The race for miniature color cameras using flat meta-optics has rapidly developed the end-to-end design framework using neural networks. Although a large body of work has shown the potential of this methodology, the reported performance is still limited due to fundamental limitations coming from meta-optics, mismatch between simulated and resultant experimental point spread functions, and calibration errors. Here, we use a HIL optics design methodology to solve these limitations and demonstrate a miniature color camera via flat hybrid meta-optics (refractive + meta-mask). The resulting camera achieves high-quality full-color imaging for a 5-mm aperture optics with a focal length of 5 mm. We observed a superior quality of the images captured by the hybrid meta-optical camera compared to a compound multi-lens optics of a mirrorless commercial camera.

Phase retrieval is an inverse problem which consists in recovering an unknown signal from a set of absolute squared projections. Recently, gradient descent algorithms have been developed to solve this problem. However, their optimization cost functions are non-convex and non-smooth. To address the non-smoothness of the cost function, some of these methods use truncation thresholds to calculate a truncated step gradient direction. But, the truncation requires designing parameters to obtain a desired performance in the phase recovery, which drastically modifies the search direction update, increasing the sampling complexity. Therefore, this paper develops the Phase Retrieval Smoothing Conjugate Gradient method (PR-SCG) which uses a smoothing function to retrieve the signal. PR-SCG is based on the smooth-ing projected gradient method which is useful for non-convex optimization problems. PR-SCG uses a nonlinear conjugate gradient of the smoothing function as the search direction to accelerate the convergence. Furthermore, the incremental Stochastic Smoothing Phase Retrieval algorithm (SSPR) is developed. SSPR involves a single equation per iteration which results in a simple, scalable, and fast approach useful when the size of the signal is large. Also, it is shown that SSPR converges linearly to the true signal, up to a global unimodular constant. Additionally, the proposed methods do not require truncation parameters. Simulation results are provided to validate the efficiency of PR-SCG and SSPR compared to existing phase retrieval algorithms. It is shown that PR-SCG and SSPR are able to reduce the number of measurements and iterations to recover the phase, compared with recently developed algorithms.

End-to-end optimization of diffractive optical elements (DOEs) profile through a digital differentiable model combined with computational imaging have gained an increasing attention in emerging applications due to the compactness of resultant physical setups. Despite recent works have shown the potential of this methodology to design optics, its performance in physical setups is still limited and affected by manufacturing artefacts of DOE, mismatch between simulated and resultant experimental point spread functions, and calibration errors. Additionally, the computational burden of the digital differentiable model to effectively design the DOE is increasing, thus limiting the size of the DOE that can be designed. To overcome the above mentioned limitations, a co-design of hybrid optics and image reconstruction algorithm is produced following the end-to-end hardware-in-the-loop strategy, using for optimization a convolutional neural network equipped with quantitative and qualitative loss functions. The optics of the imaging system consists on the phase-only spatial light modulator (SLM) as DOE and refractive lens. SLM phase-pattern is optimized by applying the Hardware-in-the-loop technique, which helps to eliminate the mismatch between numerical modelling and physical reality of image formation as light propagation is not numerically modelled but is physically done. Comparison with compound multi-lens optics of a last generation smartphone and a mirrorless commercial cameras show that the proposed system is advanced in all-in-focus sharp imaging for a depth range 0.4-1.9 m.

Super-resolution phase retrieval is an inverse problem that appears in diffractive optical imaging (DOI) and consists in estimating a high-resolution image from low-resolution phaseless measurements. DOI has three diffraction zones where the data can be acquired, known as near, middle, and far fields. Recent works have studied super-resolution phase retrieval under a setup that records coded diffraction patterns at the near and far fields. However, the attainable resolution of the image is mainly governed by the sensor characteristics, whose cost increases in proportion to the resolution. Also, these methodologies lack theoretical analysis. Hence, this work derives super-resolution models from low-resolution coded phaseless measurements at any diffraction zone that in contrast to prior contributions, the attainable resolution of the image is determined by the resolution of the coded aperture. For the proposed models, the existence of a unique solution (up to a global unimodular constant) is guaranteed with high probability, which can be increased by designing the coded aperture. Therefore, a strategy that designs the spatial distribution of the coded aperture is developed. Additionally, a super-resolution phase retrieval algorithm that minimizes a smoothed nonconvex least-squares objective function is proposed. The method first approximates the image by a spectral algorithm, which is then refined based upon a sequence of alternate steps. Simulation results show that the proposed algorithm overcomes state-of-the-art methods in reconstructing the high-resolution image. In addition, the reconstruction quality using designed coded apertures is higher than that of the non-designed ensembles.

Phase retrieval in optical imaging refers to the recovery of a complex signal from phaseless data acquired in the form of its diffraction patterns. These patterns are acquired through a system with a coherent light source that employs a diffractive optical element (DOE) to modulate the scene, resulting in coded diffraction patterns (CDPs) at the sensor. Recently, the hybrid approach of a model-driven network or deep unfolding has emerged as an effective alternative to conventional model- and learning-based phase-retrieval techniques because it allows for bounding the complexity of algorithms while also retaining their efficacy. Additionally, such hybrid approaches have shown promise in improving the design of DOEs that follow theoretical uniqueness conditions. There are opportunities to exploit novel experimental setups and resolve even more complex DOE phase-retrieval applications. This article presents an overview of algorithms and applications of deep unfolding for bootstrapped—regardless whether near, middle, or far zones—phase retrieval.

Phase retrieval is an inverse problem that consists in estimating a scene from diffraction intensities. This problem appears in optical imaging, which has three main diffraction zones where the measurements can be acquired, i.e., near, middle and far. Recent works have theoretically solved this inverse problem for the far zone, creating redundancy in the measurement process by including a coded aperture, which allows to modulate the scene and acquire coded diffraction patterns (CDP). However, in the state-of-the-art, the PR problem has not been theoretically studied for CDP at the near and middle zones. Moreover, the structure of the coded aperture is selected at random, leading to suboptimal estimations. Indeed, some of the coding elements employed in the literature are unfeasible because they increase the power of the scene in the modulation process. This paper provides theoretical guarantees for the recovery of a scene from CDP acquired at the three diffraction zones using admissible modulations. Based on the theoretical results, it is established that the image reconstruction quality directly depends on the coded aperture structure; therefore, a design strategy is proposed. In fact, when the scene can be sparsely represented in some basis, its support can be better estimated for a suitable choice of the coding elements in the modulation process. Experimental results show that the scene is successfully recovered by using designed coded apertures with up to 40% less measurements compared to non-designed ensembles.