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Conference on Optics and Photonics for Advanced Dimensional Metrology III

作者： Jeon, J. Kim, Y. Pusan Natl Univ Sch Mech Engn 2 Busandaehak Ro 63beon Gil Busan 46241 South Korea

ISBN: (纸本)9781510673120;9781510673137

In optical interferometry, phase-shifting algorithms can calculate the phase maps of the geometrical properties from measured samples with high accuracy. The phase-shifting algorithms require several interferograms captured from dynamic adjustable interferometers, with shifting occurring at uniform intervals. It is crucial to maintain the uniform shift intervals in phase-shifting algorithms because nonuniformities in intervals cause nonlinearities in the system and degrade the accuracy of measurement. However, experimental conditions inevitably introduce errors into dynamic adjustments due to environmental uncertainties. To address these drawbacks, we propose a novel method, shifte-dinterferogram generator, that eliminates the need for dynamic adjustments by utilizing a static optical interferometer with a single frame of interferogram. The proposed interferogram shifter involves capturing a single frame of an interferogram and employing deep learning to generate interferograms with ideal shifting intervals. For assessment of the proposed method, a single interferogram indicating surface shape of an optical flat was captured by Fizeau interferometer and given to the shifted-interferogram generator. The generated shifted interferograms were compared with the ideally shifted interferograms which contain exact shifting intervals and the results shows high similarities. Subsequently, the generated interferograms were used to extract phase, resulting in significantly improved accuracy comparable to more complex multi-step phase- shifting algorithms. This approach not only enhances measurement accuracy but also simplifies experimental setups, reducing susceptibility to environmental uncertainties.

关键词： deep learning optical interferometry phase-shifting algorithm shifted interferogram

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Least-squares phase-shifting algorithm of coherence scanning interferometry with windowed B-spline fitting, resampled and subdivided phase points for 3D topography metrology

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MEASUREMENT 2023年第1期217卷

作者： Duan, Yiting Li, Zexiao Zhang, Xiaodong Tianjin Univ State Key Lab Precis Measuring Technol & Instrumen Lab Micro Nano Mfg Technol Tianjin 300072 Peoples R China

3D topography metrology of optical micro-structured surfaces is critical for characterizing surface texture and form errors. The coherence scanning interferometry (CSI) faces many challenges for improving the accuracy of 3D topography metrology. In this paper, the least-squares (L-S) phase-shifting algorithm of coherence scanning interferometry with windowed B-spline fitting, resampled and subdivided phase points is proposed, which provides high accuracy of 3D surface topography. The proposed algorithm avoids the introduction of complex judgment criterion of fringe orders, and tedious phase unwrapping. Comparison with generalized phase-shifting algorithm, the wrong textures do not appear on the reconstructed 3D surfaces and 2D profiles for optical grating and Micro-lens array (MLA) surfaces using the proposed algorithm. Experimental results show that a VLSI step surface has high repeated measurement accuracy with a standard deviation of 1.6 nm, the periodic error of the proposed algorithm for PMMA MLA sub-aperture units is about 20 nm, and the mean value of PMMA MLA four random sub-aperture units are 6.66 nm (Sq), 77.63 nm (Sp), 36.38 nm (Sv), 114.18 nm (Sz) and 4.90 nm (Sa), respectively.

关键词： Coherence scanning interferometry phase-shifting algorithm Least-squares Windowed B-spline fitting Topography metrology

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Two-step gradient-assisted phase-shifting demodulation algorithm for fast 3D reconstruction

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MEASUREMENT SCIENCE AND TECHNOLOGY 2022年第2期33卷 025204-025204页

作者： Wu, Yanxue Wu, Gaoxu Yang, Shichao Yang, Tian Liu, Fei Chongqing Univ State Key Lab Mech Transmission Chongqing Peoples R China Chongqing Univ Coll Mech & Vehicle Engn Chongqing Peoples R China

The conventional multi-frequency heterodyne method is one of the most widely used methods in non-contact 3D measurement. However, it needs to project different phase-shifting patterns with different frequencies, so a large number of patterns are required. For most conventional methods, the fringe period number of the projected patterns is usually small due to its limited noise tolerance, though a larger fringe period number always means higher accuracy. We propose a two-step phase-shifting demodulation algorithm based on an intensitygradient. In this method, only two patterns for each frequency are required. With the intensity gradient of the two patterns, we obtain the wrapped phase of each frequency. Next, the absolute phase is retrieved from the three wrapped phases with the heterodyne algorithm. Because only two patterns are required for each frequency, the proposed method is more robust and has higher measuring speed compared with the traditional three-frequency four-step heterodyne method. Simulations and experiments prove the feasibility and effectiveness of the method, and demonstrate that the proposed method extends the noise tolerance and achieves highprecision with only half of the patterns required by the traditional three-frequency four-step method.

关键词： three-dimensional measurement fringe projection profilometry intensity gradient phase-shifting algorithm

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Design of a phase-shifting algorithm for Interferometric Measurement of Optical Thickness Variation 7

Design of a Phase-shifting Algorithm for Interferometric Mea...

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Conference on Photonic Instrumentation Engineering VII

作者： Bae, Wonjun Kim, Yangjin Pusan Natl Univ Sch Mech Engn 2 Busandaehak Ro 63beon Gil Busan 46241 South Korea

ISBN: (数字)9781510633384

ISBN: (纸本)9781510633384

The optical thickness is an important property of transparent plates when fabricating critical components. Spatially nonuniform errors, which are major factors in the measurement of the absolute optical thickness, can be brought about by phase errors related to the nonlinear error term. In this study, equations and a new sampling window for suppressing spatially uniform errors were constructed. Using these equations and new sampling amplitudes, we designed a new phase-shifting algorithm with 17 samples. Herein, the characteristics and advantages to the measurement of highly reflective surfaces when applying this new 17-sample algorithm are presented based on a Fourier representation. In addition, the superiority of the new algorithm in terms of its error control is demonstrated by comparing the errors occurring from a varying object phase, as well as root mean square errors, with those from different conventional algorithms.

关键词： Wavelength-scanning interferometry phase-shifting algorithm optical thickness variation spatially uniform error

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Improved 2+1 phase-shifting algorithm for suppressing ambient light influence

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OPTICAL ENGINEERING 2020年第12期59卷 124107-124107页

作者： Wu, Haitao Cao, Yiping An, Haihua Zhang, Hechen Zhang, Yujiao Yang, Na Sichuan Univ Dept Optoelect Chengdu Peoples R China

By constructing two phase-shifted fringe images and a flat image, the 2 + 1 phase-shifting algorithm can reduce the error caused by motion and realize real-time and high-resolution three-dimensional (3-D) measurement. However, the nonlinear gamma of the digital light processing and the ambient light will affect the light-field distribution of the flat image, and extensive experiments have shown that the distribution of the captured flat image is inconsistent with the DC component of the deformed patterns. Therefore, based on the linear calibration model, a more realistic DC component of the deformed patterns is deduced from the captured flat image. The AC components of the deformed patterns can be extracted more genuinely by subtracting the deduced DC component from deformed patterns. So, the influence of ambient light can be suppressed efficiently to improve 3-D measuring accuracy. The experimental results show the feasibility and validity of the proposed method. (c) 2020 Society of Photo-Optical Instrumentation Engineers (SPIE)

关键词： flat image phase-shifting algorithm ambient light linear calibration model least square method

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A novel phase retrieval method in fringe projection based on phase-shifting algorithm

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JOURNAL OF OPTICS-INDIA 2018年第4期47卷 534-541页

作者： Qiao, Naosheng Quan, Chenggen Hunan Univ Arts & Sci Hunan Prov Key Lab Photoelect Informat Integrat & Hunan Prov Cooperat Innovat Ctr Construct & Dev D Sch Phys & Elect Changde 415000 Peoples R China Natl Univ Singapore Dept Mech Engn 9 Engn Dr 1 Singapore 117576 Singapore

In order to reduce nonlinear phase error in fringe projection based on phase-shifting algorithm, a novel phase retrieval method is proposed. Firstly, on the basis of expression for wrapped phase and corresponding phase in N-step phase-shifting algorithm, the nonlinear phase error and its simple expression is deduced. Secondly, based on the four-step phase-shifting algorithm, the wrapped phase expression of actual measured object is obtained. The corresponding nonlinear phase error is derived in a simple form, and then the new phase error value is obtained by offsetting pi/4 from the nonlinear phase value. The mean of the new and original phase error values yields the final phase error;hence, the nonlinear phase errors are significantly reduced. Finally, the results of numerical simulations and experiments show that the proposed method is effective to reduce the nonlinear phase error due to system gamma nonlinearity in phase-shifting algorithm.

关键词： phase retrieval phase error System gamma nonlinearity phase-shifting algorithm Fringe projection

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Improving the measurement accuracy of shadow moire by three-step random phase-shifting algorithm

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OPTICAL ENGINEERING 2018年第5期57卷 054107-054107页

作者： Du, Hubing Yu, Jianhong Zhang, Shaofeng Xian Technol Univ Sch Mechatron Engn Xian Shaanxi Peoples R China

phase-shifting shadow moire is an efficient technique for three-dimensional (3-D) shape measurement, but the technique is always suffered from the error of phase shifter. A three-frame random phase-shifting algorithm is proposed to relax the requirements of repeatability and accuracy of the phase shifter in a shadow moire system. The proposed method can act as a bridge between the three phase-shifting analysis methods and two-shot phase-shifting methods. The value of introduced arbitrary and unknown phase shift can be calculated by a determinate formula. The algorithm has the advantages of being free from the disturbance of background elimination and less computation. In addition, the proposed method is immune to nonsinusoidal fringe patterns and can be implemented easily in many applications. Both simulation and optical experimental results verify the feasibility of this method. (C) 2018 Society of Photo-Optical Instrumentation Engineers (SPIE)

关键词： phase-shifting algorithm shadow moire phase phase shifting

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Enhanced high dynamic range 3D shape measurement based on generalized phase-shifting algorithm

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OPTICS COMMUNICATIONS 2017年 385卷 43-53页

作者： Wang, Minmin Du, Guangliang Zhou, Canlin Zhang, Chaorui Si, Shuchun Li, Hui Lei, Zhenkun Li, YanJie Shandong Univ Sch Phys Jinan 250100 Peoples R China Dalian Univ Technol Dept Engn Mech Dalian 116024 Peoples R China Jinan Univ Sch Civil Engn & Architecture Jinan 2250020 Peoples R China

Measuring objects with large reflectivity variations across their surface is one of the open challenges in phase measurement profilometry (PMP). Saturated or dark pixels in the deformed fringe patterns captured by the camera will lead to phase fluctuations and errors. Jiang et al. proposed a high dynamic range real-time three-dimensional (3D) shape measurement method (Jiang et al., 2016) [17] that does not require changing camera exposures. Three inverted phase-shifted fringe patterns are used to complement three regular phase-shifted fringe patterns for phase retrieval whenever any of the regular fringe patterns are saturated. Nonetheless, Jiang's method has some drawbacks: (1) the phases of saturated pixels are estimated by different formulas on a case by case basis;in other words, the method lacks a universal formula;(2) it cannot be extended to the four step phase-shifting algorithm, because inverted fringe patterns are the repetition of regular fringe patterns;(3) for every pixel in the fringe patterns, only three unsaturated intensity values can be chosen for phase demodulation, leaving the other unsaturated ones idle. We propose a method to enhance high dynamic range 3D shape measurement based on a generalized phase-shifting algorithm, which combines the complementary techniques of inverted and regular fringe patterns with a generalized phase-shifting algorithm. Firstly, two sets of complementary phase-shifted fringe patterns, namely the regular and the inverted fringe patterns, are projected and collected. Then, all unsaturated intensity values at the same camera pixel from two sets of fringe patterns are selected and employed to retrieve the phase using a generalized phase-shifting algorithm. Finally, simulations and experiments are conducted to prove the validity of the proposed method. The results are analyzed and compared with those of Jiang's method, demonstrating that our method not only expands the scope of Jiang's method, but also improves measuremen

关键词： phase-shifting algorithm High dynamic range (HDR) phase measuring profilometry (PMP) Fringe projection Least-square algorithm phase error

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Design and Assessment of phase-shifting algorithms in Optical Interferometer

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INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING-GREEN TECHNOLOGY 2023年第2期10卷 611-634页

作者： Kim, Sungtae Jeon, Jurim Kim, Yangjin Sugita, Naohiko Mitsuishi, Mamoru Pusan Natl Univ Sch Mech Engn 2 Busandaehak Ro Busan 46241 South Korea Univ Tokyo Dept Mech Engn 7-3-1 HongoBunkyo Ku Tokyo 1138656 Japan

Silicon wafers and transparent glass plates are major components in the semiconductor industry. In semiconductor devices, the surface shape and optical thickness of the wafers and glass plates are the key parameters for the optimal performance of the devices. phase-shifting interferometry has been widely used to achieve precision measurements of these parameters. The phase-shifting algorithm significantly affects the interferometric measurement results with phase-shifting interferometry. In this review, we introduce the design and assessment of phase-shifting algorithms in the Fizeau interferometer. Section 2 categorized the phase-shifting algorithms designed by several methods in terms of their error compensation ability. Then, the optical setup of the Fizeau interferometer used for surface and thickness measurement is explained in Sect. 3. In addition, Sect. 4 explained the principle of phase extraction using phase-shifting interferometry and discussed its error sources. Moreover, design methods for the phase-shifting algorithm to eliminate error sources are introduced in Sect. 5. Finally, the error compensation abilities of designed algorithms are estimated by several methods in Sect. 6.

关键词： Fizeau interferometer Optical thickness phase error phase-shifting algorithm phase-shifting interferometry Surface shape

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The Influence of phase-shifting algorithms on the Instrument Transfer Function in a Fizeau Interferometer 9

The Influence of Phase-shifting Algorithms on the Instrument...

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Conference on Optical Metrology and Inspection for Industrial Applications IX Part of SPIE/COS Photonics Asia Conference

作者： Zhang, Xu Lu, Qi Xu, Tianzhu Sun, Ying Liu, Shijie Silin, Dmitry Kozhevatov, Ilya Khazanov, Efim Chinese Acad Sci Precis Opt Mfg & Testing Ctr Shanghai Inst Opt & Fine Mech Shanghai 201800 Peoples R China Univ Chinese Acad Sci Beijing 100049 Peoples R China Chinese Acad Sci Shanghai Inst Opt & Fine Mech China Russian Belt & Rd Joint Lab Laser Sci Shanghai 201800 Peoples R China Fudan Univ Shanghai Engn Res Ctr Ultraprecis Opt Mfg Shanghai 200438 Peoples R China Russian Acad Sci Inst Appl Phys Nizhnii Novgorod 603950 Russia

ISBN: (纸本)9781510657052;9781510657045

The phase-shifting algorithms are essential for a Fizeau interferometer to reconstruct the topography of the optical element's surface or wavefront. There are differences between different algorithms for reconstruction results, especially for the suppression of noise. To acquire a more accurate instrument transfer function (ITF) which reflects the axial spatial frequency response of a Fizeau interferometer, the algorithm transfer function (ATF) which represents the characteristics of the calculation process in spatial frequency is proposed here. In this paper, numerical simulations were calculated and analyzed several instrument transfer functions of the well-known phase-shifting algorithms (3- frame, 4-frame, 5-frame and 13-frame algorithms). Then, the ITFs of a step plate with a height of 118 nm were measured with different algorithms by experiments and the results were analyzed. The simulations and experimental results indicate that the phase-shifting algorithm has an effect on the ITF measurement and is related to the number of interferograms. When interferograms with a similar number are selected, the ITF values calculated by different phase-shifting algorithms do not differ significantly. Therefore, the phase-shifting algorithm is not a key factor affecting the ITF measurement.

关键词： Instrument transfer function algorithm transfer function phase-shifting algorithm Fizeau interferometer

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