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Galilean invariance in Fourier optics

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Abstract

The invariance of amplitude distribution due to a converging wave front under Galilean transformation is found to lead to shift invariance of amplitude distribution. It is also established that an aberration-free off-axis converging spherical wave satisfies the Fokker-Planck equation, which reduces to the Bloch equation in the image plane. The effect of a small defocus is to reproduce periodically the image-plane amplitude distribution. Finally, the amplitude distribution and the ambiguity function of the amplitude distribution are the same in the image plane.

© 1985 Optical Society of America

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