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Zhang H, Meng K, Lou P. Fast and precise single-frame phase demodulation interferometry. OPTICS EXPRESS 2024; 32:21017-21027. [PMID: 38859467 DOI: 10.1364/oe.525359] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2024] [Accepted: 05/14/2024] [Indexed: 06/12/2024]
Abstract
To achieve real-time phase detection, this paper presents a fast and precise spatial carrier phase-shifting interferometry based on the dynamic mode decomposition strategy. The algorithm initially produces a series of phase-shifted sub-interferograms with the aid of a spatial carrier interferogram. Subsequently, the measured phases are derived with great accuracy from these sub-interferograms through the use of the dynamic mode decomposition strategy, an outstanding non-iterative algorithm. Numerical simulation and experimental comparison show that this method is an efficient and accurate single-frame phase demodulation algorithm. The paper also analyzes the performance of the proposed method based on influencing factors such as random noise level, carrier frequency size, and carrier frequency direction. The results indicate that this method is a fast and accurate phase solution method, offering another effective solution for dynamic real-time phase measurement.
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Sharma S, Kulkarni R. State-space modeling approach for fringe pattern demodulation. APPLIED OPTICS 2023; 62:7330-7337. [PMID: 37855589 DOI: 10.1364/ao.496722] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2023] [Accepted: 09/04/2023] [Indexed: 10/20/2023]
Abstract
A spatial carrier fringe demodulation technique is proposed based on a state-space modeling approach for phase estimation. The fringe background intensity, carrier frequency, and phase quadrature components are considered to be the elements of the state vector, which are estimated simultaneously. The state estimation is performed using the extended Kalman filter. The simulation and experimental results are provided to demonstrate the performance comparison of the proposed method with popular and state-of-the-art methods in terms of noise robustness and phase estimation accuracy.
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3
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Liu F, Kuang Y, Wu Y, Chen X, Zhang R. Phase retrieval from single interferogram without carrier using Lissajous ellipse fitting technology. Sci Rep 2023; 13:9917. [PMID: 37336928 DOI: 10.1038/s41598-023-36584-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2023] [Accepted: 06/06/2023] [Indexed: 06/21/2023] Open
Abstract
Phase extraction from single interferogram is of high significance and increasingly interest in optical metrology. In this contribute we propose an advanced Pixel-level Lissajous Ellipse Fitting (APLEF) method to extract the phase from single interferogram without carrier. At each pixel, a Lissajous figure is created by plotting N against D, where N and D are subtractions and additions of intensities of adjacent pixels in a small window. The so created Lissajous figure is already in phase quadrature because of the subtraction and addition process, and the Lissajous Figure is forced to be closed by taking the opposite values of N and D, i.e. -N and -D into account. The closed and in phase quadrature Lissajous Figure is the key point for APLEF to demodulate the single inteferogram without carrier in theoretically. The simulation shows its higher accuracy than existed SPT and Garbusi's method and the experiments finally corroborate its effectiveness.
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Affiliation(s)
- Fengwei Liu
- National Key Laboratory of Optical Field Manipulation Science and Technology, Chinese Academy of Sciences, Chengdu, 610209, Sichuan, China
- The Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, 610209, Sichuan, China
- Youth Innovation Promotion Association CAS, Beijing, China
| | - Yu Kuang
- National Key Laboratory of Optical Field Manipulation Science and Technology, Chinese Academy of Sciences, Chengdu, 610209, Sichuan, China.
- The Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, 610209, Sichuan, China.
- School of Electronic and Information Engineering, Sichuan University, Chengdu, 610065, China.
| | - Yongqian Wu
- National Key Laboratory of Optical Field Manipulation Science and Technology, Chinese Academy of Sciences, Chengdu, 610209, Sichuan, China.
- The Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, 610209, Sichuan, China.
| | - Xiaojun Chen
- National Key Laboratory of Optical Field Manipulation Science and Technology, Chinese Academy of Sciences, Chengdu, 610209, Sichuan, China
- The Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, 610209, Sichuan, China
| | - Rongzhu Zhang
- School of Electronic and Information Engineering, Sichuan University, Chengdu, 610065, China
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Long Y, Tang Y, Cheng X, Han C, Xiang Q, Yang Y, Zhao L, Feng J. High-order spatial phase shift method realizes modulation analysis through a single-frame image. APPLIED OPTICS 2023; 62:3422-3430. [PMID: 37132843 DOI: 10.1364/ao.488041] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
For the modulation-based structured illumination microscopy system, how to obtain modulation distribution with an image has been a research hotspot. However, the existing frequency-domain single-frame algorithms (mainly including the Fourier transform method, wavelet method, etc.) suffer from different degrees of analytical error due to the loss of high-frequency information. Recently, a modulation-based spatial area phase-shifting method was proposed; it can obtain higher precision by retaining high-frequency information effectively. But for discontinuous (such as step) topography, it would be somewhat smooth. To solve the problem, we propose a high-order spatial phase shift algorithm that realizes robust modulation analysis of a discontinuous surface with a single-frame image. At the same time, this technique proposes a residual optimization strategy, so that it can be applied to the measurement of complex topography, especially discontinuous topography. Simulation and experimental results demonstrate that the proposed method can provide higher-precision measurement.
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Cywińska M, Rogalski M, Brzeski F, Patorski K, Trusiak M. DeepOrientation: convolutional neural network for fringe pattern orientation map estimation. OPTICS EXPRESS 2022; 30:42283-42299. [PMID: 36366685 DOI: 10.1364/oe.465094] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2022] [Accepted: 09/28/2022] [Indexed: 06/16/2023]
Abstract
Fringe pattern based measurement techniques are the state-of-the-art in full-field optical metrology. They are crucial both in macroscale, e.g., fringe projection profilometry, and microscale, e.g., label-free quantitative phase microscopy. Accurate estimation of the local fringe orientation map can significantly facilitate the measurement process in various ways, e.g., fringe filtering (denoising), fringe pattern boundary padding, fringe skeletoning (contouring/following/tracking), local fringe spatial frequency (fringe period) estimation, and fringe pattern phase demodulation. Considering all of that, the accurate, robust, and preferably automatic estimation of local fringe orientation map is of high importance. In this paper we propose a novel numerical solution for local fringe orientation map estimation based on convolutional neural network and deep learning called DeepOrientation. Numerical simulations and experimental results corroborate the effectiveness of the proposed DeepOrientation comparing it with a representative of the classical approach to orientation estimation called combined plane fitting/gradient method. The example proving the effectiveness of DeepOrientation in fringe pattern analysis, which we present in this paper, is the application of DeepOrientation for guiding the phase demodulation process in Hilbert spiral transform. In particular, living HeLa cells quantitative phase imaging outcomes verify the method as an important asset in label-free microscopy.
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Moré I, Cuevas F, Jimenez J, Puris A, Sosa F. Variable mesh optimization applied to fringe pattern demodulation using a Bézier surface. APPLIED OPTICS 2021; 60:7351-7361. [PMID: 34613024 DOI: 10.1364/ao.427852] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2021] [Accepted: 07/20/2021] [Indexed: 06/13/2023]
Abstract
We present a parametric method to carry out a demodulation process in complex fringe pattern images with either open or closed fringes; this method is based on the parallel demodulation algorithm and introduces a novel way, to the best of our knowledge, to approximate the phase map using the Bezier surface control points. For this study, a recently developed population meta-heuristic called Variable Mesh Optimization is introduced to implement the optimization process. The results of the proposed method improve the phase error and the run time scores in comparison with other global optimization algorithms, which address this type of problem.
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Trusiak M. Fringe analysis: single-shot or two-frames? Quantitative phase imaging answers. OPTICS EXPRESS 2021; 29:18192-18211. [PMID: 34154081 DOI: 10.1364/oe.423336] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2021] [Accepted: 04/28/2021] [Indexed: 06/13/2023]
Abstract
Conditions of the digital recording of the fringe pattern determine the phase reconstruction procedure, which in turn directly shapes the final accuracy and throughput of the full-field (non-scanning) optical measurement technique and defines the system capabilities. In this way, the fringe pattern analysis plays a crucial role in the ubiquitous optical measurements and thus is under constant development focused on high temporal/spatial resolution. It is especially valuable in the quantitative phase imaging technology, which emerged in the high-contrast label-free biomedical microscopy. In this paper, I apply recently blossomed two-frame phase-shifting techniques to the QPI and merge them with advanced adaptive interferogram pre-filtering algorithms. Next, I comprehensively test such frameworks against classical and adaptive single-shot methods applied for phase reconstruction in dynamic QPI enabling highest phase time-space-bandwidth product. The presented study systematically tackles important question: what is the gain, if any, in QPI realized by recording two phase-shifted interferograms? Counterintuitively, the results show that single-shot demodulation exhibited higher phase reconstruction accuracy than two-frame phase-shifting methods in low and medium interferogram signal-to-noise ratio regimes. Thus, the single-shot approach is promoted due to not only high temporal resolution but also larger phase-information throughput. Additionally, in the majority of scenarios, the best option is to shift the paradigm and employ two-frame pre-filtering rather than two-frame phase retrieval. Experimental fringe analysis in QPI of LSEC/RWPE cell lines successfully corroborated all novel numerical findings. Hence, the presented numerical-experimental research advances the important field of fringe analysis solutions for optical full-field measurement methods with widespread bio-engineering applications.
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Gocłowski P, Trusiak M, Ahmad A, Styk A, Mico V, Ahluwalia BS, Patorski K. Automatic fringe pattern enhancement using truly adaptive period-guided bidimensional empirical mode decomposition. OPTICS EXPRESS 2020; 28:6277-6293. [PMID: 32225880 DOI: 10.1364/oe.382543] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2019] [Accepted: 01/24/2020] [Indexed: 06/10/2023]
Abstract
Fringe patterns encode the information about the result of a measurement performed via widely used optical full-field testing methods, e.g., interferometry, digital holographic microscopy, moiré techniques, structured illumination etc. Affected by the optical setup, changing environment and the sample itself fringe patterns are often corrupted with substantial noise, strong and uneven background illumination and exhibit low contrast. Fringe pattern enhancement, i.e., noise minimization and background term removal, at the pre-processing stage prior to the phase map calculation (for the measurement result decoding) is therefore essential to minimize the jeopardizing effect the mentioned error sources have on the optical measurement outcome. In this contribution we propose an automatic, robust and highly effective fringe pattern enhancement method based on the novel period-guided bidimensional empirical mode decomposition algorithm (PG-BEMD). The spatial distribution of the fringe period is estimated using the novel windowed approach and then serves as an indicator for the truly adaptive decomposition with the filter size locally adjusted to the fringe pattern density. In this way the fringe term is successfully extracted in a single (first) decomposition component alleviating the cumbersome mode mixing phenomenon and greatly simplifying the automatic signal reconstruction. Hence, the fringe term is dissected without the need for modes selection nor summation. The noise removal robustness is ensured employing the block matching 3D filtering of the fringe pattern prior to its decomposition. Performance validation against previously reported modified empirical mode decomposition techniques is provided using numerical simulations and experimental data verifying the versatility and effectiveness of the proposed approach.
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Trusiak M, Picazo-Bueno JA, Patorski K, Zdańkowski P, Mico V. Single-shot two-frame π-shifted spatially multiplexed interference phase microscopy. JOURNAL OF BIOMEDICAL OPTICS 2019; 24:1-8. [PMID: 31522487 PMCID: PMC6997581 DOI: 10.1117/1.jbo.24.9.096004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2019] [Accepted: 07/30/2019] [Indexed: 05/05/2023]
Abstract
Single-shot, two-frame, π-shifted spatially multiplexed interference microscopy (π-SMIM) is presented as an improvement to previous SMIM implementations, introducing a versatile, robust, fast, and accurate method for cumbersome, noisy, and low-contrast phase object analysis. The proposed π-SMIM equips a commercially available nonholographic microscope with a high-speed (video frame rate) enhanced quantitative phase imaging (QPI) capability by properly placing a beam-splitter in the microscope embodiment to simultaneously (in a single shot) record two holograms mutually phase shifted by π radians at the expense of reducing the field of view. Upon subsequent subtractive superimposition of holograms, a π-hologram is generated with reduced background and improved modulation of interference fringes. These features determine superior phase retrieval quality, obtained by employing the Hilbert spiral transform on the π-hologram, as compared with a single low-quality (low signal-to-noise ratio) hologram analysis. In addition, π-SMIM enables accurate in-vivo analysis of high dynamic range phase objects, otherwise measurable only in static regime using time-consuming phase-shifting. The technique has been validated utilizing a 20 × / 0.46 NA objective in a regular Olympus BX-60 upright microscope for QPI of different lines of prostate cancer cells and flowing microbeads.
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Affiliation(s)
- Maciej Trusiak
- Warsaw University of Technology, Institute of Micromechanics and Photonics, Warsaw, Poland
- Address all correspondence to Maciej Trusiak, E-mail: ; Vicente Mico, E-mail:
| | - Jose-Angel Picazo-Bueno
- Universitat de Valencia, Departamento de Óptica y Optometría y Ciencias de la Visión, Burjassot, Spain
| | - Krzysztof Patorski
- Warsaw University of Technology, Institute of Micromechanics and Photonics, Warsaw, Poland
| | - Piotr Zdańkowski
- Warsaw University of Technology, Institute of Micromechanics and Photonics, Warsaw, Poland
| | - Vicente Mico
- Universitat de Valencia, Departamento de Óptica y Optometría y Ciencias de la Visión, Burjassot, Spain
- Address all correspondence to Maciej Trusiak, E-mail: ; Vicente Mico, E-mail:
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Wang H, Zeng H, Chen P, Liang R, Jiang L. Fast single fringe-pattern processing with graphics processing unit. APPLIED OPTICS 2019; 58:6854-6864. [PMID: 31503656 DOI: 10.1364/ao.58.006854] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2019] [Accepted: 07/24/2019] [Indexed: 06/10/2023]
Abstract
Optical interferometric techniques provide noncontact, full-field, and high-precision measurements that are very attractive in various research and application fields. Single fringe-pattern processing (SFPP) is often required when measuring fast phenomena, which contain multiple steps including noise removal, phase demodulation, and unwrapping. However, several difficulties are encountered during SFPP, among which the processing time is of interest due to the increasing computational load brought by the large amount and high-resolution fringe patterns in recent years. In this paper, we propose a general and complete graphics processing unit (GPU)-based SFPP framework to perform a systematic discussion on SFPP acceleration. Typical methods from the spatial domain, the transform-based, and the path-related are chosen to have a variety of methods in the framework for better parallelization demonstration, namely, coherence-enhancing diffusion for denoising, spiral phase quadrature transform for demodulation, and quality-guided phase unwrapping. To the best of our knowledge, this is the first time a complete GPU-based framework has been proposed for SFPP. The advantages of performing the analysis and parallelization in framework level are demonstrated, where processing redundancy can be identified and reduced. The proposed framework can be used as an example to demonstrate the GPU-based parallelization in SFPP. Methods in the framework can be replaced but the framework level analysis, the parallel design, and the involved functions are always good references. Experiments are performed on simulated and experimental fringe patterns to demonstrate the effectiveness of the proposed work and achieve at most 29.8 times speedup compared with CPU-based sequential processing.
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12
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Cywińska M, Trusiak M, Patorski K. Automatized fringe pattern preprocessing using unsupervised variational image decomposition. OPTICS EXPRESS 2019; 27:22542-22562. [PMID: 31510545 DOI: 10.1364/oe.27.022542] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2019] [Accepted: 06/27/2019] [Indexed: 06/10/2023]
Abstract
Successful single-frame fringe pattern preprocessing comprising high-frequency noise minimization and low-frequency background removal represents often the crucial step of the fringe pattern based full-field optical metrology (i.e., interferometry, moiré, structured light). It directly determines the measurement accuracy. Data-driven decomposition by means of the 2D empirical mode decomposition (EMD) serves the filtering purpose in adaptive and detail-preserving manner. The mode-mixing phenomenon resulting in troublesome automatic grouping of modes into three main fringe pattern components (background, information part and noise) is significantly limiting this process, however. In this paper we are introducing the unsupervised variational image decomposition (uVID) model especially tailored to overcome this preprocessing problem and assure successful sparse three-component fringe pattern decomposition. Comprehensive analysis and detailed studies of accomplished significant advancements ensuring automation, versatility and robustness of the proposed approach are provided. Main advancements include: (1) tailoring the VID calculation scheme to fringe pattern preprocessing purpose by focusing onto accurate fringe extraction with tolerance parameter and custom-made decomposition parameter values; (2) fringe pattern tailored BM3D denoising algorithm with fixed parameter values. Numerical and experimental investigations corroborate that the demonstrated uVID method compares favorably with the reference 2D EMD algorithm and classical VID model. Remarkable range of acceptable local variations of the fringe pattern orientation, period, noise, contrast and background terms is to be highlighted.
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Cheng Z, Liu D. Fast and accurate wavefront reconstruction in two-frame phase-shifting interferometry with unknown phase step. OPTICS LETTERS 2018; 43:3033-3036. [PMID: 29957774 DOI: 10.1364/ol.43.003033] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
A fast and accurate wavefront reconstruction method for two-frame phase-shifting interferometry is proposed. The unknown phase step between the two interferograms is estimated directly by solving a quartic polynomial equation, and then the phase map is readily reconstructed after obtaining the phase step. The whole phase reconstruction process is nearly analytical and thus very fast and easy to realize. Good performance of the proposed method is demonstrated by reconstructing the phase maps from simulated and real fringes along with comparisons to several existing well-established algorithms.
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Picazo-Bueno JÁ, Trusiak M, García J, Patorski K, Micó V. Hilbert-Huang single-shot spatially multiplexed interferometric microscopy. OPTICS LETTERS 2018; 43:1007-1010. [PMID: 29489765 DOI: 10.1364/ol.43.001007] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2017] [Accepted: 01/18/2018] [Indexed: 05/21/2023]
Abstract
Hilbert-Huang single-shot spatially multiplexed interferometric microscopy (H2S2MIM) is presented as the implementation of a robust, fast, and accurate single-shot phase estimation algorithm with an extremely simple, low-cost, and highly stable way to convert a bright field microscope into a holographic one using partially coherent illumination. Altogether, H2S2MIM adds high-speed (video frame rate) quantitative phase imaging capability to a commercially available nonholographic microscope with improved phase reconstruction (coherence noise reduction). The technique has been validated using a 20×/0.46 NA objective in a regular Olympus BX-60 upright microscope for static, as well as dynamic, samples showing perfect agreement with the results retrieved from a temporal phase-shifting algorithm.
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Wang Y, Lu X, Liu Y, Tian J, Zhong L. Self-calibration phase-shifting algorithm with interferograms containing very few fringes based on Fourier domain estimation. OPTICS EXPRESS 2017; 25:29971-29982. [PMID: 29221032 DOI: 10.1364/oe.25.029971] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2017] [Accepted: 11/08/2017] [Indexed: 06/07/2023]
Abstract
Based on Fourier domain estimation, a novel self-calibration phase-shifting algorithm, named Mid-Band Spatial Spectrum Matching (MSSM), is proposed to achieve phase retrieval from a small amount of phase-shifting interferograms containing very few fringes (defined as ultra-sparse fringe pattern(USFP)), which is still a difficult problem for optical interferometry. Both simulation and experimental results demonstrate that the proposed MSSM algorithm can accurately and rapidly achieve the phase distribution encoded in USFP while other current self-calibration algorithms fail, and this will supply a powerful tool to extend the application of phase-shifting interferometry.
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Wang C, Kemao Q, Da F. Automatic fringe enhancement with novel bidimensional sinusoids-assisted empirical mode decomposition. OPTICS EXPRESS 2017; 25:24299-24311. [PMID: 29041375 DOI: 10.1364/oe.25.024299] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2017] [Accepted: 09/11/2017] [Indexed: 06/07/2023]
Abstract
Fringe-based optical measurement techniques require reliable fringe analysis methods, where empirical mode decomposition (EMD) is an outstanding one due to its ability of analyzing complex signals and the merit of being data-driven. However, two challenging issues hinder the application of EMD in practical measurement. One is the tricky mode mixing problem (MMP), making the decomposed intrinsic mode functions (IMFs) have equivocal physical meaning; the other is the automatic and accurate extraction of the sinusoidal fringe from the IMFs when unpredictable and unavoidable background and noise exist in real measurements. Accordingly, in this paper, a novel bidimensional sinusoids-assisted EMD (BSEMD) is proposed to decompose a fringe pattern into mono-component bidimensional IMFs (BIMFs), with the MMP solved; properties of the resulted BIMFs are then analyzed to recognize and enhance the useful fringe component. The decomposition and the fringe recognition are integrated and the latter provides a feedback to the former, helping to automatically stop the decomposition to make the algorithm simpler and more reliable. A series of experiments show that the proposed method is accurate, efficient and robust to various fringe patterns even with poor quality, rendering it a potential tool for practical use.
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Tian C, Liu S. Phase retrieval in two-shot phase-shifting interferometry based on phase shift estimation in a local mask. OPTICS EXPRESS 2017; 25:21673-21683. [PMID: 29041462 DOI: 10.1364/oe.25.021673] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2017] [Accepted: 08/03/2017] [Indexed: 06/07/2023]
Abstract
Fringe analysis in two-shot phase-shifting interferometry is important but meets challenges due to a limited number of images, corrupting noise, and background modulation. Here we propose an effective algorithm for phase retrieval from two interferograms with unknown phase shifts. The algorithm first evaluates the phase shift in a local mask through phase fitting and global optimization and then computes a full-field phase map using an arctangent function. Since the phase shift evaluation is performed within a local mask, the algorithm is fast compared with conventional optimization-based algorithms and typically needs tens of seconds to complete the processing. Computer simulation and experimental results show that the proposed algorithm has excellent performance compared with state-of-the-art algorithms. A complete software package of the algorithm in MATLAB is available at http://two-shot.sourceforge.io/.
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He A, Deepan B, Quan C. Simplified paraboloid phase model-based phase tracker for demodulation of a single complex fringe. APPLIED OPTICS 2017; 56:7217-7224. [PMID: 29047983 DOI: 10.1364/ao.56.007217] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2017] [Accepted: 08/07/2017] [Indexed: 06/07/2023]
Abstract
A regularized phase tracker (RPT) is an effective method for demodulation of single closed-fringe patterns. However, lengthy calculation time, specially designed scanning strategy, and sign-ambiguity problems caused by noise and saddle points reduce its effectiveness, especially for demodulating large and complex fringe patterns. In this paper, a simplified paraboloid phase model-based regularized phase tracker (SPRPT) is proposed. In SPRPT, first and second phase derivatives are pre-determined by the density-direction-combined method and discrete higher-order demodulation algorithm, respectively. Hence, cost function is effectively simplified to reduce the computation time significantly. Moreover, pre-determined phase derivatives improve the robustness of the demodulation of closed, complex fringe patterns. Thus, no specifically designed scanning strategy is needed; nevertheless, it is robust against the sign-ambiguity problem. The paraboloid phase model also assures better accuracy and robustness against noise. Both the simulated and experimental fringe patterns (obtained using electronic speckle pattern interferometry) are used to validate the proposed method, and a comparison of the proposed method with existing RPT methods is carried out. The simulation results show that the proposed method has achieved the highest accuracy with less computational time. The experimental result proves the robustness and the accuracy of the proposed method for demodulation of noisy fringe patterns and its feasibility for static and dynamic applications.
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Sunderland Z, Patorski K, Trusiak M. Subtractive two-frame three-beam phase-stepping interferometry for testing surface shape of quasi-parallel plates. OPTICS EXPRESS 2016; 24:30505-30513. [PMID: 28059398 DOI: 10.1364/oe.24.030505] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2016] [Accepted: 11/24/2016] [Indexed: 06/06/2023]
Abstract
We present an effective method of testing the surface shape of quasi-parallel plates which requires only two phase-shifted three-beam interferograms. We derive a general formula for difference of two three-beam interferograms as a function of the phase shift value. The phase shift does not have to be precisely determined and uniform in the image domain. We show and compare results of extracting the fringe set and corresponding phase distribution related to the plate front surface shape using the two dimensional continuous wavelet transform, Hilbert-Huang transform and Fourier transform methods. Simulated and experimental data is used to verify the algorithm performance and robustness.
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Trusiak M, Mico V, Garcia J, Patorski K. Quantitative phase imaging by single-shot Hilbert-Huang phase microscopy. OPTICS LETTERS 2016; 41:4344-7. [PMID: 27628393 DOI: 10.1364/ol.41.004344] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
We propose a novel single-shot Hilbert-Huang transform-based algorithm applied to digital holographic microscopy (DHM) for robust, fast, and accurate single-shot quantitative phase imaging in on-axis and off-axis configurations. Fringe pattern with possible defects and closed fringes are adaptively filtered and accurately phase demodulated using local fringe direction estimation. Experimental validation of the proposed techniques is presented as the DHM study of microbeads and red blood cells phase samples. Obtained results compare very favorably with the Fourier approach (off-axis) and temporal phase shifting (on-axis).
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Tian C, Liu S. Two-frame phase-shifting interferometry for testing optical surfaces. OPTICS EXPRESS 2016; 24:18695-18708. [PMID: 27505832 DOI: 10.1364/oe.24.018695] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Standard phase-shifting interferometry (PSI) generally requires collecting at least three phase-shifted interferograms to extract the physical quantity being measured. Here, we propose the application of a simple two-frame PSI for the testing of a range of optical surfaces, including flats, spheres, and aspheres. The two-frame PSI extracts modulated phase from two randomly phase-shifted interferograms using a Gram-Schmidt algorithm, and can work in either null testing or non-null testing modes. Since only two interferograms are used for phase demodulation and the phase shift amount can be random, requirements on environmental conditions and phase shifter calibration are greatly relaxed. Experimental results of three different mirrors suggest that the two-frame PSI can achieve comparable measurement precision with conventional multi-frame PSI, but has faster data acquisition speed and less stringent hardware requirements. The proposed two-frame PSI expands the flexibility of PSI and holds great potential in many applications.
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