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Mid-infrared (MIR) spectroscopy is a powerful technique employed for a variety of applications, including gas sensing, industrial inspection, astronomy, surveillance, and imaging. Thin-film narrowband interference filters, targeted to specific absorption bands of target molecules, are commonly deployed for cost-effective MIR sensing systems. These devices require complex and time-consuming fabrication processes. Also, their customization on the micro-scale for emerging miniaturized applications is challenging. Plasmonic nanostructure arrays operating in reflection and transmission modes have been developed for MIR. However, they experience undesirable characteristics, such as broad spectra and low reflection/transmission efficiencies. All-dielectric metasurfaces have low intrinsic losses and have emerged as a substitute for plasmonic metasurfaces in MIR spectroscopy. Nevertheless, they typically operate only in reflection mode. In this work, we present a hybrid metal-dielectric metasurface for MIR spectroscopy operating in transmission mode. The metasurface is composed of germanium (Ge) atop aluminum (Al) cylinders, and we show that the transmission response arises because of the hybridization of modes arising from the Ge and the Al structures. The presented metasurface has a high transmission efficiency of 80 % at $\lambda = 2.6\ \mu\text{m}$, and a narrow full-width-at-half-maximum of $0.4\ \mu\text{m}$. We show numerical simulations, successful fabrication using a straightforward fabrication method, and deployment as the in-line optical filter in a CO$_2$ gas detection with a limit of detection of ~0.04% (a few hundred ppm). Our work demonstrates the potential for hybrid metasurfaces as in-line gas sensing optical filters in MIR spectroscopy.

Computer-generated holography (CGH) is a promising technology for augmented reality displays, such as head-mounted or head-up displays. However, its high computational demand makes it impractical for implementation. Recent efforts to integrate neural networks into CGH have successfully accelerated computing speed, demonstrating the potential to overcome the trade-off between computational cost and image quality. Nevertheless, deploying neural network-based CGH algorithms on computationally limited embedded systems requires more efficient models with lower computational cost, memory footprint, and power consumption. In this study, we developed a lightweight model for complex hologram generation by introducing neural network quantization. Specifically, we built a model based on tensor holography and quantized it from 32-bit floating-point precision (FP32) to 8-bit integer precision (INT8). Our performance evaluation shows that the proposed INT8 model achieves hologram quality comparable to that of the FP32 model while reducing the model size by approximately 70% and increasing the speed fourfold. Additionally, we implemented the INT8 model on a system-on-module to demonstrate its deployability on embedded platforms and high power efficiency., Comment: 10 pages, 2 figures

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

The demands of proliferating big data and massive deep learning models, against a backdrop of a mounting climate emergency and the abating of Moore's law, push technologists to develop high-speed, high-throughput, low energy and miniaturisable computer hardware. Using light as a fundamental resource, free-space optical computing and on-chip photonic computing devices provide, respectively, powers of natural parallelism and miniaturisability. Recent work harnessing diffractive effects inside planar (or slab) waveguides has seemingly combined the best elements of each competing technology. Yet, as this paper argues, certain challenges will emerge as the clock-speeds of on-chip diffractive systems are pushed to compete with legacy technologies. Using a "time-aware" analytical approach to wave propagation, a prediction is made of the presence of a time-based error term that has not yet been accounted for in on-chip diffractive architectures. System operating frequency bounds in the gigahertz range are quantified, above which time-based errors discernibly affect the accuracy of system performance, and below which the errors can safely be ignored, using design parameters from previously published work. The analysis and related bounds presented hold value in any context where high throughput on-chip diffractive operations may be exploited, including beam-shaping, spectroscopy, sensing and communications., Comment: 19 pages, 2 figures. v2: updated arxiv ref in cited work

We implement a novel limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimisation algorithm with cross entropy (CE) loss function, to produce phase-only computer-generated hologram (CGH) for holographic displays, with validation on a binary-phase modulation holographic projector.

In a computer-generated holographic projection system, the image is reconstructed via the diffraction of light from a spatial light modulator. In this process, several factors could contribute to non-linearities between the reconstruction and the target image. This paper evaluates the non-linearity of the overall holographic projection system experimentally, using binary phase holograms computed using the one-step phase retrieval (OSPR) algorithm, and then applies a digital pre-distortion (DPD) method to correct for the non-linearity. Both a notable increase in reconstruction quality and a significant reduction in mean squared error were observed, proving the effectiveness of the proposed DPD-OSPR algorithm.

Holographic search algorithms such as direct search 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 $O(N_x N_y)$ and number of required iterations of order $O(N_x N_y)$, where $N_x$ and $N_y$ are the image dimensions. This gives a combined performance of order $O(N_x^2 N_y^2)$. In this paper we use a novel technique to reduce the iteration cost down to $O(1)$ for phase-sensitive computer generated holograms giving a final algorithmic performance of $O(N_x N_y)$. We do this by reformulating the mean-squared error metric to allow it to be calculated from the diffraction field rather than requiring a forward transform step. For a $1024\times 1024$ pixel test images this gave us a $\approx 50,000\times$ speed-up when compared with traditional direct search with little additional complexity. When applied to phase-modulating or amplitude-modulating devices the proposed algorithm converges on a global minimum mean squared error in $O(N_x N_y)$ time. By comparison, most extant algorithms do not guarantee a global minimum is obtained and those that do have a computational complexity of at least $O(N_x^2 N_y^2)$ with the naive algorithm being $O((N_xN_y)!)$.

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.

The rise of mixed reality systems such as Microsoft HoloLens has prompted an increase in interest in the fields of 2D and 3D holography. Already applied in fields including telecommunications, imaging, projection, lithography, beam shaping and optical tweezing, Computer Generated Holography (CGH) offers an exciting approach to a wide range of light shaping problems. The numerical processing required to generate a hologram is high and requires significant domain expertise. This has historically slowed the adoption of holographic techniques in emerging fields. In this paper we present HoloGen, an open-source Cuda C and C ++ 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 C # 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 C ++ 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.

We present a novel 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 judgements regarding the next iteration of the algorithm. This new 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 multi-phase device, Holographic Predictive Search offered improvements in quality of 5x as well up to 10x improvements in convergence time. This is at the cost of an increased iteration overhead.

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.

Phase and amplitude spatial light modulators (SLMs) capable of both binary and multi-level modulation are widely available and offer a wide range of technologies to choose from for holographic applications. While the replay fields generated with multi-level phase-only SLMs are of a significantly higher quality than those generated by equivalent binary phase-only SLMs, evidence is presented in this letter that this improvement is not as marked for amplitude SLMs, where multi-level devices offer only a small benefit over their binary counterparts. Heuristic and numerical justifications for this are discussed and conclusions drawn.

Holographic Predictive Search (HPS) is a novel approach to search-based hologram generation that uses a mathematical understanding of the optical transforms to make informed optimisation decisions. Existing search techniques such as Direct Search (DS) and Simulated Annealing (SA) rely on trialling modifications to a test hologram and observing the results. A formula is used to decide whether the change should be accepted. HPS operates presciently, using knowledge of the underlying mathematical relationship to make exact changes to the test hologram that guarantee the 'best' outcome for that change. In this work, we extend the scope of the original research to cover both phase and amplitude modulating Spatial Light Modulators (SLMs), both phase sensitive and phase insensitive systems and both Fresnel and Fraunhofer diffraction. In the cases discussed, improvements of up to 10x are observed in final error and the approach also offers significant performance benefits in generation time. This comes at the expense of increased complexity and loss of generality.

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.

Increasing popularity of augmented and mixed reality systems has seen a similar increase of interest in 2D and 3D computer generated holography (CGH). Unlike stereoscopic approaches, CGH can fully represent a light field including depth of focus, accommodation and vergence. Along with existing telecommunications, imaging, projection, lithography, beam shaping and optical tweezing applications, CGH is an exciting technique applicable to a wide array of photonic problems including full 3D representation. Traditionally, the primary roadblock to acceptance has been the significant numerical processing required to generate holograms requiring both significant expertise and significant computational power. This article discusses the structure and design of HoloGen. HoloGen is an MIT licensed application that may be used to generate holograms using a wide array of algorithms without expert guidance. HoloGen uses a Cuda C and C++ backend with a C# and Windows Presentation Framework graphical user interface. The article begins by introducing HoloGen before providing an in-depth discussion of its design and structure. Particular focus is given to the communication, data transfer and algorithmic aspects.

Due to the proliferation of spatial light modulators, digital holography is finding wide-spread use in fields from augmented reality to medical imaging to additive manufacturing to lithography to optical tweezing to telecommunications. There are numerous types of SLM available with a multitude of algorithms for generating holograms. Each algorithm has limitations in terms of convergence speed, power efficiency, accuracy and data storage requirement. Here, we consider probably the most common algorithm for computer generated holography - Gerchberg-Saxton - and examine the trade-off in convergent quality, performance and efficiency. In particular, we focus on measuring and understanding the factors that control runtime and convergence.

The rise in virtual and mixed reality systems has prompted a resurgence of interest in two-dimensional and three-dimensional real-time computer generated holography. Phase randomisation is an integral part of holographic projection as it ensures independence in sub-frame techniques and reduces the edge enhancement seen in flat-phase images. Phase randomisation requires, however, the availability of a pseudo-random number generator as well as trigonometric functions such as cos and sin. On embedded devices such as field programmable gate arrays and digital signal processors this can be an unacceptable load and necessitate the use of proprietary intellectual property cores. Lookup tables are able to reduce the computational load but can run to many megabytes for even low-resolution systems. This paper introduces the use of lookup tables (LUTs) in the context of two common algorithms used for real-time holographic projection: Gerchberg-Saxton and One-Step Phase-Retrieval. A simulated study is carried out to investigate the use of relatively small lookup tables where random numbers are repeated in sequence. We find that the increase in error is low and tunable to under 5\% even for small look up tables. This result is also demonstrated experimentally. Finally, the implications of this study are discussed and conclusions drawn.

Laser Induced Damage Thresholds (LIDTs) are a measure of the level of fluence an optical component may be expected to handle without observable damage. In this work we present an automated system for measurement of LIDTs for a wide range of components and include details of the data handling, image processing and code required. We then apply this system to LIDT measurements of a commercial HDP-1280-2 'BlueJay' ferroelectric display finding a LIDT of 9.2 W/cm2 {\O}27{\mu}m, 5.5 W/cm2 {\O}150{\mu}m and 3.2 W/cm2 {\O}3.1mm with wavelength 1090+-5nm. Finally, the quality of the results obtained are discussed and conclusions drawn.

Computer generated holography (CGH) has seen a resurgence in recent years due, in part, to the rise of virtual and mixed reality systems. The majority of approaches for CGH are based on a sampled Discrete Fourier Transform (DFT) and ignore the interstitial behaviour between sampling points in the replay field. In this paper we demonstrate that neighbouring replay field pixels can interfere significantly giving the visual impression of pixel movement and increased noise. We also demonstrate that increasing the separation between target pixels reduces the interference and improves pixel quality. This phenomena is demonstrated experimentally with close agreement between model and measured result. This work begins by introducing the concept of pixel differentiation before showing simulated models of pixel differentiation issues. Two mitigation approaches are introduced and an experimental system is then used to validate the simulation. Finally results are discussed and conclusions drawn.

Time multiplexed approaches for high frame-rate holographic displays have been around since the invention of One-Step Phase-Retrieval (OSPR) in the early 2000s. When discovered, formulations were created for variance reduction but other image quality metrics were ignored. This work sets out statistical models for the mean squared error (MSE) and structural similarity index (SSIM) behaviour of OSPR for a range of image types in order to better understand the effect of time multiplexing on visible images. This finds that while observed variances converges to zero as the number of frames per second increases, MSE converges to a non-zero value while SSIM converges quadratically to a non-unitary value.

The ability to form images through hair-thin optical fibres promises to open up new applications from biomedical imaging to industrial inspection. Unfortunately, deployment has been limited because small changes in mechanical deformation (e.g. bending) and temperature can completely scramble optical information, distorting images. Since such changes are dynamic, correcting them requires measurement of the fibre transmission matrix (TM) in situ immediately before imaging. TM calibration typically requires access to both the proximal and distal facets of the fibre simultaneously, which is not feasible during most realistic usage scenarios without compromising the thin form factor with bulky distal optics. Here, we introduce a new approach to determine the TM of multi-mode fibre (MMF) or multi-core fibre (MCF) in a reflection-mode configuration without access to the distal facet. A thin stack of structured metasurface reflectors is used at the distal facet to introduce wavelength-dependent, spatially heterogeneous reflectance profiles. We derive a first-order fibre model that compensates these wavelength-dependent changes in the TM and show that, consequently, the reflected data at 3 wavelengths can be used to unambiguously reconstruct the full TM by an iterative optimisation algorithm. We then present a method for sample illumination and imaging following TM reconstruction. Unlike previous approaches, our method does not require the TM to be unitary making it applicable to physically realistic fibre systems. We demonstrate TM reconstruction and imaging first using simulated non-unitary fibres and noisy reflection matrices, then using much larger experimentally-measured TMs of a densely-packed MCF, and finally on an experimentally-measured multi-wavelength set of TMs recorded from a MMF. Our findings pave the way for online transmission matrix calibration in situ in hair-thin optical fibres, Comment: Main text: 38 pages, 9 Figures, Appendices: 26 pages, 6 Figures. Corrected author affiliation

Conventional cameras, such as in smartphones, capture wideband red, green and blue (RGB) spectral components, replicating human vision. Multispectral imaging (MSI) captures spatial and spectral information beyond our vision but typically requires bulky optical components and is expensive. Snapshot multispectral image sensors have been proposed as a key enabler for a plethora of MSI applications, from diagnostic medical imaging to remote sensing. To achieve low-cost and compact designs, spatially variant multispectral filter arrays (MSFAs) based on thin-film optical components are deposited atop image sensors. Conventional MSFAs achieve spectral filtering through either multi-layer stacks or pigment, requiring: complex mixtures of materials; additional lithographic steps for each additional wavelength; and large thicknesses to achieve high transmission efficiency. By contrast, we show here for the first time a single-step grayscale lithographic process that enables fabrication of bespoke MSFAs based on the Fabry-Perot resonances of spatially variant metal-insulator-metal (MIM) cavities, where the exposure dose controls insulator (cavity) thickness. We demonstrate customizable MSFAs scalable up to N-wavelength bands spanning the visible and near-infrared with high transmission efficiency (~75%) and narrow linewidths (~50 nm). Using this technique, we achieve multispectral imaging of several spectrally distinct target using our bespoke MIM-MSFAs fitted to a monochrome CMOS image sensor. Our unique framework provides an attractive alternative to conventional MSFA manufacture, by reducing both fabrication complexity and cost of these intricate optical devices, while increasing customizability., Comment: Main manuscript: 19 pages, 5 figures; Supplementary: 43 pages 19 figures

Phase and polarisation of coherent light are highly perturbed by interaction with microstructural changes in pre-malignant tissue, holding promise for label-free early cancer detection in endoscopically accessible tissues such as the gastrointestinal tract. Flexible optical fibres used in conventional diagnostic endoscopy scramble phase and polarisation, restricting clinicians instead to low-contrast amplitude-only imaging. Here, we unscramble phase and polarisation images by exploiting the near-diagonal multi-core fibre (MCF) transmission matrix to create a novel parallelised fibre characterisation architecture, scalable to arbitrary MCFs without additional experimental overhead. Our flexible MCF holographic endoscope produces full-field en-face images of amplitude, quantitative phase and resolved polarimetric properties using a low-cost laser diode and camera. We demonstrate that recovered phase enables computational re-focusing at working distances up to 1mm over a field-of-view up to 750$\times$750 $\mu m^2$. Furthermore, we demonstrate that the spatial distribution of phase and polarisation information enables label-free visualisation of early tumours in oesophageal mouse issue that are not identifiable using conventional amplitude-only information, a milestone towards future application for early cancer detection in endoscopy., Comment: Main manuscript: 32 pages, 5 figures; Supplementary: 38 pages 11 figures