Abstract

Rotation-invariant filtering at low light levels is investigated. Low-light-level input scenes are cross correlated with a complex circular-harmonic component of a reference image stored in computer memory. Approximate expressions are given for the probability-density function of the correlation signal and for the squared modulus of the correlation signal when the number of detected photoevents is Poisson distributed as well as when the number of detected photoevents is fixed. Experimental measurements of the squared modulus of the correlation signal, obtained by using a two-dimensional, photon-counting detector and position-computing electronics, are found to be invariant with respect to rotation of the input image. In addition, when the reference object is input, its orientation can be determined from the real and imaginary parts of the correlation signal. Good discrimination between the reference image and other test images is observed, and the experimental results are in excellent agreement with theoretical predictions.

© 1986 Optical Society of America

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