## Abstract

In this paper we use our derived approximate representation of the modulation transfer function to analytically solve the problem of the extension of the depth of field for two cases of interest: *uniform quality* imaging and *task-based* imaging. We derive the optimal result for each case as a function of the problem specifications. We also compare the two different imaging cases and discuss the advantages of using our optimization approach for each case. We also show how the analytical solutions given in this paper can be used as a convenient design tool as opposed to previous lengthy numerical optimizations.

© 2008 Optical Society of America

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