An Algorithm for Precise Aperture Photometry of Critically Sampled Images

TL;DR

This paper introduces a highly precise aperture photometry algorithm for critically sampled images that uses sinc-interpolation and convolution techniques to improve accuracy and computational efficiency across various aperture geometries.

Contribution

The paper presents a novel algorithm combining sinc-interpolation and convolution in the wave-number domain for accurate and fast aperture photometry on critically sampled images.

Findings

Achieves ~10,000x faster computation using wave-number domain convolution.

Works effectively for annular and elliptical apertures.

Provides sample code for implementation.

Abstract

We present an algorithm for performing precise aperture photometry on critically sampled astrophysical images. The method is intended to overcome the small-aperture limitations imposed by point-sampling. Aperture fluxes are numerically integrated over the desired aperture, with sinc-interpolation used to reconstruct values between pixel centers. Direct integration over the aperture is computationally intensive, but the integrals in question are shown to be convolution integrals and can be computed ~10000x faster as products in the wave-number domain. The method works equally well for annular and elliptical apertures and could be adapted for any geometry. A sample of code is provided to demonstrate the method.