ISIS Application Documentation
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Fit empirical photometric functions to a Hapke model at several phase angles
Overview  Parameters  Example 1 
DescriptionThis program fits the LunarLambert or Minnaert photometric function to the complex Hapke (1981; 1984; 1986) model at several phase angles. phoempglobal adjusts the limbdarkening and the overall brightness so that the sumsquaredresidual between the two is minimized and results in a tight fit to the new empirical model. The resulting best fit limbdarkening Minnaert K or LunarLambert L and brightness values that is normalized as an empirical phase curve versus phase angle is output in a formatted table. The table, saved as a PVL file, consists of the PhaseList, KList or LList, PhaseCurveList, empirical function name, and the personal note. The output PVL file is useful for related programs discussed later in this document. Note: The fit is calculated for a portion of the visible hemisphere of an idealized spherical and uniform planet such as Mars and the Earth. phoempglobal is considered an advanced program and may not be suitable for the ISISuser novice. phoempglobal Companion Programs and Uses: The programs listed below can utilize the output file of phoempglobal as input:
User Input Requirements:
The empirical photometric function is fitted to the Hapke model over a portion of the visible hemisphere of an idealized planet using the following:
The atmospheric model is optional. It is important to define the atmospheric model based on the requirements of subsequent processing steps, which depends on whether the results will be applied to perform photometric normalization or for photoclinometry application. If an option other than "NONE" is selected, the atmospheric scattering and surface photometric properties are included as part of the physical model to which the empirical model is fitted. The parameter settings for the Hapke model have been derived, and the results published by various individuals. For the original description of the fitting process and a useful compilation of Hapke parameters from the scientific literature, see McEwen (1991). The atmospheric model used in the fits is discussed by Kirk et al. (2000, 2001). Example: Mars The following Hapke parameters for Mars are from Johnson et al. (1999) for IMP data of Photometry Flats (soil) and may be reasonably representative of Mars as a whole. Note that (HG1, HG2=1.0) is equivalent to (HG1, HG2=0.0)
Kirk et al. (2000) found that Mars wholedisk limbdarkening data of Thorpe (1973) are consistent with THETA=30, but results of Tanaka and Davis (1988) based on matching photoclinometry of local areas to shadow data are more consistent with THETA=20 when the domain of the fit is restricted to small emission angles (<= 20 degrees). Values of the photometric parameters for the Martian atmosphere, adopted from Tomasko et al. (1999) are as follows:
If result of phoempglobal will be used in photomet: All the options available in phoempglobal are also available in the photomet program. So, the best option is to forgo the atmospheric correction in phoempglobal, and instead apply the atmospheric correction in photomet. Set the parameters ATMNAME=NONE and ADDOFFSET=NO to obtain the empirical model for the surface alone. The brightness and limbdarkening values output by phoempglobal and the LunarLambertEmpirical or MinnaertEmpirical photometric function are applied with photomet to correct the image. If a correction for atmospheric scattering is desired, one of the atmospheric models can also be selected when the parameters are defined. The photometrically normalized images can then be equalized and mosaicked together. If result of phoempglobal will be used to support photoclinometry application: Fitting with an atmospheric model and setting the parameter ADDOFFSET=YES in phoempglobal is more useful for the photoclinometry application, where images are normally corrected by subtracting a uniform haze estimate rather than by applying a full atmospheric scattering model. The parameter EMAMAX should be set to a relatively small value that represents the typical range of surface slopes, and the fit will apply to images with vertical viewing. The table of fits at multiple phase angles output by phoempglobal can be interpolated, and used as input to a photoclinometry application for any given image.
Hapke, B.W., 1981, Bidirectional reflectance spectroscopy 1: Theory,
J. Geophys. Res., v. 86, p. 30393054. CategoriesRelated Applications to Previous Versions of ISISThis program replaces the following application existing in previous versions of ISIS:
Related Objects and DocumentsApplicationsHistory

Parameter GroupsFiles
User Note
HAPKE
Empirical
Atmospheric Scattering Model
Fit Range of Angles

This output is a PVL file that contains the following:
Type  filename 

File Mode  output 
Filter  *.txt *.pvl 
This is a note entered by the user. The user note parameter provides a space for digital notetaking. We recommend that the note space contain a description of how the output file will be used and the input parameter settings that were used to derive the values for the empirical photometric function. See "$ISISROOT/appdata/templates/photometry/marsred.pvl" for an example.
Type  string 

Internal Default  None Specified 
A Hapke (1981; 1984; 1986) photometric model is always used as the model to which the empirical functions are fitted. The options correspond to variants of the Hapke model with different types of model for the single particle phase (scattering) function.
Type  combo  

Default  HAPKEHEN  
Option List: 

The Hapke singlescattering albedo of surface particles, see Hapke (1981). Not to be confused with albedo WHA of the atmospheric particles.
Type  double 

Minimum  0.0 (exclusive) 
Maximum  1.0 (inclusive) 
The Hapke opposition surge width. The width parameter for the opposition effect for the surface if hapkehen or hapkeleg is used, see Hapke (1984).
Type  double 

Minimum  0.0 (inclusive) 
The Hapke opposition surge strength. The magnitude of the opposition effect for the surface if hapkehen or hapkeleg is used, see Hapke (1984).
Type  double 

Minimum  0.0 (inclusive) 
The small scale surface roughness value in degrees. The "macroscopic roughness" of the surface as it affects the photometric behavior, see Hapke (1986). The roughness correction is evaluated if theta is given any value other than 0.0, but the computation speed is extremely slow.
Type  double 

Minimum  0.0 (inclusive) 
Maximum  90.0 (inclusive) 
Asymmetry parameter used in Hapke HenyeyGreenstein model for the scattering phase function of single particles in the surface, see Hapke (1981). The twoparameter HenyeyGreenstein function is as follows:
P(phase)=(1hg2) * (1hg1**2)/(1+hg1**2+2*hg1*cos(phase))**1.5 + hg2 * (1hg1**2)/(1+hg1**22*hg1*cos(phase))**1.5
Type  double 

Minimum  1.0 (exclusive) 
Maximum  1.0 (exclusive) 
The Hapke HenyeyGreenstein coefficient for a single particle phase function. The second parameter, of the twoparameter HenyeyGreenstein model, for the scattering phase function of single particles in the surface. This parameter controls the proportions in a linear mixture of ordinary HenyeyGreenstein phase functions with asymmetry parameters equal to +hg1 and hg1. See HG1 for the full formula.
Type  double 

Minimum  0.0 (inclusive) 
Maximum  1.0 (inclusive) 
The Hapke Legendre coefficient for a single particle phase function. A twoterm Legendre polynomial is used for the scattering phase function of single particles in the surface:
P(phase) = 1 + bh * p1(cos(phase)) + ch * p2(cos(phase))Where p1 and p2 are the first and second order Legendre polynomials. Bh is not to be confused with the Legendre coefficient bha of the phase function for atmospheric particles, used when atmname=anisotropic1 or anisotropic2.
Type  double 

Minimum  1.0 (exclusive) 
Maximum  1.0 (exclusive) 
The Hapke Legendre coefficient for a single particle phase
function. A twoterm Legendre polynomial is used for the scattering
phase function of single particles in the surface:
P(phase) = 1 + bh * p1(cos(phase)) + ch * p2(cos(phase))Where p1 and p2 are the first and second order Legendre polynomials.
Type  double 

Minimum  1.0 (exclusive) 
Maximum  1.0 (exclusive) 
Specify a photometric function to fit to the Hapke model. The lists of brightness and limbdarkening values can be used with the LunarLambertEmpirical or MinnaertEmpirical photometric functions in the photometric normalization program photomet.
Type  combo  

Internal Default  LunarLambert  
Option List: 

Phoempglobal incorporates all the same atmospheric scattering models in the program photomet that is used to make photometric corrections to images. The empirical model for the surface alone is obtained by setting ATMNAME=NONE and ADDOFFSET=NO in phoempglobal, and then the atmospheric scattering parameters are applied in photomet.
If an option other than NONE is selected, an atmospheric scattering model will be included as part of the physical model to which the empirical model is fitted. Six available atmospheric models are categorized into three classes that differ in their treatment of the single particle scattering function for atmospheric particles. Each of these classes can be evaluated to a first order (faster) or second order (more accurate) approximation. Atmospheric scattering in all the models both attenuates the surface signal and adds its own (uniform) contribution to the image radiance. Therefore, unless NONE is selected, set ADDOFFSET=YES so that the additive contribution of the atmosphere will be modeled by an additive constant in the fit. This option is more useful for application to photoclinometry, where images are normally corrected by subtracting a uniform haze estimate rather than by applying a full atmospheric scattering model.
Type  combo  

Default  NONE  
Internal Default  NONE  
Option List: 

Normal atmospheric optical depth
Type  double 

Minimum  0.0 (inclusive) 
This is the singlescattering albedo of atmospheric particles, not to be confused with the albedo WH of surface particles.
Type  double 

Minimum  0.0 (exclusive) 
Maximum  1.0 (inclusive) 
Parameter used in the HenyeyGreenstein single particle phase function for atmospheric particles when ATMNAME=HAPKEATM1 or ATMNAME=HAPKEATM2. This is the asymmetry parameter for a single term HenyeyGreenstein model:
p(phase) = (1hga**2)/(1+hga**2+2*hga*cos(phase))**1.5Not to be confused with corresponding parameter HG1 for the surface particles.
Type  double 

Minimum  1.0 (exclusive) 
Maximum  1.0 (exclusive) 
Coefficient of the first order Legendre polynomial in the single particle phase function for atmospheric scattering. When ATMNAME=ANISOTROPIC1 or ATMNAME=ANISOTROPIC2, a twoterm Legendre polynomial expansion is used to represent the scattering phase function of single particles in the atmosphere:
p(phase) = 1 + bha * p1(cos(phase))Where, P1 is the first order Legendre polynomial, and not to be confused with the corresponding parameter BH for the surface.
Type  double 

Minimum  1.0 (inclusive) 
Maximum  1.0 (inclusive) 
Atmospheric shell thickness normalized to planet radius, used to correct the path lengths of atmospheric transmission for the spherical geometry of the planet. Default 0.003 is for Mars.
Type  double 

Minimum  0.0 (inclusive) 
If true, the additive contribution of the atmosphere will be modeled by an additive constant in the fit of the empirical function at each phase angle.
Because the program photomet incorporates all the same atmospheric scattering models as Phoempglobal, one would normally set ATMNAME=NONE and ADDOFFSET=NO to obtain an empirical model for the surface alone, and then apply the atmospheric scattering parameters in photomet. Fitting with an atmospheric model and ADDOFFSET=YES in phoempglobal is more useful for application to photoclinometry, where images are normally corrected by subtracting a uniform haze estimate rather than by applying a full atmospheric scattering model.
Type  boolean 

Default  false 
This is the minimum emission angle to be included. The empirical photometric function will be fitted to the Hapke model over a portion of the visible hemisphere of an idealized planet, with the following:
Type  double 

Default  0.0 
Minimum  0.0 (inclusive) 
Maximum  90.0 (exclusive) 
This is the maximum emission angle to be included. The empirical photometric function will be fitted to the Hapke model over a portion of the visible hemisphere of an idealized planet, with the following:
Type  double 

Default  90.0 
Minimum  0.0 (exclusive) 
Maximum  90.0 (inclusive) 
This parameter allows the range of emission angles included in the fit to increase slightly at high phase angles, because otherwise the region of fit becomes very small. The empirical photometric function will be fitted to the Hapke model over a portion of the visible hemisphere of an idealized planet, with the following:
Type  double 

This is the minimum incidence angle to be included. The empirical photometric function will be fitted to the Hapke model over a portion of the visible hemisphere of an idealized planet, with the following:
Type  double 

Default  0.0 
Minimum  0.0 (inclusive) 
Maximum  90.0 (exclusive) 
This is the maximum incidence angle to be included. The empirical photometric function will be fitted to the Hapke model over a portion of the visible hemisphere of an idealized planet, with the following:
Type  double 

Default  90.0 
Minimum  0.0 (exclusive) 
Maximum  90.0 (inclusive) 
This is the minimum phase angle at which a fit will be performed, corresponding to the first value (PHASELIST) in the output table.
Type  double 

Default  0.0 
Minimum  0.0 (inclusive) 
Maximum  180.0 (exclusive) 
This is the maximum phase angle at which a fit will be performed, corresponding to the last value (PHASELIST) in the output table.
Type  double 

Default  180.0 
Minimum  0.0 (exclusive) 
Maximum  180.0 (inclusive) 
Number of phase angles at which a fit will be performed, equal to the number of values in the output table, which is normally set to 20 to output results at every 10 degree increment of phase angles.
Type  integer 

Default  20 
Minimum  1 (inclusive) 
Example 1Create a PVL file with phoempglobal Description
This example shows the GUI and the input setting for each parameter name
in the phoempglobal program.
Command Line
phoempglobal
to=new_test.pvl note="phoempglobal test using photometric settings for
Mercury provided by Brett D. Parameters: to=new_test.pvl wh=0.249831313
hh=0.075 b0=2.3 theta=7.717173828 hg1=0.247542306 hg2=0.57542686
model=lunarlambert emamin=0 emamax=90 emamax_pcoeff=1 incmin=0 incmax=90
phmin=0 phmax=180 nph=20" wh=0.249831313 hh=0.075 b0=2.3 theta=7.717173828
hg1=0.247542306 hg2=0.57542686 model=lunarlambert emamin=0 emamax=90
emamax_pcoeff=1 incmin=0 incmax=90 phmin=0 phmax=180 nph=20
Run phoempglobal to generate a PVL file with the parameter values for the
LunarLambertEmpirical photometric model.
GUI Screenshot
Data File
