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Lenses in an optical imaging system are liable to defection such as pollution and thus deteriorates the imaging quality. To study the effects on imaging quality, the polluted lens can be verified equivalent to a polluted random screen set against a normal lens. In our model, the defects on random screen are assumed Poisson -distributed and can be overlapped with a random size and trans- mittance. The effect of transmittance for every individual defect is multiplicative, then, the transmittance of the random screen is computed as a product of Poisson-distributed-centered random function. This effect is named as transmittance noise that was first introduced by Chow. To compare with other models of related research, our model is more reasonable and practical. We compute not only the average optical transfer function (OTF) but the variance of the OTF for imaging system. The variance of the OTF is computed for quality analysis or restoration method designs, for the variance of the OTF is importance in image rest- oration if it is significant in value. Therefore, the variance at least stands as an indicator for determining the image restorati- on method. The computation of this statistics involves a prohibi- tive fourfold integral computation. By the help of analytic geom- etry, we simplify the fourfold integration to double integration. Thus, the computation for the variance of the OTF is a first att- empt in related researches. We simulate a polluted optical imaging system in computer to perform the experiments and check with our computed result from theory. Finally, the distorted image is restored by two techniq- ues that are designed by mean of the average OTF and the variance of the OTF.
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