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This approach was inspired by the observation that many of the constraints inherent in CGH are also present in control theory, suggesting that it might be possible to apply techniques from control engineering to advance holographic display technology. The central innovation of this work lies in re-framing the CGH problem. Rather than approaching it as a conventional iterative phase retrieval task, I model it as a multiple-input, multiple-output (MIMO) feedback control system. Within this framework, I show that system performance can be improved by adjusting a gain parameter introduced in the feedback loop. Furthermore, I derive an optimal gain value that maximises performance for a given configuration, set of constraints and a specified number of iterations. I also demonstrate that further performance improvements can be achieved by incorporating additional digital filter terms in the feedback response and that this approach generalises across different optimisation error metrics. The fact that OCF can be optimised for a fixed number of iterations is a crucial aspect. It allows the development of multi-stage hardware acceleration pipelines that have to achieve maximal performance from any given silicon or logic gate budget. Compared to iterative alternatives, OCF is readily incorporated into hardware acceleration designs. Alongside OCF, I also developed two state-of-the-art holographic projection systems. The first is a binary-phase projection system utilising HoloBlade, which is the world's first open-hardware spatial light modulator (SLM) driver platform. The technology to enable effective, reliable, and repeatable operation of the device was developed during the course of this thesis and is documented here. The second system is a multi-phase projection system which uses the Sony Phase-Only SLM. Sony is a world leader in liquid-crystal display technology, and I developed a collaboration with them during the course of this research that resulted in access to this advanced SLM. Originally developed for amplitude-modulation in high-end laser projection systems, I adapted this device and comprehensively calibrated it to achieve high performance as the modulation device in a holographic display system. Both projection systems are capable of generating high-fidelity images, which are presented in this thesis as experimental demonstrations of OCF. I developed two distinct configurations of the OCF algorithm. The first, Frame-Specific OCF, was where the key ideas and techniques behind OCF were germinated. Here, the algorithm produces optimal gain for a single target image. This yields a substantial performance improvement, but this approach requires computing a unique gain parameter for each individual image. This is impractical for most holographic projection systems that are designed to render vivid, dynamic scenes in real time. To address this limitation, I also developed General-Form OCF, which is a refined approach that allows OCF to scale across an entire population of images. Here, I utilise a comprehensive dataset, the 800-image DIV2K training set, and apply best-practice statistical sampling methods to train bulk-gain values which are optimal across the entire dataset. This enables the OCF algorithm to maintain high performance without requiring per-image optimisation, significantly enhancing its practical utility for real-world holographic display applications. I validated the effectiveness of this approach comprehensively. This was achieved by performing holdout testing, where the algorithm is assessed on data that was never used in the training, using the accompanying 100-image DIV2K validation dataset. Results demonstrate that General-Form OCF achieves substantial improvements in image quality, outperforming the conventional GS algorithm by approximately 2–3 dB in peak signal-to-noise ratio (PSNR) across a range of configurations. In order to ensure that this approach could be used on real-world devices, I also introduced Q-OCF, a variant of OCF that allows it to be used on binary-phase devices such as the HoloBlade SLM. The efficacy of both OCF and Q-OCF is demonstrated through extensive simulations as well as experimental validation on both projection systems. It is important to ensure that these algorithms can be used on real-world systems and this is what is demonstrated here. The findings confirm that OCF is both technically sound and practically viable for deployment in modern holographic systems. The results represent a step forward in practical holographic display technology.","abstract_html":"Holographic displays are a unique technology; no other display technology is able to fully replicate the light pattern of a real-world object. However the CGH (computer-generated holography) problem, where the real-world limitations of the modulation devices mean that the complex wavefront of a scene cannot be fully recreated, remains a considerable challenge. In this thesis, I present Optimal Constrained Feedback (OCF), a novel approach to addressing these limitations. This approach was inspired by the observation that many of the constraints inherent in CGH are also present in control theory, suggesting that it might be possible to apply techniques from control engineering to advance holographic display technology. The central innovation of this work lies in re-framing the CGH problem. Rather than approaching it as a conventional iterative phase retrieval task, I model it as a multiple-input, multiple-output (MIMO) feedback control system. Within this framework, I show that system performance can be improved by adjusting a gain parameter introduced in the feedback loop. Furthermore, I derive an optimal gain value that maximises performance for a given configuration, set of constraints and a specified number of iterations. I also demonstrate that further performance improvements can be achieved by incorporating additional digital filter terms in the feedback response and that this approach generalises across different optimisation error metrics. The fact that OCF can be optimised for a fixed number of iterations is a crucial aspect. It allows the development of multi-stage hardware acceleration pipelines that have to achieve maximal performance from any given silicon or logic gate budget. Compared to iterative alternatives, OCF is readily incorporated into hardware acceleration designs. Alongside OCF, I also developed two state-of-the-art holographic projection systems. The first is a binary-phase projection system utilising HoloBlade, which is the world's first open-hardware spatial light modulator (SLM) driver platform. The technology to enable effective, reliable, and repeatable operation of the device was developed during the course of this thesis and is documented here. The second system is a multi-phase projection system which uses the Sony Phase-Only SLM. Sony is a world leader in liquid-crystal display technology, and I developed a collaboration with them during the course of this research that resulted in access to this advanced SLM. Originally developed for amplitude-modulation in high-end laser projection systems, I adapted this device and comprehensively calibrated it to achieve high performance as the modulation device in a holographic display system. Both projection systems are capable of generating high-fidelity images, which are presented in this thesis as experimental demonstrations of OCF. I developed two distinct configurations of the OCF algorithm. The first, Frame-Specific OCF, was where the key ideas and techniques behind OCF were germinated. Here, the algorithm produces optimal gain for a single target image. This yields a substantial performance improvement, but this approach requires computing a unique gain parameter for each individual image. This is impractical for most holographic projection systems that are designed to render vivid, dynamic scenes in real time. To address this limitation, I also developed General-Form OCF, which is a refined approach that allows OCF to scale across an entire population of images. Here, I utilise a comprehensive dataset, the 800-image DIV2K training set, and apply best-practice statistical sampling methods to train bulk-gain values which are optimal across the entire dataset. This enables the OCF algorithm to maintain high performance without requiring per-image optimisation, significantly enhancing its practical utility for real-world holographic display applications. I validated the effectiveness of this approach comprehensively. This was achieved by performing holdout testing, where the algorithm is assessed on data that was never used in the training, using the accompanying 100-image DIV2K validation dataset. Results demonstrate that General-Form OCF achieves substantial improvements in image quality, outperforming the conventional GS algorithm by approximately 2–3 dB in peak signal-to-noise ratio (PSNR) across a range of configurations. In order to ensure that this approach could be used on real-world devices, I also introduced Q-OCF, a variant of OCF that allows it to be used on binary-phase devices such as the HoloBlade SLM. The efficacy of both OCF and Q-OCF is demonstrated through extensive simulations as well as experimental validation on both projection systems. It is important to ensure that these algorithms can be used on real-world systems and this is what is demonstrated here. The findings confirm that OCF is both technically sound and practically viable for deployment in modern holographic systems. 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Furthermore, I derive an optimal gain value that maximises performance for a given configuration, set of constraints and a specified number of iterations. I also demonstrate that further performance improvements can be achieved by incorporating additional digital filter terms in the feedback response and that this approach generalises across different optimisation error metrics. The fact that OCF can be optimised for a fixed number of iterations is a crucial aspect. It allows the development of multi-stage hardware acceleration pipelines that have to achieve maximal performance from any given silicon or logic gate budget. Compared to iterative alternatives, OCF is readily incorporated into hardware acceleration designs. Alongside OCF, I also developed two state-of-the-art holographic projection systems. The first is a binary-phase projection system utilising HoloBlade, which is the world's first open-hardware spatial light modulator (SLM) driver platform. The technology to enable effective, reliable, and repeatable operation of the device was developed during the course of this thesis and is documented here. The second system is a multi-phase projection system which uses the Sony Phase-Only SLM. Sony is a world leader in liquid-crystal display technology, and I developed a collaboration with them during the course of this research that resulted in access to this advanced SLM. Originally developed for amplitude-modulation in high-end laser projection systems, I adapted this device and comprehensively calibrated it to achieve high performance as the modulation device in a holographic display system. Both projection systems are capable of generating high-fidelity images, which are presented in this thesis as experimental demonstrations of OCF. I developed two distinct configurations of the OCF algorithm. The first, Frame-Specific OCF, was where the key ideas and techniques behind OCF were germinated. Here, the algorithm produces optimal gain for a single target image. This yields a substantial performance improvement, but this approach requires computing a unique gain parameter for each individual image. This is impractical for most holographic projection systems that are designed to render vivid, dynamic scenes in real time. To address this limitation, I also developed General-Form OCF, which is a refined approach that allows OCF to scale across an entire population of images. Here, I utilise a comprehensive dataset, the 800-image DIV2K training set, and apply best-practice statistical sampling methods to train bulk-gain values which are optimal across the entire dataset. This enables the OCF algorithm to maintain high performance without requiring per-image optimisation, significantly enhancing its practical utility for real-world holographic display applications. I validated the effectiveness of this approach comprehensively. This was achieved by performing holdout testing, where the algorithm is assessed on data that was never used in the training, using the accompanying 100-image DIV2K validation dataset. Results demonstrate that General-Form OCF achieves substantial improvements in image quality, outperforming the conventional GS algorithm by approximately 2–3 dB in peak signal-to-noise ratio (PSNR) across a range of configurations. In order to ensure that this approach could be used on real-world devices, I also introduced Q-OCF, a variant of OCF that allows it to be used on binary-phase devices such as the HoloBlade SLM. The efficacy of both OCF and Q-OCF is demonstrated through extensive simulations as well as experimental validation on both projection systems. It is important to ensure that these algorithms can be used on real-world systems and this is what is demonstrated here. The findings confirm that OCF is both technically sound and practically viable for deployment in modern holographic systems. The results represent a step forward in practical holographic display technology."]},{"key":"dc:format.checksum.md5","label":"Dc Format Checksum Md5","values":["84f4225b06f1a44fae5987db91c50acb","87eda9de84448d1f82354d60eee3eb5f"]},{"key":"dc:title","label":"Title","values":["Optimal Constrained Feedback: Computer-Generated Holography using Optimal-Gains"]}]}],"canonical_facts":{"dc:contributor.advisor":["Wilkinson, Timothy"],"dc:contributor.sponsor":["EPSRC, Sony"],"dc:creator":["Kadis, Andrew"],"dc:date.issued":["2025-08-29"],"dc:description.abstract":["Holographic displays are a unique technology; no other display technology is able to fully replicate the light pattern of a real-world object. 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Furthermore, I derive an optimal gain value that maximises performance for a given configuration, set of constraints and a specified number of iterations. I also demonstrate that further performance improvements can be achieved by incorporating additional digital filter terms in the feedback response and that this approach generalises across different optimisation error metrics. The fact that OCF can be optimised for a fixed number of iterations is a crucial aspect. It allows the development of multi-stage hardware acceleration pipelines that have to achieve maximal performance from any given silicon or logic gate budget. Compared to iterative alternatives, OCF is readily incorporated into hardware acceleration designs. Alongside OCF, I also developed two state-of-the-art holographic projection systems. The first is a binary-phase projection system utilising HoloBlade, which is the world's first open-hardware spatial light modulator (SLM) driver platform. The technology to enable effective, reliable, and repeatable operation of the device was developed during the course of this thesis and is documented here. The second system is a multi-phase projection system which uses the Sony Phase-Only SLM. Sony is a world leader in liquid-crystal display technology, and I developed a collaboration with them during the course of this research that resulted in access to this advanced SLM. Originally developed for amplitude-modulation in high-end laser projection systems, I adapted this device and comprehensively calibrated it to achieve high performance as the modulation device in a holographic display system. Both projection systems are capable of generating high-fidelity images, which are presented in this thesis as experimental demonstrations of OCF. I developed two distinct configurations of the OCF algorithm. The first, Frame-Specific OCF, was where the key ideas and techniques behind OCF were germinated. Here, the algorithm produces optimal gain for a single target image. This yields a substantial performance improvement, but this approach requires computing a unique gain parameter for each individual image. This is impractical for most holographic projection systems that are designed to render vivid, dynamic scenes in real time. To address this limitation, I also developed General-Form OCF, which is a refined approach that allows OCF to scale across an entire population of images. Here, I utilise a comprehensive dataset, the 800-image DIV2K training set, and apply best-practice statistical sampling methods to train bulk-gain values which are optimal across the entire dataset. This enables the OCF algorithm to maintain high performance without requiring per-image optimisation, significantly enhancing its practical utility for real-world holographic display applications. I validated the effectiveness of this approach comprehensively. This was achieved by performing holdout testing, where the algorithm is assessed on data that was never used in the training, using the accompanying 100-image DIV2K validation dataset. Results demonstrate that General-Form OCF achieves substantial improvements in image quality, outperforming the conventional GS algorithm by approximately 2–3 dB in peak signal-to-noise ratio (PSNR) across a range of configurations. In order to ensure that this approach could be used on real-world devices, I also introduced Q-OCF, a variant of OCF that allows it to be used on binary-phase devices such as the HoloBlade SLM. The efficacy of both OCF and Q-OCF is demonstrated through extensive simulations as well as experimental validation on both projection systems. It is important to ensure that these algorithms can be used on real-world systems and this is what is demonstrated here. 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