AT 5:30 (UNIVERSAL TIME) LAST MARCH 13 the slender cone of shadow cast by the earth extended 855,000 miles into space. The full moon then rounding the dark side of the earth was approaching the shadow on an intercepting path at a rate exceeding 2,200 miles per hour. A total eclipse of the moon was about to occur. At North Plainfield, N.J., the clock indicated approximately 12:30 a.m. (Eastern Standard Time). There, on a wooden platform atop a three-story frame house, a pair of amateur astronomers switched on a small red lamp and spent several minutes loading film into a battery of cameras that was kept trained on the stars by an automatic telescope drive. After checking the lens settings, they switched on a shortwave radio that fed precision time signals into a magnetic-tape recorder. Finally they manned the cameras in readiness for the instant when the edge of the earth's shadow made contact with the limb of the moon. Aside from gusts of cold wind that jiggled the equipment from time to time, conditions for observing were good. The amateurs, J. F. Ossanna, Jr., and L. C. Thomas, who are engineers at Bell Telephone Laboratories, were ready after months of preparation to photograph the lunar eclipse in full color.

The observers. did not seek to make unique pictures. Lunar eclipses have been photographed in color many times. Instead, Ossanna and Thomas were out to validate a reliable technique for determining the optimum camera-exposure for lunar photography. In the past most pictures of the moon have been made by the traditional technique of cut-and-try. One simply makes a series of increasing exposures and hopes that one pair will bracket the optimum exposure. In contrast, Ossanna and Thomas had computed the absolute brightness of the full moon and had taken account of the many optical and photographic variables associated with the eclipse of March 13. With these data they hoped to hit every exposure dead on the nose. A match between the color of their developed film and that of the eclipsed moon would confirm their value for the brightness of the full moon, an astrophysical quantity that had not been well established.

"We did not set out to establish anything," they write. "In the fall of 1959 we decided to photograph the eclipse in color, partly because the next one of long duration would not be visible from the East Coast until 1964, but mostly because the project presented a stimulating challenge. Would it be possible to calculate camera exposures in advance?

"The method of determining shutter speeds and lens openings that camera enthusiasts use when making casual snapshots does not work in the case of the moon. The shutterbug simply holds an exposure meter up to the scene, reads the brightness indicated by the pointer and inserts this figure, along with one representing film speed, into the little slide rule on the side of the instrument The slide rule automatically solves a built-in equation that gives the optimum lens setting and shutter speed for the scene in question. But you can't hold an exposure meter up to the moon!

"It seemed reasonable to suppose, however, that the moon's relative brightness during an eclipse could be calculated rather easily from the size and structure of the shadow. The shadow is composed of two principal regions. The largest, called the penumbra, takes the form of a truncated cone with the earth at the apex. When in the penumbra, an observer on the moon would see a partial eclipse of the sun. The second region, called the umbra, lies wholly within the penumbra and is coaxial with it. The umbra is characterized by two conical regions: (1) a short inner cone of total solar eclipse that on March 13 extended into space approximately 159,000 miles from the center of the earth, and (2) the longer surrounding cone within which an observer on the moon would sew the earth encircled by a bright ring of reddish light. The boundary between the two umbral regions is formed by rays of light from the sun's limb which are refracted by the atmosphere toward the earth's surface, then skim the surface at zero elevation and are further refracted as they traverse the atmosphere above the dark side of the earth. The shorter wavelengths (i.e., those at the blue end of the spectrum) of these rays tend scattered as they pass through the atmosphere; as a consequence the rays that divide the two regions of the umbra are deep red. The shorter wavelengths of the rays that traverse the higher levels of the atmosphere are not so strongly scattered; thus a cross section through the outer part of the umbra would appear deep red toward the center and gradually fade into orange, yellow, and finally into the white of clear sunlight at the boundary between the umbra and penumbra. When totally immersed in the umbra, the moon accordingly acquires the colors of sunset on the earth. The three major features of the shadow are depicted in the accompanying drawing [right].

"Illumination within the shadow increases progressively from full sunlight at the outer boundary of the penumbra to the deep red of the shadow's axis. To determine camera exposure, the problem is to determine the size of the umbra and penumbra and the extent to which the moon will be immersed in them. Information for computing these quantities is listed in American Ephemeris and Nautical Almanac, an indispensable reference for anyone interested in astronomy. (The ephemeris is published each year by the Government Printing Office, and is available from the Superintendent of Documents in Washington for $4.25.) Three quantities are involved in the computation. The first, P, is called the 'equatorial horizontal parallax of the sun,' and is the angle subtended at the sun's edge by lines drawn from the limb of the earth and from its center. The second quantity is similar, but applies to the moon. The equatorial horizontal parallax of the moon is used for calculating the radius of the earth's shadow at the distance of the moon. It is designated P', and is subtended at the edge of the shadow as shown in the accompanying diagram [left]. The third quantity, designated r, is also an angle. It comprises a measure of the sun's angular semidiameter (or radius).

"An inspection of the diagram will disclose that the angle P' is equal to the sum of two other angles: the umbral radius, designated s, plus half of the angle formed by the umbral cone, v. Also note that the angle representing the solar semidiameter, r, is equal to P plus v. By eliminating the angle v it is seen that the umbral radius is equal to P' plus P minus r. Similar reasoning demonstrates that the penumbral angular radius, s', is equal to the sum of P', P and r.

"For the lunar eclipse of March 13 the values of these angles were: P, 8.85 seconds of arc; P', 57 minutes 29.62 seconds of arc; and r, 16 minutes 5.3 seconds of arc. The umbral radius at the point of intersection with the moon's path (P' + P - r) was therefore 41.558 seconds of arc, and the penumbral angular radius (P' + P + r) was 73.730 seconds. The angular radius of the moon on the date of the eclipse was 15.653 seconds of arc, slightly more than a third of the umbral radius. The umbral and penumbral radii have here been calculated on the assumption that the earth has no atmosphere. It is customary to increase these values by 2 per cent to take account of the optical effects of the atmosphere. With this correction s and s' become 42.384 seconds and 75.204 seconds respectively. The length of the umbral shadow is equal to the radius of the earth divided by the trigonometric sine of the angle v. That computation yields a shadow length of 855,000 miles for this eclipse. The length of the dark portion of the umbra depends on the size of the angle, , between the outer and inner cones. This angle is equal to approximately 70 minutes of arc. To compute the length of the dark portion divide the trigonometric cosine of by the trigonometric sine of the sum of plus v and divide the quotient by the radius of the earth in miles. With these data plus the time schedule of the eclipse and related facts listed in the ephemeris we plotted the details shown on the accompanying diagram [Figure 4].

"Having thus established the size and location of the scene to be photographed, our next consideration turned to the theory of camera exposure. In simplest terms exposure is equal to the product of the illumination (in meter-candles) multiplied by the shutter speed (in seconds). The equation becomes impressively more complex when one comes to grips with an actual camera loaded with real film. It turns out that many additional factors are built into the little slide rule on the exposure meter, all of them assumptions. The illumination falling on the film increases as the product of the scene brightness in candles per square foot, the transparency of the lens system, the vignetting factor introduced by the opaque parts of the lens housing, scene distance minus the focal ratio squared, and the fourth power of the cosine of the angle through which a desired portion of the image departs from the axis of the lens system. The illumination decreases as the product of the square of the focal ratio (f number) multiplied by the square of the scene distance. If all of these factors except scene brightness and the f number are combined in a quantity q, then for a given situation the illumination in meter-candles is equal to q multiplied by the scene brightness and divided by the square of the f number. The numerical value of q of course depends on the values assumed for its component factors. The transparency of the lens system, called the transmission factor, varies with the number of lens elements and whether they are coated or not. For a typical camera with coated lenses the transmission factor usually falls between .80 and .95. In other words, 80 to 95 per cent of the light that enters the lenses gets through to the film. The rest is dissipated by the glass. The vignetting factor depends on the design of the lens barrel, relative aperture and the angular distance of the off-axis image. It can vary from .1 to 1, but typical values fall between .7 and .8. For lunar photography scene distance minus the focal ratio squared can be taken as unity. The off-axis image factor depends on the geometry of the scene. In the case of moon photography a value of 1 can be assumed, because for practical considerations the object of interest is largely confined to the axis. Considerable disagreement is found among the values listed for these factors in the photographic literature. The value of q for ordinary terrestrial scenes ranges from about 4.5 to 7.5, according to which authority you consult. We found that if a lens of 95 per cent transmission is used in lunar photography, where the image is nearly on axis, a value of 8 can be taken for q. The illumination falling on the film then becomes equal to eight times the brightness of the scene (in candles per square foot) divided by the square of the focal ratio, or f number. The exposure E is equal to this value of illumination multiplied by the time that the shutter is open.

"This formula assumes that all areas of the moon are uniformly bright. In reality the moon's brightness varies from some minimum to maximum value. The brightness of ordinary scenes (for which color films are designed) is assumed to range from 100 to 160. This means that if the dimmest part of the scene reflects light equal to the intensity of a single candle at a specified distance, the brightest part reflects light equivalent to 100 to 160 candles of the same size at the same distance. The range of brightness: that falls on the film is much narrower, however. Reflections occur within the camera, with the result that an appreciable amount of scattered light reaches: the film. This light increases the illumination of the dimmer portions of the image, an effect called the flare factor. The scattered light reduces the difference between the dimmest and brightest parts of the image by a factor of three or four. The effective brightness there fore ranges between 25 and 50; the value of 32 has frequently been assumed.

"The film must receive a certain minimum amount of light from the dimmest portion of the scene or no image will be registered. At the opposite extreme, a certain maximum exposure (in the case of color-reversal film) results in transparency. Overexposure beyond this value is not recorded by the film.

"The exposure index (S_c) that is supplied by the manufacturers of color films is based on the geometric mean of these two extremes. The geometric mean exposure, designated E_mid, is equal to the square root of the product of the maximum exposure multiplied by the minimum exposure. The exposure index for color film is defined as 8 divided by the exposure in meter-candle-seconds corresponding to E_mid. For each scene there is an effective geometric mean in the range of scene brightness, the value of B_mid, that corresponds to E_mid. We combined these relations in an equation that gives the camera exposure we used to photograph the lunar eclipse:

Here A is the relative aperture, or f number, and B_mid is expressed in candles per square foot. The exposure time, t, is in seconds.

"The latitude of color films currently available does not appear to extend much beyond that required by scenes of average effective brightness range. When the range of scene brightness exceeds the latitude of the film, the photographer must compromise and select a portion of the scene that falls within the latitude of the film by adjusting camera exposure to the midpoint B_mid of the range desired.

"From the foregoing it is evident that the exposure recommendations of film manufacturers, the exposure index specified for a given type of film and the characteristics of exposure meters rest on many assumptions about the average camera and average scene. These assumptions should be taken into account when unusual scenes are photographed.

"To determine the optimum exposure for photographing the eclipsed moon we predicted both the range of the moon's brightness during its transit through the shadow and the absolute brightness (in foot-candles) of the full moon. The brightness of a diffuse reflecting surface depends on the illumination that falls on it, the angle of incidence at which the rays strike the object and the reflectivity of the surface (the percentage of light reflected). Experiments and theory demonstrate that brightness is equal to the product of the reflectivity, the illumination and the cosine of the angle of incidence divided by 3.1416. When the illumination is measured in lumens per square foot, the equation gives brightness in terms of candles per square foot. For example, a diffuse sphere viewed from the direction of the light source appears brightest at the center, and because of the increasing angle of incidence, appears progressively dimmer toward the edge. This effect is not observed in the case of the full moon. Although the moon might be expected to be a diffuse sphere, it looks like a disk of uniform brightness. The explanation appears to be that surface irregularities on the moon, such as mountains and the walls of craters, catch sunlight at much smaller angles of incidence than would a smooth surface. This effect upsets the theoretical formula, but greatly simplifies the determination of lunar brightness during an eclipse. Normal incidence can be assumed everywhere on the moon's disk, and attention can be confined to illumination within the shadow.

"The illumination in the penumbra varies according to the proportion of the sun's disk that is covered by the earth, and on the darkening of the sun's limbs. It has been computed and measured by many observers. The relative illumination in the umbra has been similarly measured. A small area on the moon is selected for observation, and the light reflected by it is measured as the area proceeds through the shadow. Such measurements also show that the relative brightness falls slowly as the moon enters the penumbra, and rapidly at the inner edge of the penumbra. There it reaches a value of -6.2 magnitudes (a ratio of 1:302) with respect to the brightness of the full moon, to which we arbitrarily assigned a value of zero magnitude. The brightness continues to drop sharply as the small area under measurement enters the umbra, after which the rate gradually decreases.

"Sunset hues predominate in the umbra. Thus the rate of diminution that is indicated by a photometer is influenced by the color selected for measurement. We analyzed a large number of measurements made during various previous eclipses and plotted a composite curve of relative illumination for the penumbra and two of the umbra's colors: orange (wavelength 6,100 angstrom units) and green (5,400 angstroms). As shown by the accompanying graph [above] the brightness ratios of the orange curve vary from -6.2 magnitudes at the edge of the umbra to -10.3 magnitudes (a ratio of 1:13,200) at the center of umbra.

"It is obvious from the graph that the range of brightness characteristic of the lunar eclipse greatly exceeds that of color film. However, more information is required for computing camera exposure, because the graph expresses brightness with respect to that of the full moon. To compute camera exposure we need to know the absolute brightness the full moon.

"Acquiring this information proved to be rather more difficult than we had anticipated. The published data are in wide disagreement. The crux of the difficulty resides in the failure of observers to state fully the conditions and times of their measurements and calculations. Absolute lunar brightness depends on a number of variables. A major one is the intensity of sunlight. Illumination from the sun varies about 7.5 per cent, because of the approximately 3.7-per-cent variation in the moon-to-sun distance that arises from the eccentricity of the earth's orbit and that of the moon. Moreover, we cannot measure the moon's absolute brightness on earth because of the earth's atmosphere. The apparent brightness that we can measure is less than the true brightness because of absorption by the atmosphere. The absorption varies with the elevation of the moon above the horizon. Measurements of apparent brightness are meaningless, therefore, unless the observer specifies the moon's elevation at the time of observation. In addition, the intensity of moonlight falling on the earth varies some 23 per cent because of the 11-per-cent variation in earth-to-moon distance.

"Considerably less spread is found in published values for solar illumination and the moon's apparent magnitude. We decided to compute the absolute lunar brightness from these quantities by taking the reflectivity of the moon's surface into account.

"The disparity of the published values in the case of the sun is in the ratio of 1.5 to 1. We selected a value of 14.14 lumens per square centimeter for the solar light-flux outside the earth's atmosphere at the mean earth-sun distance. The surface reflectivity of the moon was taken to be .106. The full-moon brightness is equal to the product of the reflectivity and the illumination divided by 3.1416. With the quantities assumed, it comes out to 433 candles per square foot. During the March 13 eclipse the moon-sun distance was about .9967 times the mean moon-sun distance. The solar illumination was therefore .66 per cent higher, or 446 candles per square foot.

"For the alternative method of arriving at a value for lunar brightness we took the moon's visual magnitude a -12.70 (at mean earth-sun and earth-moon distances). Assuming the illumination of a zero-magnitude star to be .243 billionths of a lumen per square centimeter, the illumination of the full moon equates to .0292 thousandths of a lumen per square centimeter. The brightness of the full moon is equal to the illumination divided by 3.1416 time the square of the trigonometric sine of the angle expressing the moon's semidiameter. During the March 13 eclipse this angle was 15 minutes 39.2 seconds arc. When the moon-sun distance of .9942 multiplied by its mean value, and the earth-moon distance of 1.0079 multiplied by its mean value, are taken into account, the equation gives 418 candles per square foot as the moon's brightness-slightly lower than the value of 446 candles per square foot based on the sun's illumination. We used the average of the two: 482 candles for the brightness of the full moon.

"To find the absolute brightness of a small area on the eclipsed moon at a specified time, first determine the distance of the area from the edge of the umbra in minutes of arc, and then from the graph of brightness range calculate the relative brightness in magnitudes compared with the full moon. Convert the brightness ratio in magnitudes to a numerical ratio and multiply by the brightness of the full moon. To facilitate: this procedure, the distances of the brightest part of the moon's disk (the edge of the moon farthest from the center of the umbra), the dimmest part (the edge closest to the center of the umbra, except when the moon's disk includes the umbra center) and the center of the umbra were calculated as a function of ephemeris time. This information, together with that from the graph of brightness range, enabled us to plot against time the brightness ratio in magnitudes for these three parts of the moon [above]. The chart gives the total brightness range across the disk of the moon at all times during the eclipse.

"This information does not take into account the loss of brightness due to atmospheric absorption. We therefore charted the moon's predicted elevation above the horizon against ephemeris time for the night of March 13 at the latitude and longitude of North Plainfield, N.J. [see above]. A final graph was then made to display the visual atmospheric absorption in magnitudes with respect to the apparent angle of elevation above the horizon for a clear atmosphere [see Figure 7].

"As a demonstration of the method used to compute exposure from these data, consider a moment during the March 13 eclipse when the moon had just slipped completely into the umbra (about 7:41 ephemeris time). The graph of brightness range [Figure 5] indicates that the brightness ratio varies from -6.2 magnitudes to -9.9 magnitudes, a range of 3.7 magnitudes. This is well within the range of color transparency film (about 5 magnitudes). It would be logical to expose for the middle (B_mid) of this range: -8 magnitudes. The moon at this time is at 38.3 degrees elevation [see graph in Figure 7], which corresponds to an atmospheric absorption of about .4 magnitude. Taking the apparent brightness ratio as -8.4 magnitudes, the corresponding absolute brightness (in candles per square foot) for calculating exposure is:

"To determine the exposure we need to know the film exposure-index. For Daylight Ektachrome (sheet film, process E-3) the exposure index S_c is 50. For a relative aperture of f/6, the expression for the time in seconds (t) would be as follows (A designates the f number):

"For B_mid = .189 candle per square foot, the time is .72/.189, or 3.8 seconds. Because the brightness range in this case is less than the range of the film (3.7 magnitudes compared to 5 magnitudes), it would be logical to expose longer to attempt to capture more detail in the lunar 'seas,' or maria.

"So long as the moon is not partly out of the umbra, the brightness range across its disk is roughly within the range of color film. When the edge of the umbra does cut across the disk, the brightness range can be much greater than color film can record; for example, at 7:00 ephemeris time the total range is 8.7 magnitudes. In these cases one must decide what part of the range to try to cover. If the exposure is made for the portion of the disk in the umbra, the portion outside will be overexposed.

"It should be noted that the accuracy of these calculations should not be expected to be too great. The most serious contributions to error are the assumption that the reflectivity of the moon's disk is uniform, the use of a brightness curve within the umbra that corresponds to only one color, and variations in published physical data. We are reasonably confident that the accuracy of the calculators for the absolute brightness of an area of the moon is accurate within one magnitude.

"Four samples of the results of our predictions are herewith reproduced [see top]. The first photograph [top left] was made at 6:58 Universal Time and was exposed 1/2 second to show the irregularity of the shadow, along the umbral edge. The second photograph [top right] was made at 7:23 Universal Time and was exposed for eight seconds to show the color of the umbra. The region of the moon still immersed in the penumbra is necessarily overexposed. The third photograph [bottom left] was made at 7:35 Universal Time shortly before totality. Exposure. time was 10 seconds. It shows the difference in color and light intensity within the umbra. The upper right side of the lunar disk is nearest to the umbra center and therefore is generally darkest. Local variations in color outline the maria regions of the moon. The fourth photograph [bottom right] was made at 9:26 Universal Time and shows the moon emerging from the umbra. This exposure of 10 seconds again shows the lunar maria as well as the umbra coloring. The center of the earth's shadow zone is now beyond the upper right of the lunar disk.

"We believe that the results displayed indicate the validity of the calculated exposures. By presenting the reasoning that led to the exposure figures, we have tried to demonstrate how simple camera-exposure theory can be adapted to the special problems of eclipse photography."

Bibliography

SUNLIGHT AND SKYLIGHT AS DETERMINANTS OF PHOTOGRAPHIC EXPOSURE. I: LUMINOUS DENSITY AS DETERMINED BY SOLAR ALTITUDE AND ATMOSPHERIC CONDITIONS. Loy Jones and H. R. Condit in Journal of the Optical Society of America, 38, No. 2, pages 123-178; February, 1948.

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