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Efficient nonlinear algorithm for envelope detection in white light interferometry

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION 1996年第4期13卷 832-843页

作者： Larkin, KG []Department of Physical Optics The University of Sydney NSW 2006 Australia

A compact and efficient algorithm for digital envelope detection in white light interferograms is derived from a well-known phase-shifting algorithm. The performance of the new algorithm is compared with that of Principal criteria considered are computational efficiency and accuracy in The new algorithm is shown to be near optimal in terms of computational efficiency and can be represented as a second-order nonlinear filter. In combination with a carefully designed peak detection method the algorithm exhibits exceptionally good performance on simulated interferograms. (C) 1996 Optical Society of America

关键词： interferometry white light interferometry interference microscopy phase-shifting algorithm low coherence nonlinear filter envelope detection demodulation

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Fringe projection decamouflaging

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OPTICS AND LASERS IN ENGINEERING 2020年 134卷 106201-106201页

作者： Deng, Ji Li, Jian Ding, Shumeng Feng, Hao Xiao, Yu Han, Wenzhong Zeng, Zhoumo Tianjin Univ Sch Precis Instrument & Opto Elect Engn State Key Lab Precis Measurement Technol & Instru 92 Weijin Rd Tianjin 300072 Peoples R China North China Inst Aerosp Engn Sch Mech & Elect Engn 133 Aimin East Rd Langfang 065000 Peoples R China

Unveiling the cheating mask of camouflage is of great significance in scientific and military research, but the acquisition of detailed information about camouflaged objects remains extremely difficult. This paper presents a fringe projection decamouflaging (FPDC) approach that can provide the position, outer rim profile, and shadow information about well-camouflaged objects in a complex scenario. FPDC requires no expensive instruments, just one camera and one projector for monitoring. A bionic detection field, namely, a phase-jump field, is established to detect the intrusion of camouflaged objects. Based on local variations in this field, multiple-parameter decamouflaging is achieved for the first time. Simulations and experiments show the superiority of this technique, which has potential applications in counterespionage, discovery of wild animals, and search-and-rescue.

关键词： Decamouflaging phase-jump field phase-shifting algorithm

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Noncontact surface profiling using optical interferometric microscopy

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OPTICAL ENGINEERING 2024年第2期63卷 023104-023104页

作者： Palacios, Diego Zhai, Bowen Wang, Michael R. Univ Miami Dept Elect & Comp Engn Coral Gables FL 33124 USA

. We report the use of noncontact optical interferometric microscopy for surface topographic profiling. A Linnik optical configuration is used to create interferograms of an object's surface. When the coherence condition between the two beams is met, the phase information of the object's surface can be extracted to establish its topographic contour image. Using four pi /4 phase-shifted images, with the synchronization of a piezoelectric actuator reference mirror positioning, the present single camera optical interferometric microscope can reconstruct a surface topography with a field of view of 312 mu mx234 mu m, axial resolution of 3.31 nm, lateral resolution of 488 nm, and maximum topography height of 270 nm.

关键词： optical interferometric microscopy surface profiling phase-shifting algorithm phase map

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Two-frame wavefront reconstruction method with nonlinear optimization for Ronchi lateral

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OPTICS COMMUNICATIONS 2024年 559卷

作者： Shi, Runzhou Liu, Huiwen Shao, Yuqi Zhang, Tian Bai, Jian Zhejiang Univ State Key Lab Extreme Photon & Instrumentat Hangzhou 310027 Peoples R China Zhejiang Univ Coll Opt Sci & Engn Hangzhou 310027 Peoples R China Zhejiang Univ ZJU Hangzhou Global Sci & Technol Innovat Ctr Hangzhou 311215 Peoples R China

Ronchi lateral shearing interferometry is widely applied in wavefront measurement of advanced lithography tools. In Ronchi lateral shearing interferometry, higher-order diffraction beam interference is a common challenge, currently mitigated by introducing more phase shifts, resulting in extended measurement times and added errors. In this study, we propose a nonlinear optimization approach that combines a 2-frame phase-shifting algorithm to suppress the influence of high diffraction orders, reducing the required number of phase shifts by more than 75%. We formulate a numerical model that aligns with the interferometry, construct a highly robust error function, and enable high-precision wavefront reconstruction by optimizing Zernike coefficients. The accuracy and robustness of the proposed method are verified through simulations and experiments.

关键词： Ronchi lateral shearing interferometry Wavefront reconstruction phase-shifting algorithm Nonlinear optimization

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Measurement of Thickness and Refractive Index of Optical Samples Simultaneously Using Full-Range One-Shot Frequency-Domain Optical Coherence Tomography

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FIBER AND INTEGRATED OPTICS 2015年第3期34卷 171-182页

作者： Cheng, Hsu-Chih Huang, Chia-Tsai Natl Formosa Univ Dept Electroopt Engn Huwei Township Yunlin County Taiwan Natl Cheng Kung Univ Inst Electroopt Sci & Engn Dept Photon Tainan 70101 Taiwan

This article proposes an improved frequency-domain optical coherence tomography for simultaneously measuring the thickness and refractive index of an unknown sample. In conventional frequency-domain optical coherence tomography systems, the spectrum of interference signals generates mirror signals and autocorrelation terms that result in a restricted measurement range. This study presents an improved method that involves applying a phase-shifting algorithm to orthogonally polarized light beams to increase the measurement range and eliminate unnecessary noise. However, a disadvantage is that the proposed method is suitable for the imaging of no (or very low) birefringent samples and needs to align properly the light's states of polarization.

关键词： phase-shifting algorithm orthogonal polarized light frequency-domain optical coherence tomography

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Development of surface reconstruction algorithms for optical interferometric measurement

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Frontiers of Mechanical Engineering 2021年第1期16卷 1-31页

作者： Dongxu WU Fengzhou FANG Centre of Micro/Nano Manufacturing Technology(MNMT-Dublin) University College DublinDublin 4Ireland School of Control Engineering Northeastern University at QinhuangdaoQinhuangdao 066004China State Key Laboratory of Precision Measuring Technology and Instruments Centre of Micro/Nano Manufacturing Technology(MNMT)Tianjin UniversityTianjin 300072China

Optical interferometry is a powerful tool for measuring and characterizing areal surface topography in precision manufacturing.A variety of instruments based on optical interferometry have been developed to meet the measurement needs in various applications,but the existing techniques are simply not enough to meet the ever-increasing requirements in terms of accuracy,speed,robustness,and dynamic range,especially in on-line or on-machine *** paper provides an in-depth perspective of surface topography reconstruction for optical interferometric ***,configurations,and applications of typical optical interferometers with different capabilities and limitations are *** background and recent advances of fringe analysis algorithms,including coherence peak sensing and phase-shifting algorithm,are *** new developments in measurement accuracy and repeatability,noise resistance,self-calibration ability,and computational efficiency are *** paper also presents the new challenges that optical interferometry techniques are facing in surface topography *** address these challenges,advanced techniques in image stitching,on-machine measurement,intelligent sampling,parallel computing,and deep learning are explored to improve the functional performance of optical interferometry in future manufacturing metrology.

关键词： surface topography measurement optical interferometry coherence envelope phase-shifting algorithm

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phase-measuring algorithm to suppress inner reflection of transparent parallel plate in wavelength tuning Fizeau interferometer

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PRECISION ENGINEERING-JOURNAL OF THE INTERNATIONAL SOCIETIES FOR PRECISION ENGINEERING AND NANOTECHNOLOGY 2017年 48卷 67-74页

作者： Kim, Yangjin Sugita, Naohiko Mitsuishi, Mamoru Pusan Natl Univ Sch Mech Engn 2Busandaehak ro 63beon gil Busan 46241 South Korea Univ Tokyo Dept Mech Engn Bunkyo Ku 7-3-1 Hongo Tokyo 1138656 Japan

Optical thickness variation is a fundamental characteristic of transparent optical devices. When measuring this variation by using a wavelength-tuning Fizeau interferometer, the measurement accuracy depends on the phase-shifting algorithm being used. Therefore, the phase-shifting algorithm should compensate for any errors incurred during the measurement, including the phase-shift error, coupling errors, and bias modulation of intensity. Among these errors, however, the coupling errors between the higher harmonics resulting from the inner reflections of the transparent plate and phase-shift error have not previously been considered. This paper presents a derivation of a 19-sample phase-shifting algorithm that can compensate for the miscalibration and 1st-order nonlinearity of the phase shift, coupling errors, and bias modulation of intensity during wavelength tuning. The characteristics of the 19-sample algorithm were estimated with respect to the Fourier representation in the frequency domain. The phase error of measurements performed using the 19-sample algorithm was discussed and compared with that of measurements obtained using other conventional phase-shifting algorithms. Finally, the optical thickness variation of a fused silica parallel plate was obtained using a wavelength-tuning Fizeau interferometer and the 19-sample algorithm. The measurement accuracy was discussed by comparing the ripples in the crosstalk noise with those calculated using other phase-shifting algorithms. The experimental results indicated that the optical thickness variation measurement accuracy for the fused silica plate was approximately 2 nm. (C) 2016 Elsevier Inc. All rights reserved.

关键词： Precision measurement Interferometry Optical thickness phase-shifting algorithm phase error

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Enhanced dual-frequency pattern scheme based on spatial-temporal fringes method

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JOURNAL OF MODERN OPTICS 2018年第12期65卷 1495-1506页

作者： Wang, Minmin Zhou, Canlin Si, Shuchun Lei, Zhenkun Li, Xiaolei Li, Hui Li, YanJie Shandong Univ Sch Phys Jinan Shandong Peoples R China Dalian Univ Technol Dept Engn Mech Dalian Peoples R China Hebei Univ Technol Sch Mech Engn Tianjin Peoples R China Jinan Univ Sch Civil Engn & Architecture Jinan Shandong Peoples R China

One of the major challenges of employing a dual-frequency phase-shifting algorithm for phase retrieval is its sensitivity to noise. Yun et al proposed a dual-frequency method based on the Fourier transform profilometry, yet the low-frequency lobes are close to each other for accurate band-pass filtering. In the light of this problem, a novel dual-frequency pattern based on the spatial-temporal fringes (STF) method is developed in this paper. Three fringe patterns with two different frequencies are required. The low-frequency phase is obtained from two low-frequency fringe patterns by the STF method, so the signal lobes can be extracted accurately as they are far away from each other. The high-frequency phase is retrieved from another fringe pattern without the impact of the DC component. Simulations and experiments are conducted to demonstrate the excellent precision of the proposed method.

关键词： phase retrieval profilometry phase-shifting algorithm Fourier transform dual-frequency pattern

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Statistical and interferometric determination of the optical thickness of a multilayer transparent plate

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OPTICAL REVIEW 2017年第6期24卷 734-740页

作者： Kim, Yangjin Hibino, Kenichi Pusan Natl Univ Sch Mech Engn 2 Busandaehak Ro63beon Gil Busan 46241 South Korea Natl Inst Adv Ind Sci & Technol 1-1-1 Umezono Tsukuba Ibaraki 3058563 Japan

Wavelength-tuning Fizeau interferometry has been widely used to measure and estimate the optical thickness of optical components. However, in multilayer interferometry, the coupling errors between the higher harmonics and phase-shift error cause systematic errors in the calculated phase distribution. This paper presents the derivation of a 15-sample phase-shifting algorithm that can compensate for the phase-shift miscalibration and up-to-first-order nonlinearity of the coupling errors between the second-order harmonic and phase-shift error. The characteristics of the 15-sample algorithm are estimated with respect to the Fourier representation in the frequency domain. The optical thickness of a highly reflective lithium niobate crystal wafer is measured using a wavelength-tuning Fizeau interferometer and 15-sample algorithm. Finally, the optical thickness is determined from the measured data using the statistical Student's t test.

关键词： phase-shifting algorithm Coupling error Optical thickness Wavelength tuning Student's t test

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Suppression of multiple-beam interference noise in testing an optical-parallel plate by wavelength-scanning interferometry

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OPTICAL REVIEW 2002年第2期9卷 60-65页

作者： Hibino, K Takatsuji, T Natl Inst Ind Sci & Technol Tsukuba Ibaraki 3058564 Japan

Measurements of optical parallel plates in a Fizeau interferometer lead to problems from multiple-beam interference noise unless the back surface of the plate has an additional treatment to prevent its reflection from reaching the detector. Such internal-reflection noise can be separated from the fundamental interference signal by its modulation frequency in a wavelength-scanning interferometer. However, to completely eliminate the noise, the air-gap distance between the testing and reference surfaces of the interferometer must be adjusted to a specific value, depending on the thickness and refractive index of the plate. This adjustment requires an undesirable change in the air gap, which is related to the phase modulation rate of the interferometer, and also requires additional information regarding the testing plate, which makes the measurement laborious. We show that if we add new symmetries to the sampling functions of the phase measuring algorithm, we can obtain significantly greater tolerance for the air-gap error. A new 19-sample algorithm allows a tolerance of +/-23% while keeping the systematic errors at less than lambda/200. The periodicity of the new algorithm and an integrating bucket technique also provide more options for the thickness of the testing plate, which guarantees an air-gap distance more independent of this thickness.

关键词： phase measurement Fizeau interferometer wavelength scanning internal reflection phase-shifting algorithm optical parallel

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