Temporally and Spatially Incoherent Methods for Fourier Transform Holography and Optical Information Processing.

This thesis describes the development, analysis, and verification of techniques for constructing Fourier transform holograms in light of reduced coherence. The techniques developed are coherent in the sense that they preserve linearity in the complex amplitude associated with the object. Two complementary techniques are developed; one for use in temporally broadb and , spatially coherent illumination, and the other for use in quasi-monochromatic, spatially incoherent illumination. For the case of temporally broadb and illumination, methods of (partially) achromatizing Fourier and Fresnel transformations are developed using an approach based upon linear filter theory. This approach is shown to be quite useful in that it readily accommodates the introduction of a reference beam, physically explains the achromatization phenomena, and allows easy quantitative assessment of the achromatized transform system. A dispersion compensated reference beam is introduced by incorporating the achromatic transforming system into an achromatic grating interferometer. The resulting system is analyzed using the methods of Fourier optics. It is demonstrated that the achromatization of the Fourier transform is unaffected by the introduction of the reference beam. Experimental verification is provided by the construction of a Fourier transform hologram in polychromatic, spatially coherent light. For the spatially incoherent case, a technique based upon the concept of interferometric imaging is developed for holographically recording the Fourier transform of a complex object distribution within one beam of a grating interferometer. A paraxial Fourier optics analysis of the technique is performed and it is subsequently modeled as a superposition of four grating interferometers. It is shown with the aid of the superposition model that the underlying physical mechanism responsible for the Fourier transformation process is equivalent to interferometric imaging of the spatially incoherent source. It is also demonstrated that the overall technique is not the spatial domain counterpart to achromatization, but rather a method which utilizes, and improves with, decreased spatial coherence. Experiments to demonstrate the imaging capability of the technique and its functional equivalence to conventional coherent holography are described in detail.PhDOpticsUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/159525/1/8324158.pd