Volume 52, number 4 OPTICS COMMUNICATIONS 15 December 1984 THE USE OF A REGULAR ARRAY OF APERTURES IN PENUMBRAL IMAGING K.A. NUGENT and B. LUTHER-DAVIES LaserPhysicsLaboratory, The Department of EngineeringPhysics, The Research School of PhysicalSciences, The Australian National University, Canberra, A.C.T. 2601, Australia Received 17 August 1984 Coded aperture imaging using a regular array of apertures is investigated and a simple technique is presented whereby the recorded image may be made to appear as if it were generated by a single aperture but with a much greater collection efficiency. The technique is applied to penumbral imaging, which was the subject of a previous paper, and is shown to give significant improvements. It is also shown that the method will allow tomographic resolution of the source and that this resolution may be enhanced using super-resolution techniques. A significant amount of effort has been expended over the past few years on developing coded aperture imaging (CA/) techniques applicable to laser produced plasmas [1-7]. A prime motivation for this work has been the study of the transport of energy away from the laser focal spot by superthermal electrons. As these electrons are decelerated in the solid target or the plas- ma, high energy bremsstrahlung X-rays are emitted. Unfortunately, this high energy emission is generally too weak to be imaged with high resolution using pin- hole cameras. To overcome this problem CA/tech- niques have been developed that are able to combine large collection apertures with high resolution. This is possible by placing a coding aperture between the object and the film and then decoding the object dis- tribution from the shadow cast at the film plane. The Fresnel zone plate (FZP) [1] and the uniform- ly redundant array (URA) [2] have been the major CAI techniques used in laser-plasma interaction re- search. These two, along with an annular coding aper- ture [3] and a recently proposed off-axis multi slit coding technique [4], are also able to provide 3-D, or tomographic, imaging of the object. This com- pares with other techniques proposed for application to laser-plasmas [5-7] which do not provide tomo- graphic resolution. The purpose of this communication is to show how a regular array of apertures may be treated in such a way as to act as a single aperture as well as to provide 0 030-4018/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) tomographic resolution of the source. This result is combined with the penumbral imaging CA/technique [7] to provide an imaging method with an extremely good tolerance to noise. It will be further pointed out that super-resolution techniques (e.g. refs. [8,9] may be used to enhance the tomographic resolution. Imagine that an object O(x,y) casts a shadow of an aperture with shape A(x,y). Then the shape of the shadow so formed, I(x,y), will be given by I 1 11 y) [-ll -I 1 I(x,y) = A (I~-I-1- ~ X, l~-l ~ _* Ot-~2 x'-~2 Y J ' (1) where l 1 is the object-aperture distance, 12 is the aper- ture-detector distance and * is the convolution opera- tor. Now suppose we have an N X N array of these apertures each separated by a distance a, then the total image cast, T(x,y), will be described by T(x,y) = O(x,y) * A(x,y) * D(x,y), (2) where N[2 N/2 D(x,y) = ~ ~ *(x - na',y - ma'), (3) n=-N]2 m=-N[2 a' = (ll + 12/ll)a andN is even. We have dropped, for the purposes of the argument, the magnification fac- tors in O and A. Therefore T(x,y) may be rewritten as 287