Fidelity optimization for aberration-tolerant hybrid imaging systems

Abstract

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.

Fidelity comparison of phase masks for hybrid imaging

“…However, we show here that the optimal value of α is considerably smaller if it is possible to optimize the image-recovery kernel as for example suggested in [10]. For a maximum W 20 of 5λ, the optimal cubic phase-modulation has α ≈ 2.8λ, a five-fold reduction on the value proposed in [1], and a correspondingly higher imaging fidelity [12].…”

Extended depth-of-field imaging and ranging in a snapshot

“…In previously reported approaches to hybrid imaging, a range of phase functions have been reported that tend to fall into two classes: either the antisymmetric cubic and trefoil masks (or qualitatively similar shapes) or symmetric masks [14,13], and these provide complementary advantages. While the former offers a superior trade-off between enhanced DOF and noise amplification [15], the spatial-phase effects introduced by the asymmetry introduce highly problematic artifacts and also range-dependent image shifts [9] that are absent for symmetric phase functions. Here we demonstrate that, by recording images with complementary OTF characteristics, it is possible to benefit from the enhanced DOF of an antisymmetric mask but without introducing image artifacts, and combined with the enhancement of three-dimensional ranging.…”

“…Radially symmetric phase functions have also been proposed for increase of DOF, including quartic and logarithmic phase functions [13] and the logarithmic asphere [14], and these enable recovery of images without phase-induced artifacts but with higher levels of noise amplification than for the antisymmetric functions [15] for reasons that appear to be fundamentally associated with the antisymmetry [7].…”

Thermal imaging system using optimised wavefront coding operating in real-time

“…By measuring the mean-squared error between the ideal and modelled restored system image, it is possible to optimise the cubic phase modulation with an efficient numerical optimisation process. Using the mean-squared error it has been demonstrated that the highest imaging fidelity can be obtained at a global optimum of β ≈ 0 and secondary optimum at β ≈ 3α [5]. The secondary optimum at β ≈ 3α has broader peak than the global optimum at β ≈ 0, which allows a greater degree tolerance with a slight movement away from the peaks.…”