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# Flux, uncertainty, FWHM, shape parameters, masked pixels, fit quality.

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# PSF Photometry

Obtained from fitting a predefined PSF form to point-source images.  The quality of the fit can help determine whether a source is indeed a point source, it is exteded, or it is spurious.  PSF photometry is performed on warps by a module called PSFPHOT.  The result of the fit is reported in the Detection table.  Values reported include flux, uncertainty, position, elliptical size, and quality parameters.

## The PSF Model

The PSF model usually takes the form of an analytical function plus residuals.  The fitted parameters and residuals vary with position.

Analytical functions tested include:

• GAUSS : exp (-z)
• PGAUSS : (1 + z + z2/2 + z3/6)-1
• QGAUSS : (1 + kz + z2.25)-1
• RGAUSS : (1 + z + zk)-1
• PS1_V1 : (1 + kz + z1.67)-1

where z is the elliptical contour (akin to a radius squared):

• z = x2/(2σ2xx) + y2/(2σ2yy) + σxyXY

The PS1_V1 model is the current default value for PS1 analysis.

Variability over the image is formally represented as:

• PSF = F[dx,dy;ai(x,y)] + R0[dx,dy] + x Rx[dx,dy] + y Ry[dx,dy]

Existing documentation states that a global linear fit is performed in which the fluxes of all objects is fitted for simultaneously with the following considerations:

• Simultaneous fit of fluxes for all objects in the image
• Chi-square fit:
• χ2 = Σ(fi - Σ (Aj Fj))2 Wi (i : pixels; j : objects)
• Wi – weighting function
• now constant (from mid-2012), was inv variance
• using a constant weight removes a photometric bias found for faint sources
• minimization of Aj requires inversion of large square matrix
• N (number of objects) may be up to 100k
• but, highly diagonal, so inversion is actually fast
• ~ 1 second for 100k objects (unless they grow too large)

Unclear what constrains are placed on PSF parameters (other than flux) during the fitting.

How residuals are recorded and used to determine, e.g., aperture corrections is also unclear.

## Photometric and astrometric parameters from PSF fitting

The Detection table contains the following parameters related to PSF photometry:

 psfFlux Janskys REAL 4 -999 Flux from PSF fit. psfFluxErr Janskys REAL 4 -999 Error on flux from PSF fit. psfMajorFWHM arcsec REAL 4 -999 PSF major axis FWHM. psfMinorFWHM arcsec REAL 4 -999 PSF minor axis FWHM. psfTheta degrees REAL 4 -999 PSF major axis orientation. psfCore dimensionless REAL 4 -999 PSF core parameter k, where F = F0 / (1 + k r^2 + r^3.33). psfQf dimensionless REAL 4 -999 PSF coverage factor. psfQfPerfect dimensionless REAL 4 -999 PSF weighted fraction of pixels totally unmasked. psfChiSq dimensionless REAL 4 -999 Reduced chi squared value of the PSF model fit. psfLikelihood dimensionless REAL 4 -999 Likelihood that this detection is best fit by a PSF.
 xPos raw pixels REAL 4 -999 PSF x center location. yPos raw pixels REAL 4 -999 PSF y center location. xPosErr raw pixels REAL 4 -999 Error in PSF x center location. yPosErr raw pixels REAL 4 -999 Error in PSF y center location.

(must join the tables)

(this is from the PSPS schema browser.  must check that the PV3 version was used.)

Note that psphot actually returns PSF_MAJOR and PSF_MINOR, whose relation to FWHM depends on the value of k for the PS1_V1 profile. For k=0, FWHM=PSF_MAJOR*2*sqrt(2)*pixel_size.

## Details needed and questions

• Is a multi-parameter fit used for each detection, or are the parameters (position, PSF shape) obtained from global fits (for PSF) and detection properties (position)?  ABove notes are not fully sufficient.
• How exactly is the flux error defined?
• How are the flags set?