Several phase-modulation functions have been reported to decrease the aberration variance of the modulation-transfer-function (MTF) in aberration-tolerant hybrid imaging systems. The choice of this phase-modulation function is crucial for optimization of the overall system performance. To prevent a significant loss in signal-to-noise ratio, it is common to enforce restorability constraints on the MTF, requiring trade of aberration-tolerance and noise-gain. Instead of optimizing specific MTF characteristics, we directly minimize the expected imaging-error of the joint design. This method is used to compare commonly used phase-modulation functions: the antisymmetric generalized cubic polynomial and fourth-degree rotational symmetric phase-modulation. The analysis shows how optimal imaging performance is obtained using moderate phase-modulation, and more importantly, the relative merits of the above functions.

Foveated imaging, such as that evolved by biological systems to provide high angular resolution with a reduced space-bandwidth product, also offers advantages for manmade task-specific imaging. Foveated imaging systems using exclusively optical distortion are complex, bulky, and high cost, however. We demonstrate foveated imaging using a planar array of identical cameras combined with a prism array and superresolution reconstruction of a mosaicked image with a foveal variation in angular resolution of 5.9:1 and a quadrupling of the field of view. The combination of low-cost, mass-produced cameras and optics with computational image recovery offers enhanced capability of achieving large foveal ratios from compact, low-cost imaging systems. Conventional approaches to imaging typically aim for an approximately uniform spatial sampling frequency across the field of view, but for many applications, such as targeting, the salient requirement is for high-resolution imaging within a central, so-called foveal region of the image combined with a lowresolution periphery providing situational awareness and context. Foveated imaging offers more efficient use of a limited number of detector pixels or can be implemented as an image processing technique applied to conventional images to improve the efficiency of information transmission. Here our emphasis is to attain a large ratio between the spatial sampling frequency and image acuity for the central field of view (FOV) and a reduced sampling frequency at larger field angles. This mimics biological systems, such as the human visual system, where foveated imaging is associated with a variation in photoreceptor packing density that approximately mirrors the angular variation in the optical resolution of the eye.Imaging systems with a variation in magnification of up to a factor of 2 between a central FOV and the periphery (the foveal ratio) have been demonstrated using conventional optical approaches, but higher ratios require dramatic increases in optical complexity. Higher foveal ratios are attractive for a wide range of applications [1][2][3][4][5][6], and previous approaches include the use of multiresolution systems using single [1] or multiple sensors [2][3][4] and applications in microscopy [5,6]. In this Letter we report an experimental demonstration of computational construction of a foveated image using a multicamera array. Two mechanisms contribute to the high foveal ratio of 5.9:1 between the angular sampling frequency in the foveal and peripheral regions of the image: image distortion introduced by an array of prisms located in front of the camera array introduces nonuniform angular sampling by the sensor, and overlap of the field of regard of the cameras at the central FOV enables digital superresolution to increase the angular sampling rate at foveal regions. The use of mass-produced cameras and simple prisms enables high-performance foveated imaging at minimal cost.A 5 × 5 multicamera array is assembled on a single printed circuit board, with the relatively low ...

Received Month X, XXXX; revised Month X, XXXX; accepted Month X, XXXX; posted Month X, XXXX (Doc. ID XXXXX); published Month X, XXXX Previous reports have demonstrated that it is possible to emulate the imaging function of a single conventional lens with an NxN array of identical lenslets to provide an N-fold reduction in imaging-system track length. This approach limits the application to low-resolution imaging. We highlight how using an array of dissimilar lenslets, with an array width that can be much wider than the detector array, high-resolution super-resolved imaging is possible. We illustrate this approach with a ray-traced design and optimization of a long-wave infrared system employing a 3x3 array of free-form lenslets to provide a four-fold reduction in track length compared to a baseline system. Simulations of image recovery show that recovered image quality is comparable to that of the baseline system.

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