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

It¡¦s not easy to keep photographs clean in every day. A photograph is liable to be polluted by accumulating defects such as dusts, which can degrade the imaging quality. In the thesis, a method of image restoration is proposed for image polluted by multiplicative transmittance noise. The method is based on estimating the approximate autocorrelation function of the unpolluted image. This autocorrelation function is obtained by analyzing the relationship among the autocorrelation function for polluted image, unpolluted image and noise. Further more, the noisy image is restored by the property of the autocorrelation function. A polluted photograph in imaging system is modeled by a thin random screen against the original image. In this model, defects are Poisson-distribution and may be overlapped. Since transmittance effect of each defect is multiplicative, the transmittance of random screen is computed as a product of Poisson-distribution-centered random function. Then, the statistical autocorrelation function of random screen is accordingly computed. More specifically, we should rearrange image data as periodic signal to avoid insufficient data in computing the process autocorrelation function. The simulated polluted image is restored by the amplitude information from the estimated autocorrelation function of the original image. Simulating results is demonstrated that the RMS of the restored image computed with the polluted image is improved.