Increasing mid-frequency contrast in sparse aperture optical imaging systems

Abstract

Sparse aperture imaging systems are capable of producing high resolution images while maintaining an overall light collection area that is small with respect to a fully filled aperture yielding the same resolution. However, conventional sparse aperture systems pay the penalty of reduced contrast at mid-band spatial frequencies. The modulation transfer function (MTF), or normalized autocorrelation, provides a quantative measure of both the resolution and contrast of an optical imaging system. Numerical MTF calculations were thus used to examine mid-band contrast recovery through the systematic increase of autocorrelation redundancy in a Golay-9 sparse array. In a Golay-9 sparse aperture arrangement, three sets of three sub-apertures can be shown to lie at unique radii from the center of the array. In order to increase the mid-frequency contrast we then have two options. The first, and most influential, is to increase the size of the sub-apertures located at the intermediate radius from the array origin. This directly increases autocorrelation redundancy at mid-band frequencies. The second option, though less effective, is to increase the relative mid-band frequency response by attenuating the outer most sub-apertures. We will demonstrate that by increasing the diameters of the mid-radii sub-apertures, mid-band contrast can be increased by over 45%, compared to uniform sub-aperture diameter arrays. We will also demonstrate that attenuating the outer most sub-apertures can further increase mid-band contrast recovery, but only by less than 1%. The effects on array fill factor will also be discussed.