# PSF Photometry (`photutils.psf`

)¶

The `photutils.psf`

module contains tools for model-fitting photometry, often
called “PSF photometry”.

Warning

The PSF photometry API is currently considered *experimental* and may change
in the future. We will aim to keep compatibility where practical, but will
not finalize the API until sufficient user feedback has been accumulated.

## Terminology¶

Different astronomy sub-fields use the terms “PSF”, “PRF”, or related terms somewhat differently, especially when colloquial usage is taken into account. This package aims to be at the very least internally consistent, following the definitions described here.

For this module we take Point Spread Function (PSF), or instrumental Point Spread
Function (iPSF) to be the infinite resolution and infinite signal-to-noise flux
distribution from a point source on the detector, after passing through optics,
dust, atmosphere, etc. By contrast, the function describing the responsivity
variations across individual *pixels* is the Pixel Response Function (sometimes
called “PRF”, but that acronym is not used here for reasons that will soon be
apparent). The convolution of the PSF and pixel response function, when
discretized onto the detector (i.e. a rectilinear CCD grid), is the effective
PSF (ePSF) or Point Response Function (PRF). (This latter terminology is the
definition used by Spitzer.
In many cases the PSF/ePSF/PRF distinction is unimportant, and the
ePSF/PRF are simply called the “PSF”, but the distinction can be
critical when dealing carefully with undersampled data or detectors
with significant intra-pixel sensitivity variations. For a more
detailed description of this formalism, see Anderson & King 2000.

All this said, in colloquial usage “PSF photometry” sometimes refers to the more
general task of model-fitting photometry (with the effects of the PSF either
implicitly or explicitly included in the models), regardless of exactly what
kind of model is actually being fit. For brevity (e.g., `photutils.psf`

), we
use “PSF photometry” in this way, as a shorthand for the general approach.

## Building an effective PSF (ePSF)¶

Please see Building an effective Point Spread Function (ePSF) for documentation on how to build an ePSF.

## PSF Photometry¶

Photutils provides a modular set of tools to perform PSF photometry
for different science cases. These are implemented as separate classes
to do sub-tasks of PSF photometry. It also provides high-level classes
that connect these pieces together. In particular, it contains an
implementation of the DAOPHOT algorithm
(`DAOPhotPSFPhotometry`

) proposed by Stetson in his
seminal paper
for crowded-field stellar photometry.

The DAOPHOT algorithm consists in applying the loop FIND, GROUP, NSTAR,
SUBTRACT, FIND until no more stars are detected or a given number of
iterations is reached. Basically, `DAOPhotPSFPhotometry`

works
as follows. The first step is to estimate the sky background. For this task,
photutils provides several classes to compute scalar and 2D backgrounds, see
`background`

for details. The next step is to find an initial
estimate of the positions of potential sources.
This can be accomplished by using source detection algorithms,
which are implemented in `detection`

.

After finding sources, one would apply a clustering algorithm in order
to label the sources according to groups. Usually, those groups are
formed by a distance criterion, which is the case of the grouping
algorithm proposed by Stetson. In `DAOGroup`

, we
provide an implementation of that algorithm. In addition,
`DBSCANGroup`

can also be used to group sources with
more complex distance criteria. The reason behind the construction of
groups is illustrated as follows: imagine that one would like to fit
300 stars and the model for each star has three parameters to be
fitted. If one constructs a single model to fit the 300 stars
simultaneously, then the optimization algorithm will have to search
for the solution in a 900 dimensional space, which is computationally
expensive and error-prone. Reducing the stars in groups effectively
reduces the dimension of the parameter space, which facilitates the
optimization process.

Provided that the groups are available, the next step is to fit the sources
simultaneously for each group. This task can be done using an astropy
fitter, for instance, `LevMarLSQFitter`

.

After sources are fitted, they are subtracted from the given image and, after fitting all sources, the residual image is analyzed by the finding routine again in order to check if there exist any source which has not been detected previously. This process goes on until no more sources are identified by the finding routine.

Note

It is important to note the conventions on the column names of the
input/output astropy Tables which are passed along to the source detection
and photometry objects. For instance, all source detection
objects should output a table with columns named as `xcentroid`

and
`ycentroid`

(check `detection`

). On the other hand,
`DAOGroup`

expects columns named as `x_0`

and `y_0`

,
which represents the initial guesses on the sources’ centroids.
Finally, the output of the fitting process shows columns named as
`x_fit`

, `y_fit`

, `flux_fit`

for the optimum values and
`x_0`

, `y_0`

, `flux_0`

for the initial guesses.
Although this convention implies that the columns have to be renamed
along the process, it has the advantage of clarity so that one can
keep track and easily differentiate where input/outputs came from.

### High-Level Structure¶

Photutils provides three classes to perform PSF Photometry:
`BasicPSFPhotometry`

, `IterativelySubtractedPSFPhotometry`

,
and `DAOPhotPSFPhotometry`

. Together these provide the core
workflow to make photometric measurements given an appropriate PSF (or other)
model.

`BasicPSFPhotometry`

implements the minimum tools for
model-fitting photometry. At its core, this involves finding sources
in an image, grouping overlapping sources into a single model, fitting
the model to the sources, and subtracting the models from the image.
In DAOPHOT parlance, this is essentially running the “FIND, GROUP,
NSTAR, SUBTRACT” once. Because it is only a single cycle of that
sequence, this class should be used when the degree of crowdedness of
the field is not very high, for instance, when most stars are
separated by a distance no less than one FWHM and their brightness are
relatively uniform. It is critical to understand, though, that
`BasicPSFPhotometry`

does not actually contain the
functionality to *do* all these steps - that is provided by other
objects (or can be user-written) functions. Rather, it provides the
framework and data structures in which these operations run. Because
of this, `BasicPSFPhotometry`

is particularly useful
for build more complex workflows, as all the stages can be turned on
or off or replaced with different implementations as the user desires.

`IterativelySubtractedPSFPhotometry`

is similar to
`BasicPSFPhotometry`

, but it adds a parameter called
`n_iters`

which is the number of iterations for which the loop
“FIND, GROUP, NSTAR, SUBTRACT, FIND…” will be performed. This class enables
photometry in a scenario where there exists significant overlap between stars
that are of quite different brightness. For instance, the detection algorithm
may not be able to detect a faint and bright star very close together in the
first iteration, but they will be detected in the next iteration after the
brighter stars have been fit and subtracted. Like
`BasicPSFPhotometry`

, it does not include implementations of the
stages of this process, but it provides the structure in which those stages run.

`DAOPhotPSFPhotometry`

is a special case of
`IterativelySubtractedPSFPhotometry`

. Unlike
`IterativelySubtractedPSFPhotometry`

and
`BasicPSFPhotometry`

, the class includes specific implementations
of the stages of the photometric measurements, tuned to reproduce the algorithms
used for the DAOPHOT code. Specifically, the `finder`

,
`group_maker`

, `bkg_estimator`

attributes are set to the
`DAOStarFinder`

, `DAOGroup`

, and
`MMMBackground`

, respectively. Therefore, users need to
input the parameters of those classes to set up a
`DAOPhotPSFPhotometry`

object, rather than providing objects to
do these stages (which is what the other classes require).

Those classes and all the classes they *use* for the steps in the
photometry process can always be replaced by user-supplied functions
if you wish to customize any stage of the photometry process. This
makes the machinery very flexible, while still providing a “batteries
included” approach with a default implementation that’s suitable for
many use cases.

### Basic Usage¶

The basic usage of, e.g., `IterativelySubtractedPSFPhotometry`

is
as follows:

```
>>> # create an IterativelySubtractedPSFPhotometry object
>>> from photutils.psf import IterativelySubtractedPSFPhotometry
>>> my_photometry = IterativelySubtractedPSFPhotometry(
... finder=my_finder, group_maker=my_group_maker,
... bkg_estimator=my_bkg_estimator, psf_model=my_psf_model,
... fitter=my_fitter, niters=3, fitshape=(7,7))
>>> # get photometry results
>>> photometry_results = my_photometry(image=my_image)
>>> # get residual image
>>> residual_image = my_photometry.get_residual_image()
```

Where `my_finder`

, `my_group_maker`

, and `my_bkg_estimator`

may be any
suitable class or callable function. This approach allows one to customize every
part of the photometry process provided that their input/output are compatible
with the input/ouput expected by `IterativelySubtractedPSFPhotometry`

.
`photutils.psf`

provides all the necessary classes to reproduce the DAOPHOT
algorithm, but any individual part of that algorithm can be swapped for a
user-defined function. See the API documentation for precise details on what
these classes or functions should look like.

### Performing PSF Photometry¶

Let’s take a look at a simple example with simulated stars whose PSF is assumed to be Gaussian.

First let’s create an image with four overlapping stars:

```
>>> import numpy as np
>>> from astropy.table import Table
>>> from photutils.datasets import (make_random_gaussians_table,
... make_noise_image,
... make_gaussian_sources_image)
>>> sigma_psf = 2.0
>>> sources = Table()
>>> sources['flux'] = [700, 800, 700, 800]
>>> sources['x_mean'] = [12, 17, 12, 17]
>>> sources['y_mean'] = [15, 15, 20, 20]
>>> sources['x_stddev'] = sigma_psf*np.ones(4)
>>> sources['y_stddev'] = sources['x_stddev']
>>> sources['theta'] = [0, 0, 0, 0]
>>> sources['id'] = [1, 2, 3, 4]
>>> tshape = (32, 32)
>>> image = (make_gaussian_sources_image(tshape, sources) +
... make_noise_image(tshape, distribution='poisson', mean=6.,
... random_state=1) +
... make_noise_image(tshape, distribution='gaussian', mean=0.,
... stddev=2., random_state=1))
```

```
>>> from matplotlib import rcParams
>>> rcParams['font.size'] = 13
>>> import matplotlib.pyplot as plt
>>> plt.imshow(image, cmap='viridis', aspect=1, interpolation='nearest',
... origin='lower')
>>> plt.title('Simulated data')
>>> plt.colorbar(orientation='horizontal', fraction=0.046, pad=0.04)
```

Then let’s import the required classes to set up a `IterativelySubtractedPSFPhotometry`

object:

```
>>> from photutils.detection import IRAFStarFinder
>>> from photutils.psf import IntegratedGaussianPRF, DAOGroup
>>> from photutils.background import MMMBackground, MADStdBackgroundRMS
>>> from astropy.modeling.fitting import LevMarLSQFitter
>>> from astropy.stats import gaussian_sigma_to_fwhm
```

Let’s then instantiate and use the objects:

```
>>> bkgrms = MADStdBackgroundRMS()
>>> std = bkgrms(image)
>>> iraffind = IRAFStarFinder(threshold=3.5*std,
... fwhm=sigma_psf*gaussian_sigma_to_fwhm,
... minsep_fwhm=0.01, roundhi=5.0, roundlo=-5.0,
... sharplo=0.0, sharphi=2.0)
>>> daogroup = DAOGroup(2.0*sigma_psf*gaussian_sigma_to_fwhm)
>>> mmm_bkg = MMMBackground()
>>> fitter = LevMarLSQFitter()
>>> psf_model = IntegratedGaussianPRF(sigma=sigma_psf)
>>> from photutils.psf import IterativelySubtractedPSFPhotometry
>>> photometry = IterativelySubtractedPSFPhotometry(finder=iraffind,
... group_maker=daogroup,
... bkg_estimator=mmm_bkg,
... psf_model=psf_model,
... fitter=LevMarLSQFitter(),
... niters=1, fitshape=(11,11))
>>> result_tab = photometry(image=image)
>>> residual_image = photometry.get_residual_image()
```

Note that the parameters values for the finder class, i.e.,
`IRAFStarFinder`

, are completely chosen in an arbitrary
manner and optimum values do vary according to the data.

As mentioned before, the way to actually do the photometry is by using
`photometry`

as a function-like call.

It’s worth noting that `image`

does not need to be background subtracted.
The subtraction is done during the photometry process with the attribute
`bkg`

that was used to set up `photometry`

.

Now, let’s compare the simulated and the residual images:

```
>>> plt.subplot(1, 2, 1)
>>> plt.imshow(image, cmap='viridis', aspect=1, interpolation='nearest',
origin='lower')
>>> plt.title('Simulated data')
>>> plt.colorbar(orientation='horizontal', fraction=0.046, pad=0.04)
>>> plt.subplot(1 ,2, 2)
>>> plt.imshow(residual_image, cmap='viridis', aspect=1,
... interpolation='nearest', origin='lower')
>>> plt.title('Residual Image')
>>> plt.colorbar(orientation='horizontal', fraction=0.046, pad=0.04)
>>> plt.show()
```

### Performing PSF Photometry with Fixed Centroids¶

In case that the centroids positions of the stars are known a priori, then
they can be held fixed during the fitting process and the optimizer will
only consider flux as a variable. To do that, one has to set the `fixed`

attribute for the centroid parameters in `psf`

as `True`

.

Consider the previous example after the line
`psf_model = IntegratedGaussianPRF(sigma=sigma_psf)`

:

```
>>> psf_model.x_0.fixed = True
>>> psf_model.y_0.fixed = True
>>> pos = Table(names=['x_0', 'y_0'], data=[sources['x_mean'],
... sources['y_mean']])
```

```
>>> photometry = BasicPSFPhotometry(group_maker=daogroup,
... bkg_estimator=mmm_bkg,
... psf_model=psf_model,
... fitter=LevMarLSQFitter(),
... fitshape=(11,11))
>>> result_tab = photometry(image=image, init_guesses=pos)
>>> residual_image = photometry.get_residual_image()
```

```
>>> plt.subplot(1, 2, 1)
>>> plt.imshow(image, cmap='viridis', aspect=1,
... interpolation='nearest', origin='lower')
>>> plt.title('Simulated data')
>>> plt.colorbar(orientation='horizontal', fraction=0.046, pad=0.04)
>>> plt.subplot(1 ,2, 2)
>>> plt.imshow(residual_image, cmap='viridis', aspect=1,
... interpolation='nearest', origin='lower')
>>> plt.title('Residual Image')
>>> plt.colorbar(orientation='horizontal', fraction=0.046, pad=0.04)
```

## Fitting additional parameters¶

The PSF photometry classes can also be used to fit more model parameters than
just the flux and center positions. While a more realistic use case might be
fitting sky backgrounds, or shape parameters of galaxies, here we use the
`sigma`

parameter in `IntegratedGaussianPRF`

as the simplest
possible example of this feature. (For actual PSF photometry of stars you would
*not* want to do this, because the shape of the PSF should be set by bright
stars or an optical model and held fixed when fitting.)

First, let us instantiate a PSF model object:

```
>>> gaussian_prf = IntegratedGaussianPRF()
```

The attribute `fixed`

for the `sigma`

parameter is set to `True`

by
default, i.e., `sigma`

is not considered during the fitting process.
Let’s first change this behavior:

```
>>> gaussian_prf.sigma.fixed = False
```

In addition, we need to indicate the initial guess which will be used in during
the fitting process. By the default, the initial guess is taken as the default
value of `sigma`

, but we can change that by doing:

```
>>> gaussian_prf.sigma.value = 2.05
```

Now, let’s create a simulated image which has a brighter star and one
overlapping fainter companion so that the detection algorithm won’t be
able to identify it, and hence we should use
`IterativelySubtractedPSFPhotometry`

to measure the fainter
star as well. Also, note that both of the stars have `sigma=2.0`

.

```
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import LogNorm
from photutils.datasets import (make_random_gaussians_table,
make_noise_image,
make_gaussian_sources_image)
from photutils.psf import (IterativelySubtractedPSFPhotometry,
BasicPSFPhotometry)
from photutils import MMMBackground
from photutils.psf import IntegratedGaussianPRF, DAOGroup
from photutils.detection import DAOStarFinder
from photutils.detection import IRAFStarFinder
from astropy.table import Table
from astropy.modeling.fitting import LevMarLSQFitter
sources = Table()
sources['flux'] = [10000, 1000]
sources['x_mean'] = [18, 9]
sources['y_mean'] = [17, 21]
sources['x_stddev'] = [2] * 2
sources['y_stddev'] = sources['x_stddev']
sources['theta'] = [0] * 2
tshape = (32, 32)
image = (make_gaussian_sources_image(tshape, sources) +
make_noise_image(tshape, distribution='poisson', mean=6.,
random_state=1) +
make_noise_image(tshape, distribution='gaussian', mean=0.,
stddev=2., random_state=1))
vmin, vmax = np.percentile(image, [5, 95])
plt.imshow(image, cmap='viridis', aspect=1, interpolation='nearest',
origin='lower', norm=LogNorm(vmin=vmin, vmax=vmax))
```

Let’s instantiate the necessary objects in order to use an
`IterativelySubtractedPSFPhotometry`

to perform photometry:

```
>>> daogroup = DAOGroup(crit_separation=8)
>>> mmm_bkg = MMMBackground()
>>> iraffind = IRAFStarFinder(threshold=2.5*mmm_bkg(image), fwhm=4.5)
>>> fitter = LevMarLSQFitter()
>>> gaussian_prf = IntegratedGaussianPRF(sigma=2.05)
>>> gaussian_prf.sigma.fixed = False
>>> itr_phot_obj = IterativelySubtractedPSFPhotometry(finder=iraffind,
... group_maker=daogroup,
... bkg_estimator=mmm_bkg,
... psf_model=psf_model,
... fitter=fitter,
... fitshape=(11, 11),
... niters=2)
```

Now, let’s use the callable `itr_phot_obj`

to perform photometry:

```
>>> phot_results = itr_phot_obj(image)
>>> phot_results['id', 'group_id', 'iter_detected', 'x_0', 'y_0', 'flux_0']
id group_id iter_detected x_0 y_0 flux_0
--- -------- ------------- ------------- ------------- -------------
1 1 1 18.0045935148 17.0060558543 9437.07321281
1 1 2 9.06141447183 21.0680052846 977.163727416
>>> phot_results['sigma_0', 'sigma_fit', 'x_fit', 'y_fit', 'flux_fit']
sigma_0 sigma_fit x_fit y_fit flux_fit
------- ------------- ------------- ------------- -------------
2.05 1.98092026939 17.9995106906 17.0039419384 10016.4470148
2.05 1.98516037471 9.12116345703 21.0599164498 1036.79115883
```

We can see that `sigma_0`

(the initial guess for `sigma`

) was assigned
to the value we used when creating the PSF model.

Let’s take a look at the residual image:

```
>>> plt.imshow(itr_phot_obj.get_residual_image(), cmap='viridis',
... aspect=1, interpolation='nearest', origin='lower')
```

## Additional Example Notebooks (online)¶

## References¶

## Reference/API¶

This subpackage contains tools to perform point-spread-function (PSF) photometry.

### Functions¶

`create_matching_kernel` (source_psf, target_psf) |
Create a kernel to match 2D point spread functions (PSF) using the ratio of Fourier transforms. |

`extract_stars` (data, catalogs[, size]) |
Extract cutout images centered on stars defined in the input catalog(s). |

`get_grouped_psf_model` (template_psf_model, …) |
Construct a joint PSF model which consists of a sum of PSF’s templated on a specific model, but whose parameters are given by a table of objects. |

`prepare_psf_model` (psfmodel[, xname, yname, …]) |
Convert a 2D PSF model to one suitable for use with `BasicPSFPhotometry` or its subclasses. |

`resize_psf` (psf, input_pixel_scale, …[, order]) |
Resize a PSF using spline interpolation of the requested order. |

`subtract_psf` (data, psf, posflux[, subshape]) |
Subtract PSF/PRFs from an image. |

### Classes¶

`BasicPSFPhotometry` (group_maker, …[, …]) |
This class implements a PSF photometry algorithm that can find sources in an image, group overlapping sources into a single model, fit the model to the sources, and subtracting the models from the image. |

`CosineBellWindow` (alpha) |
Class to define a 2D cosine bell window function. |

`DAOGroup` (crit_separation) |
This class implements the DAOGROUP algorithm presented by Stetson (1987). |

`DAOPhotPSFPhotometry` (crit_separation, …[, …]) |
This class implements an iterative algorithm based on the DAOPHOT algorithm presented by Stetson (1987) to perform point spread function photometry in crowded fields. |

`DBSCANGroup` (crit_separation[, min_samples, …]) |
Class to create star groups according to a distance criteria using the Density-based Spatial Clustering of Applications with Noise (DBSCAN) from scikit-learn. |

`EPSFBuilder` ([oversampling, shape, …]) |
Class to build an effective PSF (ePSF). |

`EPSFFitter` ([fitter, fit_boxsize]) |
Class to fit an ePSF model to one or more stars. |

`EPSFModel` (data[, flux, x_0, y_0, normalize, …]) |
A class that models an effective PSF (ePSF). |

`EPSFStar` (data[, weights, cutout_center, …]) |
A class to hold a 2D cutout image and associated metadata of a star used to build an ePSF. |

`EPSFStars` (stars_list) |
Class to hold a list of `EPSFStar` and/or `LinkedEPSFStar` objects. |

`FittableImageModel` (data[, flux, x_0, y_0, …]) |
A fittable 2D model of an image allowing for image intensity scaling and image translations. |

`GriddedPSFModel` (data[, flux, x_0, y_0, …]) |
A fittable 2D model containing a grid PSF models defined at specific locations that are interpolated to evaluate a PSF at an arbitrary (x, y) position. |

`GroupStarsBase` |
This base class provides the basic interface for subclasses that are capable of classifying stars in groups. |

`HanningWindow` () |
Class to define a 2D Hanning (or Hann) window function. |

`IntegratedGaussianPRF` ([sigma, x_0, y_0, flux]) |
Circular Gaussian model integrated over pixels. |

`IterativelySubtractedPSFPhotometry` (…[, …]) |
This class implements an iterative algorithm to perform point spread function photometry in crowded fields. |

`LinkedEPSFStar` (stars_list) |
A class to hold a list of `EPSFStar` objects for linked stars. |

`NonNormalizable` |
Used to indicate that a `FittableImageModel` model is non-normalizable. |

`PRFAdapter` (psfmodel[, renormalize_psf, …]) |
A model that adapts a supplied PSF model to act as a PRF. |

`SplitCosineBellWindow` (alpha, beta) |
Class to define a 2D split cosine bell taper function. |

`TopHatWindow` (beta) |
Class to define a 2D top hat window function. |

`TukeyWindow` (alpha) |
Class to define a 2D Tukey window function. |

### Class Inheritance Diagram¶

## photutils.psf.sandbox Module¶

This module stores work related to photutils.psf that is not quite ready for prime-time (i.e., is not considered a stable public API), but is included either for experimentation or as legacy code.

### Classes¶

`DiscretePRF` (prf_array[, normalize, subsampling]) |
A discrete Pixel Response Function (PRF) model. |

`Reproject` (wcs_original, wcs_rectified) |
Class to reproject pixel coordinates between unrectified and rectified images. |