Abstract

A joint transform correlator in which the size of the joint transform spectrum (JTS) can be varied by using diverging or converging white light illumination is analyzed. A JTS is formed where the illuminating source is focused. Certain coherence requirements should be met for the joint transform hologram (JTH) to be formed successfully. The separation between the input object to be identified and the reference object should be smaller than the lateral coherence length of the source in the corresponding direction. The number of overlapped spatial frequency spectra (SFS) is proportional to the SFS bandwidth of the object in the direction perpendicular to the grating line over the SF of the grating. Hence, both input and reference objects should lie on a line parallel to the grating line for successful recording of the JTH. In the readout process, white light is dispersed by a pair of gratings to shine on the recorded JTH. Light of different wavelength transmitted by the JTH is Fourier transformed by a lens and is superimposed to give the correlation output. In the experiment with a black-and-white reference object, from the color of the correlation spot we can identify that the object with a specific color is present. For detection of an object with a primary color, the reference object with a primary color can be used. If the reference object is replaced by one harmonic component of the object, the proposed system can readily be extended to rotation-invariant and scale-invariant pattern recognition.

© 1991 Optical Society of America