is the radial distance of the nth subaperture from the origin of the system and is expressed in terms of multiples of the subaperture radius and u and v are the coordinate in the image plane the expression for h u v is the impulse response which is proportional to the fourier transform of the transmittance of the exit pupil of the multiple aperture system the exit pupil can be expressed as the convolution of one aperture with an array of delta functions which describe the location of the centers of each aperture the subapertures which are contained within each multi aperture are identical equation 1 is a generalized expression for the impulse response of any multi aperture system which contains identical circular subapertures this equation may be used to form a subset of equations which describe the impulse responses of multiple rings of identical circular subapertures in identifying an expression for the generalized subaperture radii for any system of multi apertures arranged in concentric rings to just fit inside a single large aperture of radius a ref the radius of each subaperture comprising the concentric ring multi aperture system may be described as equ2 where rings number of rings which comprise the multi aperture system a ref 1 2 the diameter 112 in fig1 the radial distance from the origin to the circle on which the centers of the subapertures of.