phoempglobal

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.

Description

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

Description

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.

Description

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.

Description

The Hapke single-scattering albedo of surface particles, see Hapke (1981). Not to be confused with albedo WHA of the atmospheric particles.

Description

The Hapke opposition surge width. The width parameter for the opposition effect for the surface if hapkehen or hapkeleg is used, see Hapke (1984).

Description

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

Description

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.

Description

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

Description

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.

Description

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))

Description

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))

Description

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.

Description

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.

Description

Normal atmospheric optical depth

Description

This is the single-scattering albedo of atmospheric particles, not to be confused with the albedo WH of surface particles.

Description

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

Description

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))

Description

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.

Description

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.

Description

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

Description

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

Description

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

Description

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

Description

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

Description

This is the minimum phase angle at which a fit will be performed, corresponding to the first value (PHASELIST) in the output table.

Description

This is the maximum phase angle at which a fit will be performed, corresponding to the last value (PHASELIST) in the output table.

Description

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.