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The insertion of a suitably designed phase plate in the pupil of an imaging system makes it possible to encode the depth dimension of an extended three-dimensional scene by means of an approximately shift-invariant PSF. The so-encoded image can then be deblurred digitally by standard image recovery algorithms to recoup the depth dependent detail of the original scene. A similar strategy can be adopted to compensate for certain monochromatic aberrations of the system. Here we consider two approaches to optimizing the design of the phase plate that are somewhat complementary -one based on Fisher information that attempts to reduce the sensitivity of the phase encoded image to misfocus and the other based on a minimax formulation of the sum of singular values of the system blurring matrix that attempts to maximize the resolution in the final image. Comparisons of these two optimization approaches are discussed. Our preliminary demonstration of the use of such pupil-phase engineering to successfully control system aberrations, particularly spherical aberration, is also presented.

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An examination of recent trends in imaging reveals a movement toward systems that balance processing between optics and electronics. Imaging applications include conventional imaging to produce visually pleasing images, special purpose imaging whose output is also an image but with enhanced characteristics, and functional imaging to produce information about a scene from optical data. We identify three approaches to computational imaging that are capable of achieving these goals: wavefront encoding, multiplex imaging, and feature extraction.