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 d_e rather than the physical diameter of the aperture. The expressions commonly used for d_e, 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 d_re. Unlike those for d_e, expressions for d_re 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) d_re 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 d_e 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