Classical signal detection theory and reconstruction problems in holographic imaging systems

A new "circuit" model is developed to study non-linear effects in holography. The model links classical signal detection theory to holography, for it clearly shows that the reconstructed images in a thin hologram can be computed from mathematical formulas obtained for the output of non-linear detectors. In preparation for hologram analysis, the results for the (time-) autocorrelation of electrical ʋth-law devices in response to signal plus noise are extended to memoryless non-linear detectors with arbitrary characteristics. Mathematical parallels are next established between holography and the non-linear detection of signals, and these are incorporated in the model. The ready-made formulas for electrical detectors apply directly to give formulas for the (space-)autocorrelation of holograms of diffuse objects. The autocorrelation function predicts distorted multi-pie images, their relative positions, orientations, widths, and strengths. The multiplicity of images is due to the generation of harmonics; the background halo-like noise components added to the faithful images are mainly due to the multiplicity of the first harmonic itself. The analysis is further expanded to include a still more general case in which the reflected light from the object is depolarized. A decrease in signal-to-noise ratio (decrease in fringe visibility); a loss of information, and an augmentation of non-linear distortion could be expected. A simple way of reducing these effects is suggested. Finally, holography with more than one reference beam is studied. An exact formulation is given for double-reference-beam holograms. For multiple-reference-beam holograms, only approximate closed forms are presented. It is shown that the addition of extra reference beams during the recording step of the hologram may amplify the faithful images without increasing their background noise significantly. Experiments confirm the theoretical expectations.Applied Science, Faculty ofElectrical and Computer Engineering, Department ofGraduat