Cosinusoidal transforms in white light

Abstract

Theory and techniques of white light interferometry have been studied to devise an optoelectronic hybrid for diffraction pattern sampling. For an incoherently illuminated input scene, we obtain an output intensity that is the 2-D spatial cosine transform of the input plus a bias term. The bias can be subtracted electronically to within shot noise fluctuation limitations. The optical system consists of a double-imaging interferometer with a beam-splitter cube and crossed right-angle-prism reflectors followed by an achromatic-optical-transform lens pair. A photodiode array is placed in the optical transform plane, and this is coupled to a digital computer for further signal processing. Theoretical results are presented for the synthesis of the cosinusoidal transform configuration. From Fresnel-zone theory, a general form is derived for the impulse response of a cascade of ideal thin lenses, and this is used to design Fourier transform achromats that are well suited to this application. Experiments are presented showing cosine transforms for rough objects and for objects in reflection using illumination of negligible spatial coherence at the object. Excellent sensitivity is obtained with the bias subtraction, and a high space–bandwidth product is attained for the system.