PNP - A New Class of Coded Aperture Arrays

Fast decoding algorithms for coded aperture systems

“…Because the technique is now available to the square MURAs [9], a subset of which has been shown to be antisymmetric on 901 rotation [11], fast decoding is now available if an antisymmetric aperture is desired. Also, because the technique applies to the self-supporting PNP, M-P or M-M apertures, it is possible to use fast decoding while enjoying the benefits of these self-supporting apertures, such as rigidity of structure [12] or active collimation [32]. Note also that these latter systems possess a much greater range of eccentricity of rectangular pattern than that available to the almost square URAs.…”

“…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.…”

“…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 .…”

“…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].…”