by A. Levin, S. W. Hasinoff, P. Green, F. Durand and W. T. Freeman
Although many types of cameras are invented to extend their depth of field (DoF), none of them optimize the quality of the resulting image or, equivalently, maximize the modulation transfer function (MTF). In this paper, the authors perform a 4D frequency analysis to estimate the maximal frequency spectrums of optical systems.
The key of the analysis lies in the observation of the dimensional gap between the 3D MTF and the 4D ambiguity function that characterizes a camera: the former was a manifold embedded in the latter, called “the focal segments”. To maximize the MTF, therefore, the ambiguity function is desired to uniformly distribute all the energy on these segments. This analysis leads to an upper bound of the MTF.
Unfortunately, most contemporary computational cameras waste energy out of the region. The only exception is the focal sweep camera, but the phase incongruence of its OTF across various focus settings lowers the spectrum magnitude. The authors propose the lattice-focal lens. This lens is composed of a number of sub-squares, each responsible for focusing light rays from a specific depth. This spatial division of aperture also concentrates energy on the focal region, but achieves a much higher spectrum than the focal sweep camera.
The ambiguity function, defined as auto-correlation of the 2D scalar field of an optical system, is a redundant representation. This prohibits the authors from determining the tight upper bound of the frequency spectrum. Still, the proposed analysis sheds much light on this question. Although there is no explicit analysis, it indicates that the key of maximizing MTFs may lie in phase incoherence of the optical system.
The key of the analysis lies in the observation of the dimensional gap between the 3D MTF and the 4D ambiguity function that characterizes a camera: the former was a manifold embedded in the latter, called “the focal segments”. To maximize the MTF, therefore, the ambiguity function is desired to uniformly distribute all the energy on these segments. This analysis leads to an upper bound of the MTF.
Unfortunately, most contemporary computational cameras waste energy out of the region. The only exception is the focal sweep camera, but the phase incongruence of its OTF across various focus settings lowers the spectrum magnitude. The authors propose the lattice-focal lens. This lens is composed of a number of sub-squares, each responsible for focusing light rays from a specific depth. This spatial division of aperture also concentrates energy on the focal region, but achieves a much higher spectrum than the focal sweep camera.
The ambiguity function, defined as auto-correlation of the 2D scalar field of an optical system, is a redundant representation. This prohibits the authors from determining the tight upper bound of the frequency spectrum. Still, the proposed analysis sheds much light on this question. Although there is no explicit analysis, it indicates that the key of maximizing MTFs may lie in phase incoherence of the optical system.
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