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 Citation:

# Iterative projection meets sparsity regularization: towards practical single-shot quantitative phase imaging with in-line holography

• Light: Advanced Manufacturing  4, Article number: 6 (2023)
• Corresponding author:
Liangcai Cao (clc@tsinghua.edu.cn)
Revised: 01 February 2023
Accepted: 03 February 2023
Accepted article preview online: 04 February 2023
Published online: 11 March 2023
• Holography provides access to the optical phase. The emerging compressive phase retrieval approach can achieve in-line holographic imaging beyond the information-theoretic limit or even from a single shot by exploring the signal priors. However, iterative projection methods based on physical knowledge of the wavefield suffer from poor imaging quality, whereas the regularization techniques sacrifice robustness for fidelity. In this work, we present a unified compressive phase retrieval framework for in-line holography that encapsulates the unique advantages of both physical constraints and sparsity priors. In particular, a constrained complex total variation (CCTV) regularizer is introduced that explores the well-known absorption and support constraints together with sparsity in the gradient domain, enabling practical high-quality in-line holographic imaging from a single intensity image. We developed efficient solvers based on the proximal gradient method for the non-smooth regularized inverse problem and the corresponding denoising subproblem. Theoretical analyses further guarantee the convergence of the algorithms with prespecified parameters, obviating the need for manual parameter tuning. As both simulated and optical experiments demonstrate, the proposed CCTV model can characterize complex natural scenes while utilizing physically tractable constraints for quality enhancement. This new compressive phase retrieval approach can be extended, with minor adjustments, to various imaging configurations, sparsifying operators, and physical knowledge. It may cast new light on both theoretical and empirical studies.

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• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

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### Research Summary

Compressive holography: Seeing transparent samples with a snap shot

Holography provides access to the phase of an optical field that contains various sources of information. Yet recovering the accurate phase remains a challenging task for holography due to the existence of the twin-image artifacts. Liangcai Cao from China’s Tsinghua University and colleagues now report development of a compressive holographic reconstruction framework that enables the quantitative analysis of optical phase from a single shot. It utilizes physical knowledge and the sparsity nature of the real-world samples to eliminate the twin image and achieve high imaging fidelity. The team conducted holographic reconstruction of various optically transparent samples, demonstrating its potential applications in surface metrology and biomedical imaging

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## Iterative projection meets sparsity regularization: towards practical single-shot quantitative phase imaging with in-line holography

• State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China
• ###### Corresponding author: Liangcai Cao, clc@tsinghua.edu.cn

Abstract:

Holography provides access to the optical phase. The emerging compressive phase retrieval approach can achieve in-line holographic imaging beyond the information-theoretic limit or even from a single shot by exploring the signal priors. However, iterative projection methods based on physical knowledge of the wavefield suffer from poor imaging quality, whereas the regularization techniques sacrifice robustness for fidelity. In this work, we present a unified compressive phase retrieval framework for in-line holography that encapsulates the unique advantages of both physical constraints and sparsity priors. In particular, a constrained complex total variation (CCTV) regularizer is introduced that explores the well-known absorption and support constraints together with sparsity in the gradient domain, enabling practical high-quality in-line holographic imaging from a single intensity image. We developed efficient solvers based on the proximal gradient method for the non-smooth regularized inverse problem and the corresponding denoising subproblem. Theoretical analyses further guarantee the convergence of the algorithms with prespecified parameters, obviating the need for manual parameter tuning. As both simulated and optical experiments demonstrate, the proposed CCTV model can characterize complex natural scenes while utilizing physically tractable constraints for quality enhancement. This new compressive phase retrieval approach can be extended, with minor adjustments, to various imaging configurations, sparsifying operators, and physical knowledge. It may cast new light on both theoretical and empirical studies.

### Research Summary

Compressive holography: Seeing transparent samples with a snap shot

Holography provides access to the phase of an optical field that contains various sources of information. Yet recovering the accurate phase remains a challenging task for holography due to the existence of the twin-image artifacts. Liangcai Cao from China’s Tsinghua University and colleagues now report development of a compressive holographic reconstruction framework that enables the quantitative analysis of optical phase from a single shot. It utilizes physical knowledge and the sparsity nature of the real-world samples to eliminate the twin image and achieve high imaging fidelity. The team conducted holographic reconstruction of various optically transparent samples, demonstrating its potential applications in surface metrology and biomedical imaging

show all

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