Synthesis of binary arrays with perfect correlation properties — coded aperture imaging

Fast decoding algorithms for coded aperture systems

“…During the induction method of the main optimisation algorithm in Section 4.1, consider a point in the induction given by Eq. (14). Using this equation we can write…”

“…In many cases, a coded aperture system based on a rectangular geometry is defined by a unit pattern of size v  w elements [3,9,14]. Exposure to the source typically generates a detector shadowgram, Pði; jÞ, where 0 ri r v À 1 and 0 r jr w À 1.…”

“…The product apertures are synthesised using the products of single coded aperture systems, called primitive systems [14]. The PNP [12], M-P and M-M [13] apertures are all subsets of the product apertures.…”

“…Firstly we study the square MURA configurations [9], of which a subset is antisymmetric on 901 rotation [11]. Secondly we analyse those configurations described by the author that are created from products of individual onedimensional coded aperture systems [14]. For ease of discussion, we refer to these as product apertures.…”

“…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].…”