focusing of the telescope is also facilitated at this viewing tended by postponing space-charge Umited operation with­ ·port. ln the "out" position, light is allowed to pass into the out the problem of the gain instal>ilioty that would attend the balance of the photometer. Next, the wheel that is perpen­ accomplishment of the same end by lowering the supply dicular to the optical axis houses fix filters, three of which voltage. are now kept opaque and three of which contain the UBV E8 CONTRIBUTIONS TO ASTROGEOLOGY

of Schott GG 13 and 0.7 mm of Schott BG 12. The ultra­ ABSOLUTE CALIBRATION violet filter is a Corning 9863. The focal-plane dia­ Of the four photoelectric scans taken on the night of phragm transmits a circular beam of light 2.64" of arc June 2-3, one scan of the southern lunar highlands was in diameter corresponding to a spot 4.8 kilometers across rejected because its location eould not be precisely de­ at the center of the lunar disk. termined, and a second scan taken centrally on the disk The photogr3!phic data were reduced on the Joyce­ was rejected because a large atmospheric extinction cor­ Loebl microphotometer-Beckman and Wl1itley Isoden­ rection was required. The two remaining soans, one near sitracer (IDT) combination using a square aperture the equator and the other aJt about lat 25° N., were taken 0.173 mm on a side. This aperture setting resulted in immedia.tely before and after the photographic plate a sampling resolution for the photographic plate that was exposed. Scanning time was approximately 25 min­ was comparable to the resolution inherent in the spatial utes per scan; each extended from limb to limb. To in­ scans made with the photoelectric photometer at the sure coverage of the extremes of brightness of the lunar telescope. It is also consistent with the maximum amount disk, single points in Aristarchus, Tycho, and LeMon­ of information that can be portrayed on a 1 : 5,000,000- nier were also measured. scale map, even though the plate can yield additional For precise calibration the requirements were a sele­ information at finer sampling resolution. nographic congruence of points measured both photo­ The interva.l between scan centers on the plate was electrically at the telescope and densitometrically on the 75p. and provided an overlap of 57 percent between suc­ cessive scans. The c.a.libra.tion wedge used in the IDT lunar photograph. The photographic · plate was posi­ had a dynamic range of 0-2.4 in optical density, with tioned on the IDT (operating in tJ1e scan mode) to re­ step increments of 0.1195 in density. The range of nor­ produce exactly the selenogr.aphic traverses of the scans mal albedo was thus divided into 20 unequal contour which were obtained by the photoelectric photometer intervals. The maximum (23 percent) and minimum (7 directly at the telescope (fig. 5). In addition, densities of percent) values of the moon's normal albedo have been the control points in Aristarchus, Tycho, and LeMon­ satisfactorily bounded by the scale. nier were individually measured on the plate.

Photographic scan

Photoelectric scan L

FIGURE 5.-A comparison of signal traces adjusted to the same scale of abscissa. Both follow the same track across the mOQD.. Lower curve: amplified photoelectric voltage as ordinate on the same voltage scale used for recording flux voltages of standard stars. Upper curve: conrtinuous record of density of the simultaneous1y recorded photographic plate on the same vertical density scale that is coded by the Joyce-Loebl-Beckman and Whitley I sodensitracer. PHOTOELECTRIC-PHOTOGRAPIDC STUDY OF THE NORMAL ALBEDO OF THE MOON E9

It is most convenient to convert the signal scale of from an independent photoelectric measurement of ratio the photoelectric charts to normal albedo before relat­ of blue to yellow signals-reasonably the invadanlt over ing the photoelectric photomeJtry to the photography. the lunar disk-can therefore be reduced to dbtain, in Determination of normal albedo from photoelectric sig­ sequence, a V magnitude,- a specific intensity, and a nor­ nal proceeds in three steps (for more details see specified maJ albedo for a full-scale deflection. With these limits sections in "Conversion and calibration data") : ( 1) Cor­ of normal albedo, the rest of the scale follows by a direct rection of the photometry for differences in spectral proportioning over the ordinUAte interval. response and power scale between the operational sys­ By obtaining absolute spectral radiometry on any one tem of the telescope-photometer (after correcting for of the UBV standard stars, or any nonvariable star atmospheric extinction) and an intermediate standard whose V magnitude and B-V color index will at some system, in this case, the Johnson-Morgan UBV system time be determined by photoelectric measurement, an (sec section on "The theory of astronomical photometry absolute calibration of ~the entire U BV system can be and systems of stellar magnitudes and colors") ; ( 2) determined. Such data were collected by Willstrop conversion of the intermediate V magnitude to a wave­ ( 1960) , and the resulting calib:ration was determined length-averaged absolute specific intensity or surface by Wildey and Murray ( 1963). The conversion from a brightness (see section "The theory of Lambert scatter­ V magnitude of a known solid angle to a specific inten­ ing and the absolute calibr,ation of normal albedo") and sity can thus be obtained. a corresponding effective wavelength (see section on In the determination of normal albedo from observed "Specific intensity and effective wavelength"); (3) de­ specific intensity, a hypothetical Lambert surface must termination of the normal specific intensity of a Lam­ be placed at the point in space occupied by the moon, bertian scattering surface at the same distance from the and the specific intensity tha.t it would exhibit because sun on the basis of published absolUJte solar photometry of its diffuse reflection of sunlight must be calculated. (see section on "The theory of Lambert scattering and The distance from the sun to the earth-moon system at tho absolute calibration of normal albedo"). the time of the dbservations is obtained from the ephem­ .A small correction ( 0.05 magll.itude), obtained from eris. A hypothetic.al Lambert scattering surface has a the brightness versus phase curves at small angles specific intensity under normal illumination which is (Wildey and Pohn, 1964), was applied to extrapolrute completely specified by the properties of (1) total re­ magnitudes to zero phase angle. Within about 5° of flection, ( 2) a specific intensity constant over all positive zero phase angle, variation in size of the ext:vapolation directions and zero over all negative directions, ,and ( 3) does not correlate with class of lunar feature (within the a known apparent V magnitude for the sun (Stebbins precision of the investigation), and the waxing and and Kron, 1957). An observational normal albedo is waning branches of the brightness versus phase curves obtained by dividing the observed specific intensity by coincide regardless of selenographic coordinates. This the calculated specific intensity of the Lambert surface. asymptotic coincidence demonstrates the mathematical Once a normal albedo scale had been established for degeneracy of the photometric function, in the neigh­ the photoelectric photometry, the next step was to de­ borhood of zero phase angle, in all its geometric de­ termine its relationship to photographic density. The grees of freedmn except phase angle. This degeneracy is maximums and minimums of the curves obtained from of course essential to the labeling of the full-moon photo­ the photographic and photoelectric scans (fig. 5) were graph with values of normal albedo, because the phase intercompared, and a calibration plot (fig. 6) was con­ angle is the only geometric degree of freedom in the structed using the density values from the photographic photometric function which is reasonably constant over plate and the absolute albedo values obtained from the the entire moon. photoelectric photometry. The choice of the extrema of Photoelectric voltages are scaled to normal albedo in the scans as calibration points was based on the assump­ the following way. The ordinate of the photoelectric tion that the necessary geographic correspondences trace in the lower part of figure 5 is linear in the num­ would thereby be assured. Several values near the limb ber of photons received per second and thus linear in were rejected owing to the severe positional effects in specific intensity and normal albedo. The zero point on limb regions of the differences in lunar libration be­ the trace (corresponding both to zero photoelectric volt­ tween ~the time of the photographic exposure and the age and zero normal albedo) is determined by the signal times of the photoelectric measurements. The point plot of the adjacent sky, which is negligible compared with for the calibration curve shows the maximum possible that of the moon. The hypothetical full-scale signal of random error, since the extremes of the signal traces are the yellow trace, together with a :blue signal obtained most likely to be subject to errors due to astronomical ElO CONTRIBUTIONS TO ASTROGEOLOGY

• •

150 •

140 0 • 0 r • 000 • 130 • 0

120

~ z 110 EXPLANATION :::> t: 0 ~ Scan A·l J: u 100 • z Scan BA·BG 0 1- u 90 w ...J u. w c 80 1-c • 70

60 0 0 ~·0

50 •: ~Oe ~oo :o9..• oo o 0 (;00 40 ~0 0 0 30 ffooo0~

20 .060 .070 .090 .100 .110 .120 .130 .140 .150 .160 .170 .180 .190 .200

ALBEDO (PHOTOELECTRIC)

FIGURE 6.-Calibration plot of points on the moon measured simultaneously by photoelectric photometry and photography. Corresponding maximums and minimums of the photoelectric and photographic spatial scans from figure 5 were used.

"seeing" and any residual positional inaccuracy. The albedo (see fig. 6). This is an unavoidable limitation in magnitude of the scatter about the calibration curve the present operation of the IDT. Despite this, the implies a nominal error of about + 1 percent. authors felt that the labeling of contours by albedo would be more practical than the imprinting of optical THE ABSOLUTE ALBEDO MAP density, which would require frequent reference to the One major departure from standard mapping proce­ calibration curve. dure was used in constructing the absolute albedo map, For the albedo map to ~ used to maximum advan­ and a brief explanation of this departure will enable the tage, it must be understood that the quantization inter­ reader to better utilize the data. The contour intervals val of the IDT is not sufficiently small to permit an as recorded by the isodensitra'Cings of the full-moon adequate linear interpolation between contours in all plate are constant in photographic density but not in cases. The print of the photographic plate (see pl. 1) PHOTOELECTRIC-PHOTOGRAPmC STUDY OF THE NORMAL ALBEDO OF THE MOON Ell should therefore be used as an interpolation device. As not affect an albedo reading at a point on the map if it an example of an associated problem, contacts between is considered as a ratio to a reading at some other point different types of lunar surficial materials will not on the map. (2) The brightness gradients of very small always be demarcated by a contour line. The IDT shifts bright lunar features, such as some bright halo craters, operational mode at predetermined equal increments of were too steep for the IDT to follow, and the peak density. Therefore, if the machine is set to change mode values indicated are too low by an uncertain amount. at density increments corresponding, at a certain level, ( 3) In a broader sense, additional information can be to 5 percent variation in surface brightness, a contact obtained from the photographic plate by increasing the corresponding to a 3 percent brightness change, at that number of contour intervals and sampling with a nar­ level, may or may not show on the tracing because it rower aperture setting on the IDT. This is warranted might conceivably be contained entirely within one con­ by the "seeing" conditions that existed when the plate tur interval, depending on the arbitrary zero point of was exposed but can ·be realized only by mapping at the density encoding process. An example is shown in a larger scale. figure 7. The area measured is in Mare Serenitatis. In REFERENCES figure 7A, the setting of the zero point of the machine Carr, M. H., 1966, Geologic map of the Mare Serenitatis region fortuitously caused the mode switch to be correlated of the moon: U.S. Geol. Survey Misc. Geol. Inv. Map I-489. with the border of dark materials which surround Mare Johnson, H. L., 1955, Spectral responses of a precisely transform­ Serenitatis (fig. 8). In figure 7B, the zero point was able two-color system which excludes the Balmer jump: shifted slightly, and thus the contour lines no longer Annales Astrophys., v. 18, p. 292-295. have geologic significance in this region. The effect is Johnson, H. L., and Morgan, W. W., 1953, Photometry of 200 1stars in three colors: Astrophys. Jour., v. 117, p. 313-823. subtle in that the border pattern, which appears in both, Minnaert, M. G. J ., 1961, Photometry of the moon, Chapter 6 in is the proper size to coincide with the contact in only Kuiper, G. P., and Middlehurst, B. M., eds., Planets and one case. and satellites, Volume 3 of The solar system: Chicago, Univ. Areas with extremely steep brightness gradients Chicago Press, p. 213-248. present another problem. When the IDT reaches an Shoemaker, E. M., and Hackman, R. J., 1962, Stratigraphic basis for a lunar time scale, ·in Kopal, Zdenek, and Mikhai­ area of large change in brightness over an interval which lov, Z. K., eds. The moon-Internat. Astron. Union Sym­ is small with respect to the aperature, the finite speed posium 14, Leningrad 1960: London, Academic Press, p. of the plate carriage forces the IDT to change modes 289-300. as rapidly as it can. The contours in ;a small bright Stebbins, Joel, and Kron, G. K., 1957, Six-color photometry of region, therefore, will tend to assume a symmetrical stars ; X, The stellar magnitude and color index of the sun : Astrophys. Jour., v. 126, p. 266-280. shape even if the true brightness configuration is actu­ Wildey, R. L., and Murray, B. C., 1963, Ten micron stellar ally asymmetrical. photometry-First results and future prospects: Colloque In summary, this is the first reliable map of the abso­ Internat. d' Astrophys. tenu a l'Univ. de Liege, 24-26 lute normal albedo of the moon in which real-time juin 1963, v. 26, p. 460-468. photoelectric calibration is utilized and for which the Wildey, R. L., and Pohn, H. A., 1964, Detalled photoelectric necessary uniformity in plate parameters is known. The ll>hotometcy of the moon: Astron. Jour., v. 69, p. 619--634. map is, however, considered provisional in three aspects: Wilhems, D. E. 1966, Summary of telescopic lUiliar stratigraphy, (1) The absolute scale of normal albedo may undergo in Lunar and planetary investigation, Part A of Astrogeo­ logic studies annual progress report, July 1, 1965 to July 1, a blanket correction factor of a few percent difference 1966: U.S. Goo!. Survey open-file report, p. 235--298. (relative) from the present data owing to a refinement Willstrop, R. V., 1960, Absolute measures of stellar radiation: in absolute calibration presently under study. This will Royal Astron. Soc. Monthly Notices, v. 121, p. 17-26. E12 CONTRIBUTIONS TO ASTROGEOLOGY

A

B

FIGURE 7.-lsodensitracings made from the photographic plate used in the present lunar photometry. A. Contours corresponding to areas of geologic significance. B. Contours showing no geologic significance. PHOTOELECTRIC-PHOTOGRAPHIC STUDY OF THE NORMAL ALBEDO OF THE MOON E13

Mare Serenitatis

IS • N

FIGURE 8.-Sketch of Mare SerenitaJtis s·howing extenJt of dark mare unit (dashed and dotted line). Stipple indicateil

CONVERSION AND CALIBRATION DATA E16 CONTRIBUTIONS TO ASTROGEOLOGY

SPECIFIC INTENSITY AND EFFECTIVE WAVELENGTH tensity may be realized as follows (see fig. 9) : The Specific intensity is the most general parameter asso­ radiative power accepted originates in an area of ci-ated with a radiation field. It is the one from which lunar surface corresponding to the fraction of image all others (for example, mean intensity, flux, radiation encircled by the aperture in the :focal plane dia­ pressure) are derivable, and it is defined in the follow­ phragm. The size of this ,area, as direction away from ing way: Consider a truncated cone where the apex the surface varies, accommodates itself so that the pro­ angle of the fully extended cone defines a solid angle jection of this area onto a plane perpendicular to the and the truncating cap defines an area. Measure the line of sight remains fixed in size for a given earth­ radiative power for all photons which pass first through moon distance. Furthermore, the photons originating the truncating cap and then through the base of the in this area are constrained to travel on rays within the cone; divide by the product of the area of the cap and solid angle subtended at the moon by the telescope the solid angle of the cone. In the limit as the cone objective. If the earth-moon distance is changed, the angle approaches zero, the quantity so defined is the spe­ diminution of solid angle is exactly compensated by the cific intensity. The following equations show the mathe­ increase in the geographic area of the moon being meas­ matical relations between quantities defined in the text ured. The signal will thus remain unchanged if reso­ and figure 9 for unit time interval. lution is not a consideration, in which case the solid angle and the area considered are small enough to be I a Energy considered as mathematical differentials. Their prod­ aA.an uct, which would be divided into the signal, is thus a constant. Hence, the signal is proportional to specific I' a Energy intensity. M' .an' THE THEORY OF ASTRONOMICAL PHOTOMETRY AND 2 M' =a0(381 ,ooo) SYSTEMS OF STELLAR MAGNITUDES AND COLORS AO' =M/(381,000)2 Normally, standards of celestial photometry are established by measuring a collection of stars of con­ :.1'=1 stant luminosity over a period of time during which Specific intensity is characterized by a direction and equipment response parameters can be kept constant. is measured in watts per square centimeter (of area The photometric investigation of other objects (under­ normal to the direction) per steradian (of solid angle taken at arbitrarily later times), when coordinated with surrounding the direction) per unit wavelength (if not the measurement of some of these standard stars on the bolometric). As mathematically shown above specific same nights, can then be rendered on a highly homo­ intensity does not vary with distance in a nonabsorbing genous photometric system. Extremely accurate com­ medium. If not bolometric, it may be truly monochro­ parison with other objects measured in the same way matic or an average associated with some broad spectral is possible because corrections can be made not only response function. In the l-atter case, it can be associated for ( 1) the nightly deviation of the average atmos­ with an effective wavelength. At lease two kinds of pheric extinction from the secular average used in the effective wavelength can be defined, the most Ineaning­ reductions and (2) the uncertainty in the bolometric ful of which is probably responsitivity of a given photometer, but also for (3) small color deviations in the spectral response cha~acter­ istics of a given photometer from those of the original photometer used to establish the collection of standard stars. To do this, the photometry must be at least two­ color (in two different wavelength bands). where The reduced form of stellar photometry is on a loga­ A=wavelength, rithmic scale. The flux measurement is given as a "mag­ !,.=specific intensity, and nitude," and the colorimetry (magnitude difference) as R,.=spectral response of photometer. a "color index." The unit, or zero point of the magnitude system, is essentially arbitrary though it stems ulti­ The effective wave length for the present observations mately from the naked -eye observations by Aristar­ is approximately 5,540 .A (angstroms). chus of Samos, whose brightest stars were "stars of the That the number of photons per second registered by first magnitude." Although the original reason for a the photometer is directly proportional to specific in- logarithmic scale was physiological, a more scientific ~ D,. Energy 0 ~ t_:rj t"' t_:rj c;a Admittance 1-1 aperture to c photoelectric photometer 0~ D,.A t-3 0 0 ~

c~

q~ 1------381.000 km------~---1 ~ 0 l:l;j ~ ~ ~ ~ ~ tD t_:rj t:::1 0 0 l:l;j ~ a:: 0 ~ FIGURE 9.-0ptical schematic diagram of the unfolded geometry relating the photoelectric photons captured to their origin on the moon's terrain. Two equiva­ lent views of the transduction process are shown. They define the distance-independence of specific intensity and relate specific intensity to point-source fluxes. Peripheral beams as well as the beams on the optical axis are shown in each view. The locus of such beams ovel! the areas shown in each case yields the total radiative power. t;:l..... ~ E18 CONTRIBUTIONS TO ASTROGEOLOGY rationale can now be developed for its preservation. These equations are called the color equations or the Consider the monochromatic radiation of a black­ transformation equations from the natural magnitude­ body at four different wavelengths. Let us then define color system of the telescope-photometer to the BV four monochromatic magnitudes as follows: system. On a given night one obtains the observed parameters in the above equations for all objects meas­ mJ=-2.5log [~/(ehc~>-i!!1)J ured. Among these are the standard stars for which V and B-V are also known. The constant coefficients The expression on the right is the Planck function and additive constan•ts .A., 0, D, and E in the color multiplied by a convenient constant which need not equations can therefore be determined by a least-square concern us since the zero point of the m1 magnitude is fit to the data. The transformation is then used to reduce arbitrary, needing only to be preserved after once being the photometry to the BV system. chosen. Of course a star is not exactly a blackbody because For stellar temperatures and the wavelengths of of its complicated opacity and radiative equilibrium, ordinary photometry, Wien's approximation holds; and there is a gradual variation with wave length of the hence moon's reflectivity. Furthermore, our photometry is he rather broad band and not monochromatic. However, m1=12.5 1og X1+(2.5log e) XJkT. if response variations with the wavelength for V andy Color indices are, for a given T, (and Band b) do not differ by more than the commercial tolerances for a filter and a photoemissive surface of Xt he 1 ( 1 1) mt-m1=12.5log x +2.5 k (log e) T x,-x • the same type as was originally used to establish the 1 1 BV system, these effects will produce errors much less By writing down the foregoing equation for i, j=1, 2 than 1 percent. This is true even when the color correc­ and again fori, j=3, 4, one can readily solve simul­ tions themselves are in a range of as high as 10-15 taneously for the relationships: percent. A useful check on the photometry is the close­ ness of D to unity and of A to zero. It should also be made clear that although the V m1-m2=[~' ~·] (ma-m4)+12.5[log(~:) magnitude can be defined in the following way: Xa X4 .J:CX) F.,.R.,.d'A] V=-2.5log +constant, [ J:co-- 1 cxa)l R.,.d'A ~1-~~ 0 -[ 1 _ 1 · og X4 J· Xa X where Fx is the stellar flux and Rx is the spectral The important feature of this equation is that it does response of the V system, spectrophotometric control not contain T. It is therefore a canonical equation of can be maintained indefinitely by the use of the color blackbody photometry which is the same for any four equations without ever knowing anything about Rx. spectral measurements of a blackbody regardless of its Indeed, the precision is superior to what would be ob­ temperature. tained by ordinary laboratory techniques for measuring Suppose we now have a photoelectric chart deflection, and correcting for Rx using a nominal spectral shape for Fx and evaluating integrals. d11, at relative amplifier gain, G11, expressed in magni­ tudes rather than decibels. Let t}le subscript refer to a The photoelectric observations which calibrate the particular radiation wavelength band, y for yellow and albedo map of the present investigation employed 10 b for blue, and presume that the observations have been BV standard stars measured bef~re, during, and after corrected for atmospheric extinction. Let there be a the lunar photoelectric observations. Actually, a photo­ standard magnitude-color system (in practice we have electric ultraviolet color was also measured, the overall used the Johnson BV system) called B and V. From the system being the Johnson-Morgan VBV system. foregoing equation the following formulas must be The ensuing calibra•tion of the photography, accord­ valid: ing to the technique discussed in· the text, implicitly d assumes that in the connection between the spectral V-(-2.5log d11+G11 )+A(2.5Iog d:-G11 +Gb)+O bands of photoelectric V and 649F + GG 14, there is and no color term (that is, in •the connection between the BV system and a photoelectric system for which the blue response is spectrometrically identical with B and the PHOTOELECTRIC-PHOTOGRAPmC STUDY OF THE NORMAL ALBEDO OF THE MOON E19 yellow response is identical with 649F + GG 14, the Because the surface is lambertian, I vL can be taken coefficient A is zero) . The color equation shows that this outside the integral and we obtain will not lead to error even if such an assumption is poorly founded, provided that the moon does not show I vL = F v (power in the band per unit area per steradian). 'If' a large dispersion in color index. This appears to be the case. Although Eastman Kodak emulsion 103a-D + Stebbins and Kron (1957) have measured the apparent 2.0 mm of Schott GG 11 filter has a spectral response V magnitude of the sun. Willstrop (1960) has measured 2 almost identical with that of V, this spectroscopic emul­ the absolute value ofF-,. (watts per A per cm ) for 100 sion is very grainy and is also too fast for a photometric A bandwidths at various points in stellar spectra of exposure by our presently operational technique. stars of known V and B-V. This is sufficiently wide to effectively smooth the Fraunhofer lines and sufficiently THE THEORY OF LAMBERT SCATTERING AND THE narrow to be a reasonable mesh for a numerical inte­ ABSOLUTE CALIBRATION OF NORMAL ALBEDO gration over the V spectral response function. We can Given a magnitude corresponding to full scale on a thus write photoelectric trace from which points for the plate cali­ li>ration are taken, the normal albedo to which it corre­ sponds must be determined. This is done in two steps. first, determine the absolute specific intensity that iv-ould be exhibited by a Lambert scattering surface when placed at the distance from the sun corresponding to the time of the observation. Then, convert the V mag­ nitude to an absolute specific intensity. Carrying out the integration in the second equation .by A. Lambert surface is the ideal diffuse reflooting sur­ using Willstrop's data and Johnson's (1955) tabulatiOn face which absorbs no light and shines with a specific of the V response function, one then solves for the intensity constant over all directions. For the surf,ace constant in the first equation. F v is thus evaluated. The V magnitude corresponding to the lunar photo­ brightness thus defined to be consistent with the first electric observational scale of this study is also trans­ law of thermodynamics, it must be proportional to the latable into a flux using the foregoing two equations. cosine of the angle of incidence ( i) of the illuminator. The calibration of F v thus provided is independent of For considerations of the noDmal albedo, the desired color; however, the effective wavelength of the lunar geometry requires that cos i= 1. F v is somewhat longer than that of the sun because the The specific intensity of a Lambert surface under moon is redder than the sun. Values have not been nor­ solar illumination is derived as follows: Let the solar malized to the same monochromatic wavelength, but flux in the V band be F v at the position in space oc­ normalization would lead to a small change at worst. cupied by the earth-moon system. Then the energy There is also no a priori reason why a monochromatic striking the Lambert surface in a unit area per unit evaluation will be more meaningful than one corre­ time is F v· Let the specific intensity in the V band sponding to a broad band. The F v of a star is its ~~a­ exhibited by the surface be lvL· In a given direction, ,tive flux density at earth. In terms of the total radiative (J (polar), c/J (azimuth), with respect to the local normal, power the telescope receives from the sta~, F ""!' is ~erely the total area perpendicular to this direction through this power divided by the area of the obJective rmrror, which the beams passing in this direction will have which is the area within which all the stellar photons come from the unit area is cos 9. Thus the radiant count toward the energy transfer and outside of which (V band) power per unit solid angle in this direction none do (see fig. 9). Obviously the mirror has the neces­ that comes from the unit area of Lambert surface is sary properties of being an area element that is pelf>en­ IvL cos 9. The total V band power that is leaving the dicular to the stellar direction ·and also one that Is lo­ surface is obtained by integrating over the half space cated a;t earth rather than somewhere closer to or farther of solid angle above the surface. Equating this to the from the star. The F v of the moon can be changed to a power arriving per unit area, specific intensity by dividing it by the solid angle of fr/2 f2r the celestial sphere imaged within the focal plane aper­ F v= Jo Jo (I vL cos 9) sin (J d(J d c/J. ture. This is the correct solid .angle because the area of E20 CONTRIBUTIONS TO ASTROGEOLOGY integration of specific intensity that is characteristic of all the. lunar light that is responsible for the photoelec­ the measurement, although it can be chosen anywhere tric signal and (2) the entire stellar image and there­ along the light bea.m, will be com;mon to both the stellar fore the stellar flux-hence, the rationale for the above and the lunar measurement if it is chosen at the telescope conversion to specific intensity. entrance pupil (and, hence, is the circular area of the With both the Lambertian and the observed lunar spe­ telescope objective mirror). If the area is thus chosen, cific intensities evaluated as above, the normal ·albedo in thB corresponding solid angle is that stated above, as tho Johnson V band is evaluated according to definition can be seen in the object-image geometry (fig. 9). With by dividing the latter by the former. the solid angle- chosen as above, one accounts for (1)

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