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# PSF Photometry

## The PSF Model

## Photometric and astrometric parameters from PSF fitting

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PSF photometry is one of the major ways to measure the flux of sources (= detections) in PanSTARRS1 data. It is based on fitting a predefined a= nalytical shape to the counts reported for each detection, and then applyin= g a zero point conversion to the total object count rate thus obtained.

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The starting point for the PS1 data archive is at Pan-STARRS1 data archive h= ome page.

Obtained from fitting a predefined PSF form to all detections. The quali= ty of the fit can help determine whether a source is indeed a point source,= it is extended, or it is spurious. PSF photometry is performed on wa= rps by a module called PSFPHOT and on stacks by PSPHOTSTACK. The result of = the fit is reported in the Detection table (or StackDetection table for sta= cks). Values reported include flux, uncertainty, position, elliptical= size, and quality parameters.

The PSF model takes the form of an analytical function plus residuals.&n= bsp; The fitted parameters and residuals vary with position, but are actual= ly determined at 9 positions (in a regular 3x3 grid pattern) per skycell th= en interpolated to other positions.

Analytical functions tested include:

- GAUSS : exp (-z)
- PGAUSS : (1 + z + z
^{2}/2 + z^{3}/6)^{-1}<= /li> - 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 =3D x
^{2}/(2=CF=83^{2}_{xx}) + y^{2}/= (2=CF=83^{2}_{yy}) + =CF=83_{xy}XY

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

Variability over the image is formally represented as:

- PSF =3D 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 w= hich the fluxes of all objects is fitted for simultaneously with the follow= ing considerations:

- Simultaneous fit of fluxes for all objects in the image
- Chi-square fit:
- =CF=87
^{2}=3D =CE=A3(f_{i}- =CE=A3 (A_{j}F~~j))~~^{2}W_{i}(i : pixels; j : objects)<= /li> - W
_{i}=E2=80=93 weighting function- now constant (from mid-2012), was inv variance
- using a constant weight removes a photometric bias found for faint sour= ces

- =CF=87
- 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)

The **PS=
1 Detection table fields** table contains the following paramete=
rs related to PSF photometry:

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. |

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 =3D 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.<= /td> |

psfLikelihood |
dimensionless | REAL | 4 | -999 | Likelihood that this detection is best fit by a = PSF. |

The equivalent stack measurements are to be found in **PS1 StackObjectA=
ttributes table fields**.

Note that psphot actually returns PSF_MAJOR and PSF_MINOR, whose relatio= n to FWHM depends on the value of k (reported as psfCore) for the PS1_V1 pr= ofile. For k=3D0, FWHM=3DPSF_MAJOR*2*sqrt(2)*pixel_size.

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