phohillier

phohillier implements a photometric correction based upon a paper titled "Multispectral Photometry of the Moon and Absolute Calibration of Clementine UV/Vis Camera" by Hillier, Burratti and Hill, published in Icarus 141, 205-225 (1999). The equation for I/F photometric correction from this source is:

      I/F = (mu0/(mu+mu0)*F(phase)

              where:
                  mu0 = cos(incidence)
                  mu   = cos(emission)
                  F(phase) = b0*e(-b1*phase) + a0 + a1*phase + a2*phase^2 + 
                                      a3*phase^3 + a4*phase^4
    

The equation described there utilizes the Lommel-Seeliger function to account for scattering dependance on incidence and emission angles. Lunar Reflectance approximately follows this function and this is the dependence expected for signly scattered light. Thus is should be a good approximation for dark objects such as the Moon where singly scattered light dominates reflectance. The phase function is a fourth order polynomial with an exponential term to better account for opposition surge.

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

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

Object = PhotometricModel 
  HillierUnits = Degrees
  Group = Algorithm
    Name = Hillier
    FilterName = "Filter1"
    BandBinCenter = 100.1
    B0 = 0.0432753
    B1 = 0.0644091
    A0 = -0.0207532
    A1 = 0.00165219
    A2 = -3.94007e-05
    A3  = 4.19325e-07
    A4 = -1.69163e-09
  EndGroup

  Group = Algorithm
    Name = Hillier
    FilterName = "Filter2"
    BandBinCenter = 112.5
    B0 = 0.0332283
    B1 = 0.00667452
    A0 = -0.0258405
    A1 = -9.04379e-05
    A2 = 7.59709e-06
    A3 = -1.06395e-07
    A4 = 5.18268e-10
  EndGroup

  Group = Algorithm
    Name = Hillier
    FilterName = "Filter8"
    BandBinCenter = 545.3
    BandBinCenterTolerance = 1.0E-2
    B0 = 0.0347020
    B1 = 0.0211712
    A0 = -0.0244440
    A1 = 0.000388924
    A2 = 4.72860e-07
    A3 = -5.00731e-08
    A4 = 3.07309e-10
  EndGroup
EndObject
  

The NormalizationModel object will (currently) always apply an Albedo normalization. The value of the Name parameter is ignored here. Also ignored is the value if PhotoModel as it is always "Hillier". 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 Hillier photometry at the given Incref, 
                                     Emaref and Pharef angles
                         ph        is the photometric correction for the 
                                     incidence, emission and phase at each pixel
      

In the above example, parameters B0-B1 and A0-A4 are the parameters for the Hillier equation. Additional parameters area needed in order to apply a specific set of parameters in an Algorithm group to selected bands. The set of parameters, B0-B1, A0-A4, within an Algorithm group are applied to a band if (ABS(Center-BandBinCenter) <= ABS(BandBinCenterTolerance)). 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 HillierUnits 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.

Below is an example of a small PVL file that will process all bands that have a center wavelength of 100.0 to 900.0 (units do not matter as long as the PVL ALgorithm groups contain the same units as the BandBin Center keyword in the input cube file). The units of phase is provided in Radians for this particular example and is overridden from the keyword in the PhotometricModel object:

Object = NormalizationModel 
  Group = Algorithm 
    Name = Albedo 
    PhotoModel = Hillier
    Incref=30.0
    Emaref=0.0
    Pharef=30.0
  EndGroup 
EndObject 
      
Object = PhotometricModel 
  HillierUnits = Degrees
  Group = Algorithm
    Name = Hillier
    FilterName = "AllFilters"
    BandBinCenter = 500.0
    BandBinCenterTolerance = 400.0
    HillierUnits = Radians
    B0 = 0.0347020
    B1 = 0.0211712
    A0 = -0.0244440
    A1 = 0.000388924
    A2 = 4.72860e-07
    A3 = -5.00731e-08
    A4 = 3.07309e-10
  EndGroup
EndObject      
    

Additional consequences of the photometric correction processing is any incidence angle greater than i90 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.