How to specify the beta_t to reduce the reflectance of overcorrected bright areas?

[rese_support]

Two output files are generated during the atmospheric / topographic correction: the processed scene and the illumination image cos(beta) which is coded as byte data, i.e. illumination illu = 100*cos(beta). Link both files (e.g. with the ENVI software) and look for the dark areas in the illumination image. These correspond to steep slopes oriented away from the sun and these areas usually show strong BRDF effects, i.e. they correspond to the bright overcorrected areas in the processed scene. Example: the scaled overcorrected reflectance is 320 (scale factor 4), i.e., rho(isotropic) = 80%. The illumination file for this pixel says illu=34, i.e., beta = arccos(illu/100)=70 degree. Let us assume the 80% reflectance should be reduced to 40%, which is the value for pixels in the flat-terrain neighborhood. Then the threshold angle beta_t has to be specified such that cos(beta) / cos(beta_t) = 0.5, in this case beta_t=47 degree. So if the desired geometry-dependent reflectance reduction factor is G the required threshold angle can be calculated as beta_t = arccos { cos(beta) / G } = arccos { illu / (100*G) } Unfortunately, there is no general solution to this problem, the threshold parameter is scene dependent and has to be defined interactively. A rule of thumb is beta_t = solar_zenith_angle + 20 [degrees].