Diffractive achromats (DAs) promise ultra-thin and light-weight form factors for full-color computational imaging systems. However, designing DAs with the optimal optical transfer function (OTF) distribution suitable for image reconstruction algorithms has been a difficult challenge. Emerging end-to-end optimization paradigms of diffractive optics and processing algorithms have achieved impressive results, but these approaches require immense computational resources and solve non-convex inverse problems with millions of parameters. Here, we propose a learned rotational symmetric DA design using a concentric ring decomposition that reduces the computational complexity and memory requirements by one order of magnitude compared with conventional end-to-end optimization procedures, which simplifies the optimization significantly. With this approach, we realize the joint learning of a DA with an aperture size of 8 mm and an image recovery neural network, i.e., Res-Unet, in an end-to-end manner across the full visible spectrum (429–699 nm). The peak signal-to-noise ratio of the recovered images of our learned DA is 1.3 dB higher than that of DAs designed by conventional sequential approaches. This is because the learned DA exhibits higher amplitudes of the OTF at high frequencies over the full spectrum. We fabricate the learned DA using imprinting lithography. Experiments show that it resolves both fine details and color fidelity of diverse real-world scenes under natural illumination. The proposed design paradigm paves the way for incorporating DAs for thinner, lighter, and more compact full-spectrum imaging systems.

Deconvolution is widely used to improve the contrast and clarity of a 3D focal stack collected using a fluorescence microscope. But despite being extensively studied, deconvolution algorithms can introduce reconstruction artifacts when their underlying noise models or priors are violated, such as when imaging biological specimens at extremely low light levels. In this paper we propose a deconvolution method specifically designed for 3D fluorescence imaging of biological samples in the low-light regime. Our method utilizes a mixed Poisson-Gaussian model of photon shot noise and camera read noise, which are both present in low light imaging. We formulate a convex loss function and solve the resulting optimization problem using the alternating direction method of multipliers algorithm. Among several possible regularization strategies, we show that a Hessian-based regularizer is most effective for describing locally smooth features present in biological specimens. Our algorithm also estimates noise parameters on-the-fly, thereby eliminating a manual calibration step required by most deconvolution software. We demonstrate our algorithm on simulated images and experimentally-captured images with peak intensities of tens of photoelectrons per voxel. We also demonstrate its performance for live cell imaging, showing its applicability as a tool for biological research.

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State-of-the-art snapshot spectral imaging (SI) systems introduce color-coded apertures (CCAs) into their setups to obtain a flexible spatial-spectral modulation, allowing spectral information to be reconstructed from a set of coded measurements. Besides the CCA, other optical elements, such as lenses, prisms, or beam splitters, are usually employed, making systems large and impractical. Recently, diffractive optical elements (DOEs) have partially replaced refractive lenses to drastically reduce the size of the SI devices. The sensing model of these systems is represented as a projection modeled by a spatially shift-invariant convolution between the unknown scene and a point spread function (PSF) at each spectral band. However, the height maps of the DOE are the only free parameters that offer changes in the spectral modulation, which causes the ill-posedness of the reconstruction to increase significantly. To overcome this challenge, our work explores the advantages of the spectral modulation of an optical setup composed of a DOE and a CCA. Specifically, the light is diffracted by the DOE and then filtered by the CCA, located close to the sensor. A shift-variant property of the proposed system is clearly evidenced, resulting in a different PSF for each pixel, where a symmetric structure constraint is imposed on the CCA to reduce the high number of resulting PSFs. Additionally, we jointly design the DOE and the CCA parameters with a fully differentiable image formation model using an end-to-end approach to minimize the deviation between the true and reconstructed image over a large set of images. Simulation shows that the proposed system improves the spectral reconstruction quality in up to 4 dB compared with current state-of-the-art systems. Finally, experimental results with a fabricated prototype in indoor and outdoor scenes validate the proposed system, where it can recover up to 49 high-fidelity spectral bands in the 420–660 nm.

achieves state-of-the-art results for HS-D imaging and that the optimized DOE outperforms alternative optical designs.