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Kindergarten children (n=161) screened with the 'Early Prevention of School Failure' (EPSF) measure were examined several years later. Students who had been retained, referred to special education, or placed in special education demonstrated significantly lower EPSF scores. Buy Genuine Nissan Fluid 999MP-EPSF00P Electric Power Steering Fluid - 1 Quart: Hydraulic Oils - Amazon.com FREE DELIVERY possible on eligible purchases. In terms of placement in special education, EPSF modality scores were accurate predictors for approximately 80% of cases (Table 3). In the stepwise discriminant analysis on retention status, EPSF subtest scores on expressive language were the most powerful predictors, followed by scores.

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• Definition & Sources

Definitions: Percent of entering public school kindergarteners performing at or above age level in selected areas, according to Early Prevention of School Failure (EPSF) assessment.

Data Source: VI Department of Education

Footnotes: *Please note that this assessment is no longer in use. Data provided here are for historical reference only.
The Early Prevention of School Failure (EPSF) test is a nationally valid assessment that measures kidergarten students' proficiency in vital cognitive and physical areas. EPSF is administered as a pre-test to all kindergarteners, and as a post-test to those identified as high risk. Scores reported are the pre-test scores.
Data for St. Thomas reflects scores for the St. Thomas/St. John district.
N/A: Data not available

• Definition & Sources

Definitions: Percent of entering public school kindergarteners performing at or above age level in selected areas, according to Early Prevention of School Failure (EPSF) assessment.

Data Source: VI Department of Education

Footnotes: *Please note that this assessment is no longer in use. Data provided here are for historical reference only.
The Early Prevention of School Failure (EPSF) test is a nationally valid assessment that measures kidergarten students' proficiency in vital cognitive and physical areas. EPSF is administered as a pre-test to all kindergarteners, and as a post-test to those identified as high risk. Scores reported are the pre-test scores.
Data for St. Thomas reflects scores for the St. Thomas/St. John district.
N/A: Data not available

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

Terminology¶

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

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For this module we take Point Spread Function (PSF), or instrumentalPoint Spread Function (iPSF) to be the infinite resolution andinfinite signal-to-noise flux distribution from a point source onthe detector, after passing through optics, dust, atmosphere, etc.By contrast, the function describing the responsivity variationsacross individual pixels is the Pixel Response Function (sometimescalled “PRF”, but that acronym is not used here for reasons that willsoon be apparent). The convolution of the PSF and pixel responsefunction, when discretized onto the detector (i.e., a rectilinearCCD 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/PRFdistinction is unimportant, and the ePSF/PRF are simply calledthe “PSF”, but the distinction can be critical when dealingcarefully with undersampled data or detectors with significantintra-pixel sensitivity variations. For a more detaileddescription of this formalism, see Anderson & King 2000.

All this said, in colloquial usage “PSF photometry” sometimes refersto the more general task of model-fitting photometry (with the effectsof the PSF either implicitly or explicitly included in the models),regardless of exactly what kind of model is actually being fit. Forbrevity (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 PSFphotometry for different science cases. These are implementedas separate classes to do sub-tasks of PSF photometry. Italso provides high-level classes that connect these piecestogether. In particular, it contains an implementation of theDAOPHOT algorithm (DAOPhotPSFPhotometry)proposed by Stetson in his seminal paper forcrowded-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 ofiterations is reached. Basically, DAOPhotPSFPhotometryworks as follows. The first step is to estimate the sky background. Forthis task, photutils provides several classes to compute scalar and 2Dbackgrounds, see background for details. The next step isto find an initial estimate of the positions of potential sources. Thiscan be accomplished by using source detection algorithms, which areimplemented in detection.

After finding sources, one would apply a clustering algorithm inorder to label the sources according to groups. Usually, thosegroups are formed by a distance criterion, which is the case of thegrouping algorithm proposed by Stetson. In DAOGroup,we provide an implementation of that algorithm. In addition,DBSCANGroup can also be used to group sources with morecomplex distance criteria. The reason behind the construction of groupsis illustrated as follows: imagine that one would like to fit 300 starsand the model for each star has three parameters to be fitted. If oneconstructs a single model to fit the 300 stars simultaneously, then theoptimization algorithm will have to search for the solution in a 900dimensional space, which is computationally expensive and error-prone.Reducing the stars in groups effectively reduces the dimension of theparameter space, which facilitates the optimization process.

Provided that the groups are available, the next step isto fit the sources simultaneously for each group. Thistask 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 findingroutine again in order to check if there exist any source which has notbeen detected previously. This process goes on until no more sources areidentified by the finding routine.

Note

It is important to note the conventions on the column names of theinput/output astropy Tables which are passed along to the sourcedetection and photometry objects. For instance, all source detectionobjects should output a table with columns named as xcentroidand ycentroid (check detection). On the otherhand, DAOGroup expects columns named as x_0and y_0, which represents the initial guesses on the sources’centroids. Finally, the output of the fitting process shows columnsnamed as x_fit, y_fit, flux_fit for the optimum valuesand x_0, y_0, flux_0 for the initial guesses. Althoughthis convention implies that the columns have to be renamed alongthe process, it has the advantage of clarity so that one can keeptrack and easily differentiate where input/outputs came from.

High-Level Structure¶

Photutils provides three classes to perform PSFPhotometry: BasicPSFPhotometry,IterativelySubtractedPSFPhotometry, andDAOPhotPSFPhotometry. Together these provide the coreworkflow to make photometric measurements given an appropriate PSF (orother) model.

BasicPSFPhotometry implements the minimum tools formodel-fitting photometry. At its core, this involves finding sourcesin an image, grouping overlapping sources into a single model, fittingthe model to the sources, and subtracting the models from the image. InDAOPHOT parlance, this is essentially running the “FIND, GROUP, NSTAR,SUBTRACT” once. Because it is only a single cycle of that sequence, thisclass should be used when the degree of crowdedness of the field is notvery high, for instance, when most stars are separated by a distance noless than one FWHM and their brightness are relatively uniform. It iscritical to understand, though, that BasicPSFPhotometrydoes 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 theseoperations run. Because of this, BasicPSFPhotometry isparticularly useful for build more complex workflows, as all the stagescan be turned on or off or replaced with different implementations asthe user desires.

IterativelySubtractedPSFPhotometry is similar toBasicPSFPhotometry, but it adds a parameter calledn_iters which is the number of iterations for which the loop“FIND, GROUP, NSTAR, SUBTRACT, FIND…” will be performed. This classenables photometry in a scenario where there exists significant overlapbetween stars that are of quite different brightness. For instance,the detection algorithm may not be able to detect a faint and brightstar very close together in the first iteration, but they will bedetected in the next iteration after the brighter stars have been fitand subtracted. Like BasicPSFPhotometry, it does notinclude implementations of the stages of this process, but it providesthe structure in which those stages run.

DAOPhotPSFPhotometry is a special case ofIterativelySubtractedPSFPhotometry. UnlikeIterativelySubtractedPSFPhotometry andBasicPSFPhotometry, the class includes specificimplementations of the stages of the photometric measurements, tuned toreproduce the algorithms used for the DAOPHOT code. Specifically, thefinder, group_maker, bkg_estimator attributes are set tothe DAOStarFinder, DAOGroup,and MMMBackground, respectively. Therefore,users need to input the parameters of those classes to set up aDAOPhotPSFPhotometry object, rather than providingobjects to do these stages (which is what the other classes require).

Those classes and all the classes they use for the steps in thephotometry process can always be replaced by user-supplied functionsif you wish to customize any stage of the photometry process. Thismakes the machinery very flexible, while still providing a “batteriesincluded” approach with a default implementation that’s suitable formany use cases.

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Basic Usage¶

The basic usage of, e.g.,IterativelySubtractedPSFPhotometry is as follows:

Where my_finder, my_group_maker, and my_bkg_estimatormay be any suitable class or callable function. This approach allowsone to customize every part of the photometry process provided thattheir input/output are compatible with the input/ouput expected byIterativelySubtractedPSFPhotometry. photutils.psfprovides all the necessary classes to reproduce the DAOPHOT algorithm,but any individual part of that algorithm can be swapped for auser-defined function. See the API documentation for precise details onwhat these classes or functions should look like.

Performing PSF Photometry¶

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

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

(Source code, png, hires.png, pdf, svg)

Then let’s import the required classes to set up aIterativelySubtractedPSFPhotometry object:

Let’s then instantiate and use the objects:

Note that the parameters values for the finder class, i.e.,IRAFStarFinder, are completely chosen in anarbitrary manner and optimum values do vary according to the data.

As mentioned before, the way to actually do the photometry is by usingphotometry as a function-like call.

It’s worth noting that image does not need to be backgroundsubtracted. The subtraction is done during the photometry process withthe attribute bkg that was used to set up photometry.

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

(Source code, png, hires.png, pdf, svg)

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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 optimizerwill only consider flux as a variable. To do that, one has to set thefixed attribute for the centroid parameters in psf as True.

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

(Source code, png, hires.png, pdf, svg)

Fitting additional parameters¶

The PSF photometry classes can also be used to fit more model parametersthan just the flux and center positions. While a more realistic use casemight be fitting sky backgrounds, or shape parameters of galaxies, herewe use the sigma parameter in IntegratedGaussianPRFas the simplest possible example of this feature. (For actual PSFphotometry of stars you would not want to do this, because the shapeof the PSF should be set by bright stars or an optical model and heldfixed when fitting.)

First, let us instantiate a PSF model object:

The attribute fixed for the sigma parameter is set to Trueby default, i.e., sigma is not considered during the fittingprocess. Let’s first change this behavior:

In addition, we need to indicate the initial guess which will be used induring the fitting process. By the default, the initial guess is takenas the default value of sigma, but we can change that by doing:

Now, let’s create a simulated image which has a brighter starand one overlapping fainter companion so that the detectionalgorithm won’t be able to identify it, and hence we should useIterativelySubtractedPSFPhotometry to measurethe fainter star as well. Also, note that both of the stars havesigma=2.0.

(Source code, png, hires.png, pdf, svg)

Let’s instantiate the necessary objects in order to use anIterativelySubtractedPSFPhotometry to performphotometry:

Now, let’s use the callable itr_phot_obj to perform photometry:

We can see that sigma_0 (the initial guess for sigma) wasassigned to the value we used when creating the PSF model.

Let’s take a look at the residual image:

(Source code, png, hires.png, pdf, svg)

References¶

Reference/API¶

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

Functions¶

Classes¶

Class Inheritance Diagram¶

Inheritance diagram of photutils.psf.photometry.BasicPSFPhotometry, photutils.psf.matching.windows.CosineBellWindow, photutils.psf.groupstars.DAOGroup, photutils.psf.photometry.DAOPhotPSFPhotometry, photutils.psf.groupstars.DBSCANGroup, photutils.psf.epsf.EPSFBuilder, photutils.psf.epsf.EPSFFitter, photutils.psf.models.EPSFModel, photutils.psf.epsf_stars.EPSFStar, photutils.psf.epsf_stars.EPSFStars, photutils.psf.models.FittableImageModel, photutils.psf.models.GriddedPSFModel, photutils.psf.groupstars.GroupStarsBase, photutils.psf.matching.windows.HanningWindow, photutils.psf.models.IntegratedGaussianPRF, photutils.psf.photometry.IterativelySubtractedPSFPhotometry, photutils.psf.epsf_stars.LinkedEPSFStar, photutils.psf.models.NonNormalizable, photutils.psf.models.PRFAdapter, photutils.psf.matching.windows.SplitCosineBellWindow, photutils.psf.matching.windows.TopHatWindow, photutils.psf.matching.windows.TukeyWindow

photutils.psf.sandbox Module¶

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

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Classes¶

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Class Inheritance Diagram¶

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Inheritance diagram of photutils.psf.sandbox.DiscretePRF, photutils.psf.sandbox.Reproject