Kalman filter addresses an estimation problem defined by two models: the signal model and the observation model. In this thesis, the signal model is obtained from a ratio of the defected and clean pictures in frequency domain. The observation model is built for an additive measurement noise from electronic sampling. The statistics of the generating noise for the signal model is important in Kalman filtering. The focus of this thesis is to derive the variance of the generating noise in the middle band for the signal model. By this derived variance, the Kalman filter is thus possible to be applied to estimate the optical transfer function for a defected imaging system in the future.

The lenses are important elements in optical imaging systems. However, lenses are liable to defects such as dusts and thus deteriorate their imaging quality. These kinds of imaging systems are investigated in this thesis .The polluted lens can be verified equivalent to a polluted random screen set against a clean lens .In our model ,the defects on random screen are assumed poisson-distribution ,overlapped and the transmittance effect of each defect is multiplicative .The autocorrelation function of screen is obtained by defects' density ,radius ,and transmittance. The evaluation of the optical transfer function for this imaging system can be achieved by the autocorrelation of the above random screen. This thesis includes computer simulation, experiments and comparison with other model and restoration method. The experiments are set up by the instruments including the video camera , capture card ,and personal computer. We may estimate the key parameters of our theoretical autocorrelation function by the real optical transfer function obtained from experiment. Accordingly, two methods are applied to image restoration in this thesis. One is to use the theoretical autocorrelation, the other is to use a second-order statistics of optical transfer function. The computation of second-order statistics involves a fourfold integration .By the help of changing variables and geometric analysis, we simplify the fourfold integration to double integration. Both of our methods are better for image restoration in RMS value than the method proposed by Tamas Daboczi

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Quadratic pupils representing Gaussian apodization and defocus are expanded into Zernike polynomials. Combinations of the pupil expansion coefficients are used, in turn to expand the Optical Transfer Function into a novel set of basis functions.

We derive the expression for the three-dimensional incoherent optical transfer function when third-order spherical aberration is present. The normalized version of the transfer function is numerically calculated for various amounts of spherical aberration. We find the effects of the aberration to be highly dependent on the spatial frequency in the longitudinal direction. We also calculate a structure content parameter, as a quality criterion, from the normalized transfer function. Remarkably, the structure content parameter dependence on spherical aberration is well-fit by a simple Cauchy curve for aberrations out to two waves at the margin.

The lenses are important elements in optical imaging systems. However, lenses are liable to defects such as dusts and thus deteriorate their imaging quality. The polluted lens can be verified equivalent to a polluted random screen set against a clean lens. In our model, the defects on random screen are assumed poison-distribution, overlapped and the transmittance effect of each defect is multiplicative. In this thesis, we will apply Kalman filter to estimate the optical transfer function for a defected imaging system. The experiments are set up by the instruments including the video camera, capture card, and personal computer. Kalman filter addresses an estimation problem defined by two models: the signal model and the observation model. Kalman filter was originally developed in the field of optimal estimation for application of controlling and tracking. Recently Kalman filter has been very often applied to the problems of image restoration. In this thesis, the signal model is obtained from a ratio of the defected and clean pictures in frequency domain. The observation model is built for an additive measurement noise from electronic sampling. Experimental results have demonstrated that the estimated optical transfer function is useful for image restoration.

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Thesis (M.S.)--Rochester Institute of Technology, 1989. / Includes bibliographical references (leaves 102-103).