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The bilinear transform between the optical apodization functions derived from VanderLugt's filter and Wiener's filter is exploited to provide filters of which a new minimax filter can trade the minimum mean-square distance with the maximum detection spot intensity. Their optical power efficiencies are analytically compared with their estimated error distances. Since a complex two-object cross-correlation product can be replaced by an algebraic sum of the real intensities of three objects, 〈ÕO*〉 + 〈Õ*O〉 = 〈|Õ|2+ 〈|O|2〉 − 〈|Õ − O |2〉, quantitative measurement of the matched filter performance is readily possible. Digital simulation results of Airy patterns are given to illustrate the identity for target detections.
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Harold Szu (1985) studied this question.
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