Non-iterative complex wave-field reconstruction based on Kramers–Kronig relations

Shen, Cheng; Liang, Mingshu; Pan, An; Yang, Changhuei

doi:10.1364/prj.419886

Cited by 47 publications

(23 citation statements)

References 41 publications

(41 reference statements)

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“…The Kramers–Kronig relations connects the imaginary and real parts of a complex function, which is analyzed in the upper half‐plane (UHP). [ 37,39,57,58 ] The transformation of the real and imaginary parts of a complex function satisfies

Im [H (r)] = - \frac{1}{π} p . v . \int_{- \infty}^{\infty} \frac{Re false[H false(τ false) false]}{τ - {boldr}_{∥}} d τ

where p.v. is Cauchy's principal value.…”

Section: Principle and Methodsmentioning

confidence: 99%

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High Bandwidth‐Utilization Digital Holographic Multiplexing: An Approach Using Kramers–Kronig Relations

Huang

Cao

2022

Advanced Photonics Research

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Modern quantitative optical imaging is developing toward high throughput and powerful data processing capabilities. Holography is a powerful technique to characterize quantitative phase delays introduced by light–matter interactions. The spatial bandwidth utilization of imaging sensors in digital holography can be expanded via an off‐axis multiplexing technique, which is a powerful tool for high‐throughput quantitative optical imaging. However, the highest bandwidth utilization of sensor is limited at 58.9% to keep the signal spectra away from the zeroth spectra. Kramers–Kronig relation is introduced into the off‐axis multiplexing technology to allow for the overlapping between the signal spectra and unwanted spectra. The bandwidth utilization of sensor in a diffraction‐limited optical system can reach 78.5% in one hologram. It opens a new route to multiplexing quantitative optical imaging and helps to improve the performance of iterative‐free and constraint‐free modern optical microscopes in various spectral regimes.

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Im [H (r)] = - \frac{1}{π} p . v . \int_{- \infty}^{\infty} \frac{Re false[H false(τ false) false]}{τ - {boldr}_{∥}} d τ

where p.v. is Cauchy's principal value.…”

Section: Principle and Methodsmentioning

confidence: 99%

“…Noniterative pupil modulation on band‐limited signal analyticity is also an effective method. [ 37 ] In‐line DH is of great research interest because it allows the reconstruction of complex wavefronts with a larger field of view (FOV), which is suitable for imaging large static or quasi‐static samples.…”

Section: Introductionmentioning

confidence: 99%

High Bandwidth‐Utilization Digital Holographic Multiplexing: An Approach Using Kramers–Kronig Relations

Huang

Cao

2022

Advanced Photonics Research

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“…It leverages the analyticity of band-limited signals. Its extendibility to KKSAI has then been proved in [22].…”

Section: mentioning

confidence: 99%

“…It is not the most efficient since redundancy not necessary for KKSAI. In principle, as long as the scanning of any convex aperture covers the whole pupil and its edge crosses the origin, the scanning scheme should work for KKSAI [22]. We can choose a rectangular aperture with 2 non-overlapping measurements shown in Fig.…”

Section: Scanning Schemementioning

confidence: 99%

Non-interferometric and non-iterative complex wave-field reconstruction based on Kramers-Kronig relations

Shen

Zhou

Yang

2022

Quantitative Phase Imaging VIII

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We reported a novel non-interferometric and non-iterative computational imaging method, synthetic aperture imaging based on Kramers-Kronig relations (KKSAI), to reconstruct complex wave-field. By collecting images through a modified microscope system with pupil modulation capability, we show that the phase and amplitude profile of the sample at pupil limited resolution can be extracted from as few as two intensity images by exploiting Kramers-Kronig relations. KKSAI reconstruction is non-iterative, free of parameter tuning and applicable to a wider range of samples. Simulation and experiment results have proved that it has much lower computational burden and achieves the best reconstruction quality when compared with two existing phase imaging methods.

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“…Currently, FPM has been written into the Introduction to Fourier Optics (4th edition) by Goodman [12]. Given its flexible setup without mechanical scanning and interferometric measurement, FPM has improved rapidly, and it not only acts as a tool to obtain both HR and a large FOV but is also regarded as a paradigm to solve a series of trade-off problems, including whole slide imaging [13][14][15][16][17][18], circulating tumor cell (CTC) analysis [19], high-throughput drug screening [20,21], label-free (single shot) high-throughput imaging in situ [22][23][24], retina imaging [25], 3D imaging [26][27][28], wafer detection [29], HR optical field imaging [30], optical cryptosystem [31] and remote sensing [9,32].…”

Section: Introductionmentioning

confidence: 99%

Fourier Ptychographic Microscopy via Alternating Direction Method of Multipliers

Wang

Zhang

Wang

et al. 2022

Cells

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Fourier ptychographic microscopy (FPM) has risen as a promising computational imaging technique that breaks the trade-off between high resolution and large field of view (FOV). Its reconstruction is normally formulated as a blind phase retrieval problem, where both the object and probe have to be recovered from phaseless measured data. However, the stability and reconstruction quality may dramatically deteriorate in the presence of noise interference. Herein, we utilized the concept of alternating direction method of multipliers (ADMM) to solve this problem (termed ADMM-FPM) by breaking it into multiple subproblems, each of which may be easier to deal with. We compared its performance against existing algorithms in both simulated and practical FPM platform. It is found that ADMM-FPM method belongs to a global optimization algorithm with a high degree of parallelism and thus results in a more stable and robust phase recovery under noisy conditions. We anticipate that ADMM will rekindle interest in FPM as more modifications and innovations are implemented in the future.

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Non-iterative complex wave-field reconstruction based on Kramers–Kronig relations

Cited by 47 publications

References 41 publications

High Bandwidth‐Utilization Digital Holographic Multiplexing: An Approach Using Kramers–Kronig Relations

High Bandwidth‐Utilization Digital Holographic Multiplexing: An Approach Using Kramers–Kronig Relations

Non-interferometric and non-iterative complex wave-field reconstruction based on Kramers-Kronig relations

Fourier Ptychographic Microscopy via Alternating Direction Method of Multipliers

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