Photometry Module (sbpy.photometry
)¶
Introduction¶
photometry
provides routines for photometric phase curve
modeling of small bodies, and for retrieving sbpy
’s builtin filter
bandpasses.
Diskintegrated Phase Function Models¶
Diskintegrated phase function refers to the brightness or reflectance of
an asteroid, often measured in magnitude, with respect to phase angle. The IAU
adopted a number of models to describe the phase function of asteroids,
including the twoparameter H, G system (Bowell et al. 1989), the
threeparameter H, G1, G2, and the twoparameter H, G12 system derived from
the threeparameter system (Muinonen et al. 2010). The H, G12 system was
further revised by Penttilä et al. (2016). photometry
provides
classes for all four models HG
, HG1G2
,
HG12
, and HG12_Pen16
, respectively.
The photometric model class can be initialized with the default parameters,
by supplying the model parameters as either dimensionless numbers or
Quantity
:
>>> import astropy.units as u
>>> from sbpy.photometry import HG, HG1G2, HG12, HG12_Pen16
>>> m = HG()
>>> print(m)
Model: HG
Inputs: ('x',)
Outputs: ('y',)
Model set size: 1
Parameters:
H G
 
8.0 0.4
>>> m = HG(H = 3.34 * u.mag, G = 0.12, radius = 460 * u.km, wfb = 'V')
>>> print(m)
Model: HG
Inputs: ('x',)
Outputs: ('y',)
Model set size: 1
Parameters:
H G
mag
 
3.34 0.12
The calculations that involve conversion between magnitude and reflectance
requires valid object size and wfb
(wavelength/frequency/band) parameter to
be set for the photometric model. The corresponding solar flux at the wfb
of the photometric model object has to be available through calib
system, or set by set
, which works with context
management with
syntax.
Calculate geometric albedo, Bond albedo, and phase integral:
>>> import astropy.units as u
>>> from sbpy.calib import solar_fluxd
>>> solar_fluxd.set({'V': 26.77 * u.mag})
<ScienceState solar_fluxd: {'V': <Quantity 26.77 mag>}>
>>> print(m.geomalb)
0.09557298727307795
>>> print(m.bondalb)
0.03482207291799989
>>> print(m.phaseint)
0.3643505755292945
Note that the current version of astropy.modeling.Model
doesn’t support
astropy.units.MagUnit
instance as model parameters. For now one has to use
the dimensionless magnitude mag
in the phase function
parameter, and manually set solar flux in order for the conversion between
magnitude and reflectance to work.
The model class can also be initialized by a subclass of sbpy
’s
DataClass
, such as Phys
, as long as it contains the
model parameters:
>>> from sbpy.data import Phys
>>> phys = Phys.from_sbdb('Ceres')
>>> m = HG.from_phys(phys)
INFO: Model initialized for 1 Ceres (A801 AA). [sbpy.photometry.core]
>>> print(m)
Model: HG
Inputs: ('x',)
Outputs: ('y',)
Model set size: 1
Parameters:
H G
mag
 
3.31 0.12
Note that in this case, model set is not supported. Only one model can be
initialized with the first set of valid parameters in the input
DataClass
.
To fit a photometric model, one may follow the standard procedure defined in
astropy.modeling
submodule, first initializing a model, then using one of
the fitter classes defined in astropy.modeling.fitting
submodule, such as SLSQPLSQFitter
. Note that
the HG1G2
model requires that the G1 and G2 parameters
are bounded within [0, 1], as well as an inequality constraint,
0 <= 1  G1  G2 <= 1. These constraints are implemented in sbpy via the
bounds
parameter of Parameter
and the ineqcons
parameter of Model
. Some fitters, such as
astropy.modeling.LevMarLSQFitter
, do not support constrained fit via
the ineqcons
parameter, though.
>>> import numpy as np
>>> import astropy.units as u
>>> from astropy.modeling.fitting import SLSQPLSQFitter
>>> # generate data to be fitted
>>> model1 = HG(3.34 * u .mag, 0.12)
>>> alpha = np.linspace(0, 40, 20) * u.deg
>>> mag = model1(alpha) + (np.random.rand(20)*0.2  0.1) * u.mag
>>> # fit new model
>>> fitter = SLSQPLSQFitter()
>>> model2 = HG()
>>> model2 = fitter(model2, alpha, mag, verblevel=0)
Alternatively, one may use the class method
from_obs
to
initialize a model directly from an Obs
object by fitting the
data contained therein.
>>> # use class method .from_obs
>>> from astropy.modeling.fitting import SLSQPLSQFitter
>>> fitter = SLSQPLSQFitter()
>>> from sbpy.data import Obs
>>> obs = Obs.from_dict({'alpha': alpha, 'mag': mag})
>>> model3 = HG12.from_obs(obs, fitter, 'mag', verblevel=0)
One can also initialize a model set from multiple columns in the input
Obs
object if it contains more than one columns of brightness
measurements. The columns to be fitted are specified by a keyward argument
fields
. By default, the column 'mag'
will be fitted.
>>> # Initialize model set
>>> model4 = HG(5.2 * u.mag, 0.18)
>>> mag4 = model4(alpha) + (np.random.rand(20)*0.2  0.1) * u.mag
>>> fitter = SLSQPLSQFitter()
>>> obs = Obs.from_dict({'alpha': alpha, 'mag': mag, 'mag1': mag4})
>>> model5 = HG.from_obs(obs, fitter, fields=['mag', 'mag1'], verblevel=0)
Filter Bandpasses¶
A few filter bandpasses are included with sbpy
for internal tests and your convenience. The function bandpass
will return the filter transmission as a SpectralElement
(requires synphot
):
>>> from sbpy.photometry import bandpass
>>> bp = bandpass('Cousins R')
>>> print(bp.avgwave())
6499.914781904409 Angstrom
For other bandpasses, obtain the photoncounting relative spectral response curves as a twocolumn file. If the first column is wavelength in Angstroms, and the second is the response, then read the file with:
>>> from synphot import SpectralElement
>>> bp = SpectralElement.from_file('filename.txt')
See synphot.spectrum.SpectralElement
for other options and file format details.
Reference/API¶
sbpy Module for small body photometry
Functions¶

Retrieve bandpass transmission spectrum from sbpy. 
Classes¶

Base class for diskintegrated phase function model 

HG photometric phase model (Bowell et al. 1989). 

HG12 photometric phase model (Muinonen et al. 2010). 

Revised H, G12 model by Penttil"a et al. (2016). 

HG1G2 photometric phase model (Muinonen et al. 2010). 

Linear phase function model 