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In this paper, we present a novel computational imaging system using a dual off-axis color filtered aperture (DCA) for distance estimation in a single-camera framework. The DCA consists of two off-axis apertures that are covered by red and cyan color filters. The two apertures generate misaligned color channels in which the amount of misalignment of points in the image plane are a function of the distance from the camera of the corresponding points in the object plane. The primary contribution of this paper is the derivation of a mathematical model of the relationship between the color shifting values and distance of an object from the camera when the camera parameters and the baseline distance between the two apertures in the DCA are given. The proposed computational imaging system can be implemented simply by inserting an appropriately sized DCA into any general optical system. Experimental results show that the DCA camera is able to estimate the distances of objects within a single-camera framework. (C) 2013 Optical Society of America

We consider the problem of reconstructing either a one-dimensional or a two-dimensional signal from its Fourier intensity and the Fourier intensity of another signal that is related to the first by the addition of a known reference signal. Several theorems are given that give conditions under which a unique reconstruction is possible, and a recursive algorithm is provided that allows for the reconstruction of the signal from the pair of Fourier intensities.

The phase-retrieval problem for discrete multidimensional fields is investigated. In particular, a recursive procedure is developed for reconstructing a signal from the modulus of its Fourier transform. The information necessary to begin the recursion is the boundary values of the signal. Although it is not always possible to determine these boundary values from Fourier modulus data only, if the sequence has a region of support with a certain geometry then these boundary values can be determined. These geometries represent a generalization of the conditions for off-axis holography.

Deconvolution is an important problem in many branches of physics and engineering, and many different algorithms have been considered for deconvolving two signals. Iterative algorithms based on the method of successive approximations have become popular for signal deconvolution because of the flexibility that they allow for the incorporation of signal constraints into the restoration. One of the limitations with these iterative algorithms, however, is that they achieve only a linear rate of convergence. In this paper an accelerated iterative deconvolution algorithm is presented that is based on the idea of updating the observation equation after each iteration. With this approach it is shown that the modified iterative algorithm achieves a quadratic rate of convergence. Although with this new algorithm there is a significant increase in the convergence rate, the incorporation of signal constraints into the iteration is more difficult than with the algorithms based on the method of successive approximation.