An algorithm for precise aperture photometry of critically sampled images

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 centres. Direct integration over the aperture is computationally intensive, but the integrals in question are shown to be convolution integrals and can be computed >= 10 000 times faster as products in the wavenumber 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.