arXiv subjects

Peter J. Christopher

Publications and source records attributed to Peter J. Christopher.

14 recordsLinked to original sources

arXiv2021

HoloGen: An open source toolbox for high-speed hologram generation

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.

eess.IV↗

arXiv2020

Linear time algorithm for phase sensitive holography

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 $O((N_xN_y)!)$.

physics.optics↗

arXiv2020

Improving performance of single-pass real-time holographic projection

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.

eess.IV↗

arXiv2020

Relative limitations of increasing the number of modulation levels in computer generated holography

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.

eess.IV↗

arXiv2020

Holographic Predictive Search: Extending the Scope

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.

eess.IV↗

arXiv2020

Sympathetic quantisation -- a new approach to hologram quantisation

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.

eess.IV↗

arXiv2020

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 (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.

eess.IV↗

arXiv2020

Novel Predictive Search Algorithm for Phase Holography

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.

eess.IV↗

arXiv2020

Structure and Design of HoloGen

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.

cs.GR↗

arXiv2020

Benchmarking the Gerchberg-Saxton Algorithm

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.

eess.IV↗

arXiv2020

Lookup tables for phase randomisation in hardware generated holograms

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.

eess.SP↗

arXiv2020

Automated laser induced damage threshold testing applied to a ferroelectric spatial light modulator

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 Ø27μm, 5.5 W/cm2 Ø150μm and 3.2 W/cm2 Ø3.1mm with wavelength 1090+-5nm. Finally, the quality of the results obtained are discussed and conclusions drawn.

physics.ins-det↗

arXiv2019

Improving pixel differentiation in holographic images

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.

physics.optics↗

arXiv2019

Variance and Error in One-Step Phase-Retrieval

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.

eess.IV↗