Television photometry: The Mariner 9 experience

ICARUS 21,

262-282 (1974)

Television Photometry: The Mariner 9 Experience A. T. Y O U N G 1 Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, California 91103

Received July 20, 1973 Television photometry is compared to conventional techniques. Reduced data from the Mariner 9 cameras should, under optimum conditions, have been accurate to a few percent. However, a combination of unstable camera properties and various unfortunate circumstances (see Appendix A) produced serious nonlinearities (typically 20-40%) and other systematic errors. The means of estimating these errors are described in detail ; they lean heavily on the fortuitous presence of a few specks of dust on the faceplate of one vidicon (see Appendix B). Crude corrections, shown in Figs. 2 and 4, will (if applied by hand to "reduced" data) probably improve the photometric quality from that of the Bonner Durchmu~terung to nearly that of the Revised Harvard Photometry, for the two most-used filter positions of the A camera. It would be very difficult to improve the photometry further (Appendix C). In view of their low photometric accuracy and detective quantum efficiency (Appendix D), vidicons do not seem likely to replace conventional photography, except for special applications. INTRODUCTION

p. 288). The lesson of h i s t o r y is t h a t one m u s t critically examine each new device Astronomical p h o t o m e t r y has a long and before accepting its p h o t o m e t r i c results a t painful history, beautifully reviewed in a face value. Thus, the p h o t o m e t r i c limitaclassical p a p e r b y W e a v e r (1946) t h a t tions of well-understood imaging detectors should be required reading for a n y o n e (viz., the eye and the photographic plate) presuming to enter this difficult and should guide us in discovering the limitatreacherous field. This history is replete tions o f doing p h o t o m e t r y with poorlywith novel devices t h a t were supposed to u n d e r s t o o d imaging detectors (such as eliminate the problems of existing tech- television systems). niques, and m a k e fast, accurate measureTelevision systems suffer from m a n y o f m e n t s with a m i n i m u m of effort. Again the worst problems of b o t h the eye and a n d again such hopes have been dis- the photographic plate. Like the eye, the appointed, as new difficulties have been television camera " r e m e m b e r s " the r e c e n t discovered. P h o t o m e t r y has improved, past, and varies m a r k e d l y in response b u t only slowly: the accuracy of m o d e r n across its field of view. Like the photod a t a (FitzGerald, 1973) is only a factor of graphic plate, the television s y s t e m has a 30 b e t t e r t h a n P t o l e m y ' s estimates made limited useful d y n a m i c range because o f n e a r l y 2000 y r ago, according to d a t a saturation a t high light levels and noise a t t a b u l a t e d b y W e a v e r (1946 ; p. 228). low levels. Like both, its characteristics T h e current fad is for television and v a r y with the color and brightness o f the related electronic image detectors; some light being measured, and with time. o f the enthusiastic claims made for F u r t h e r m o r e , all these variations depend television systems t o d a y (Disney, 1972) on b o t h t e m p e r a t u r e and position. Because r e m i n d one of those m a d e over a c e n t u r y T V systems have n o t been t h o r o u g h l y ago for p h o t o g r a p h y (cf. Weaver, 1946; studied from a p h o t o m e t r i c point o f l Present address: Department of Physics, view, additional problems m a y r e m a i n Texas A&M University, College Station, Texas undiscovered. These complex, multidimensional effects 77843. Copyright © 1974 by Academic Press, Inc. 262 All rights of reproduction in any form reserved, Printed in Great Britain

TELEVISION PHOTOMETRY

cannot be completely and accurately measured in practice. At best, we can sample the expected domain of operating conditions. The accuracy of interpolations between calibration points depends on both the density of the sampling net (limited by the money, people, and computers available) and the stability of the measured characteristics. As in all photometric work, 2 the results cannot be accepted uncritically, but must be carefully tested to determine both internal precision and external accuracy. A critical comparison of the Mariner 9 TV photometry with t h a t from other imaging detectors is appropriate at present, not only because of the continuing use of such systems, but also because the unprecedented efforts spent on both preflight calibration and data reduction (Levinthal et al., 1973) will not be duplicated in the foreseeable future; thus, better television d a t a cannot he expected for some time to come. PHOTOMETRIC ANALYSIS: G E N E R A L REMARKS

This paper is based entirely on the socalled "reduced data record" or " R D R " . The preparation of reduced from raw data involves corrections for geometric distortion (Seidman and Kreznar, 1972) nonlinearity (Green and Ruiz, 1972), residual image (Jepsen and Schwartz, 1972), and other artifacts of the TV system (see also Lcvinthal et al., 1973). The R D R (which is the final product available from the National Space Science Data Center) is intended to be a faithful representation of the scene before the TV camera. In particular, the numerical value or " d a t a number" (DN) assigned to each picture element is supported to be proportional to the brightness of the corresponding element of solid angle in the actual scene. Our basic question is whether the R D R 2 " W h e n t h e h i g h e s t p h o t o m e t r i c a c c u r a c y is r e q u i r e d one s h o u l d a l w a y s use a t l e a s t t w o systems of... calibration and check their results a g a i n s t e a c h o t h e r , since h i d d e n errors o f t e n creep in from unexpected sources." (Harrison, 1934).

263

contains useful photometric data, as is intended. Experience with previous Mariner TV data (Young, 1969; Young and Collins, 1971) has shown t h a t reduced data numbers (RDR DN) were not proportional to light intensity. However, the arguments leading to this conclusion for Mariner 4, 6, and 7 data necessarily made some assumptions about the photometric properties of Mars. Although these assumptions were, and still are, plausible, one cannot have 100% confidence in such arguments, and they have been criticized from time to time. Therefore the Mariner 9 photometry was meant to have a much firmer foundation, not only by measuring the cameras' characteristics more thoroughly before launch, but also by taking extensive picture sequences at Mars to check, and, if need be, re-establish these characteristics during the actual mission. Unfortunately, most of the intended "calibration sequences" at Mars were not obtained (see Appendix A), so once again it was necessary to fall back on various make-do schemes. All the discussion is of R D R data corrected for residual image (Jepsen and Schwartz, 1972), unless noted otherwise. The major emphasis is on photometric linearity, although some shading anomalies are mentioned as well. One should realize t h a t the algorithms used in producing the R D R are necessarily limited by the small number of light levels at which calibration data were taken, 3 and thus by interpolation and extrapolation ambiguities. A common extrapolation problem occurs when a frame follows one containing saturated areas; this causes an overcorrection for residual image, which produces a blotchy discontinuity in the residual-corrected version of the later frame. Such difficulties either produce obvious anomalies, or else are too subtle to detect in the present analyses. Finally, anyone interested in using Mariner 9 data photometrically should read the essential calibration report (Snyder, s M a r i n e r c a l i b r a t i o n d a t a are g e n e r a l l y s p a c e d a t i n t e r v a l s of 0.3 i n l o g l o I ; L a t h a m (1969) r e c o m m e n d s a t l e a s t 10, a n d p r e f e r a b l y 15, levels

per decade (AlogloI = 0.1 to 0.06).

264

A.T. YOUNG

1971), as well as the R D R Users' Guide (Seidman et al., 1973), and the references therein. The c o m p l e x i t y of the processing t h r o u g h which the R D R dat~ h a v e been squeezed is almost inconceivable to the outsider; perhaps it can be compared to w h a t a F O R T R A N compiler does in turning a source deck into a machinelanguage program. I n b o t h cases, the process appears simple to the novice, b u t the experienced user is painfully aware of m a n y u n w a n t e d side effects; naive or incautious use can produce wrong answers. ANTICIPATED ACCURACY Before taking up flight data, we shall use preflight calibrations to indicate the accuracy possible u n d e r ideal circumstances. The most usethl d a t a are the flat-field calibrations t a k e n on Feb. 4, 1971, called " B e n c h 3" b y S n y d e r (1971). B o t h s t a n d a r d (9-point) transfer curves (A log I ~ 0.3) and e x t e n d e d (21-point)

transfer curves (A log I ~ 0.1) were measured. I f the 21-point d a t a are reduced using the 9-point calibration, the errors due to interpolation, u n c o r r e c t e d residualimage effects, and f r a m e - t o - f r a m e reproducibility u n d e r constant conditions can be estimated. Figure 1 shows the D N histogram of a typical reduced frame. I f the d a t a were noiseless, this would be a single spike; Gaussian noise would spread it into a parabolic peak, because of the logarithmic scale. Although such a peak appears in Fig. 1, a b o u t 14% of the d a t a belong, to a m u c h broader population; 6.6% of the d a t a are zero, and 4.5% are saturated. This pathological error distribution renders straight means and s t a n d a r d deviations meaningless, for t h e y are efficient, unbiased statistics only for the n o r m a l error law. However, the mode is clearly an efficient estimator; so we c o m p u t e a m e a n and s t a n d a r d deviation for a symmetrical region a b o u t the mode, chosen s~ PERCENTILES

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TELEVISION PHOTOMETRY

t h a t the lowest histogram frequency on the high-DN side is not below 500 ( ~ 0.07%). This cutoff is marked on Fig. 1 ; it includes most of the Gaussian peak, and excludes most of the non-normal noise. The mean and standard deviation of the peak, computed in this way, are given in Table I for each reduced frame. Clearly the RMS noise is underestimated by the truncation, but it does indicate the width of the peak. Flight data contain additional nonnormal (bit) errors, introduced in transmitting the data to Earth; as highorder bit errors would create aliased peaks in the histogram, they are clearly unimportant in Fig. 1. Some of the low-DN data are due to reseau marks and the edges of the frame, but these do not explain why fully one-seventh of all picture elements have abnormal errors. In any case, the RMS errors in Table I are optimistic; flight data are about twice as noisy. The general behavior of the noise suggests a constant (additive) component at low levels, plus about 1% of the average light level. This quasi-multiplicative com-

265

ponent includes spatial variations in sensitivity ("shading") t h a t are not fully corrected in the data reduction. Besides the RMS error estimates, Table I gives the absolute errors of the (truncated) means, in the sense of inferred minus true light level. As the 21-point sequence repeats the light levels of the separate 9-point sequence, comparison at these points (marked by an asterisk in column 1) mainly measures frame-to-frame reproducibility and residual-image correction. On the other hand, the errors at intermediate light levels also include interpolation errors, and are more realistic estimates of the errors to be expected in actual use. Clearly, the systematic errors are larger than random noise for wellexposed frames; over the one useful decade of dynamic range (92-920ft-L), the RMS relative error of the mean is 2.5%, about twice the random noise. Systematic errors in local contrast can be estimated by ln[(out/in)i + (out/in)i_l] where " o u t " and "in" are respectively the light level inferred from the reduced data and the input light level, and the subscript

TABLE

I

REDUCTION OF B-CAMERA, "BENCH 3" 2 1 - P o i n t SEQUENCE

RDR DN

Output (ft-L)

RMS noise per picture element

Error of m e a n

Slope error

Input (~-L)

mode

mean

mode

mean

DN

f t -L

%

*39 52 *75 92 117 "152 171 192 229 260 *305 372 440 520 *595 670 *760 920

10 16 24 30 38 51 58 66 78 87 102 129 152 179 -237 260 314

9.594 16.317 23.816 30.272 37.619 50.681 57.627 66.382 77.662 87.359 101.705 129.017 151.550 178.754 -237.269 259.522 313.973

29.7 47.6 71.4 89.2 113.0 151.7 172.5 196.3 232.0 258.8 303.4 383.7 452.1 532.4

28.538 48.536 70.842 90.046 111.900 150.754 171.415 197.457 231.010 259.854 302.527 383.769 450.794 531.714

1.678 0.917 0.935 0.950 0.958 0.936 0.872 0.930 0.899 0.958 1.169 1.248 1.357 1.816

5.051 2.728 2.781 2.826 2.850 2.784 2.594 2.766 2.674 2.850 3.477 3.712 4.036 5.402

13.0 5.2 3.7 3.1 2.4 1.8 1.5 1.4 1.2 1.1 1.1 1.0 0.9 1.0

--26.9 --6.7 --5.5 --2.1 --4.4 --0.8 .1.0.2 .1.2.8 .1.0.9 --0.1 --0.8 +3.2 -t-2.5 +2.3

-.1.0.243 .1.0.012 .1.0.036 --0.023 .1.0.036 +0.011 .1.0.026 --0.019 --0.009 --0.008 .1.0.039 --0.007 --0.002

705.0 773.4 934.0

705.770 771.963 933.931

1.951 1.930 2.I22

5.803 5.741 6.312

0.9 0.8 0.7

.1.5.3 .1.1.6 .1.1.5

.1.0.030 --0.036 --0.001

%

266

A.T. YOUNG

denotes the line of Table I. On a log-log plot of " o u t " against "in", this quantity would be the logarithm of the slope between the ith and ( i - 1)th points, or (as the correct slope is unity) the logarithmic error in this slope. This quantity, called "slope error", appears in the last column of the Table; it is a measure of local deviations from linearity. Over the dynamic range mentioned above, the RMS slope error is 2.4%, very similar to the absolute errors. For comparison, the unaided eye can achieve, at best, systematic errors of about 20%, and random errors near 10% (Weaver, 1946; pp. 228-229). However, photometric instruments employing the eye as detector reduced both random and systematic errors to 5%, or a little less, by the end of the last century. 4 Somewhat better results are obtained photographically; with care, systematic differences from plate to plate need not exceed 3-4%, and systematic variations across a single plate can be 1-2% or less (Latham, 1966, 1968). Thus the TV errors should be similar to photographic ones, under ideal conditions. Of course, the accuracy achieved with single (point) detectors is better still. In a table of " Th e Sensitivity and Accuracy of Various Representative Photometers", ~ e a v e r (1946; p. 514) gives the probable error of measurement as ½ to 1% for observations made around World War I, and 0.3% for observations in the 1940's. The nonlinearity of modern data is near 0.1%, much better t han any imaging system. The errors given for the Mariner-9 B camera are underestimates, not only because of noise truncation, but also because the effects of temperature, aging, etc. should be negligible. T hey are lower bounds on photometric errors of a practical TV system under laboratory conditions; in field or flight use, we must expect larger errors. The n ex t sections examine the actual photometric quality of Mariner 9 TV data returned from Mars, for each camera separately. 4 These figures apply to stellar photometry. For extended, uniform areas, visual comparisons can reach 1% precision or better.

THE A CAMERA Figure 2 shows data from seven orange frames from the 76th orbit, the only inflight transfer-curve calibration for this filter. The exposures range from 3.9 (nominally 3) to 96 msec, and the points denoted MIN and MAX are the R D R DN levels at the 2nd and the 98th percentile points respectively, in the reduced dat a histograms (excluding saturated and zero DN levels) of these frames. I f the field of view covered the same area on Mars in each picture, and if we can neglect brightness changes due to the motions of Mars and Mariner 9, a fixed percentile in each histogram corresponds to a fixed scene brightness. Then, if the R D R DN were (as intended) proportional to exposure, and if the vidicon shows no reciprocity failure, 5 the DN level for a given percentile would be proportional to exposure time. The abscissae of the two sets of points in Fig. 2 are proportional to the times measured by Snyder (1971); the MAX points have been shifted horizontally by a factor of about 2.3, for comparison with the MIN points in the region of overlap. The two sets of dat a agree in sho~ing a very non-linear relation between R D R DN and exposure. In the region between 100 and 150 R D R DN, where most of the orangefilter data lie, the contrast of the reduced data (i.e., the slope in Fig. 3) is too low b y about 30%. This slope error is an order of magnitude larger than those in Table I. At low DN values, such as occur in atmospheric hazes beyond the limb or terminator, the contrast m ay be too high by a factor of two or more. These scale errors would appear as similar errors in the scale heights of atmospheric hazes determined b y the method of Young (1969), for example; such large systematic errors are clearly unacceptable. 5 While the mechanism that causes reciprocity failure in photographic materials is not present in vidicons, this does not guarantee that vidicons are free of reciprocity problems. The calibration data (Snyder, 1971) show no large effect, but the question has not been thoroughly investigated. See Appendix C.

267

TELEVISION PHOTOMETRY

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Fro. 2. T h e p r e l i m i n a r y in-flight c a l i b r a t i o n c u r v e for M a r i n e r 9 A - c a m e r a d a t a t a k e n t h r o u g h t h e o r a n g e filter. T h e p o i n t s m a r k e d " M A X " a n d " M I N " are t a k e n f r o m a u t o m a t i c "stretch" limits based on the histogram of p i c t u r e d a t a a n d p r i n t e d o n R D R p i c t u r e labels. T h e d a s h e d line c o r r e s p o n d s t o l i n e a r p h o t o m e t r y . ( D a t a are c o r r e c t e d for r e s i d u a l image.)

~ORANGE

F i G . 3. A p p a r e n t c o n t r a s t o f t h e d a r k e s t A - c a m e r a d u s t - s p e c k s h a d o w i n selected f r a m e s t h a t lack M a r t i a n detail. D o t s are residualc o r r e c t e d o r a n g e d a t a ; crosses are u n c o r r e c t e d , Violet-filter d a t a are m a r k e d w i t h a " V " , a n d also a n " R " i f c o r r e c t e d for r e s i d u a l image. A t a g i v e n D N level, t h e o r d i n a t e o f Fig. 3 s h o u l d b e p r o p o r t i o n a l t o t h e slope of Fig. 2 (see A p p e n d i x B). T h e i n d i c a t e d e r r o r levels are c o m p u t e d f r o m

Eq. (B8). Various explanations of the nonlinearity in Fig. 2 have been offered. F o r example, a change (i.e., an error) in either the exposure times or the dark-signal level would m a k e the curve nonlinear. However, either effect would be most severe at the left end of the curve, and could only account for a m o n o t o n i c error in contrast (always too high, or always too low), not the observed reversal of the error near 50 R D R DN. F u r t h e r m o r e , the q u a n t i t a t i v e changes required are quite implausible: the d a r k level observed in star pictures is v e r y close to t h a t in prelaunch data, and an exposure error of tens of msec would be needed to account for the nonlinearity above 100 DN. Finally, the MAX and M I N d a t a would not agree if the exposure times were in error. Nevertheless, because of the large n u m ber of assumptions and the small n u m b e r of calibration frames involved in Fig. 2, it is desirable to test the shape of the curve with entirely i n d e p e n d e n t evidence. Perhaps t h e most sensitive such test deals with

the a p p a r e n t contrast of the shadows of dust specks on the vidicon faceplate. As the analysis is r a t h e r lengthy, the details are given in A p p e n d i x B ; the results (see Fig. 3) confirm the correctness of Fig. 2. F u r t h e r information can be o b t a i n e d for the polarizing filter, where the filter wheel stuck after orbit 118. A set of 5 A frames t a k e n at 3 exposure levels on orbit 225 are useful for transfer-curve calibration. Because some Martian features are visible, one can splice together d a t a for several scene brightness levels. Instead of the two levels of Fig. 2, we can use those of the eight features given in Table II. The average RDI~ D N for an 11 × 11sample square centered on each feature is given in Table I I I . (Note t h a t these are clearly n o t proportional to exposure). One can plot the d a t a for each feature as in Fig. 2 ; errors can be e s t i m a t e d from the RMS dispersion of the 121 D N values for each square. Because of strong brightness gradients in the scene, and difficulties in

268

A.T.¥OUNG TABLE II

FEATURES MEASURED ON P-225 CALIBRATION FRAMES

RDR Coordinates on DAS 09666624 Feature line

sample

name

420

186

A

272

260

B

122 414 364 206 710 165

258 748 810 644 442 804

C D E F G H

Description lower edge of large crater halo at right of dark spot bright patch small ring crater dark spot double dark spot large bright blob small bright spot

locating some features precisely, I have a d o p t e d this dispersion (rather t h a n the formal error of the mean) as the error estimate for each m e a n value in Table I I I . The log-log plots for the eight features can t h e n be fitted t o g e t h e r b y sliding t h e m horizontally, just as the M A X a n d M I N d a t a are fitted t o g e t h e r in Fig. 2; the result is Fig. 4. The fitting depends to some e x t e n t on one's own j u d g e m e n t ; also, no change in scene brightness with time has been allowed for. Consequently, Fig. 4 m a y still be systematically wrong, b u t p r o b a b l y n o t b y more t h a n 5 or 10%. The t o t a l deviation from linearity over a decade of d y n a m i c range is a b o u t 40%.

The dust-speck analysis of A p p e n d i x B can again serve as a check. Fig. 5 shows a p p a r e n t dust-speck c o n t r a s t for residualcorrected frames between orbits 119 a n d 165, using only frames t h a t show little or no Martian detail in or a r o u n d the dust speck. The great scatter of the data, m u c h larger t h a n the internal errors, m a y he due to weak Martian detail; the semiinterquartile range (external probable error) of the d a t a is a b o u t 0.4%, c o m p a r e d to 0.2% in Fig. 3, where the dust s t o r m concealed surface features. However, picture detail does n o t seem to correlate with large deviations in Fig. 5, so the increased scatter m a y simply be due to increased bit-error noise later in the mission. U n f o r t u n a t e l y , there are few residualcorrected frames with v e r y high or v e r y low D N levels at the dust speck for this filter position, so the general shape of Fig. 4 c a n n o t be checked b y using Fig. 5. However, we can compare the two figures near 200 R D R DN, where the slope of Fig. 4 is a b o u t 0.84 ± .12 (max. error) and the a p p a r e n t contrast is 5.1 ± 0.4% (probable error). I f we estimate the probable error in the slope as half the m a x i m u m , we infer a true contrast of 6.1 ± 0.5% for the dust-speck shadow, which agrees well with the values derived in A p p e n d i x B. F u r t h e r m o r e , the shape of Fig. 4 is similar to t h a t of Fig. 2. On the whole, it seems likely t h a t RDI~ d a t a corrected b y the function shown in

TABLE I I I MEAN RDR DN OF FEATURESIN TABLEI I DAS Time (exposure) 09666624 (95.6 ms) 09666694 (190.4 ms) 09666764 (95.6 ms) 09666834 (48.1 ms) 09666904 (95.6 ms)

A

B

325.7 281.4 ___8.0 --+2.4 --(Saturated) 335.3 290.0 -+11.6 -+5.6 192.2 162.0 ___9.8 ___2.5 328.1 280.9 -+8.4 -+3.7

C

D

E

F

G

H

243.2 -+3.2 403.4 -+7.3 248.5 _+3.1 135.7 _+2.5 244.8 +3.4

150.0 -+5.1 248.5 +6.3 152.1 -+4.6 79.2 -+3.9 144.5 -+5.6

125.4 -+2.4 210.6 -+3.3 123.6 _+2.5 59.1 -+2.0 117.3 ___4.1

140.3 -+2.2 234.7 -+3.3 141.0 -+1.8 70.2 -+1.7 135.7 -+2.8

202.4 -+2.1 338.0 _+1.7 212.5 -+2.1 117.1 _+1.5 206.5 ±1.9

99.1 -+2.0 172.7 -+2.8 96.7 _+1.6 42.5 -+2.1 91.1 +2.5

269

TELEVISION PHOTOMETRY 500

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RELATIVE EXPOSURE

FIO. 4. C o r r e c t i o n c u r v e for A - c a m e r a filter p o s i t i o n 5, c o n s t r u c t e d f r o m t h e d a t a in T a b l e 3. T h e i n d i c a t e d e r r o r levels are r e l a t i v e t o a line of u n i t slope t a n g e n t t o t h e c u r v e (near 100 DN).

Fig. 4 will have probable errors on the order of 5% (i.e., probably half of such corrected data will still deviate from linearity b y more t han 5%), and small contrasts m such corrected data can be measured with errors of about 10%. These estimates do not include errors between widely-separated frames, or between widely-separated points in the same frame (shading effects).

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The A-camera shading pattern in fact seems to have changed. Fig. 6 shows an orange A-frame taken early in the mission, when surface features were completely obscured. As is shown below, this condition produced a roughly Lambertian photometric function, so the expected brightness distribution over the frame is roughly proportional to cos i, where i is the angle of incidence of the sunlight. Figure 6 is only about 0.1 rad across, so deviations from Lambertian behavior should produce very small effects. The data shown in Fig. 6 are the ratio o f R D R DN to cos i ; if the reduced data were linear, and if the surface were Lambertian, the ratio should be constant. Neither assumption is correct, but an error in either should produce a one-dimensional gradient in brightness across the ratio picture from limb to terminator. Instead, Fig. 6 (and other ratio pictures distributed over the planet) shows a circular shading pat t ern t h a t is quite symmetrical: the center is about 10% darker t han the edges. The s y m m e t r y about the camera axis, and the lack of correlation with position on Mars or viewing geometry, clearly show t h a t this shading is an instrumental effect.

270

A. T. YOUNG

FIG. 6. A featureless A-frame, corrected for an assumed Lambertian photometric the symmetrical shading pattern, and the three prominent dust-speck shadows.

function.

271

TELEVISION PHOTOMETRY

predict

THE B-CAMERA

Several pictures taken with the B camera shortly before arrival at Mars are useful for calibration. These include several pictures of Saturn and a few of the Pleiades. Also, shading problems are easy to identify in B pictures, which cover small regions of nearly uniform brightness. The Pleiades frame showing the most stars was analyzed. The integrated brightness of each star image was measured by summing the RDI~ DN for a 15 × 15 square of picture elements centered on the star, and subtracting from this the sum for an adjacent 15 × 15 square of blank sky. This is exactly analogous to the method used at the telescope in photoelectric stellar photometry. Because the TV data showed faint vertical stripes due to powersupply noise, the sky region was always vertically above or below the region centered on the star. The Mariner camera does not duplicate the spectral response of any standard photometric system. However, it is not far from the V response of the UBV system (A~usienis and Strai~ys, 1966). Figure 7 compares the B and V response curves with t h a t of the Mariner B camera (Snyder, 1971). I f we call the Mariner system V*, and assume the usual linear relation between reciprocal effective wavelengths and stellar magnitude, we can ..............

~ .......... ~ t ~

V* = V -

0.07 ( B - V ) + const.

Thus the accurately known values of V and ( B - V) for Pleiades stars (Blanco et al., 1968) can be used to compute expected values of V*. Observed values of V* were computed from the integrated R D R brightnesses described above. Figure 8 shows the residuals ( 0 - C) as a function of V*. The TV data are clearly not on a Pogson scale, but show large scale errors, on the order of 20%. Such scale errors are typical of the crude eyeestimates used a century ago in compiling the Bonn and Cordoba Durchmusterungen (Weaver, 1946; pp. 228-229). Of course, the nonlinearity indicated here is not characteristic of Martian data taken with the same camera because (a) most of the star data are near threshold, (b) a star image is not uniform in brightness but covers a wide range from zero to some peak value, and (c) the vidicon probably does not respond in the same way to point and extended images. However, the nonlinearity is real and is not due to a color error; for all the brighter Pleiades have nearly the same (B - V) color index, and a very red star in the field (HD 23712 = I

I

i

L

4000

~: '$ .............

.\

../ /

,~VM9B V° ~ V-O.O7 (B-V}

4500 5000 k. ANGSTROI~S

5500

bOO0

b500

7000

FIG. 7. Response curves for the B and V bands of the U, B, V system (A~usienis and Strai~ys, 1966) and the Mariner 9 B camera (Snyder, 1971). Effective wavelengths for solar illumination are indicated, taken from the same sources.

J

\

./

/.

3500

I

/\. /

\" " .~i\" \

/"

3000

(1)

/

o.~ i

o.71

L

3

I

4

I

5

L

6

L

7

|

:B

FIG. 8. M a g n i t u d e r e s i d u a l s for P l e i a d e s s t a r s , t a k e n f r o m a M a r i n e r 9 B f r a m e . T h e circled p o i n t is t h e r e d field s t a r m e n t i o n e d i n t h e text.

272

A.T. ¥ o u N a

B ] ) + 24 ° 571, B - V = +1.7 ; m a r k e d b y a circled dot in Fig. 8) agrees well with bluer stars of similar magnitude. The linearity of the B camera can also be tested with the S a t u r n pictures. Table I V summarizes results obtained from 26 images of S a t u r n t a k e n on N o v e m b e r 30, 1971. The t o t a l brightness of each image was obtained in the same w a y as the total brightness o f stars, e x c e p t t h a t a slightly larger area (19 × 23 picture elements) was used because of partial resolution of the planet and ring. These d a t a confirm the Pleiades result t h a t the R D R D N values are too low at b o t h high and low extremes, just as in the A camera (Figs. 2-5). However, only the single frames t a k e n a t the shortest and longest exposure times show significant deviations from the mean, and (as with the star images) there is considerable averaging over a large D N range, so no q u a n t i t a t i v e correction can be found. The values at 96 and 384msec do not differ significantly; more surprisingly, the errors do n o t differ significantly ( F = 2.5, n~=2, n 2=4; P=0.2) a t these two exposures, although one would e x p e c t m u c h larger errors at the shorter exposure for pure additive noise. The relative error per frame is 9.4% at 96msec, and 6.3% at 384msec ; clearly nonadditive (multiplicative?) noise is i m p o r t a n t at the higher exposure (cf. Table I). The geometrical image size is a b o u t 3 × 7 picture elements, so these errors a p p l y to areas of a b o u t 20 elements. Also, most o f these d a t a were n o t corrected for residual image. Ten o f the 192-msec frames were corrected for residual image, TABLE IV BRIGHTNESS OF SATURN IN S PICTb~I~ES Nominal exposure t i m e s (m.sec)

n

Mean and standard deviation ( a r b i t r a r y units)

48 96 192 384 768

1 3 16 5 1

2.049 2.574 _+0.139 2.528 -+_0.033 2.426 ___0.068 1.946

and their scatter (1.7%) is m u c h less t h a n t h a t of the u n c o r r e c t e d images (8.4%) at the same exposure time. The difference is highly significant ( F = 2 4 . 7 , nl = 5 , n 2 = 9; for F = 11.7 and these degrees o f freedom, P = 0.001). This is surprising, as the images do not overlap and the "resid u a l " is black sky in e v e r y case. One m u s t be cautious in a t t r i b u t i n g all this difference to residual removal, however, p a r t l y because o f the a p p a r e n t u n i m p o r t a n c e o f additive noise, and p a r t l y because all the corrected frames have S a t u r n n e a r l y in the center, so t h a t shading effects are smaller. The corrected and u n c o r r e c t e d means differ b y only 3.5%, which is not significant (t -- 1.01, n d = 14; P ~ 0.33). Shading problems occur in the u p p e r left corner o f B frames, b u t none o f the S a t u r n images falls in the affected area, which extends a b o u t 200 picture elements from the corner in each coordinate. Depending on the average exposure level, this corner m a y a p p e a r either too d a r k or too bright in R D R data. This anomalous area should, at present, be excluded from a n y a t t e m p t to use B - c a m e r a d a t a photometrically. I t will be m u c h more difficult to m e a s u r e nonlinearity in the B - c a m e r a t h a n in Acamera data, because the dust-speck shadows have an order of m a g n i t u d e lower contrast, and the seven in-flight calibration frames do not cover the full D N range. P r e l i m i n a r y indications suggest fair line a r i t y between 55 and 110 RDI~ DN, with considerable nonlinearity a t higher levels (which, u n f o r t u n a t e l y , include most of the data). D a t a near 300 R D R D N a p p e a r to be m u c h too low, perhaps b y a f a c t o r of nearly two. Very extensive studies will be needed to produce reliable information on B-camera nonlinearity, however. (See Appendix C.) PHOTOMETRY OF MARS

Because of the lack of reliable photom e t r y from the Mariner 9 T V cameras, a n y inferences a b o u t Mars must be based on qualitative r a t h e r t h a n q u a n t i t a t i v e data. T h e dangers of misusing such television d a t a h a v e been pointed out b y Suomi a n d

T E L E V I S I O N 1)I-IOTOMETRY

Vender H a a r (1972). W e therefore m u s t confine ourselves to distinctions such as b r i g h t e r / d a r k e r relationships. A convenient way to display such relationships is to t r u n c a t e a few of the most significant bits in the RDI~ DN, and scale the remaining bits to cover the range from 0 to 511 (the n o r m a l d y n a m i c range of the data). This is equivalent to multiplying all d a t a b y 2" (if n bits are discarded) and ignoring overflow bits. W h e n the resulting d a t a are displayed, there is a black-white transition wherever the original (n + 1 )st bit changes from 0 to 1. F o r example, if we discard four bits, the whole d y n a m i c range is divided into 16 subranges; the d a t a from

273

(original) D N 0-31 are e x p a n d e d to cover the full range of grey from black to white, b u t (original) 32 is displayed as black again, increasing to white at 63; and SO o n .

Figure 9 is a preorbital B frame t h a t has been " c o n t o u r e d " b y five-bit truncation. In spite of a r a t h e r large residualimage effect, which displaces the brighter contours b y a b o u t their own spacing, the general shape of the contours is clear. The m a x i m u m brightness occurs v e r y nearly at the subsolar point, as would be e x p e c t e d if the storm-shrouded planet had a L a m b e r t i a n p h o t o m e t r i c function. However, a t r u l y L a m b e r t i a n globe would

FIG. 9. A contoured preorbital B-frame of Mars. Note the large effects of residual image, shown by the gray area above the planet, and the kinks in contours near the bottom. 10

274

A.T.

YOUNG

have elliptical isophotes, the projections colors (which are brightness ratios in of small circles with their pole at the sub- different wavelengths) at this stage, for a solar point; whereas Mars shows nearly different "sensitivity" factor applies to straight isophotes extending close to the each DN level as long as the scale is nonlimb at high latitudes. Qualitatively, linear. The present RDI~ data correspond, the greater-than-Lambertian brightness both in photometric quality and in sciennear the limb indicates a substantial tific results, to mid-nineteenth-century single-scattering contribution from the visual observations. To quote Suomi and atmospheric dust; this is reasonable, Vonder Haar (1972), " A vidicon is a as multiply-scattered light from absorbing notoriously poor photometer . . . . The particles should be weak. Quantitatively, answers can never be obtained with a the shape of the contours remains to be vidicon camera system. We should all explained. I t is especially noteworthy that get on with the task of developing a fully the shape of the contours cannot be fit by acceptable system." any Minnaert function: k = 1 is needed to place the maximum brightness at the subsolar point, but a substantially lower value THE FUTURE OF TV PHOTOMETRY of k would be needed to produce the bright limb at high latitudes. Although the Finally, what should be done in future cloud-covered state is abnormal for Mars, work~. Can TV photometry be improved? this result emphasizes the danger of Alternatively, can other imaging detectors assuming the applicability of the Minnaert provide better photometry? function in general. First, we must face the dismal photoThe quasi-Lambertian behavior of metric record produced by vidicon cameras clouds, in contrast to the normal (less (Suomi and Vonder Haar, 1972; Young, limb-darkened) behavior of Mars, is hardly 1969; Young and Collins, 1971). All a new result. It was remarked by William Mariner cameras have produced reduced Huggins (1867) in a paper which sum- data with systematic nonlinearities of marizes most of what is known about the some tens of percent, while visual photophotometric properties of the planet, even metry has been better than this for about today. Huggins also calls attention to the a century, and photographic photometry redder color of the center of the disc, which has done as well for many decades. appears in the Mariner isophotes as a The television difficulties must be aslimbward displacement of the maximum cribed (if we suppose the laboratory brightness at shorter wavelengths, as calibrations to have been done correctly) shown by contoured A-camera pictures. to changes in the vidicons some time There appears to be little prospect of between pre-launch calibration and their learning anything new from Mariner TV use at Mars. Possibly, some other type "photometry" without reducing R D R of television tube may prove more stable; DN values to a linear photometric scale. but, at present, we are far from underOne attempt to do this was made by standing the photometric properties of Thorl~e (1972) who published approximate TV systems (and their changes with time) correction factors to be applied to nominal as we understand photographic and photoR D R DN values for both cameras. electric detectors. It is remarkable that Thorpe's corrected R D R DN values are vidicon cameras have been repeatedly used in two recent papers--one dealing flown on spacecraft, at least in part for with the average photometric function of photometric purposes, without their ability Mars (Thorpe, 1973), the other, with the to produce valid photometry ever having polarization properties of Phobos and been demonstrated; indeed, the available Deimos (Noland et al., 1973). The prospects evidence suggests the contrary. for future improvement are given in ApThe stability problem can be avoided by pendix C. I t is of course meaningless to putting enough effort into calibrations at discuss either absolute brightnesses or the same temperature, age, etc. as occur

T E L E V I S I O N PHOTOMETRY

during actual data-taking. Table I shows that performance similar to photographic photometry may then be possible. However, vidicons still have limitations, compared to photography, including smaller format and inferior geometric accuracy, as well as lower detective quantum efficiency (see Appendix D). In addition, TV systems use telescope time and storage space very inefficiently. The high uniformity of photographic materials allows us to make calibration exposures simultaneously with the observations, but with TV a large amount of observing time must be lost while the system is calibrated. Furthermore, the variations over the field enormously complicate TV data reduction; a 1000 × 1000 format requires the construction of a million different characteristic curves, a million residual-image corrections, etc. Skipping over unused picture elements (such as blank sky) also consumes much computer time, especially if only a few elements (such as star images) are of interest. Finally, the bulk of digitized pictures is enormous: a few fill a roll of magnetic tape, and even a few inches of digitized spectrum fills a box of punched cards. The 7000 Mariner 9 pictures, on magnetic tape, fill 1000 magnetic tapes; the corresponding photographs, on microfiche cards, are about the size of a shoebox. While computer technologists plan to use photographic storage for compact mass memories, Disney (1972) proposes to replace photographs with computer memory; surely this is going the wrong way. Of course, better TV systems are being developed. The silicon vidicon is more linear than the vidicons used in Mariner cameras, for example; b u t so are the finegrained spectroscopic emulsions, and electronography. And as television systems improve, so do photographic ones. I f TV systems remain inferior to photography, is there ever any justification for using television? Television has practical advantages over photography for remote space probes. It avoids the weight and bulk of processing chemicals, it provides an electrical signal directly for transmission b y radio, and

275

it does not integrate cosmic-ray exposure. However, one could probably avoid this last problem, or reduce it to an acceptable level, b y utilizing the Herschel effect, suitable desensitizing dyes, etc. The superior detective quantum efficiency of film (see Appendix D) would allow smaller, lighter optics to be used; the superior uniformity and dynamic range are desirable for photometry; and the superior photographic resolution and geometrical stability are useful in mapping. Although even the proponents of photography admit that "the photographic emulsion is often the subject of criticism because of its low sensitivity (quantum efficiency) as compared with a photoelectric cell, its lower photometric accuracy, and its nonlinear response" (Stock and Williams, 1962), these maladies are shared b y television systems, which in addition have residual-image problems, severe non-uniformity, and a resolution that varies with light level. We m a y be contemptuous of photography because better detectors (though not better imaging detectors) exist, and because it has been around a long time. B u t we are the beneficiaries of over a hundred years of research on the silverbromide-in-gelatine emulsion, which has been brought to a high degree of perfection. Perhaps, in another century, television too will be capable of the performance we routinely expect from photography today. Of course, if photometry of the highest accuracy is desired, there is no substitute for the photoelectric photometer, as was realized b y the designers of the Soviet Mars-2 and Mars-3 probes. I t may be possible to use such data to help correct the errors in television data, just as photoelectric data are routinely used to standardize photographic photometry (Stock and Williams, 1962). However, the shading problems of TV systems, combined with the rapidly-changing scene viewed from a spacecraft, make this more difficult to do than with photography. Finally, unless television systems vastly superior to the Mariner systems are

276

A.T. YOUNG

produced, one must question the wisdom of using TV instead of the conventional combination of photography and photoelectric photometry on the Large Space Telescope (O'Dell, ]972). The circumstances t h a t favor television--space and weight limitations, nonretrievable equipment, etc.--do not apply to the LST; and high-quality data will be required, as well as efficient use of telescope time. Thus television, at least in its present state, appears ill-suited to the circumstances of the LST. ACKNOWLEDGMENTS I am deeply indebted to T. E. Thorpe and W. B. Green, who made truly Herculean efforts to plan and obtain adequate calibration data, to determine the in-flight performance of the cameras, and to produce reliable photometric results. L. M. Snyder and L. L. Simmons provided useful information about the cameras and helpful discussions. I thank R. G. Roosen and W. B. Green for helpful suggestions concerning the presentation of results. This paper presents the results of one phase of research carried out at the J e t Propulsion Laboratory, California Institute of Technology, under contract NAS 7-100, sponsored by the National Aeronautics and Space Admi~fistration. APPENDIX A

What Happened to Calibration? Because reduced television data from Mariner 4 (Young, 1969) and Mariner 6 and 7 (Young and Collins, 1971) had systematic errors one to two orders of magnitude larger than is considered tolerable in normal astronomical photometry, I was reluctant to become involved in another similar experiment. Nevertheless, at the urging of C. Sagan and G. de Vaucouleurs, I did accept an invitation to become a co-investigator in the 1971 Mariner Mars TV Team, largely because some of the several thousand pictures expected could be devoted to checking the photometry. A detailed plan for in-flight calibration was based on the following arguments: (1) We do not know the time scale of

significant changes in the vidicon, but experience with other detectors suggests weeks, or months. I t would be prudent to check the calibration frequently at first, and then (supposing t h a t no severe drift is apparent) less often; a reasonable plan is once a week for three weeks, then once a month for three months (the duration of the nominal 90-day mission). Thus at least 6 full calibrations are needed. (2) As the properties of the camera are wavelength-dependent, a complete calibration is needed for each of the 8 filters in the A camera, plus one more for the B camera (fixed filter)--a total of 9 per spacecraft. (3) Each calibration requires a star field for geometric calibration ; a planet (Jupiter or Saturn) for absolute photometric reference; several pictures of a target fixed in the field taken with different exposure times, to check the transfer curve; and several pictures of a moving target with fixed exposure to measure shading {spatial nonuniformity of response). The "shading" test should be made at (at least) 3 different exposure levels, as the shading pattern is light-level dependent. Furthermore, both the shading and the transfer-curve sequence require frequent interpolation of a "reference" picture, to allow measurement and removal of brightness changes due to spacecraft motion and planetary rotation. In addition, the first picture of a sequence is useless for photometry because it cannot be corrected for residual image (incomplete target erasure in the vidicon). The tot:fi number of pictures per calibration sequence is thus about 32. I f we multiply this by the 9 filter positions, and then by the 6 temporal samples, we have a total of about 1800 frames per spacecraft--on the order of i of the total picture budget. Unfortunately, this excellent plan, which, in many ways, would have stand:~rdized the Mariner 9 photometry, never materialized. In astronomical photometry, one normally spends about ½of the observing time on sta.ndard stars; however, this was regarded as excessive by most of the TV team members, who are geologists rather than astronomers. The compromise adopted was to budget only about 10% of the pictures for calibration, by abandon-

TELEVISION PHOTOMETRY

ing all calibration of the polarizing filter positions, and by doing much less calibration of the spacecraft used for mapping. That was before Mariner 8 went down instead of up. When the full burden of the mission fell on Mariner 9, the geologists still wanted the same number of frames to get complete mapping coverage. However, as a concession to the minority interested in photometry, they would allow part of a day at the end of each 21-day mapping cycle to be used for calibration. This reduced the calibration budget to about 3% of the total, which required giving up all time-dependent effects. These severe sacrifices were justified with the following argument: (a) photometrically reduced data would be available within a few days after picture-taking, so t h a t any serious photometric errors could be detected within a week or two of the first calibration sequence; and (b) if unacceptable photometric errors were detected, an intensive effort could be immediately devoted to calibration because of the adaptive character of the mission. ("Unacceptable" was estimated by most team members as errors in the neighborhood of 10-15%.) However, it was already clear t h a t such in-flight "calibration" data would not suffice to establish correct photometric data, but would only provide crude corrections and some estimate of their uncertainty. In actual fact, things turned out to be much worse. The failure of several major soi~ware systems (on whose existence the whole mission plan had been predicated) made the time-scale for production of reduced data many weeks rather than a few days; largely prevented the detailed planning and execution of the few calibration sequences remaining in the nominal mission plan; and delayed the accurate information on illumination and viewing geometry, needed in the reduction of calibration frames, for m a n y months. As is shown in the text, large systematic errors exist in reduced data. Thus the tiny amount of calibration data actually obtained is inadequate to reveal more than the most serious deficiencies of the Mariner 9 television "photometry".

277

~PPENDIX B

Dust-Speck Analysis To begin with, we establish t h a t these features, which appear at the same positions in all the Mariner 9 TV pictures, really are dust-speck shadows. Four such features appear in raw Acamera pictures, and two much weaker ones in B-camera pictures. In both cases, the features in a given camera are all the same size, and agree in diameter with the expected size calculated from the thickness and refractive index of the faceplate, and the focal ratio of the camera. I f we regard the dust-speck as an antipinhole, it should form (anti-) pinhole-camera images of the entrance pupil of the optics ; such an image is a uniform circle in the case of the A-camera, and a uniform annulus in the case of the B-camera. The images have this character; in the B-camera, one can even see the displacement of the central obstruction as seen from off-axis points. Similar annular shadows occur in other Mars pictures (Humason, 1961; Plate 5). Finally, as will be shown below, the size of the largest A-camera speck estimated from the profile of its shadow agrees well with the size estimated from the contrast of the shadow. Figure 3 shows the apparent contrast of this shadow in RDR data, as a function of R D R DN. To measure the contrast precisely, one must average the DN values of many picture elements. Existing software can do this for any specified rectangular block in a picture ; but the shadow is circular, not rectangular. Thus to obtain the values shown in Fig. 3, the basic data were mean values for an inscribed square, and for a larger square enclosing the shadow. Let the inner square have side s (area s2), the outer square have side S (area $2), and the circular shadow have diameter d and contrast c, on a background of brightness B. The measured quantities are the mean DN values, m and M respectively, of the inner and outer squares. To find the background brightness B and contrast c of the circular shadow, we note that m =- B(1 --c) (B1)

278

A.T.

YOUNO

and M

=

B[1

-

(c~d2/4S2)] =

B[] - .c].

(B2)

Solving for c and B, we find c =

(M

-

m)/(i

(B3)

-- am)

and B = ( i -- am)/(1 -- a),

(B4)

H o w is the a p p a r e n t contrast shown in Fig. 3 related to the shape of the transfer curve in Fig. 27 Suppose Fig. 2 were on linear instead of log-log paper, so t h a t y=RDI~ D N and x = exposure. The a p p a r e n t contrast is (B9)

c = Ay/y

and the true contrast is

where (B5)

a = ~rd2/4S 2,

as defined in Eq. (B2). In our case, d = 30 picture elements, b o t h from direct m e a s u r e m e n t and from the calculation based on the thickness and refractive index of the faceplate and the solid angle of t h e f/4 beam incident on it. I have chosen s = 19 and S = 49 ; as b o t h squares have the same center (line 548, sample ]57 in R D R picture format), a uniform gradient across this region has no effect on the result. I f the s t a n d a r d deviation of the individual D N values in the smaller square from m is at, an estimate of the error in c is a,(1 - - a ) ( 1 +fl)~/2 M % =

(M -

~m) 2

s

(B6)

where fl = (s/S) 2

(B7)

This involves some dubious assumptions, such as the statistical independence of values at individual picture elements, and does n o t properly take account of the partial correlation between m and M due to the picture elements in common, nor the contribution of a local gradient to a 1. However, it provides some estimate of precision. F o r our particular situation, c < 1 so m ~ M. This allows a simplification of Eq. (B6) to a I [(1 + fl),/2]

(B8)

or a c ~ 0 . 0 8 a l / M for our p a r t i c u l a r values. Figure 3 is a plot of c vs. B, with error flags representing (c ~-ac) for each point. Typically, % is on the order of 0.1%, so the large variations in c with B are certainly real.

(B10)

C = Ax/x,

where ,dx and A y are the diminution of light in the shadow and the corresponding diminution of response in the R D R . Then c Ay/y x Ay x dy . . . . . . . ~ -. C Ax/x y Ax y dx

-

dlny dlnx"

(Bll)

T h a t is, if the contrasts are infinitesimally small, the ratio of a p p a r e n t contrast to true contrast is the logarithmic derivative of y(x), or the slope of the log-log plot of Fig. 2. Now, Fig. 2 shows unit slope (i.e., correct contrast) near 50-60 D N ; in this range, Fig. 3 shows an a p p a r e n t contrast in orange light of a b o u t 6 . 3 ± 0 . 2 % , which we can a d o p t as an estimate of C, the true contrast. Below 50 DN, Fig. 3 shows c > C, so the slope of Fig. 2 should be greater t h a n u n i t y - - a n d it is. Above 60 DN, Fig. 3 shows c/C < l, so the slope of Fig. 2 should also be less t h a n 1 - - a n d it is. The general decrease in c from 30 to 150 D N has its exact c o u n t e r p a r t in the continuous decrease in slope of Fig. 2 in this same range. I n fact, there is fairly good quantit a t i v e agreement between the slope of Fig. 2 and the contrast shown for the dustspeck shadows in orange pictures in Fig. 3. Thus the dust-speck analysis provides i n d e p e n d e n t confirmation of the nonlinearity shown in Fig. 2 - - Q . E . D . I n principle, if one knew the true contrast C, he could use d a t a like those shown in Fig. 3 to integrate the difference equation ( B l l ) and obtain the true relation between R D R D N and light intensity. Thus there is a practical reason for t r y i n g to determine the true contrast of the shadow. I n this sense, we can regard the dust-speck shadow as a one-step

T E L E ¥ I S I O N PHOTOMETRY

calibration wedge (Latham, 1972), and our task is to learn its true value. The contrast of the shadow could be calculated if we knew the geometrical area A occulted by the dust-speck, since c = 4A/Trd 2

(B12)

We can try to estimate the dimensions of the speck, and hence its area, from the DN profile across its shadow. The edges of the shadow profile are not sharp, but are sloping ; the width of the sloping region is the width of the speck of dust. From the average of five individual frames, I have estimated the width of the sloping edge as six picture elements vertically and eight elements-horizontally, with an uncertainty of about one in each direction. This gives a contrast of 5.4 ± 1.0%, in good agreement with the 6.3% contrast estimated from Figs. 2 and 3. It is important to realize t h a t the shadow contrast found from the geometrical size of the dust-speck (cf. Eq. (B12)) is an upper limit, because the speck is assumed to be perfectly opaque. A semitransparent dust-speck would produce a less-contrasty shadow. Thus the very high apparent contrast (~7-8%) of the shadow in violet pictures (see Fig. 3) implies correspondingly severe nonlinearities in these data, and cannot be explained by a colored (yellowish) dust-speck. The above results have been checked by reducing a group of flat-field frames taken just before launch for calibration verification. These R D R data show linearity within about five per cent between exposure and DN, and a more nearly constant apparent contrast of 5.7 ± 0.4% for the dust-speck shadow, in good agreement with the previous estimates. The direct verification of linearity in these pre-launch data not only shows t h a t the calibration files and reduction algorithms used in computing R D R values are correct, but also t h a t the nonlinearity of the flight data represents a real change in the camera characteristics either during launch or en route to Mars. Finally, reduction of both flight data and prelauneh frames, using calibration files for different temperatures, have shown t h a t although the ab-

279

solute sensitivity of the camera is quite temperature-dependent, with a variation of 2.5% per degree, the linearity (e.g., apparent dust-speck contrast) is not. Thus the nonlinearities of reduced flight data are not due to temperature effects (such as using an incorrect camera temperature for reduction). APPENDIX C Future Improvements in the Mariner Data

The measured systematic errors can be used to correct the RDI% data. The present uncertainty, after such corrections, is about 10% (over a limited dynamic range). Our use of time-scale sensitometry (Figs. 2 and 4) assumes no reciprocity effects; in preflight testing, no systematic effect was found in data with about 10% scatter. Furthermore, exposure variations of about 0.1 msec may cause several per cent error at the left side of Fig. 2 (3msec data). Our corrections may also contuin several per cent systematic errors due to uncorrected residual-image effects. Possibly 5% accuracy could be achieved for the orange filter position of the Acamera if all suitable frames were reduced and analyzed for dust-speck contrast (Appendix B). We have already analyzed about one-third of all suitable frames taken with the polarizer; these are limited not only in dynamic range, but also by their higher noise level, so not much improvement seems likely. There are so few data available for the other filter positions t h a t only a very crude correction, at best, can be made; one might hope to achieve 15% accuracy over a limited dynamic range. Similarly, the lack of a good dust-speck shadow in the B-camera (as well as very limited in-flight calibration data) means t h a t 10-15% accuracy is the best one could expect if corrections were generated. Much of the B-camera correction would have to be based on comparison with A-camera data, the bulk of which involve the polarizer, so t h a t polarization effects would compound the errors transferred from the A-camera. The accurate measurement of these

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corrections involves large amounts of magnitude, or 10%, corresponding to labor and computer time. For example, about 100 detected photons per 7th the complete dust-speck analysis requires magnitude star. In the 6.144-sec exposure, visual inspection of several thousand about l06 photons are received by the frames to select those with "clean" 2 × 10Zcm z collecting area of the Bdust-speck shadows; computer processing camera; thus the DQE is about 10-4 , of the selected frames to measure apparent about 50 times lower than the detective contrast (about 75 hr of computer time); quantum efficiency of a good photographic and integration of the resulting difference emulsion. This comparison can be checked equation (B 11) for several plausible values by comparing the limiting magnitudes of of the true contrast. Comparison of B film and Mariner cameras. The limiting with A frames, to establish the scale of magnitude of the Mariner B-camera pictures is near V* = 8.2, for a 6-sec exposure the B-camera, is a job of similar size. Whether correcting the TV photometry with the 8-in. (20-cm) camera aperture. to the accuracy of visual measurements Eighth-magnitude stars can also be photomade in the 1880's (cf. Weaver, pp. graphed in 6sec with a 35-mm camera 229-230) will provide enough new scientific from the surface of the Earth, using an information to justify this effort is debat- f/1.8 lens of 70-mm focal length (Nielson, able. Ten per cent accuracy is barely ]957). Allowing for atmospheric extincadequate to detect differences in photo- tion, the limiting magnitudes are practicmetric function between different regions ally equal; but the film camera has only a of Mars, for example (Young and Collins, 40-mm aperture, or about 1/25 the col1971). The expected accuracy for color lecting area of the Mariner B-camera. measurements is likewise marginal for the Thus the DQE of the Mariner camera is detection of the subtle color differences on between 25 and 50 times worse than that of Mars. The little improvement available normal photography. This comparison is slightly unfair, as at high and low DN levels probably is insufficient for photometric study of at- the vidicon may not be as sensitive to mospheric haze at limb and terminator, stars as it is to extended areas. Let us or for polar-cap work. The most likely compare Mars pictures with photography. uses of improved data are for the study of The B-camera's unobstructed collecting variable surface features, the general area is equivalent to t h a t of an f/2.8 lens photometric function, and possibly in the of the same focal length, and typical Mars photometric estimation of slopes, all of exposures (through a GG 495 filter) are which require only good local photometry about 24 msec (1/40 sec). The reflectance of Mars is about twice t h a t (~12%) of an in the normal range of exposures. Each worker must judge for himself "average outdoor scene ''6, which just whether improved data are worth the compensates for the reduced brightness effort of generating improved corrections. of sunlight at Mars; so nearly the same I do not feel t h a t possible small improve- exposure is required to photograph Mars ments in the photometry are worth this as to photograph terrestrial scenes. The effort; but anyone who wants to extract spectral response of the Mariner vidicon better photometry from the Mariner data resembles that of ordinary panchromatic films, so we can adopt the same filter is welcome to try. factor (about 2) for the yellow filter in both cases. Thus, a film like Panatomic-X APPENDIX D (ASA 32; normal daylight exposure 4 or Comparative Quantum Ej~ciencies of 5msec at f/5.6) would require about two Vidicons and Films milliseconds to photograph Mars through The scatter in Fig. 8 allows us to estimate the B-camera optics and filter; in other the detective quantum efficiency (DQE) words, the ASA "film speed" of the B of the Mariner B-camera. For example, vidicon is 2/24 of 32, or about 3. 6 According to Kodak publication AF-13. the scatter near V * = 7.0 is about 0.1

TELEVISION PHOTOMETRY

Such a slow detector can be e x p e c t e d to have good signal/noise ratio. U n f o r t u n ately, no commercial film this slow exists for comparison. The nearest p a n c h r o m a t i c emulsion seems to be K o d a k Spectroscopic Film, T y p e V-F (ASA 10), for which ~ 4.7 and the RMS density fluctuation with a 48-t~m scanning aperture is 9 × 10 -3. This corresponds to an equivalent input noise of 2 × 10 -3 in the c o m m o n logarithm of the exposure, or less t h a n ½% I%MS error in relative i n t e n s i t y per 48-t~m sample. The RMS noise per picture element in flight d a t a from the B-camera is 2.2%, b u t the sample size is smaller (about 13tLm across). I f we assume noise from adjacent picture elements is uncorrelated, the RMS noise of a 48-~m p a t c h would be 0.27 of this or 0.6%; t h u s a V-F emulsion would give slightly lower noise with only t h r e e - t e n t h s as m u c h exposure. Actually, the noise from adjacent picture elements is partially correlated, so the D Q E of the vidicon is more t h a n a factor of 5 below t h a t of V-F spectroscopic emulsion; correlation effects are discussed below. I f it is objected t h a t the d y n a m i c range of the vidicon exceeds t h a t of a slow, c o n t r a s t y emulsion, we could instead choose a fast film of m e d i u m contrast like 103-F or T r i - X Pan, whose characteristic curves are similar to the vidicon's. A t ASA 400, we would need to change the optics to nearly f/40 to p h o t o g r a p h Mars in 24 msec on such films; the nearly 14-fold increase in focal length would e x p a n d the B-camera's picture element (about 6" of arc across) to some 180tLm. Since the RMS film noise corresponds to a b o u t 0.025 in logl0 E ( ~ 6 % exposure error) for a 48-t~m spot, the relative RMS noise in the p h o t o m e t r y would be a b o u t 1.6% for a 180-t~m resolution element. Again, the photographic noise level is below t h a t of the vidicon camera. F u r t h e r m o r e , the films would have superior resolution (higher M T F curves) at this sample size, and b e t t e r large-scale uniformity. Finally, if we use the scatter in Fig. 3 or Fig. 5 to allow for correlation effects, we have an RMS error 7 of 0.3% (Fig. 3) or Assumed to be 1.0/0.67 times the probable errors estimated previously.

281

0.6% (Fig. 5) for one m e a s u r e m e n t of a p p a r e n t spot contrast. E q u a t i o n (BS) t h e n teils us t h a t the equivalent uncorrelated RMS noise in the A-camera is a 1 = 3 . 7 5 to 0 7.5% per sample. These figures lower the D Q E b y factors of 2.9 to 11.6, so the D Q E of the vidicon is some 14 to 55 times lower t h a n t h a t of V-F film. Similarly, the residual-corrected S a t u r n images have RMS noise of 1.7°/o for a b o u t 20-element areas; this corresponds to al = 7.6%, or a b o u t 56 times lower D Q E t h a n V-F. These more realistic estimates agree well with the earlier ones based on star images. W e m u s t conclude t h a t photographic emulsions are considerably superior to vidicons, c o n t r a r y to the opinions expressed b y O'Dell (1972) and Disney (1972). Of course, the D Q E of vidicons can be i m p r o v e d b y an image-tube preamplifier; b u t the same is true of film. Comparison of intensifier-vidicons with unintensified p h o t o g r a p h y is unfair; such tubes should be compared to p h o t o g r a p h y w i t h image tubes, or to electronography.

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WILLIAM (1867). On the spectrum of Mars, with some remarks on the colour of that planet. Mort. Not. Roy. Astron. Soc. 27, 178. HUI~ASON, M. n . (1961). Photographs o f P l a n e t s with the 200-inch telescope. I n "Planets and Satellites" (G. P. Kuiper and B. M. MiddleHUGGII~S,

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hurst, eds.), Ch. 16 Univ. of Chicago Press, Chicago. JEPSON, P. L., AND SCHWARTZ,A. A. (1972). Correction for residual image effects in Mariner 9 television images. J. Opt. Soc. Am. LATHA~, D. W. (1972). Private communication. LATHAlVl,D. W. (1966). Some experiments on the limits of photographic spectrometry. Astron. J. 71, 168. LATHAM, D. W. (1968). Some performance data for E a s t m a n Kodak I I a emulsions. Astron. J. 73, 515. LATHAM, I). W. (1969). Amer. Astron. Soc. Photo-Bull. 1, 3. LEVINTHAL, E. C., GREEN, W. B., CUTTS, J. A., JAHELKA, E. D., JOHANSEN, R. A., SANDER, M. J., SEID!VIAN, J. B., YOUNG, A. T., AND SODERBLOM, L. A. (1973). Mariner 9--image processing and products, Icarus 18, 75. NIELSON, A. (1957). High-speed star photography. Sky and Telescope 16, 350. NOLAND, M., VEVERKA, J., AND POLLACK, J. B. (1973). Mariner 9 polarimetry of Phobos and Deimos. Icarus 20, 490. O'DELL, C. R. (1972). The large space telescope program. Sky and Telescope 44, 369. SEIDI~A~, J. G., GREEN, W. B., ..TEPSO]~', P. L., RuIz, R. M., AND T~ORPE, T. E. (1973). A user's guide to the Mariner 9 television reduced data record. J P L Technical Memora n d u m 33-628, Aug. 1, 1973.

SEIDYIAN, J. B., AND KREZNAR, J. E. (1972). Geometric calibration of the Mariner 9 vidicon camera system. J. Opt. Soc. Amer. 62, 1351. SNYDER, L. M. (1971). Internal Report. Mariner 9 TV subsystem calibration report. J P L Report 610-202, 15 November 1971. STOCK, J., AND WILHA~S, A. D. (1962). Photographic photometry. I n "Astron. Tech." (W. A. Hiltner, ed.), Ch. 17. Univ. of Chicago Press, Chicago. Suol~I, V. E., AND YONDER HAAa~, T. H. (1972). Reply. J. Atmos. Sci. 29, 602. THORPE, T. (1972). Mariner 9 TV Imaging Performance Evaluation. Vol. 2 of Mariner 9 ~[V subsystem calibration report No. 610-237. JPL. THORPE, T. (1973). Mariner 9 photometric observations of Mars from November 1971 through March 1972. Icarus 20, 482. WEAVER, H. F. {1946). The development of astronomical photometry. Pop. Astron. 54, 211-230, 287-299, 339-351,384-404, 451-464, and 504--526. YOUNG, A. T. (1969). High-resolution photo. metry of a thin planetary atmosphere. Icarus 11, 1. You~o, A. T., Am) COLLINS, S. A. (1971). Photometric properties of the mariner camera and of selected regions on Mars. J. Geophys. Res. 76, 432.