Lloyd's Mirror As An Optical Processor

This paper describes the use of Lloyd's mirror in two optical processing applications. First it is shown that if the narrow slit in the usual Lloyd's mirror set up is illuminated by polychromatic light, the interference pattern is the Fourier Cosine transform of the spectral intensity distribution of the light. Lloyd's mirror may thus be used as the transforming element in a Fourier transform spectrometer of exceedingly simple and rugged design. An experimental realization of this process is displayed. Second it is shown that if the narrow slit in the Lloyd's mirror set up is replaced by a wide slit or, more generally, by a one dimensional object illuminated by non-coherent monochromatic light, the interference pattern obtained is the Fourier transform of the intensity distribution of the object. Lloyd's mirror may thus be used to produce Fourier holograms in non-coherent light of one dimensional objects. An experimental realization of this process is displayed. If the object is two dimensional the interference pattern is the Fourier transform of the intensity distribution of the object along one direction. If the transform of the object is obtained in several orientations of the object, the object may be recovered by the same process used in CAT SCAN.