Noncoherent-object hologram: its reconstruction and optical processing

Encoding a complex-amplitude diffraction pattern on a photographic film by addirtg a suitably chosen coherent reference beam forms a conventional hologram. A hologram of a spatially noncoherent object, referred to as a Γ hologram in this paper, is formed by encoding the complex-valued spatial-coherence function on a square-law detector such as photographic film. This record is made possible by means of a self-refetencing interferometer. Such a record behaves much as a hologram does; it permits reconstruction of the original object by illuminating it with a spatially noncoherent planar source of uniform (constant) intensity. If a conventional coherent-light setup is used with a Γ hologram, the intensity distribution of the reconstruction equals the square of the intensity of the original object. In the research reported in this paper, optical processing of spatially noncoherent objects is accomplished by using and modifying the spatial-coherence function. The Γ hologram is used to gain access to this function. This procedure opens new possibilities of noncoherent-object information processing. Examples of matched filtering, low-pass filtering, and high-pass filtering are discussed. The underlying theory has its roots in the fundamental Van Cittert–Zernike theorem of the theory of partial coherence.