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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.

Recent experimental work has demonstrated the potential to combine the merits of diffractive and on-chip photonic information processing devices in a single chip by making use of planar (or slab) waveguides. Researchers have adapted key results of 3D Fourier optics to 2D, by analogy, but rigorous derivations in planar contexts have been lacking. Here, such arguments are developed to show that diffraction formulas familiar from 3D can be adapted to 2D under certain mild conditions on the operating speeds of the devices in question. Equivalents to the Rayleigh-Sommerfeld diffraction (RS) formulas in 2D are provided and a Radiation Condition of validity proved. The equivalence of the first 2D RS formula with an angular spectrum formulation is demonstrated. Finally Fresnel approximations are derived starting from the RS formulation and that of the angular spectrum. In addition to serving those working with slab waveguides, this letter provides analytical tools to researchers in any field where 2D diffraction is encountered, including the study of surface plasmon polaritons, surface waves, 3D diffraction with line-sources or corresponding symmetries, and the optical, acoustic and crystallographic properties of 2D materials., Comment: 13 pages, 2 figures. v2: updated arxiv ref for cited preprint, style changes, added acknowledgment

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.

The Cimmino algorithm is an iterative algorithm used for solving linear equations (Ax = b) and is part of a wider family of algebraic reconstruction algorithms. Despite being used in computed tomography and digital signal processing, we present an approach for using it in holographic projections in the Fraunhofer region. Following the work carried out by our group on Kaczmarz holography, an earlier algebraic linear equation solver, we compare the performance and speed of Cimmino against this algorithm. Three versions of the Cimmino algorithm, Cimmino full, Cimmino eye, and Cimmino FFT, are evaluated and compared to both Kaczmarz and Gerchberg-Saxton. Interestingly, the derivation and simplification of Kaczmarz and Cimmino leads to the input-output algorithm originally derived by Fienup and while the solution is well-known, the link between these algorithms is not and despite being around since the 1930s, it was originally used to solve linear equations and not phase retrieval. While the Cimmino full and Cimmino eye reflect fairly poorly against Cimmino FFT and Kaczmarz in terms of image quality and speed, the Cimmino FFT delivers better results in terms of image quality than all algorithms considered. It is significantly faster than Kaczmarz, being only a few milliseconds slower than Gerchberg-Saxton.

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.

Pixel by pixel brightness control was achieved in the 3D 4k holographic replay field results. High accuracy and brightness control is required for maps in military applications and real-time head-up displays.

—A general method is presented for exciting discrete modes in waveguides of arbitrary geometry. Guided modes supported by the waveguide are first calculated using a finite difference frequency domain model. High efficiency holograms to excite these discrete modes are then generated using the Direct Search hologram generation algorithm. The Direct Search algorithm is optimised such that the inherent properties of waveguide modes are exploited to give faster execution times. A nodeless antiresonant photonic crystal fibre is considered as a test geometry, in which high-purity modes are experimentally excited and in-coupling efficiencies of up to 32.8% are obtained.

Imaging through optical fibres has recently emerged as a promising method of micro-scale optical imaging within a hair-thin form factor. This has significant applications in endoscopy and may enable minimally invasive imaging deep within live tissue for improved diagnosis of disease. Multi-mode fibres (MMF) are the most common choice because of their high resolution but multicore fibres (MCF) offer a number of advantages such as widespread clinical use, ability to form approximate images without correction and an inherently sparse transmission matrix (TM) enabling simple and fast characterisation. We present a novel experimental investigation into properties of MCF important for imaging, specifically: a new method to upsample and downsample measured TMs with minimal information loss, the first experimental measurement of MCF spatial eigenmodes, a novel statistical treatment of behaviour under bending based on a wireless fading model, and an experimental observation of TM drift due to self-heating effects and discussion of how to compensate this. We next present practical techniques for imaging through MCFs, including alignment, how to parallelise TM characterisation measurements to improve speed and how to use non-interferometric phase and polarisation recovery for improved stability. Finally, we present two recent applications of MCF imaging: polarimetric imaging using a robust Bayesian inference approach, and entropic imaging for imaging early-stage tumours.

The Kaczmarz algorithm is an iterative method for solving linear equations in the form of Ax = b. It is widely used in computed tomography (CT) and digital signal processing (DSP) but has yet to be adopted in computer-generated holography (CGH). Phase retrieval algorithms such as Gerchberg-Saxton or Fienup are significantly more popular in this field, however, in this paper we propose a unique and alternative approach to projecting a replay field through Discrete Fourier Transform (DFT) matrices and have shown that there are legitimate benefits to implementing this approach. The gradient descent iteration mechanism adopted by Kaczmarz, for instance, provides finer granularity control over the individual pixels in the replay field. We consequently demonstrate the quality of the image is significantly improved when compared to Gerchberg-Saxton.

The rise of virtual and augmented reality systems has prompted an increase in interest in the fields of 2D and 3D computer-generated holography (CGH). The numerical processing required to generate a hologram is high and requires significant domain expertise. This has historically slowed the adoption of CGH in emerging fields. In this paper we introduce HoloGen, an open-source Cuda C and [Formula presented] framework for computer-generated holography. HoloGen unites, for the first time, a wide array of existing hologram generation algorithms with state of the art performance while attempting to remain intuitive and easy to use. This is enabled by a [Formula presented] and Windows Presentation Framework (WPF) graphical user interface (GUI). A novel reflection based parameter hierarchy is used to ensure ease of modification. Extensive use of [Formula presented] templates based on the Standard Template Library (STL), compile time flexibility is preserved while maintaining runtime performance. The current release of HoloGen unites implementations of well known generation algorithms including Gerchberg-Saxton (GS), Liu-Taghizadeh (LT), direct search (DS), simulated annealing (SA) and one-step phase-retrieval (OSPR) with less known specialist variants including weighted GS and Adaptive OSPR. Benchmarking results are presented for several key algorithms. The software is freely available under an MIT license. Program summary: Program title: HoloGen v2.2.1.17177 CPC Library link to program files: https://doi.org/10.17632/nzk4swwsrg.1 Developer's repository link: https://gitlab.com/CMMPEOpenAccess/HoloGen Licensing provisions: MIT Programming language: Cuda, [Formula presented], [Formula presented] External packages: Cuda, ManagedCuda, MathNet, Newtonsoft.Json, NUnit, AForge, Accord, ClosedXML, CefSharp, PdfiumViewer, Xceed, NHotkey, SharpDX, MaterialSkin, Xamarin.forms, HelixToolkit, Dragablz, LiveCharts, MahApps Nature of problem: Hologram generation for two-dimensional Fourier and Fresnel holograms displayed on amplitude or phase modulating spatial light modulators with binary or multi-level control Solution method: Algorithmic variants including Gerchberg-Saxton, Liu-Taghizadeh, Direct Search, Simulated Annealing and One-Step Phase-Retrieval. Includes real-time reporting, batch processing and complex field manipulation Additional comments include restrictions and unusual features: Graphical user interface only exposes access to two-dimensional hologram generation. Includes a novel reflection based parameter hierarchy for ease of modification.

Current display technologies are limited in projecting floating ultra-high definition images on multiple layers, preventing applications in augmented reality for medical education. Computer-generated holography (CGH) with custom algorithms allows for displaying floating 3D images for augmented reality applications. The limitation of existing 3D display technologies is the lack of clearly-defined anatomical structures and models for medical education The custom algorithm was based on microoptical adaptation of the natural superposition compound human eye with the help of a virtual Gabor superlens and a layering technique. High-resolution Spatial Light Modulators (SLMs) can enable increasing the field of view and display size in CGH. The 3D holographic projection applications require an enlarged field of view for multi-user purposes and can be implemented to deliver presentations from remote settings and as non-invasive practical education in medicine. This technology targets academic medical centres, hospitals and clinics as well as research laboratories. In this work, a layered holographic projection method was developed to display high-resolution (3840×2160 px) 3D floating images in direct-view mode targeting medical education. A computational algorithm was created based on a phase retrieval algorithm and a virtual Gabor superlens to project a hologram on the Liquid Crystal on Silicon (LCoS) display panel of an UHD SLM. A code was programmed for generating multilayer 3D in-eye projections by adding multiple retrieved holograms with an independent Gabor zone plate into each single hologram. The reconstructions were obtained with a HeNe laser (633 nm, 5 mW) and the UHD SLM with reflective phase modulation. 3D holograms were directly observed floating as a ghost image at variable focal distances.

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.

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

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.

We present a DST-based Gerchberg-Saxton search algorithm for generating binary-phase holograms. The new algorithm is shown to give an order of magnitude speed improvement for a small reduction in image quality.

We present a method to create the holographic foveated rendering effect based on the iterative phase retrieval algorithm. We validated our proposing algorithm using an optical setup with a multi-phase spatial light modulator.

We present an embedded implementation using the Raspberry-Pi cluster system for One-Step Phase-Retrieval hologram generation. The results indicate a promising direction towards a lower cost and more compact embedded hologram generation system.

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.

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.

© 2020 Society of Photo-Optical Instrumentation Engineers (SPIE). Holographic search algorithms such as direct search (DS) and simulated annealing allow high-quality holograms to be generated at the expense of long execution times. This is due to single iteration computational costs of O (NxNy) and number of required iterations of order O (NxNy), where Nx and Ny are the image dimensions. This gives a combined performance of order O(Nx2Ny2). We use a technique to reduce the iteration cost down to O (1) for phase-sensitive computer-generated holograms, giving a final algorithmic performance of O (NxNy). We do this by reformulating the mean-squared error (MSE) metric to allow it to be calculated from the diffraction field rather than requiring a forward transform step. For a 1024 × 1024-pixel test images, this gave us a ≈50,000 × speed-up when compared with traditional DS with little additional complexity. When applied to phase-modulating or amplitude-modulating devices, the proposed algorithm converges on a global minimum MSE in O (NxNy) time. By comparison, most extant algorithms do not guarantee that a global minimum is obtained. Those that do, have a computational complexity of at least O(Nx2Ny2) with the naive algorithm being O [ (NxNy) ! ].

This work describes a novel approach to time-multiplexed holographic projection on binary phase devices. Unlike other time-multiplexed algorithms where each frame is the inverse transform of independently modified target images, Single-Transform Time-Multiplexed (STTM) hologram generation produces multiple sub-frames from a single inverse transform. Uniformly spacing complex rotations on the diffraction field then allows the emulation of devices containing 2 N modulation levels on binary devices by using N sub-frames. In comparison to One-Step Phase Retrieval (OSPR), STTM produces lower mean squared error for up to N = 5 than the equivalent number of OSPR sub-frames with a generation time of 1 N of the equivalent OSPR frame. A mathematical justification of the STTM approach is presented and a hybrid approach is introduced allowing STTM to be used in conjunction with OSPR in order to combine performance benefits.

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.

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 π / 9 at 4.6 V/µm for the chiral-doped nematic mixtures E7.

We have demonstrated a Liquid crystal (LC) analog phase modulator based on the flexoelectric-optic effect that can achieve full 2π phase modulation with sub-millisecond switching speed. The LC mixture in the device consists of the bimesogen CBC7CB with chiral dopant R5011 that can exhibit ±𝜋/4 rotation of the optic axis for an electric field of ±4.2Vμm^(-1). This is then converted to a ±π phase modulation with the aid of a chiral reflector and a quarter waveplate. The residual amplitude modulation is found to be very low, and we show how these elements can be combined to form a integrated device.

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 (HSAs) that offers Mean Square Error (MSE) 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.

We present HoloBlade, a collection of open and accessible technologies to advance the field of holography and serve the wider research community. The initial implementation is presented and functionality demonstrated.

© 2020 Elsevier B.V. Spatial light modulators can typically only modulate the phase or the amplitude of an incident wavefront, with only a limited number of discrete values available. This is often accounted for in computer-generated holography algorithms by setting hologram pixel values to the nearest achievable value during what is known as quantisation. Sympathetic quantisation is an alternative to this nearest-neighbour approach that takes into account the underlying diffraction relationships in order to obtain a significantly improved post-quantisation performance. The concept of sympathetic quantisation is introduced in this paper and a simple implementation, soft sympathetic quantisation, is presented which is shown to improve mean squared error and structural similarity index error metrics by 50% for the considered case of single-transform algorithms.

Computer-generated holography (CGH) is a technique to generate holographic interference patterns. One of the major issues related to computer hologram generation is the massive computational power required. Hardware accelerators are used to accelerate this process. Previous publications targeting hardware platforms lack performance comparisons between different architectures and do not provide enough information for the evaluation of the suitability of recent hardware platforms for CGH algorithms. We aim to address these limitations and present a comprehensive review of CGH-related hardware implementations.

Ferroelectric liquid crystals (FLCs) couple the direction of their spontaneous electric polarization to the direction of tilt of their optic axis. Consequently, reversal of the electric polarization by an electric field gives rise to an immediate and lasting optical response when an appropriately aligned FLC is observed between crossed polarizers, with one field direction yielding a dark image, and the opposite direction yielding a bright image. Here this peculiar electro-optic response is used to image, with high optical contrast, 180{\deg} ferroelectric domains in a crystalline substrate of magnesium-doped lithium niobate. The lithium niobate substrate contains a few domains with upwards electric polarization surrounded by regions with downward electric polarization. In contrast to a reference non-chiral liquid crystal that is unable to show ferroelectric behavior due to its high symmetry, the FLC, which is used as a thin film confined between the lithium niobate substrate and an inert aligning substrate, reveals ferroelectric domains as well as their boundaries, with strong black and white contrast. The results show that FLCs can be used for non-destructive read-out of domains in underlying ferroelectrics, with potential applications in e.g. photonic devices and non-volatile ferroelectric memories., Comment: 12 pages, 3 figures

We present a hardware architecture for generating Fresnel holograms for 3D holography on a small scale field-programmable gate arrays. Our hardware implementation can achieve similar performance to a high-end CPU enabled software implementation.