Digital Incoherent Compressive Holography Using a Geometric Phase Metalens

We propose a compressive self-interference incoherent digital holography (SIDH) with a geometric phase metalens for section-wise holographic object reconstruction. We specify the details of the SIDH with a geometric phase metalens design that covers the visible wavelength band, analyze a spatial distortion problem in the SIDH and address a process of a compressive holographic section-wise reconstruction with analytic spatial calibration. The metalens allows us to realize a compressive SIDH system in the visible wavelength band using an image sensor with relatively low bandwidth. The operation of the proposed compressive SIDH is verified through numerical simulations.

Imaging biological tissue with high-throughput single-pixel compressive holography

Single-pixel holography (SPH) is capable of generating holographic images with rich spatial information by employing only a single-pixel detector. Thanks to the relatively low dark-noise production, high sensitivity, large bandwidth, and cheap price of single-pixel detectors in comparison to pixel-array detectors, SPH is becoming an attractive imaging modality at wavelengths where pixel-array detectors are not available or prohibitively expensive. In this work, we develop a high-throughput single-pixel compressive holography with a space-bandwidth-time product (SBP-T) of 41,667 pixels/s, realized by enabling phase stepping naturally in time and abandoning the need for phase-encoded illumination. This holographic system is scalable to provide either a large field of view (~83 mm2) or a high resolution (5.80 μm × 4.31 μm). In particular, high-resolution holographic images of biological tissues are presented, exhibiting rich contrast in both amplitude and phase. This work is an important step towards multi-spectrum imaging using a single-pixel detector in biophotonics.

Non-uniform Recovery Guarantees for Binary Measurements and Infinite-Dimensional Compressed Sensing

Due to the many applications in Magnetic Resonance Imaging (MRI), Nuclear Magnetic Resonance (NMR), radio interferometry, helium atom scattering etc., the theory of compressed sensing with Fourier transform measurements has reached a mature level. However, for binary measurements via the Walsh transform, the theory has long been merely non-existent, despite the large number of applications such as fluorescence microscopy, single pixel cameras, lensless cameras, compressive holography, laser-based failure-analysis etc. Binary measurements are a mainstay in signal and image processing and can be modelled by the Walsh transform and Walsh series that are binary cousins of the respective Fourier counterparts. We help bridging the theoretical gap by providing non-uniform recovery guarantees for infinite-dimensional compressed sensing with Walsh samples and wavelet reconstruction. The theoretical results demonstrate that compressed sensing with Walsh samples, as long as the sampling strategy is highly structured and follows the structured sparsity of the signal, is as effective as in the Fourier case. However, there is a fundamental difference in the asymptotic results when the smoothness and vanishing moments of the wavelet increase. In the Fourier case, this changes the optimal sampling patterns, whereas this is not the case in the Walsh setting.

Imaging biological tissue with high-throughput single-pixel compressive holography

Single-pixel holography (SPH) is capable of generating holographic images with rich spatial information by employing only a single-pixel detector. Thanks to the relatively low dark-noise production, high sensitivity, large bandwidth, and cheap price of single-pixel detectors in comparison to pixel-array detectors, SPH is becoming an attractive imaging modality at wavelengths where pixel-array detectors are not available or prohibitively expensive. Moreover, SPH is particularly advantageous when imaging through scattering media or in scarce illumination with compressive sensing. In the current practice of SPH, the throughput of the system is mainly limited by the phase-encoded illumination and the ways to realize phase stepping. In this work, we developed a high-through single-pixel compressive holography, achieving a space-bandwidth-time product (SBP-T) of 41,667 pixels/s. This result indicates that by using a single-pixel detector, information of holographic images containing up to 65,536 pixels can be collected within only 3 seconds. The high-throughput was realized by enabling phase stepping naturally in time and abandoning the need for phase-encoded illumination. We further show that compressive sensing can be conveniently adapted to significantly reduce the acquisition time. Besides being high throughput, we also show that this holographic system is scalable to provide either a large field of view (~83 mm2) or a high resolution (5.8 μm × 4.3 μm). In particular, high-resolution holographic images of a piece of rat tail were presented, exhibiting rich information of mussel, cortical bone, and cancellous bone. Given that microscopic images of biological tissue has rarely been explored in the current practice of SPH, we anticipate the developed high-throughput SPH is promising to nourish the development of multi-spectrum imaging by providing high-quality holographic images for biological tissues.