On self-supporting coded aperture arrays

Sensitivity of coded mask telescopes

“…Discussion of the choice of algorithm for placing the holes has concentrated on designs in which the (cyclic) autocorrelation function of the pattern, sampled at shifts corresponding to a whole number of cells of the grid, is bivalued with a central peak and flat wings. An extensive literature [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] exists on arrays which have this property, which are usually termed 'Uniformly Redundant Arrays' (URAs). For URA-based masks, in certain well defined circumstances, cross-correlation of the recorded data with an array which corresponds to the mask pattern (with a scaling and offset applied) leads to images with a point source response function (PSF) having a central peak and perfectly flat side-lobes.…”

Fast decoding algorithms for coded aperture systems

“…We demonstrate the methods of the previous sections by considering the specific cases of the PNP [12], M-P and M-M [13] apertures. These will occur when n ¼2 with the orders of the two primitive systems being p 1 and p 2 .…”

“…The PNP [12], M-P and M-M [13] apertures are all subsets of the product apertures. Although some primitive systems can have orders that are non-prime (for example a PN sequence can be of order 63), because of the methods used, we are concerned here with primitive systems that have prime orders.…”

“…Early examples of perfect apertures are the uniformly redundant arrays (URAs) [3] and the modified uniformly redundant arrays (MURAs) [9]. Discoveries of other perfect apertures were motivated by the desire to tackle certain problems, such as having antisymmetric apertures [10,11], selfsupporting apertures [12,13] and apertures with low throughput [14,15]. Although perfect apertures are often seen as desirable, it should be noted that in a practical context other effects such as imperfections in the detector, variations in detector efficiencies and various mechanical constraints, such as artifacts in the shadowgram caused by the grid structure used to support the aperture elements, can dominate noise created by using imperfect apertures [16].…”

“…For ease of discussion, we refer to these as product apertures. The product apertures have low throughput and are all fully self-supporting, special cases of which are the pseudo noise product (PNP) arrays [12] and the M-P and M-M arrays [13].…”