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ISIS Documentation

phoempglobal

Fit empirical photometric functions to a Hapke model at several phase angles

This program fits the Lunar-Lambert or Minnaert photometric function to the complex Hapke (1981; 1984; 1986) model at several phase angles. phoempglobal adjusts the limb-darkening and the overall brightness so that the sum-squared-residual between the two is minimized and results in a tight fit to the new empirical model. The resulting best fit limb-darkening Minnaert K or Lunar-Lambert 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 ISIS-user novice.

phoempglobal Companion Programs and Uses:

The programs listed below can utilize the output file of phoempglobal as input:

  • photemplate - used to create a template file consisting of parameter values for a selected photometric function to normalize images
  • photomet - used to apply photometric normalization to an image

User Input Requirements:

  • Output PVL filename
  • Empirical model (LunarLambert or Minnaert)
  • Photometric function (HapkeHen or HapkeLeg)
  • Parameter values for the Hapke model
  • Atmospheric model (optional)
  • User note that documents the input parameter values and its use
  • Minimum and maximum incidence angle
  • Minimum and maximum emission angle
  • Minimum and maximum phase angle
  • Fraction of phase angle to add to maximum emission angle
  • Number of phase angles to report to output file

The empirical photometric function is fitted to the Hapke model over a portion of the visible hemisphere of an idealized planet using the following:

  • INCMIN <= incidence angle <= INCMAX
  • EMAMIN <= emission angle <= EMAMAX + EMAMAX_PCOEFF * phase angle
  • INCMIN and EMAMIN are normally set to 0
  • INCMAX and EMAMAX are set to values approaching 90 to exclude only limited regions near the limb and terminator from the fit

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)

Band WH B0 HH HG1 HG2
Red 0.52 0.025 0.170 0.213 1.000
Green 0.29 0.290 0.170 0.190 1.000
Blue 0.16 0.995 0.170 0.145 1.000

Kirk et al. (2000) found that Mars whole-disk limb-darkening 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:

Band WHA HGA
Red 0.95 0.68
Blue 0.76 0.78

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 limb-darkening 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.


References:

Hapke, B.W., 1981, Bidirectional reflectance spectroscopy 1: Theory, J. Geophys. Res., v. 86, p. 3039-3054.

Hapke, B., 1984, Bidirectional reflectance spectroscopy 3: Corrections for macroscopic roughness, Icarus, v. 59, p. 41-59.

Hapke, B., 1986, Bidirectional reflectance spectroscopy 4: The extinction coefficient and the opposition effect, Icarus, v. 67, p. 264-280.

Johnson, J.R., et al., 1999, Preliminary Results on Photometric Properties of Materials at the Sagan Memorial Station, Mars. J. Geophys. Res., v. 104, p. 8809-8830.

Kirk, R.L., Thompson, K.T., Becker, T.L., and Lee, E.M., 2000, Photometric modeling for planetary cartography, Lunar Planet. Sci., XXXI, Abstract #2025, Lunar and Planetary Institute, Houston (CD-ROM).

Kirk, R.L., Thompson, K.T., and Lee, E.M., 2001, Photometry of the martian atmosphere: An improved practical model for cartography and photoclinometry, Lunar Planet. Sci., XXXII, Abstract #1874, Lunar and Planetary Institute, Houston (CD-ROM).

McEwen, A.S., 1991, Photometric functions for photo-clinometry and other applications, Icarus, v. 92, p. 298-311.

Tanaka, K.L., and and Davis, P.A., 1988, Tectonic History of the Syria Planum Provice of Mars, J. Geophys. Res., v. 93, p. 14893-14917.

Thorpe, T.E., 1973, Mariner 9 Photometric Observations of Mars from November 1971 through March 1972, Icarus, v. 20, p. 482-489.

Tomasko, M.G., et al., 1999, Properties of Dust in the Martian Atmosphere from the Imager on Mars Pathfinder, J. Geophys. Res., v. 104, p. 8987-9007.

Categories

Related Applications to Previous Versions of ISIS

This program replaces the following application existing in previous versions of ISIS:
  • pho_emp_global

Related Objects and Documents

Applications

History

Randy Kirk1999-11-16 USGS Flagstaff Original Version
Janet Barrett2003-01-13 Ported pho_fit_global from the VAX and renamed it pho_emp_global in isis2
Sharmila Prasad2011-08-24 Isis3 Original version, pho_emp_global ported from isis2 to isis3 phoempglobal
Randy Kirk2011-09-25 Updated documentation for the phoempglobal program.
Ella Mae Lee2013-01-25 Updated documentation, and added links to the glossary and an example, fixes #451.
Lynn Weller2013-02-25 Removed links to applications imbedded in text and replaced with italicized application name. Added application links to the "Related Objects and Documents" section of the documentation. Fixes mantis ticket #1525.

Parameters

Files

This output is a PVL file that contains the following:
  • User note - description entered by the user
  • Function name - LunarLambertEmpirical or MinnaertEmpirical
  • PhaseList - list of phase angles
  • KList or LList - list of best fit limb-darkening values
  • PhaseCurveList - list of brightness values
The output file is formatted so it can be used by the program photemplate (used to edit the parameters) or photomet (used to apply photometric normalization to an image).
Type filename
File Mode output
Filter *.txt *.pvl

User Note

This is a note entered by the user. The user note parameter provides a space for digital note-taking. 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

HAPKE

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:
Option Brief Description
HAPKEHEN Hapke Henyey-Greenstein photometric model This is the two-parameter version of the Henyey-Greenstein single particle phase function, with parameters HG1 and HG2.

Exclusions

  • BH
  • CH
HAPKELEG Hapke Legendre photometric model This is a two-term Legendre Polynomial expansion of the single particle phase function, with parameters BH and CH.

Exclusions

  • HG1
  • HG2

The Hapke single-scattering 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 Henyey-Greenstein model for the scattering phase function of single particles in the surface, see Hapke (1981). The two-parameter Henyey-Greenstein function is as follows:
P(phase)=(1-hg2) * (1-hg1**2)/(1+hg1**2+2*hg1*cos(phase))**1.5 + hg2 * (1-hg1**2)/(1+hg1**2-2*hg1*cos(phase))**1.5
Type double
Minimum -1.0 (exclusive)
Maximum 1.0 (exclusive)

The Hapke Henyey-Greenstein coefficient for a single particle phase function. The second parameter, of the two-parameter Henyey-Greenstein model, for the scattering phase function of single particles in the surface. This parameter controls the proportions in a linear mixture of ordinary Henyey-Greenstein 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 two-term 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 two-term 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)

Empirical

Specify a photometric function to fit to the Hapke model. The lists of brightness and limb-darkening values can be used with the LunarLambertEmpirical or MinnaertEmpirical photometric functions in the photometric normalization program photomet.
Type combo
Internal Default LunarLambert
Option List:
Option Brief Description
LUNARLAMBERT LunarLambert photometric function Fit the LunarLambert photometric function to the Hapke Model to derive the parameters for the LunarLambertEmpirical photometric function. The LunarLambertEmpirical model as defined by McEwen (1991) and used by the program photomet is
func=b(phase) * ((1-l(phase))*u0 + 2*l(phase)*u0/(u0+u))
where phase is the phase angle, and u0 and u are the cosines of the incidence and emission angles, respectively.
MINNAERT Minnaert photometric function Fit the Minnaert photometric function to the Hapke Model to derive the parameters for the MinnaertEmpirical photometric function. The MinnaertEmpirical model as defined by McEwen (1991) and used by the program photomet is
func=b(phase) * u0**k(phase) * u**(k(phase)-1)
where phase is the phase angle, and u0 and u are the cosines of the incidence and emission angles, respectively.

Atmospheric Scattering Model

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:
Option Brief Description
NONE No atmospheric scattering model The radiance from the Hapke surface is not modified by atmospheric scattering.

Exclusions

  • TAU
  • WHA
  • HGA
  • HNORM
  • ADDOFFSET
  • BHA
ISOTROPIC1 First order isotropic Atmospheric particles are assumed to scatter light isotropically. The effects of this scattering are calculated exactly to first order.

Exclusions

  • HGA
  • BHA

Inclusions

  • TAU
  • WHA
  • HNORM
  • ADDOFFSET
ISOTROPIC2 Second order isotropic Atmospheric particles are assumed to scatter light isotropically. The effects of this scattering are calculated exactly to second order.

Exclusions

  • HGA
  • BHA

Inclusions

  • TAU
  • WHA
  • HNORM
  • ADDOFFSET
ANISOTROPIC1 First order anisotropic Atmospheric particles are assumed to scatter light according to a Legendre polynomial model with a single term. The effects of this scattering are calculated exactly to first order.

Exclusions

  • HGA

Inclusions

  • TAU
  • WHA
  • BHA
  • HNORM
  • ADDOFFSET
ANISOTROPIC2 Second order anisotropic Atmospheric particles are assumed to scatter light according to a Legendre polynomial model with a single term. The effects of this scattering are calculated exactly to second order.

Exclusions

  • HGA

Inclusions

  • TAU
  • WHA
  • BHA
  • HNORM
  • ADDOFFSET
HAPKEATM1 First order Henyey-Greenstein Atmospheric particles are assumed to scatter light according to a single-parameter Henyey-Greenstein function (see the description of the surface scattering parameter HG1 for the equation that combines two such functions for surface particles). The effects of this scattering are approximated by using a first order solution for multiple scattering by isotropic particles and making a correction to the distribution of singly scattered radiation. The model is called HAPKEATM1 because this correction for the single particle phase function is similar to the one developed by Hapke (1981) for surface scattering.

Exclusions

  • BHA

Inclusions

  • TAU
  • WHA
  • HGA
  • HNORM
  • ADDOFFSET
HAPKEATM2 Second order Henyey-Greenstein Atmospheric particles are assumed to scatter light according to a single parameter Henyey-Greenstein function (see the description of the surface scattering parameter HG1 for the equation that combines two such functions for surface particles). The effects of this scattering are approximated by using a second order solution for multiple scattering by isotropic particles and making a correction to the distribution of singly scattered radiation. The model is called HAPKEATM2 because this correction for the single particle phase function is similar to the one developed by Hapke (1981) for surface scattering.

Exclusions

  • BHA

Inclusions

  • TAU
  • WHA
  • HGA
  • HNORM
  • ADDOFFSET

Normal atmospheric optical depth
Type double
Minimum 0.0 (inclusive)

This is the single-scattering 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 Henyey-Greenstein single particle phase function for atmospheric particles when ATMNAME=HAPKEATM1 or ATMNAME=HAPKEATM2. This is the asymmetry parameter for a single term Henyey-Greenstein model:
p(phase) = (1-hga**2)/(1+hga**2+2*hga*cos(phase))**1.5
Not 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 two-term 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

Fit Range of Angles

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:
  • INCMIN <= incidence angle <= INCMAX
  • EMAMIN <= emission angle <= EMAMAX + EMAMAX_PCOEFF * phase angle
  • INCMIN and EMAMIN are normally set to 0
  • INCMAX and EMAMAX are set to values approaching 90 to exclude only limited regions near the limb and terminator from the fit
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:
  • INCMIN <= incidence angle <= INCMAX
  • EMAMIN <= emission angle <= EMAMAX + EMAMAX_PCOEFF * phase angle
  • INCMIN and EMAMIN are normally set to 0
  • INCMAX and EMAMAX are set to values approaching 90 to exclude only limited regions near the limb and terminator from the fit
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:
  • INCMIN <= incidence angle <= INCMAX
  • EMAMIN <= emission angle <= EMAMAX + EMAMAX_PCOEFF * phase angle
  • INCMIN and EMAMIN are normally set to 0
  • INCMAX and EMAMAX are set to values approaching 90 to exclude only limited regions near the limb and terminator from the fit
Use EMAMAC_PCOEFF=0.1111 to output phase angles at 10 degree increments.
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:
  • INCMIN <= incidence angle <= INCMAX
  • EMAMIN <= emission angle <= EMAMAX + EMAMAX_PCOEFF * phase angle
  • INCMIN and EMAMIN are normally set to 0
  • INCMAX and EMAMAX are set to values approaching 90 to exclude only limited regions near the limb and terminator from the fit
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:
  • INCMIN <= incidence angle <= INCMAX
  • EMAMIN <= emission angle <= EMAMAX + EMAMAX_PCOEFF * phase angle
  • INCMIN and EMAMIN are normally set to 0
  • INCMAX and EMAMAX are set to values approaching 90 to exclude only limited regions near the limb and terminator from the fit
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 1

Create a PVL file with phoempglobal

This example shows the GUI and the input setting for each parameter name in the phoempglobal program.

Command Line

Run phoempglobal to generate a PVL file with the parameter values for the LunarLambertEmpirical photometric model.
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

GUI Screenshot

phoemglobal GUI

phoempglobal GUI

phoemglobal GUI

Screenshot of GUI version of the application. The parameter values are entered by the user, and the results are output to a text file.

Data File

Links open in a new window.
Output PVL file The output PVL file contains the photometric parameter settings for the LunarLambertEmpirical photometric function. This file can be used as input to the photomet program with the FROMPVL parameter name.

Note: The phase angles listed in the PVL file is not in 10 degree increments. The setting for EMAMAX_PCOEFF influences the phase angle values that are output. Use EMAMAC_PCOEFF=0.1111 to output phase angles at 10 degree increments.