PSF Measurement Improvements


The point-spread function (PSF) measurement tasks imexamine, psfmeasure, starfocus, and kpnofocus have been modified to include a Moffat profile model. The profile has the functional form:

	I(r)/I(0) = (1 + (r/alpha)^2)^(-beta)
where I is the profile intensity, r is the radius from the profile center, alpha and beta are profile parameters, and ^ is the exponentiation operator. The new profile fitting allows fixing beta at a specified value or having it be determined simultaneously with alpha.

In imexamine there are three new parameters in the rimexam parameter set; fittype, beta, and iterations. These may be set in the parameter set or changed interactively with colon commands. The fittype parameter may be "moffat" (the new default) or "gaussian". The beta parameter may be a fixed value or INDEF (the default) to have the parameter be fit. The iterations parameter allows the fitting radius to be adjusted based on the result of the previous fit if the value is greater than one. This makes the fitting slower but the results are more independent of the initial fitting radius.

The changes to imexamine apply to the 'a' and 'r' keys. The output from the 'a' key and when logging is turned on has labels that identify the type of profile and the measured quantities. The 'r' key prints the same quantities without the labels. One change in the output is that the moment full-width at half maximum (FWHM) is no longer output. The output for the Moffat profile includes the beta parameter. An example of fitting a Moffat profile with beta free is below.

Example of Moffat Fit with IMEXAMINE

# [1] obj2601 - Leo II uBVI 1996 Mar 12-13
#   COL    LINE                                      --------- FWHM ---------
#    R    MAG    FLUX     SKY    PEAK    E   PA BETA ENCLOSED   MOFFAT DIRECT
 965.75 1122.55
 13.46  17.84  73334.    327.   2359. 0.04  -13 2.68     4.45     4.54   4.49
The same star measured using a Gaussian profile is shown next.

Example of Gaussian Fit with IMEXAMINE

#   COL    LINE                                      --------- FWHM ---------
#    R    MAG    FLUX     SKY    PEAK    E   PA      ENCLOSED GAUSSIAN DIRECT
 965.75 1122.55
 13.46  17.84  73334.    327.   2321. 0.04  -13          5.30     4.69   4.49

In the output also notice that the first column is now the radius used in deriving the measurements. This radius is now determined iteratively using preceding estimates of the direct FWHM (as defined below). In the examples above the initial radius was 5 pixels but using 3 iterations gave a final radius of 13.46 pixels.

The PSF measuring tasks previously had two types of size measurements, the radius enclosing a specified fraction of the flux and the FWHM of a Gaussian profile that has the same enclosed flux radius at the specified fraction of the flux. The latter measurement is model dependent. In the revised tasks the radius measurement is still available along with three new FWHM estimates. One is the FWHM of the Gaussian which best fits the enclosed flux profile. Note that this is different than the previous Gaussian FWHM in that it is a fit rather than the profile that matches the enclosed flux at just one point. The second new estimate is the FWHM of the Moffat profile which best fits the enclosed flux profile. The last estimate is the direct FWHM determined from half-flux radius of the radial profile. In this case the radial profile is computed as the derivative of the enclosed flux profile so it is azimuthally average and sampled finely and smoothly in radius unlike using the pixel values directly.

The FWHM of the profile fit to the enclosed flux profile is also what is reported in the ENCLOSED column of the imexamine output above for the appropriate model. Similarly the imexamine DIRECT column is the direct FWHM using the radial profile derived from the enclosed flux profile.

The four possible size estimates that may be reported by the PSF tools is set with the size having values of "Radius", "FWHM", "GFWHM", "MFWHM" for the enclosed flux radius, the direct FWHM, the Gaussian fit, and the Moffat fit. The default is now the direct FWHM. As with imexamine a new beta parameter has been added to allow fixing or determining the value in the profile fitting.

An example of measuring the same star as above using psfmeasure is shown below. The figure shows the enclosed flux profile with a Moffat profile fit, the derived radial profile with the Moffat profile fit, and Moffat profile FWHM that yeilds the same enclosed flux at each fraction of the enclosed flux. The last plot indicates departures from the model profile such that if the enclosed flux came from the profile it would be constant at all fraction values.

PSFMEASURE Example

NOAO/IRAF V2.11DEVELOP valdes@puppis Fri 11:41:45 05-Apr-96

          Image  Column    Line     Mag    FWHM   Ellip      PA SAT
        obj2601  965.75 1122.55    0.00   4.488    0.04     -11

  Full width at half maximum (FWHM) of 4.4882

The changes have been made to the nmisc external package available in the IRAF ftp archive (get nmisc.tar.Z and nmisc.readme). The new imexamine is called newimexamine in the nmisc package to avoid conflicts with the distributed version.


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Last updated: 5April1996