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Point spread function

Introduction

The point spread function (PSF) (Wikipedia - PSF) represents the spatial probability distribution of reconstructed event positions for a point source. So far we're only considering radially symmetric PSFs here.

Probability distributions

  • dP/dΩ(r), where dP is the probability to find an event in a solid angle dΩ at an offset r from the point source. This is the canonical form we use and the values we store in files.
  • Often, when comparing observered event distributions with a PSF model, the dP/dr2 distributions in equal-width bins in r2 is used. The relation is dΩ = πdr2, i.e. dP/dr2 = (1/π)(dP/dΩ).
  • Sometimes, the distribution dP/dr(r) is used. The relation is dP/dr = 2πrdP/dΩ.

TODO: explain "encircled energy" = "encircled counts" = "cumulative" representation of PSF and define containment fraction and containment radius.

Normalisation

PSFs must be normalised to integrate to total probability 1, i.e.


∫0∞2πrdP/dr(r)dr = 1, wheredP/dr = 2πrdP/dΩ

This implies that the PSF producer is responsible for choosing the Theta range and normalising. I.e. it's OK to choose a theta range that contains only 95% of the PSF, and then the integral will be 0.95.

We recommend everyone store PSFs so that truncation is completely negligible, i.e. the containment should be 99% or better for all of parameter space.

Comments

  • Usually the PSF is derived from Monte Carlo simulations, but in principle it can be estimated from bright point sources (AGN) as well.
  • Tools should assume the PSF is well-sampled and noise-free. I.e. if limited event statistics in the PSF computation is an issue, it is up to the PSF producer to denoise it to an acceptable level.

PSF formats

psf_table/index psf_3gauss/index psf_king/index psf_gtpsf/index