Contents

# 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 + z
^{2}/2 + z^{3}/6)^{-1} - QGAUSS : (1 + kz + z
^{2.25})^{-1} - RGAUSS : (1 + z + z
^{k})^{-1} - PS1_V1 : (1 + kz + z
^{1.67})^{-1}

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

- z = x
^{2}/(2σ^{2}_{xx}) + y^{2}/(2σ^{2}_{yy}) + σ_{xy}XY

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:
- χ
^{2}= Σ(f_{i}- Σ (A_{j}F_{j)})^{2}W_{i}(i : pixels; j : objects) - W
_{i}– weighting function- now constant (from mid-2012), was inv variance
- using a constant weight removes a photometric bias found for faint sources

- χ
- minimization of A
_{j}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)

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?

## Papers explored:

http://adsabs.harvard.edu/abs/2007ASPC..364..153M

http://adsabs.harvard.edu/abs/2012ApJ...756..158S

http://adsabs.harvard.edu/abs/2012ApJ...750...99T

All these papers provide good information on the calibration process - correction for airmass, reduction to a standard magnitude system, other instrumental effects, etc - but none describe explicitly (or even implicitly) how the *flux* itself is determined. There must be such a paper, but I have not found it.