Resolution-equivalent vs. sensitivity-equivalent effective diameter in pinhole collimation: experimental verification

Abstract

To account for photon penetration, the formulas used to calculate the geometric resolution of a pinhole collimator use an effective diameter de rather than the physical diameter of the aperture. The expressions commonly used for de, however, were originally derived to include penetration in sensitivity calculations. To predict the full width at half maximum (FWHM) resolution of the point spread function (PSF) of a pinhole collimator, we have previously proposed simple expressions for a resolution-equivalent effective diameter dre. Unlike those for de, expressions for dre predict both a dependence on the polar angle of the source (thetas) and a non-isotropic PSF. The new theory was tested with a novel setup to measure experimentally the FWHM of the PSF as a function of several geometric parameters always at the same location on the detector, so that its intrinsic response was independent of thetas. Our first results confirm the theoretical predictions that: (a) dre provides the best estimates of the experimental FWHM as a function of thetas and of the direction in the plane of the pinhole; (b) Paix's expression for de tends to overestimate the FWHM; (c) Anger's is a better approximation, but it is still inaccurate and cannot predict the dependence on thetas; and (d) the FWHM decreases with decreasing thetas, i.e. resolution improves for sources at the edge of the field-of-view