Photometric properties of the Moon: Phase curves at small phase angles (0 – 10°) by clementine images

A&. Space Res. Vol. 23. No. 11, pp. 1841-1844.1999

0 1999 COSPAR. Published by Elsevier Science Ltd. All rights reserved

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PHOTOMETRIC PROPERTIES OF THE MOON: PHASE CURVES AT SMALL PHASE ANGLES (0 - 10’) BY CLEMENTINE IMAGES Y.

Yokotal, Y. Iijimal, R. Honda2, T. Okadal, and H. Mizutanil

1 Institute of Space and Astronautical Science, 3-l-l Yoshinodai, Sagamihara, 229-8510, Japan 2 Kochi University, 2-5-l Akebono cho, Kochi, 464-0814, Japan

ABSTRACT Using Clementine data, the phase curves of the lunar surface were investigated at small phase angles (0” to 10’) by direct comparison with standard phase angle (30”) data. We found the geological type dependence and wavelength dependence of the phase curve. Additionally, we found a negative correlation between the reflectance at standard phase angle 30” and the brightness ratio [(small phase angle)/Z(30”). ‘Ihe dependencies on the terrain type and wavelength can be simply approximated by the dependence on the reflectance. 0 1999 COSPAR.Published by Elsevier Science Ltd. intensity. The calibration procedure for the Clementine images by the Clementine science team was made public on the Brown University web site (1995). Their equations for the correction to the reflectance are expressed as follows:

INTRODUCTION The surface brightness of the moon depends on viewing geometry. Viewing geometry is specified by three angles; i is the incidence angle, e is the emission angle, and g is the solar phase angle illustrated in Figure 1. The bidirectional reflectance equation (Hapke, 198 1) describes the relation between surface brightness and viewing geometry. The equation can be approximated as follows:

NT6 g) = w

,osf~~os f(g) e

i(i,e,g) is the observed intensity, scattering albedo, cosil(cosi+cose) Seeliger function, and f(g) is the phase function. The phase curve phase angle dependence of the

Z(3OO)=

(11

Qg)F

& = 1(30”) x Correction factor

w is the single is the Lommelphase curve or expresses the reflected light

Note that the notations and forms are not same as the original. I(307 is the intensity and R30 is the reflectance at standard viewing geometry. i=30”, GO”, and g=30” are used as the standard viewing

Table 1. Data sets Apollo 16 highland

Mare Tranquillitatis

15.O”E to 15.4’E

26.0’ E to 26.2” E

Latitude

0.0’ to 10.0’s

0.0’ to 10.0-N

Orbits

162, 295

158, 291

Longitude

Wavelength

(4)

Ml-*u,, /

415, 750, 1000 nm

Lunar Surface

Fig. 1. Viewing geometry. 1841

1842

Y.

geometry in the Reflectance Laboratory of the Brown University (RELAB). f(g) is given by a fourth order ~lynomial for the phase angles larger than 5”. Although an accurate phase curve is necessary for precise analysis of UV-VIS-NIR spectral data, the phase curve at small phase angle exhibits complicated behavior. Buratti et al. (1996) investigated the phase curves in detail at phase angles ranging from 0” to 4’. However, it was difficult to extrapolate their curves up to standard phase angle 30”. It is also known that the phase function depends on place and wavelength (e.g., Buratti ef al., 1996; Shkuratov and Kreslavsky, 1998). Those effects have made the problem difficult. The objectives of this study are summarized as follows: (1) Determination of the phase curve for the small phase angIe ranging from 0” to IO’. (2) Examination of the geoIogica1 type dependence of the phase curve within this range of phase angle. (3) Examination of the wavelength dependence of the phase curve within this range of phase angle. (4) Consideration of the method to predict the phase curve for any geological types and wavelength.

et al.

albedo w that explicitly appears in Eq. (1). In this analyses, we normalized observed intensities of light by using overlapping images at g=30”. Shkuratov and Kreslavsky (1998) used 10,000 pairs of overlapping images for each band, and derived an average phase function with a new photometric model. In this study, the approximate Hapke model (Eq. 1) was chosen for its simpiicity to separate the phase function from the influence of i, e, and w. We selected two areas to examine the difference between the highlands and maria. One area is a part of the highlands, near the Apollo 16 landing site. The other area is a part of Mare Tranquillitatis. The data sets are listed in Table 1. Three band images (415, 750, and 1000 nm) were used to examine wavelength dependence. Only short exposure images were used to avoid saturated data. We defined square grids on lunar surface for analyzing units, along with ovedapping zones of two orbits’ images. E&h grid had width of 0.1 degrees which corresponds to about 3 km. Two assumptions were required for our processing: (1) There is only one phase curve which can be applied to the same terrain types and wavelength. (2) The Brown University phase functions are accurate within the phase angle range g = 3of3”.

ANALYSES Clementine UV-VIS camera took lunar images with 5 filters (415, 750, 900, 950, 1000 nm) in high spatial resolution (125 to 200 m/pixel). A Iittle portion of the lunar surface was imaged twice under different phase angles. These images allow us to separate the phase function and the single scattering (Phase angle g=3M3”)

The processing procedure is shown in Figure 2. Calibrations of hardware settings and flat field were done to the raw images, using the Brown University procedure. Preliminary position data in header files were used to calculate longitude and latitude. The grids which had been observed under different phase angles, were selected by using the longitude

(Small g)

Picking up pixels in the overlapping grid (grid width = -3km) 1 Correction of i and e (The Lommel-Seeliger function) 1 I

Calculation of long. and lat. t + Calculation of i, e and g

Fig. 2. Processing procedure. Image A and Image B have overlapping zone on the lunar surface. Header A and Header B are the header files of the images, including position data of the space craft.

1843

Photometric Properties

and latitude. Pixels‘ intensities in the grids were averaged for each observation. Geometrical parameters (i, e, g) were calculated, approximating the lunar surface as a horizontal plane in each grid. Next, the Lommel-Seeliger correction was applied to the data. A small correction of phase angle was applied to the data at g=30*3” by the Brown University phase function. In Figure 2, the symbols IA and IB denote the intensities derived from the observations at phase angle 3OY3” and small phase angles, respectively. The intensity IB(~> was divided by the lA(3O*) of the overlapping grid, and it became a relative intensity normalized at phase angle 30°.

2.2 2

1.2 1 0

10

5

15

20

25

30

Phase angle g [‘I REStnTS

AND DISCUSSION

Results from the 750 nm band are plotted in Figure 3 with the Brown University phase curve. Our phase curves were derived in small phase angle ranges from g=O* to 10’. The wavelength 750 nm is used in many analyses as the standard band to bring out the absolute value of the reflectance. It is seen that the Brown University curve approximates the average curve of the highlands and maria well. However, it has 4 - 8% error for each terrain type at phase angles ranging from 5’ to IO’. Ail Results from Apollo 16 Highland and Mare Tranquillitatis are plotted in Figure 4 (a) and (b), respectively. The geological type dependencies for each band are seen by a comparison of Figure 4 (a) and (b). For instance, the curve of the maria is nearly 17% higher than the curve of the highlands at phase angle 2” for the 1000 nm band. In Figure 4 (a) and (b), it is clearly seen that the curves also depend on wavelength. At small phase angles, the normalized intensity increases as the wavelength decreases. The amplitude of the spectral change of the highlands is larger than the amplitude of the maria. We discuss a method to treat these d~~nden~ies comprehensively. Theoretically, the phase functions at small phase angles depend on the directional scattering property of the particles, and on the opposition surge which is occurred by the shadow hiding (e.g., Hapke, 1981) and coherent effect (e.g., Helfenstein et al., 1997). The single scattering albedo w affects directional scattering property of the particle. It is known that individual particles which have low albedo exhibit back scattering property (e. g., Hapke, 1963). When the particles have low w, the reflectance would be low, and the normalized intensity lB(g)/f,.+(30’) would

increase

by

the

back

scattering

of

the

Fig. 3. Phase curves at 750 nm. Circle: Data from the highlands. Plus: Data Rom the maria. The curve of the Brown Univ. is also shown for comparison. The crowds at phase angle 3053” are the data used for normalizing.

L

b) Mare Tranquillitatis :

2.2 Qg- 2E 21.8 G 5.6 i 1.4 1 1.2 t.. 0

. ‘. 2

”

“, 4

. ’ *. 6

i ‘, 8

’ 1’. 10

.I 12

Phase angle g [‘I Fig. 4. Phase curves derived by this study. The data from the highlands and maria are plotted in (a).and (b), respectively. All plots are normalized at phase angle 30”. Tbe wavelength of the bands used in the analysis are 41.5, 750, and 1000 nm.

Y. Yokota et al.

1844

Mare Tranqujllitatis M Apollo 16 highland 2.4

~:““““““““““.““““““1

1.6

Fig. 5. Ampiitu~ Of~B(g)/~A(3~O)again% refleCtanCe.The reflectance f?30 was obtained ffom the data at phase angles g=30&3” by using the procedure of the Brown university. 0pen symbol: Data from the maria. Closed symbol: Data from the highlands. The data at the wavelength 415 nm, 750 nm, and 1000 nm are plotted together for each symbol, and they have wide range of the R30. The error bars indicate l-sigmas of the pixels’ intensities within the grids. Although the data also contains an error about overlapping of the CIementine images, this couldn’t estimate in this analysis. The fitted lines are also shown in the

figure. incident light. Figure 5 shows the normatized intensity at small phase angles against the bidirectional reflectance R30 [%I. The data were derived by the procedure illustrated in Figure 2. The data at g=l.~.Z” and 7.0+_0.25’ are plotted in Figure 5. The reflectance R30 was obtained from the data of g=30&3” by using the Brown University correction factor. In Figure 5, a relation between R30 and ~B(g)/zA(30°) was found as discussed above. We fitted linear iines, zB(g~/fA(30*) = ARjo+B, to the data at phase angles 1°(rt0.250), 4*, and 7’. The parameters of the fitted lines and lsigmas are listed in Table 2. From these rest&s, it appears that the dependencies on the terrain type and wavelength are simply approximated by the dependence on the reflectance. Using this relationship , it will be possible to know the phase functions to first order for any other geological types or wavelength. Further study at different

Table 2. Parameters

of the line fitting

points on the lunar surface is required to construct a more precise method for predicting phase curves, In addition, it is also required to take into account other optical effects, such as the shadow hiding.

The authors would like to thank the anonymous reviewer for the helpful comments. REFERENCES Buratti, B. J., J. K. Hillier, and M. Wang, The Lunar Opposition Surge: Observations by Clementine, Icarus, 124, 490 (1996) Hapke, B., A Theoretical Photometric Function for the Lunar Surface, J. of Geo~~ys. Res., 68, 4571 (1963) Hapke, B., Bidirectional Reflectance Spectroscopy: 1. Theory, J. of Geophys. Res., 86, 3039 (1981) Helfenstein, P., J. Veverka, and J. Hillier, The Lunar Opposition Effect: A Test of Alternative Models, ha-us, 128,2 (1997) Shkuratov, Y. G., and M. A. Kreslavsky, A Model of Lunar Photometric Function, LPSC XXIX, (1998)