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] It was named after the astronomer Marcel Minnaert. This function expresses the radiance factor (RADF) as a function the phase angle (), 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