Optical Transforms in White Light

An optoelectronic hybrid has been developed for implementation of optical transforms in natural light. Specifically, a two-dimensional cosine, sine, or Hartley transform plus a bias term is obtained interferometrically from an intensity -distributed object under spatially incoherent broadband illumination. The bias term can be subtracted electronically within shot noise fluctuation limitations. The hybrid system consists of a double-imaging interferometer with a beam splitter and crossed right-angle-prism reflectors, an achromatic transform lens pair, a 2-D CCD array and a digital computer. A close relationship has been shown between the system-possessed space-bandwidth product and the spatial and temporal coherence of illumination. Theoretical investigations are presented, showing the capabilities and limitations of the system. Requirements on both spatial and temporal aspects are derived, which enable our designing of the optical system for a diffraction-limited performance. Experiments are presented showing optical transforms of 2-D and 3-D objects. Excellent sensitivity is obtained with the bias subtraction, and a high space-bandwidth product is in a good agreement with theoretical predictions. Applications of cosinusoidal transforms for correlation experiments and image reconstructions are also demonstrated.