Minnaert function

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The Minnaert function is a photometric function used to interpret astronomical observations [1][2] and remote sensing data for the Earth.[3] This function expresses the radiance factor (RADF) as a function the phase angle () and the photometric latitude () and the photometric longitude ().

where is the Minnaert albedo, is an empirical parameter, is the scattered radiance in the direction , is the incident radiance, and

The phase angle is the angle between the light source and the observer with the object as the center.

The assumptions made are:

  • the surface is illuminated by a distant point source.
  • the surface is isotropic and flat.

Minnaert's contribution is the introduction of the parameter , having a value between 0 and 1,[4] originally for a better interpretation of observations of the Moon. In remote sensing the use of this function is referred to as Minnaert topographic correction, a necessity when interpreting images of rough terrain.


  1. ^ "Probing Titan’s lower atmosphere with acousto-optic tuning". Icarus 163: 150–163. Bibcode:2003Icar..163..150C. doi:10.1016/S0019-1035(03)00075-7. 
  2. ^ "Martian phase function: Modeling the visible to near-infrared surface photometric function using HST-WFPC2 data". Icarus 184: 401–423. Bibcode:2006Icar..184..401S. doi:10.1016/j.icarus.2006.05.006. 
  3. ^ "The use of the Minnaert correction for land‐cover classification in mountainous terrain". International Journal of Remote Sensing 26: 3831–3851. doi:10.1080/01431160500104194. 
  4. ^ http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1941ApJ....93..403M&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf