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Table of Contents
(adapted from Figure 5 in Buratti et al., 1996)
The solid curve shows the general increase in brightness of the lunar surface approaching zero
, with an estimate of the magnitude of the anomalous extra surge at very small phase angles.
A sudden and significant increase in the brightness of an object as the
of observation approaches zero.
It has long been known that the brightness of solar system objects lit by the Sun increases as the
decreases. Part of this is due to the increase in the illuminated area (growing from a thin crescent to a full disk), and part to an increase in the intrinsic surface brightness of the part that is in sunlight. For many objects, the increase over a considerable range is roughly linear when plotted on a logarithmic scale (such as the system of stellar magnitudes).
Early work on the variation in the brightness of the Moon with phase was summarized by Russell in 1916. According to Russell, the first reliable investigation was made, inadvertently, by John Herschel in the early 1800's. Herschel, observing from Cape Town, South Africa, had hoped to be able to use the Moon as a brightness standard against which he could monitor changes in the brightness of stars. Using a very small lens of very short focal length, he focused the moonlight into a star-like point whose brightness he could vary according to its distance from his eye. However, he discarded the results as unreliable when he found his reference star didn't vary in the way he expected during the lunar cycle. Zöllner later turned Herschel's measurements around by assuming the stars were constant, thereby producing what was apparently the first accurate curve of the variation of the Moon's brightness with phase.
Both Zöllner and Bond made additional observations of their own, comparing the lunar "star" to a standard lamp; and concluded that the variation did not fit any of the existing theories. Many others followed, but none of these early observers seem to have detected any special anomalous surge in brightness at very small phase angles. Indeed, even now, most claims about the magnitude of the lunar opposition surge are based on the behavior of small regions of the surface as photographed at close range by spacecraft.
The best modern Earth-based study of the variation of the brightness of the Moon as a whole is probably that of Lane and Irvine (1973), who made measurements over the range of 6 to 120 degrees in phase angle. Although they were aware that an opposition surge reportedly occurred at smaller angles, they did not attempt to study it themselves.
refers to an addition sudden brightening at very small phase angles.
The existence of such a surge was first noticed by Thomas Gehrels, in 1956, while studying the light curve of an asteroid. He coined the term
to describe this phenomenon. The word "opposition" when used in this astronomical sense means basically that the Sun and the object being observed are in opposite directions (almost identical to the definition of zero
). However, to the uninformed the term
could mean either the general increase in brightness, or the sudden additional increase at very small phase angles, so the term
(used by many recent authors) seems better.
In 1964, Gehrels obtained data demonstrating that the Moon also exhibited a surge in brightness at phase angles less than about 5 degrees.
Since then, an
has been observed in the light curves of nearly all airless solar system bodies that can be seen in opposition. Sometimes the magnitude of the surge is greater than for the Moon, and sometimes it is less. Note that cloud-covered bodies, such as the gas giants and some of their moons, show an increase in brightness as phase angle decreases, but they
show an extra surge at small angles.
When the Moon is viewed at close range (as from an orbiting spacecraft or from on the lunar surface itself), the range of phase angle displayed in a single photo can be quite large including points at zero phase angle. A bright glow, or hot spot in the image, is observed around this anti-solar point (which occurs at the point where one expects to find the shadow of the camera). For example, if an astronaut holds a camera to their eye and takes a photo looking away from the Sun, a glow will be seen around the shadow of his head. This resembles a common terrestrial phenomenon that can be seen when shadows are cast on dew-covered grass -- an effect that has long been called the "Heiligenschein". Because of the resemblance in appearance, the
on the Moon that produces a comparable effect has been frequently called the
. It has been applied both to the haloes around the shadows of astronauts heads and to the more general brightening of features seen at Full Moon from Earth. This is again a somewhat unfortunate term because the lunar
(which produces both of these effects) is obviously not produced by dewdrops on grass. See
This is a very active field of study, but information as to the exact magnitude of the Moon's
, the angles over which it operates, how it varies with wavelength and whether it is different for different kinds of surface features is confusing and often contradictory. The mechanism that produces the
is also hotly debated.
Hapke (1966) originally attributed the small-angle surge to shadow hiding. He later (1993) decided it was almost entirely due to an obscure mechanism called "coherent backscatter". A few years latter (1998) we are informed it an equal mix of coherent backscatter and shadow hiding; and so on.
Throughout this, the exact shape of the light curve has been touted as means of inferring the detailed structure of the surface by remote sensing, yet recent laboratory studies by, for example, Shepard and Helfenstein (2007), suggest the signatures of different possible surface structures are intermixed in so complicated a way that it is virtually impossible to reach any firm conclusion about the nature of a surface based on its light curve.
(1996), based on their study of Clementine data, estimated a 40% increase in brightness in going from a phase angle of 4 degrees to 0 degrees (some unstated part of which could be regarded as a surge over the increase that would be expected from the general trend at higher angles). They also concluded that the opposition surge was about 10% greater for bright highlands areas than for dark mare. Yokota
(1999), also studying Clementine data, seem to show an increase of only some 20-30% going from 4 to 0 degrees (somewhat dependent on wavelength). And they found that the mare actually brightened by a higher factor (~1.7x) than the highlands (~1.5x) in going form a phase angle of 30 degrees to 7 degrees. The additional brightening in going from 7° to 1° (~1.27x) was, if anything, very slightly greater for the darker (mare) features.
Burrati, B. J.; Hillier, J. K.; Wang, M. 1996.
The Lunar Opposition Surge: Observations by Clementine
. 124: 490-499.
Gehrels, T. 1956.
Photometric Studies of Asteroids. V: The Light-Curve and Phase Function of 20 Massalia
Gehrels, T.; Coffeen, T.; Owings, D. 1964.
Wavelength dependance of polarization. III. The lunar surface
, 69, 826-852.
Hapke, Bruce. 1966.
An Improved Theoretical Lunar Photometric Function
, Vol. 71, pp. 333-339.
Hapke, B. W.; Nelson, R. M.; Smythe, W. D. 1993.
The opposition effect of the moon - The contribution of coherent backscatter
, vol. 260, pp. 509-511.
Hapke, Bruce; Nelson, Robert; Smythe, William. 1998.
The Opposition Effect of the Moon: Coherent Backscatter and Shadow Hiding
, Volume 133, pp. 89-97.
Lane, Adair P.; Irvine, William M. 1973.
Monochromatic phase curves and albedos for the lunar disk
, Vol. 78, pp. 267-277.
Russell, Henry Norris. 1916.
The Stellar Magnitudes of the Sun, Moon and Planets
, vol. 43, pp. 103-129.
Shepard, Michael K.; Helfenstein, Paul. 2007.
A test of the Hapke photometric model
Journal of Geophysical Research
, Volume 112, E03001 (17 pp).
Yokota, Y.; Iijima, Y.; Honda, R.; Okada, T.; Mizutani, H. 1999.
Photometric properties of the moon: phase curves at small phase angles (0 - 10°) by Clementine images
Advances in Space Research
, Volume 23, Issue 11, p. 1841-1844.
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