Hapke

The Hapke BRDF depends on three parameters and is usually used independently, not in a linear combination with other kernels. It is similar to the Rahman kernel but the hotspot, a peak in reflectivity back in the direction of the incident light due to the absense of shadowing effects, is treated differently.

This is one of eight BRDF kernels listed by Spurr in his 2002 paper.

Equation A.18 from Spurr is implemented with the following changes:

• cos(phi) is replaced with -cos(phi)

• the reflectance is divided by pi

Example

import sasktranif.sasktranif as skif
import math

brdf = skif.ISKBrdf('HAPKE')
mjd            = 52393.3792987115;
location       = [0.0, 0.0, 25000.0, mjd];
[ok,brdfvalue] = brdf.BRDF( 600.0, location, 0.6, 0.7, -0.8)

References

Hapke B., “Theory of reflectance and emittance spectroscopy”. Cambridge University Press, 1993. Robert J. D. Spurr, “A new approach to the retrieval of surface properties from earthshine measurements”, Journal of Quantitative Spectroscopy & Radiative Transfer, vol. 83, pp. 15-46, Oct. 9, 2002. doi:10.1016/S0022-4073(02)00283-2 url: http://www.sciencedirect.com/science/article/pii/S0022407302002832