Isis 3 Application Documentation
Fit empirical photometric functions to Hapke
Description
This program finds lunar-Lambert or Minnaert photometric functions
to approximate a more realistic but more complex Hapke model. The fit
is performed at a single geometry rather than for a range of phase
angles. The user specifies the phase angle and the incidence and emission
angles of the mean ground plane (datum), as well as the RMS (root mean
squared) slope relative to the dataum. Artificial data are then created,
with slopes drawn from an isotropic Gaussian distribution relative to the
datum. The simpler model is fit at these orientations to the Hapke model
by adjusting its one parameter and its overall brightness so that the
sum-squared-residual between the two is minimized. Both the parameter
(which, for both types of simple model, mainly controls limb darkening)
and the brightness (normalized as an empirical phase curve) are reported.
This program should serve as a clear example for developing a new program
to fit the parameter of an empirical photometric function to part of an
actual image. The differences can be summarized as follows:
1) Fit is done only once (not in a table vs. phase angle)
since the input image has a fixed geometry.
2) The data to be fit *to* are obtained from an ISIS cube plane
rather than modeled in in the code.
3) Similarly, the incidence, emission, and phase angles are
obtained from backplanes of the same cube and maintained
in buffers corresponding point-for-point with the image.
4) Both image data and angles should be converted to double
precision before being used.
5) Optionally, a region-of-interest mask could be obtained
from a backplane and only those pixels in the ROI used
in the fit. This would be in addition to the incidence
and emission angle tests already done in the code.
Categories
History
Randy Kirk | 1999-11-16 |
USGS Flagstaff Original Version
|
Janet Barrett | 2003-01-13 |
Ported pho_fit_local from the VAX and renamed it
pho_emp_local in isis2
|
Sharmila Prasad | 2011-08-04 |
Isis3 Original version, pho_emp_local ported from isis2 to isis3
phoemplocal
|
Randy Kirk | 2011-09-25 |
Updated documentation for the phoemplocal program
|
|
Parameter Groups
Files
Name
|
Description
|
TO |
Output text file to contain fit parameters
|
APPEND |
Append Output to File
|
User Note
Name
|
Description
|
NOTE |
User note to be added to output file
|
Hapke
Name
|
Description
|
PHTNAME |
Surface Photometric Model
|
WH |
Single Scattering Albedo
|
HH |
Opposition Surge Width
|
B0 |
Opposition Surge Strength
|
THETA |
Surface roughness in degrees
|
HG1 |
Henyey-Greenstein coefficient 1
|
HG2 |
Henyey-Greenstein coefficient 2
|
BH |
Legendre coefficient 1
|
CH |
Legendre coefficient 2
|
Empirical
Name
|
Description
|
MODEL |
Type of empirical photometric function fitted to the Hapke model.
|
Atmospheric Scattering Model
Name
|
Description
|
ATMNAME |
Type of atmospheric scattering model (if any) modifying the surface
scattering
|
TAU |
Normal atmospheric optical depth
|
WHA |
Single-scattering albedo
|
HGA |
Henyey-Greenstein coefficient for atmospheric particles
|
BHA |
Atmospheric particle Legendre coefficient
|
HNORM |
Atmospheric shell thickness
|
ADDOFFSET |
Allow additive offset in fit
|
Mean Ground Plane(Datum) Geometry
Random Number Generator
|
Files:
TO
Description
The output file will contain the phase angle, best-fit limb
darkening parameter, best-fit brightness both in absolute units
and relative to the zero phase model and RMS residual to the fit.
Type
| filename |
File Mode
| output |
Internal Default
|
None Specified
|
Filter
|
*.txt
|
Files:
APPEND
Description
If this option is selected, the output from the application will be appended to the file.
If it is not selected, any information in the TO file will be overwritten.
Type
| boolean |
Default
| FALSE |
User Note:
NOTE
Description
The user can specify a note to be added to the output file using this parameter.
Type
| string |
Internal Default
| None Specified |
Hapke:
PHTNAME
Description
A Hapke (1981; 1984; 1966) photometric model is always used as the model
to which 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
|
Internal Default
| HAPKEHEN |
Option List:
|
Option |
Brief |
Description |
HAPKEHEN |
Use Henyey-Greenstein scattering function in Hapke photometric model
|
This is the two-parameter version of the Henyey-Greenstein single
particle phase function, with parameters HG1 and HG2.
Exclusions
|
HAPKELEG |
Use Legendre-Polynomial in Hapke photometric model
|
This is a two-term Legendre Polynomial expansion of the single
particle phase function, with parameters BH and CH.
Exclusions
|
|
Hapke:
WH
Description
Single-scattering albedo of surface particles. See Hapke
(1981). Not to be confused with albedo WHA of the atmospheric
particles.
Type
| double |
Internal Default
| None Specified |
Hapke:
HH
Description
Opposition Surge Width. ZEROs are strongly advised as the simple models
do not fit the opposition effect well. See Hapke (1984).
Type
| double |
Internal Default
| None Specified |
Hapke:
B0
Description
Opposition Surge Strength. Magnitude of the opposition effect for
the surface. ZEROs are strongly advised as the simple models do
not fit the opposition effect well. See Hapke (1984).
Type
| double |
Internal Default
| None Specified |
Hapke:
THETA
Description
Small scale surface roughness in degrees. "Macroscopic roughness"
of the surface as it affects the photometric behavior. This is the
root mean squared (RMS) slope at scales larger than the distance
photons penetrate the surface but smaller than a pixel. See
Hapke (1986).
Type
| double |
Internal Default
| None Specified |
Hapke:
HG1
Description
Asymmetry parameter used in the Henyey-Greenstein model for the
scattering phase function of single particles in the surface,
used if PHTNAME=HAPKEHEN. See Hapke (1981). The two-parameter
Henyey-Greenstein function is 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 |
Internal Default
| None Specified |
Hapke:
HG2
Description
Second parameter of the two-parameter Henyey-Greenstein model
for the scattering phase function of single particles in the
surface, used if PHTNAME=HAPKEHEN. This parameter controls the
proportions in a linear mixture of ordinary Heneyey-Greenstein
phase functions with asymmetry parameters equal to +HG1 and -HG1.
See HG1 for the full formula.
Type
| double |
Internal Default
| None Specified |
Hapke:
BH
Description
Coefficient of the first order Legendre polynomial in the
single particle phase function. When PHTNAME=HAPKELEG, a
two-term Legendre polynomial expansion is used to represent
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 |
Internal Default
| None Specified |
Hapke:
CH
Description
Coefficient of the second order Legendre polynomial in the
single particle phase function. When PHTNAME=HAPKELEG, a
two-term Legendre polynomial expansion is used to represent
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 |
Internal Default
| None Specified |
Empirical:
MODEL
Description
Determines which empirical photometric function will be fitted
to the Hapke model. The values of brightness and limb darkening
can be used with the lunar-Lambert empirical or Minnaert empirical
photometric functions in the photometric normalization program
photomet.
Type
| combo |
Internal Default
| LunarLambert |
Option List:
|
Option |
Brief |
Description |
LUNARLAMBERT |
Lunar-Lambert Empirical Photometric Function
|
Fit the Lunar-Lambert Empirical Photometric Function to the
Hapke Model. The empirical lunar-Lambert model as defined by
McEwen (1991) and used by the program photomet is:
Lunar-Lambert FUNC=B(PHASE) * ((1-L(PHASE))*u0 + 2*L(PHASE)*u0/(u0+u))
|
MINNAERT |
Minnaert Empirical Photometric Function
|
Fit the Minnaert Empirical Photometric Function to the
Hapke Model. The empirical Minnaert model as defined by
McEwen (1991) and used by the program photomet is:
Minnaert FUNC=B(PHASE) * u0**K(PHASE) * u**(K(PHASE)-1)
|
|
Atmospheric Scattering Model:
ATMNAME
Description
If an option other than NONE is selected, an atmospheric scattering
model will be included in addition to the surface Hapke model as
part of the physical model to which the empirical model is fitted.
Six atmospheric models are currently provided, falling into three
classes that differ in their treatment of the single particle
scattering function for atmospheric particles. Each of these classes
of model can be evaluated to a first order (faster) or second order
(more accurate) approximation. Atmospheric scattering in all these
models both attenuates the surface signal and adds its own (uniform)
contribution to the image radiance. Therefore, unless NONE is
selected, it makes sense to also set ADDOFFSET=YES so that the additive
contribution of the atmosphere will be modeled by an additive
constant in the fit. This approach is useful in preparing for
photoclinometry (shape from shading), for which images are normally
preprocessed by subtracting a uniform haze component that corresponds
to the additive term in the fit with ADDOFFSET=YES.
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
Inclusions
|
ISOTROPIC2 |
Second Order Isotropic
|
Atmospheric particles are assumed to scatter light isotropically.
The effects of this scattering are calculated exactly to second
order.
Exclusions
Inclusions
|
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
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
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
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
Inclusions
- TAU
- WHA
- HGA
- HNORM
- ADDOFFSET
|
|
Atmospheric Scattering Model:
TAU
Description
Normal atmospheric optical depth
Type
| double |
Internal Default
| None Specified |
Atmospheric Scattering Model:
WHA
Description
Single-scattering albedo of atmospheric particles, not to be
confused with the albedo WH of surface particles.
Type
| double |
Internal Default
| None Specified |
Atmospheric Scattering Model:
HGA
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
Not to be confused with corresponding parameter HG1 for the
surface particles.
Type
| double |
Internal Default
| None Specified |
Atmospheric Scattering Model:
BHA
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)) where P1 is the first order
Legendre polynomial. Not to be confused with the corresponding
parameter BH for the surface.
Type
| double |
Internal Default
| None Specified |
Atmospheric Scattering Model:
HNORM
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.
Type
| double |
Internal Default
| None Specified |
Atmospheric Scattering Model:
ADDOFFSET
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.
Type
| boolean |
Default
|
false
|
Mean Ground Plane(Datum) Geometry:
EMISSION
Description
This is the emission angle of the ground plane at a representative
point in the image of interest, measured between the local vertical
and the vector from the point on the ground to the spacecraft.
Type
| double |
Internal Default
| None Specified |
Mean Ground Plane(Datum) Geometry:
PHASE
Description
This is the phase angle at a representative point in the image,
measured between the vector from that point to the sun and the
vector from that point to the spacecraft.
Type
| double |
Internal Default
| None Specified |
Mean Ground Plane(Datum) Geometry:
INCIDENCE
Description
This is the incidence angle of the ground plane at a representative
point in the image of interest, measured between the local vertical
and the vector from the point on the ground to the sun.
Type
| double |
Internal Default
| None Specified |
Mean Ground Plane(Datum) Geometry:
RMS_SLOPE
Description
The fit will be performed over a set of synthesized data with
different orientations. Each component (E-W and N-S) of slope
of these data points is normally distributed with a mean of
zero and a standard deviation given by this parameter. The fit
results should be only weakly dependent on this parameter.
Type
| double |
Internal Default
| None Specified |
Random Number Generator:
SEED
Description
If enabled, this program uses the user defined number as the starting
seed for the randomn number generator which is used to generate
slopes at which the fit is performed, allowing the same random number
sequence to be used multiple times for testing purposes. If disabled,
the random number sequence will be initialized from the system clock
and the numbers will be different each time the program is run.
Type
| boolean |
Default
| false |
Inclusions
|
|
Random Number Generator:
SEED_NUMBER
Description
Starting seed number for randomn number generator
Type
| integer |
Internal Default
| None Specified |