LROC Empirical implements a photometric correction

      I/F = F(mu, mu0,phase)
              where
                  mu0 = cos(incidence)
                  mu = cos(emission)
                  (2014 version)
                    F(mu, mu0, phase) = e(A0 + A1 * phase + A2 * mu + A3 * mu0)
                  (2019 version)
                    F(mu, mu0, phase) = mu0 / (mu + mu0) * exp(B0 +
                     B1 * (alpha * alpha) + B2 * alpha +
                     B3 * sqrt(alpha) + B4 * mu + B5 * mu0 +
                     B6 * (mu0 * mu0) );
    

The equation described accounts for scattering dependance on incidence, emission, and phase angles. Lunar Reflectance approximately follows this function and has been tested with repeat coverage at different illumination geometries. The exponential equation has been derived from over 760,000 NAC image tiles. More information can be found at:

http://www.hou.usra.edu/meetings/lpsc2014/pdf/2826.pdf

This application provides features that allow LROC NAC image cubes to be photometrically corrected with a properly formatted PVL input file much like that of the ISIS program photomet. This application restricts much of the options available to the more sophisticated photomet application. Below is an example input parameter file for this application:

      Object = NormalizationModel
        Group = Algorithm
          Name = LROC_Empirical
          PhotoModel = LROC_Empirical
          Incref=30.0
          Emaref=0.0
          Pharef=30.0
        EndGroup
      EndObject

      Object = PhotometricModel
        Units = Degrees
        Group = Algorithm
          Name = LROC_Empirical
          FilterName = "Broadband"
          BandBinCenter = 600.0
          A0 = -2.9811422 (2014 version)
          A1 = -0.0112862 (2014 version)
          A2 = -0.8084603 (2014 version)
          A3 = 1.3248888 (2014 version)
          B0 = -1.479654495
          B1 = -0.000083528
          B2 =  0.012964707
          B3 = -0.237774774
          B4 =  0.556075496
          B5 =  0.663671460
          B6 = -0.439918609
        EndGroup
      EndObject
  

The Normalization object is the PhotometricModel evaluated at the given Incref, Emaref and Pharef angles. The value of the Name parameter is ignored here. The Incref, Emaref, and Pharef are the incidence, emission and phase angles to be used as the photometric standard. It will be used to normalize the photometric correction parameter to these angles. The equation used to create the photometrically corrected I/F dn is:

          odn = idn * (phostd  / ph)

              where phostd is the photometry model evaluated at the given Incref,
              Emaref and Pharef angles. ph is the photometric correction for the
              incidence, emission and phase at each pixel
      

The "Center" parameter in the above equality comes from the Center keyword in the BandBin group of the input cube file specified in the FROM parameter. This keyword must exist in the input cube or an error is generated and the program aborts. BandBinCenter and BandBinCenterTolerance are contained in each Algorithm group. Only BandBinCenter is required. If BandBinCenterTolerance is not present in an Algorithm group a value of 1.0E-6 is used. All input bands in the FROM file must be matched to at least one of the Algorithm parameters otherwise an error is generated and the application is aborted.

The parameter Units is provided to specify if the phase angle is in units of degrees or radians. It does not have to exist in any group or even in the top Object section. If it does not exist, "Radians" is the default.

An additional feature of the PVL structure is that any keyword that exists in the Object section of the PhotometricModel Object is propagated to each Algorithm group when it is read in unless the keyword already exists in the Algorithm group. If a keyword exists in both the PhotometricModel object and an Algorithm group, the keyword in the Algorithm group has precedence.

Additional consequences of the photometric correction processing is any incidence angle greater than 90 degrees is set to the ISIS special Null pixel value. And, of course, any ISIS special pixel encountered on input is propagated to the output TO file without modification. Function is only valid for phase angles between 15 and 65 degrees.