Abstract

In an earlier paper¹ we described an incoherent optoelectronic Fourier transformation scheme based on reduction of dimensionality via the projection-slice theorem. The scheme offers high sensitivity and speed, wide dynamic range (because of a novel method for eliminating the dynamic-bias problem that plagues most incoherent optoelectronic processing schemes), and an ability to perform Fourier transformation of real scenes (hence the name Fourier camera) or of 2-D complex functions through color coding. The scheme lends itself readily to trade-off between the degrees of serial and parallel processing that may be utilized to tailor throughput and cost to the constraints of specific applications. In this paper we will review the concept of Fourier camera emphasizing the case of a natural (positive real) object scene. It is shown that for this class of objects the throughput of the camera can be doubled and that it performs the Fourier analysis of a scene in a manner similar to that suggested by Fourier models of human vision.² With certain modifications in architecture, which we describe, the camera can also provide multispectral Fourier analysis of a scene. The connection between this capability and the measurement of the cross-power spectral density $w\left({\overline{r}}_1,{\overline{r}}_2,\upsilon \right)$ is also discussed together with its usefulness in the design of associated automated recognition and classification systems. The above features make the Fourier camera a valuable tool in the study and imitation of human vision and machine vision. Preliminary results obtained with an optical bench implementation of the Fourier camera concept using several elementary test objects are presented. These are shown to be in good agreement with the results of numerical simulations.

© 1985 Optical Society of America