Reflected Radiation from Natural Surfaces

Spring 2003

Definitions and Relationships

1. Solar Phase Angle,

   Angle subtended at object by vectors to Earth (or s/c) and sun.

2. Normal Reflectance, r_n

   Ratio of flux backscattered from flat surface when observed at normal incidence.

3. Phase Integral, q

   
   where J(x)= disk integrated brightness, q = 0.6 for Moon

4. Geometric Albedo, P

   Ratio of J(0) to flux expected from flat, perfectly reflecting plate of same area as object.
   
   where F = incident flux.
   For Moon p = r_n. For Lambert, r_n=1 and p = (2/3)r_n

5. Bond Albedo, A_B

   Ratio of total reflected energy to incident energy (but needs solar spectrum). A_B = pq

6. Radiometric Albedo, A_V

   A_B over all incident wavelengths.

Reflection of Sunlight from Moon

1. Integral Phase Curve
• No limb darkening at L=O
• Opposition Effect
2. Bond Albedo; Phase Integral; Geometric and Normal Albedo; Photometric Functions
3. Polarization vs. Phase, Theoretical vs Actual
4. Slightly Reddish Color

Interpretation

1. "Fairy Castle Structure"
• Fine dark porous powder covering all surfaces - self shadowing. Olivine powder example.
• Nearly all front surface reflection off individual grains vs. little multiple scattering
• Slightly increasing real index with wavelength
2. Coherent Back Scatter - Hapke, 1993
• Opposition effect; polarization curve
• Doesn't simulate lunar dust texture - e.g., no limb darkening

Other Atmosphereless Bodies

1. Mercury
2. Phobos / Deimos
3. Asteroids

Mars and Effects of Thin Atmosphere

1. Rayleigh Scattering
2. Dust Particle Scattering and Absorption
3. Clouds, ice, CO₂, crystals
4. Shadow Filling on Surface
5. Variable Local Photometric Function (no uniform "fairy castles")

Relationship to Thermal Emission

Tutorial 1: Reflectance from Planetary Surfaces
Tutorial 2: Thermal Emission from Planetary Surfaces

Radar Reflection

1. Observed Return From the Moon, Power vs time, Wavelength dependence
2. Range Doppler Measurements, Geometry

References

Avanesov, G. et. al. "Results of TV Imaging of Phobos (Experiment VSK-FREGAT)". Planet. Space Sci. 39, no. 1/2, January/February 1991. pp. 281-295.

Hapke, Bruce W. et. al. "The Opposition Effect of the Moon: The Contribution of Coherent Backscatter". Science 260, 23 April 1993. pp. 509-511.

Hapke, Bruce W. Optical Properties of the Lunar Surface. Pittsburgh, 1971.

Thomas, P. et. al. "Satellites of Mars: Geologic History". in Mars, Kieffer, H.H. et. al., ed., Tucson: The University of Arizona Press, 1992. pp. 1257-1282.

Veverka, J. et. al. "Photometry and Polarimetry of Mercury". in Mercury, Vilas, Faith et. al., ed., Tucson: The University of Arizona Press, 1988. pp. 37-58.

- Murray -

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Last updated 06/05/2003