Nano-optic imagers that modulate light at sub-wavelength scales could enable new applications in diverse domains ranging from robotics to medicine. Although metasurface optics offer a path to such ultra-small imagers, existing methods have achieved image quality far worse than bulky refractive alternatives, fundamentally limited by aberrations at large apertures and low f-numbers. In this work, we close this performance gap by introducing a neural nano-optics imager. We devise a fully differentiable learning framework that learns a metasurface physical structure in conjunction with a neural feature-based image reconstruction algorithm. Experimentally validating the proposed method, we achieve an order of magnitude lower reconstruction error than existing approaches. As such, we present a high-quality, nano-optic imager that combines the widest field-of-view for full-color metasurface operation while simultaneously achieving the largest demonstrated aperture of 0.5 mm at an f-number of 2.

an optimization procedure with a spatial-spectral prior, specifically designed for deconvolution-based spectral reconstruction. Finally, we demonstrate hyperspectral imaging with a fabricated DOE attached to a conventional DSLR sensor. Results show that our method compares well with other stateof-the-art hyperspectral imaging methods in terms of spectral accuracy and spatial resolution, while our compact, diffraction-based spectral imaging method uses only a single optical element on a bare image sensor. CCS Concepts: • Computing methodologies → Hyperspectral imaging.

Capturing appearance often requires dense sampling in light-view space, which is often achieved in specialized, expensive hardware setups. With the aim of realizing a compact acquisition setup without multiple angular samples of light and view, we sought to leverage an alternative optical property of light, polarization. To this end, we capture a set of polarimetric images with linear polarizers in front of a single projector and camera to obtain the appearance and normals of real-world objects. We encountered two technical challenges: First, no complete polarimetric BRDF model is available for modeling mixed polarization of both specular and diffuse reflection. Second, existing polarization-based inverse rendering methods are not applicable to a single local illumination setup since they are formulated with the assumption of spherical illumination. To this end, we first present a complete polarimetric BRDF (pBRDF) model that can define mixed polarization of both specular and diffuse reflection. Second, by leveraging our pBRDF model, we propose a novel inverse-rendering method with joint optimization of pBRDF and normals to capture spatially-varying material appearance: per-material specular properties (including the refractive index, specular roughness and specular coefficient), per-pixel diffuse albedo and normals. Our method can solve the severely ill-posed inverse-rendering problem by carefully accounting for the physical relationship between polarimetric appearance and geometric properties. We demonstrate how our method overcomes limited sampling in light-view space for inverse rendering by means of polarization.

Abstract. It is known that a semi-cubically hyponormal weighted shift need not satisfy the flatness property, in which equality of two weights forces all or almost all weights to be equal. So it is a natural question to describe all semi-cubically hyponormal weighted shifts Wα with first two weights equal. Let α : 1, 1,∧ be a backward 3-step extension of a recursively generated weight sequence with 1 < x < u < v < w and let Wα be the associated weighted shift. In this paper we characterize completely the semicubical hyponormal Wα satisfying the additional assumption of the positive determinant coefficient property, which result is parallel to results for quadratic hyponormality.

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

Holographic displays promise to deliver unprecedented display capabilities in augmented reality applications, featuring a wide field of view, wide color gamut, spatial resolution, and depth cues all in a compact form factor. While emerging holographic display approaches have been successful in achieving large étendue and high image quality as seen by a camera, the large étendue also reveals a problem that makes existing displays impractical: the sampling of the holographic field by the eye pupil. Existing methods have not investigated this issue due to the lack of displays with large enough étendue, and, as such, they suffer from severe artifacts with varying eye pupil size and location. We show that the holographic field as sampled by the eye pupil is highly varying for existing display setups, and we propose pupil-aware holography that maximizes the perceptual image quality irrespective of the size, location, and orientation of the eye pupil in a near-eye holographic display. We validate the proposed approach both in simulations and on a prototype holographic display and show that our method eliminates severe artifacts and significantly outperforms existing approaches.

In this paper, we discuss the semi-cubic hyponormality of recursively generated weightedgive a new bridge between cubically hyponormal and quadratically hyponormal weighted shifts. Using weight sequences with first two equal weights, we show that two notions of quadratic hyponormality and semi-cubic hyponormality are different one from another. Moreover, we characterize the semi-cubic hyponormality of weighted shifts.

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