Planar Fourier optics for slab waveguides, surface plasmon polaritons, and 2D materials.

Recent experimental work has demonstrated the potential of combining the merits of diffractive and on-chip photonic information processing devices in a single chip by making use of planar (or slab) waveguides. Here, arguments are developed to show that diffraction formulas familiar from 3D Fourier optics can be adapted to 2D under certain mild conditions on the operating speeds of the devices in question. In addition to serving those working in on-chip photonics, this Letter provides analytical tools for the study of surface plasmon polaritons, surface waves, and the optical, acoustic, and crystallographic properties of 2D materials.

Multi-depth phase-only hologram optimization using the L-BFGS algorithm with sequential slicing.

We implement a limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimization of phase-only computer-generated hologram for a multi-depth three-dimensional (3D) target. Instead of computing the full 3D reconstruction of the hologram, we use a novel method using L-BFGS with sequential slicing (SS) for partial evaluation of the hologram during optimization that only computes loss for a single slice of the reconstruction at every iteration. We demonstrate that its ability to record curvature information enables L-BFGS to have good quality imbalance suppression under the SS technique.

Effects of measurement noise on the construction of a transmission matrix.

The effects of time-varying measurement noise on transmission matrix acquisition processes are considered for the first time, to our knowledge. Dominant noise sources are discussed, and the noise properties of a typical interferometer system used for characterizing a multimode fiber transmission matrix are quantified. It is demonstrated that an appropriate choice of measurement basis allows a more accurate transmission matrix to be more quickly obtained in the presence of measurement noise. Finally, it is shown that characterizing the noise figure of the experimental system allows the inverse transmission matrix to be constructed with an ideal amount of regularization, which can in turn be used for optimal image acquisition.

Dynamic phase measurement of fast liquid crystal phase modulators.

We present dynamic time-resolved measurements of a multi-pixel analog liquid crystal phase modulator driven at a 1 kHz frame rate. A heterodyne interferometer is used to interrogate two pixels independently and simultaneously, to deconvolve phase modulation with a wide bandwidth. The root mean squared optical phase error within a 30 Hz to 25 kHz bandwidth is <0.5° and the crosstalk rejection is 50 dB. Measurements are shown for a custom-built device with a flexoelectro-optic chiral nematic liquid crystal. However, the technique is applicable to many different types of optical phase modulators and spatial light modulators.

Robust correction of interferometer phase drift in transmission matrix measurements.

A complex-valued transmission matrix describing a scattering medium can be constructed from a sequence of many interferometric measurements. A major challenge in such experiments is to correct for rapid phase drift of the optical system during the data acquisition process, especially when the phase drifts significantly between consecutive measurements. Therefore, a new method is presented where the exact phase drift between two measurements is characterized and corrected using a single additional measurement. This approach removes the need to continuously track the phase and significantly relaxes the phase stability requirements of the interferometer, allowing transmission matrices to be constructed in the presence of fast and erratic phase drift.

Automated Computer Vision-Enabled Manufacturing of Nanowire Devices.

We present a high-throughput method for identifying and characterizing individual nanowires and for automatically designing electrode patterns with high alignment accuracy. Central to our method is an optimized machine-readable, lithographically processable, and multi-scale fiducial marker system─dubbed LithoTag─which provides nanostructure position determination at the nanometer scale. A grid of uniquely defined LithoTag markers patterned across a substrate enables image alignment and mapping in 100% of a set of >9000 scanning electron microscopy (SEM) images (>7 gigapixels). Combining this automated SEM imaging with a computer vision algorithm yields location and property data for individual nanowires. Starting with a random arrangement of individual InAs nanowires with diameters of 30 ± 5 nm on a single chip, we automatically design and fabricate >200 single-nanowire devices. For >75% of devices, the positioning accuracy of the fabricated electrodes is within 2 pixels of the original microscopy image resolution. The presented LithoTag method enables automation of nanodevice processing and is agnostic to microscopy modality and nanostructure type. Such high-throughput experimental methodology coupled with data-extensive science can help overcome the characterization bottleneck and improve the yield of nanodevice fabrication, driving the development and applications of nanostructured materials.

Perceptually motivated loss functions for computer generated holographic displays.

Understanding and improving the perceived quality of reconstructed images is key to developing computer-generated holography algorithms for high-fidelity holographic displays. However, current algorithms are typically optimized using mean squared error, which is widely criticized for its poor correlation with perceptual quality. In our work, we present a comprehensive analysis of employing contemporary image quality metrics (IQM) as loss functions in the hologram optimization process. Extensive objective and subjective assessment of experimentally reconstructed images reveal the relative performance of IQM losses for hologram optimization. Our results reveal that the perceived image quality improves considerably when the appropriate IQM loss function is used, highlighting the value of developing perceptually-motivated loss functions for hologram optimization.

Computer-generated holography in the intermediate domain.

Iterative Fourier transform algorithms are widely used for hologram generation for phase-modulating spatial light modulators. In this paper, we introduce a new technique called the "intermediate domain," which decomposes the Fourier transforms used into multiple subtransforms, the combination of which can offer major performance benefits over traditional approaches. To demonstrate this, we introduce ID-GS, an implementation of the intermediate domain technique for possibly the best known hologram generation algorithm, Gerchberg-Saxton. We discuss the performance of this across a wide range of configurations with a focus on computational performance.

Automotive Holographic Head-Up Displays.

Driver's access to information about navigation and vehicle data through in-car displays and personal devices distract the driver from safe vehicle management. The discrepancy between road safety and infotainment must be addressed to develop safely operated modern vehicles. Head-up displays (HUDs) aim to introduce a seamless uptake of visual information for the driver while securely operating a vehicle. HUDs projected on the windshield provide the driver with visual navigation and vehicle data within the comfort of the driver's personal eye box through a customizable extended display space. Windshield HUDs do not require the driver to shift the gaze away from the road to attain road information. This article presents a review of technological advances and future perspectives in holographic HUDs by analyzing the optoelectronics devices and the user experience of the driver. The review elucidates holographic displays and full augmented reality in 3D with depth perception when projecting the visual information on the road within the driver's gaze. Design factors, functionality, and the integration of personalized machine learning technologies into holographic HUDs are discussed. Application examples of the display technologies regarding road safety and security are presented. An outlook is provided to reflect on display trends and autonomous driving.

LiDAR-derived digital holograms for automotive head-up displays.

A holographic automotive head-up display was developed to project 2D and 3D ultra-high definition (UHD) images using LiDAR data in the driver's field of view. The LiDAR data was collected with a 3D terrestrial laser scanner and was converted to computer-generated holograms (CGHs). The reconstructions were obtained with a HeNe laser and a UHD spatial light modulator with a panel resolution of 3840×2160 px for replay field projections. By decreasing the focal distance of the CGHs, the zero-order spot was diffused into the holographic replay field image. 3D holograms were observed floating as a ghost image at a variable focal distance with a digital Fresnel lens into the CGH and a concave lens.

HoloBlade: an open-hardware spatial light modulator driver platform for holographic displays.

Spatial light modulators (SLMs) are key research tools in several contemporary applied optics research domains. In this paper, we present the argument that an open platform for interacting with SLMs would dramatically increase their accessibility to researchers. We introduce HoloBlade, an open-hardware implementation of an SLM driver-stack, and provide a detailed exposition of HoloBlade's architecture, key components, and detailed design. An optical verification rig is constructed to demonstrate that HoloBlade can provide Fourier imaging capability in a 4f system. Finally, we discuss HoloBlade's future development roadmap and the opportunities that it presents as a research tool for applied optics.

Cost-optimized heterogeneous FPGA architecture for non-iterative hologram generation.

The generation of computer-generated holograms (CGHs) requires a significant amount of computational power. To accelerate the process, highly parallel field-programmable gate arrays (FPGAs) are deemed to be a promising computing platform to implement non-iterative hologram generation algorithms. In this paper, we present a cost-optimized heterogeneous FPGA architecture based on a one-step phase retrieval algorithm for CGH generation. The results indicate that our hardware implementation is 2.5× faster than the equivalent software implementation on a personal computer with a high-end multi-core CPU. Trade-offs between cost and performance are demonstrated, and we show that the proposed heterogeneous architecture can be used in a compact display system that is cost and size optimized.

Analog modulation by the flexoelectric effect in liquid crystals.

We have solved the long-standing problems of stability and hysteresis, and we are able to obtain the homogeneous uniform lying helix structure in polymer-free cholesteric liquid crystals. This is instrumental for the present work to demonstrate the analog modulation at high speed and high precision. The device is configured for the transverse field switching wherein the substrate surface is flat. In addition to the response time of 10 ms at room temperature, we have obtained the R-squared and the adjusted R-squared as a measure of true sine wave for the sinusoidal responding transmissions from 1 Hz to 100 kHz that are all greater than 0.9993. In a Michelson interferometer, the phase shift at wavelength 633 nm after two passes has been measured to be equal to about $\pi /{9}$π/9 at 4.6 V/µm for the chiral-doped nematic mixtures E7.

Robustness to misalignment of low-cost, compact quantitative phase imaging architectures.

Non-interferometric approaches to quantitative phase imaging could enable its application in low-cost, miniaturised settings such as capsule endoscopy. We present two possible architectures and both analyse and mitigate the effect of sensor misalignment on phase imaging performance. This is a crucial step towards determining the feasibility of implementing phase imaging in a capsule device. First, we investigate a design based on a folded 4f correlator, both in simulation and experimentally. We demonstrate a novel technique for identifying and compensating for axial misalignment and explore the limits of the approach. Next, we explore the implications of axial and transverse misalignment, and of manufacturing variations on the performance of a phase plate-based architecture, identifying a clear trade-off between phase plate resolution and algorithm convergence time. We conclude that while the phase plate architecture is more robust to misalignment, both architectures merit further development with the goal of realising a low-cost, compact system for applying phase imaging in capsule endoscopy.

Predictive search algorithm for phase holography.

We present an algorithm for generating high-quality holograms for computer generated holography: holographic predictive search. This approach is presented as an alternative to traditional holographic search algorithms such as direct search (DS) and simulated annealing (SA). We first introduce the current search-based methods and then introduce an analytical model of the underlying Fourier elements. This is used to make prescient judgments regarding the next iteration of the algorithm. This approach is developed for the case of phase-modulating devices with phase-sensitive reconstructions. When compared to conventional iterative approaches such as DS and SA on a multiphase device, holographic predictive search offered a fivefold improvement in quality as well as up to a 10-fold improvement in convergence time. This comes at the cost of an increased iteration overhead.

Quantitative phase and polarization imaging through an optical fiber applied to detection of early esophageal tumorigenesis.

Phase and polarization of coherent light are highly perturbed by interaction with microstructural changes in premalignant tissue, holding promise for label-free detection of early tumors in endoscopically accessible tissues such as the gastrointestinal tract. Flexible optical multicore fiber (MCF) bundles used in conventional diagnostic endoscopy and endomicroscopy scramble phase and polarization, restricting clinicians instead to low-contrast amplitude-only imaging. We apply a transmission matrix characterization approach to produce full-field en-face images of amplitude, quantitative phase, and resolved polarimetric properties through an MCF. We first demonstrate imaging and quantification of biologically relevant amounts of optical scattering and birefringence in tissue-mimicking phantoms. We present an entropy metric that enables imaging of phase heterogeneity, indicative of disordered tissue microstructure associated with early tumors. Finally, we demonstrate that the spatial distribution of phase and polarization information enables label-free visualization of early tumors in esophageal mouse tissues, which are not identifiable using conventional amplitude-only information.

Full-field quantitative phase and polarisation-resolved imaging through an optical fibre bundle.

Flexible optical fibres, used in conventional medical endoscopy and industrial inspection, scramble phase and polarisation information, restricting users to amplitude-only imaging. Here, we exploit the near-diagonality of the multi-core fibre (MCF) transmission matrix in a parallelised fibre characterisation architecture, enabling accurate imaging of quantitative phase (error <0.3 rad) and polarisation-resolved (errors <10%) properties. We first demonstrate accurate recovery of optical amplitude and phase in two polarisations through the MCF by measuring and inverting the transmission matrix, and then present a robust Bayesian inference approach to resolving 5 polarimetric properties of samples. Our method produces high-resolution (9.0±2.6µm amplitude, phase; 36.0±10.4µm polarimetric) full-field images at working distances up to 1mm over a field-of-view up to 750×750µm 2 using an MCF with potential for flexible operation. We demonstrate the potential of using quantitative phase for computational image focusing and polarisation-resolved properties in imaging birefringence.

Improving holographic search algorithms using sorted pixel selection.

Traditional search algorithms for computer hologram generation such as Direct Search and Simulated Annealing offer some of the best hologram qualities at convergence when compared to rival approaches. Their slow generation times and high processing power requirements mean, however, that they see little use in performance critical applications. This paper presents the novel sorted pixel selection (SPS) modification for holographic search algorithms that offers mean square error reductions in the range of 14.7-19.2% for the test images used. SPS operates by substituting a weighted search selection procedure for traditional random pixel selection processes. While small, the improvements seen are observed consistently across a wide range of test cases and require limited overhead for implementation.

Dynamic response of large tilt-angle flexoelectro-optic liquid crystal modulators.

We present here the first time-resolved tilt-angle and retardance measurements for large-tilt (>45°) flexoelectro-optic liquid crystal modulators. These devices have potential for next generation fast switching (>1 kHz), 0-2π analog phase spatial light modulators (SLMs), with applications in optical beamsteering, microscopy and micromachining. The chiral nematic device used consisted of a mixture of CBC7CB and the chiral dopant R5011 in a nominally 5 µm-thick cell, aligned in the uniform lying helix mode. As the device is dynamically switched over angles of ± 54°, retardance changes of up to 0.17λ are observed. Furthermore, the time-resolved measurements reveal an asymmetry in the tilt in the optic-axis depending on the polarity of the applied electric field. The change in the optic-axis exhibits a pattern dependence, whereby it is determined by both the pulse history and the applied field. This pattern dependence results in tilt-angle errors of up to 8.8°, which could manifest as phase errors as large as 35.2° in potential SLMs. These time domain measurements may allow correction of these deterministic errors, to realize practical devices.

Fast and low loss flexoelectro-optic liquid crystal phase modulator with a chiral nematic reflector.

In this paper, we demonstrate a flexoelectro-optic liquid crystal phase-only device that uses a chiral nematic reflector to achieve full 2π phase modulation. This configuration is found to be very tolerant to imperfections in the chiral nematic reflector provided that the flexoelectro-optic LC layer fulfils the half-wave condition. Encouragingly, the modulation in the phase, which operates at kHz frame rates, is also accompanied by low amplitude modulation. The configuration demonstrated herein is particularly promising for the development of next-generation liquid crystal on silicon spatial light modulators.