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.
