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Apply Hapke bidirectional reflectance model photometric correction to multiband cubes
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lrowacphomap implements photometric correction based on the full form of bidirectional reflectance model by Hapke (2012). See below for full description of the model. It takes an input cube to be corrected, an output cube to write the results to, a parameter cube that defines the Hapke parameters to be used for the correction, a PVL input file to define the algorithm and an optional backplane cube. Here's an example command line:
lrowacphomap from=input.cub+1 to=output.cub phoalgo=hapke.pvl phoparcube=params.cub backplane=input.cub+2,3,4,5,6
The input cube (from) must have a BandBin label.
Example (containing image and backplane bands): Group = BandBin FilterNumber = (1, 2, 3, 4, 5, 6) Center = (321, 321, 321, 321, 321, 321) Width = (32, 32, 32, 32, 32, 32) Name = (Image, Phase, Emission, Incidence, lat, lon) End_Group
The PVL file (phoalgo) contains the algorithm name, reference values for normalization, and a Parameters group to define the parameter bands from the parameter cube to use.
Example: Object = PhotometricModel Name = HapkeLROC Units = Degrees Incref = 60.0 Emiref = 0.0 Pharef = 60.0 Group = Parameters BandBinCenter = 321 Bands = (1, 2, 3, 4, 5, 6, 7, 8, 9) EndGroup EndObjectThe Incref, Emiref and Pharef are the incidence, emission and phase angles to be used as the common illumination and viewing angles. It will be used to normalize the photometric correction parameter to these angles. The equation used to create the photometrically corrected I/F is:
n_IOF = IOF / Model(g,e,i) * Model(Pharef,Emiref,Incref) where Model(g,e,i) is the model value for phase (g), emission (e), and incidence (i) at each pixel, Model(Pharef,Emiref,Incref) is the model value at the given common geometric angles.
The parameter cube (phoparcube) should be a 9 band cube with the parameters in the order:
backplane cube must contain 5 bands (in order): Phase Angle, Emission Angle, Incidence Angle, Latitude, Longitude
In full form of bidirectional reflectance model by Hapke (2012), the radiance factor I/F is
I is radiance, F is perfectly diffuse surface illuminated at i = e = g = 0 (corresponds to the flatfield).
The bidirectional reflectance r(i,e,g) is
where i is incidence angle, e is emission angle, and g is phase angle, i_{e} and e_{e} are the effective angle of incidence and emission respectively.
Then, K is (porosity effect)
p(g) is, (HG phase function)
B_{S}(g) is, (Shadow Hiding Opposition surge Effect: SHOE )
M(i,e) is, (Isotropic Multiple Scattering Approximation: IMSA)
where H(x) is,
where r_{0} is,
B_{C}(g) is, (Coherent Backscatter Opposition surge Effect: CBOE)
Then, S(i,e,g) is, (Shadow effect)
When i e,
where and are,
When e i,
where and are,
where is,
and is, (y corresponds to i or e)
where E_{1} and E_{2} are, (y corresponds to i or e)
is given by,
is given by,
Thus it can be written as,
Finally, free parameters are,
w (Single scattering albedo) b (HG phase function asymmetry) c (HG phase function amplitude) B_{C0} (CBOE amplitude) h_{C} (CBOE angular width) B_{S0} (SHOE amplitude) h_{S} (SHOE angular width) (Roughness parameter) (Filling factor)
Reference:
Hapke, B. (2012) Theory of Reflectance and Emittance Spectroscopy, Cambridge Univ. Press.
Name  Description 

FROM  Input cube 
TO  Output cube 
BACKPLANE  Backplane Cube 
PHOALGO  Pvl file 
PHOPARCUBE  Parameter cube 
Name  Description 

MINPHASE  Minimum phase angle to trim 
MAXPHASE  Maximum phase angle to trim 
MINEMISSION  Minimum emission angle to trim 
MAXEMISSION  Maximum emission angle to trim 
MININCIDENCE  Minimum incidence angle to trim 
MAXINCIDENCE  Maximum incidence angle to trim 
Name  Description 

USEDEM  Use DEM instead of ellipsoid for photometric angle calculations 
PHOTOMETRYONLY  Output only photometry value in output cube. 
NORMALIZED  Normalize photometry value before applying to input image. 
Use this parameter to select the input filename.
Type  cube 

File Mode  input 
Filter  *.cub 
This file will contain the photometrically corrected image data after being corrected.
Type  cube 

File Mode  output 
Pixel Type  real 
This file will contain the backplane data. It must have "Phase Angle", "Emission Angle", "Incidence Angle", "Latitude" and "Longitude".
Type  cube 

File Mode  input 
Pixel Type  real 
Internal Default  Calculate the photometry on the fly 
This file will contain the photometric correction algorithm information. Here's an example pvl file for Hapke photometric correction:
Object = PhotometricModel Name = HapkeLROC Units = Degrees Incref = 60.0 Emiref = 0.0 Pharef = 60.0 Group = Parameters BandBinCenter = 321 Bands = (1, 2, 3, 4, 5, 6, 7, 8, 9) EndGroup EndObject
Type  filename 

File Mode  input 
Filter  *.pvl 
This file will contain the parameters (in order) Wh, Hg1, Hg2, Bc0, hc, B0, Hh, Theta, phi. See the main program documentation for a full description.
Type  cube 

File Mode  input 
Filter  *.cub 
Pixels which have a phase angle less than this value will be trimmed.
Type  double 

Default  0.0 
Minimum  0.0 (inclusive) 
Maximum  180.0 (inclusive) 
Less Than or Equal 

Pixels which have a phase angle greater than this value will be trimmed.
Type  double 

Default  180.0 
Minimum  0.0 (inclusive) 
Maximum  180.0 (inclusive) 
Greater Than or Equal 

Pixels which have an emission angle less than this value will be trimmed.
Type  double 

Default  0.0 
Minimum  0.0 (inclusive) 
Maximum  90.0 (inclusive) 
Less Than or Equal 

Pixels which have a emission angle greater than this value will be trimmed.
Type  double 

Default  90.0 
Minimum  0.0 (inclusive) 
Maximum  90.0 (inclusive) 
Greater Than or Equal 

Pixels which have an incidence angle less than this value will be trimmed.
Type  double 

Default  0.0 
Minimum  0.0 (inclusive) 
Maximum  180.0 (inclusive) 
Less Than or Equal 

Pixels which have a incidence angle greater than this value will be trimmed.
Type  double 

Default  90.0 
Minimum  0.0 (inclusive) 
Maximum  180.0 (inclusive) 
Greater Than or Equal 

Phase, Emission, and Incidence angles can be calculated from the elipsoid (default) or from the DEM. The difference is that using the DEM the surface roughness is taken into account.
Type  boolean 

Default  False 
Only the photometry value will be written to the output cube, not the original image data. Used for testing photometry calculation.
Type  boolean 

Default  False 
Set to False to cause the photometry value to not be normalized. Used for testing photometry calculation.
Type  boolean 

Default  True 
Kris Becker  20100221  Original version. 
Dan Clarke  20120928  Added full Hapke model. Optimized processing. Updated documentation. 
Adam Licht  20130118  Fixed an error in how parameters were loaded for use in the refrence model calculation. 
Cordell Michaud  20220510  Refactored lrowacphomap for testability and added functional tests. 