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Li Z, Yin D, Yang Y, Zhang Q, Gong H. Specular Surface Shape Measurement with Orthogonal Dual-Frequency Fourier Transform Deflectometry. SENSORS (BASEL, SWITZERLAND) 2023; 23:674. [PMID: 36679465 PMCID: PMC9861365 DOI: 10.3390/s23020674] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Revised: 12/27/2022] [Accepted: 01/04/2023] [Indexed: 06/17/2023]
Abstract
Three-dimensional (3D) shape measurement for specular surfaces is becoming increasingly important in various applications. A novel orthogonal dual-frequency fringe is proposed in the specular surface shape measurement to overcome the phase jumping and discontinuities in spatial phase unwrapping. The fringe recalibrated high-accuracy phase information from its high-frequency fringe component with low-ambiguity phase information from its low-frequency fringe component. An improved Fourier transform deflectometry method based on the orthogonal dual-frequency fringe is proposed to measure 3D specular surface shapes. Simulation results showed that the orthogonal dual-frequency Fourier transform deflectometry (ODD) method could precisely reconstruct flat surfaces with an error of 2.16 nm rms, and concave surfaces with an error of 1.86 μm rms. Experimental results showed that the reconstructed shapes of both the flat mirror and the concave mirror measured by the ODD measurement system were highly comparable to those obtained by the phase-measuring deflectometry (PMD) method. This new fringe provides a distinctive approach to structured pattern construction and reduces the phase unwrapping ambiguities in specular surface shape measurement. The ODD method can achieve accurate 3D shape measurement for specular surfaces by sampling only one fringe, providing a possible basis for future real-time measurement of specular surfaces.
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Affiliation(s)
- Zhiming Li
- Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China
- School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China
- School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Dayi Yin
- Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China
- School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yuanyu Yang
- Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China
- School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Quan Zhang
- Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China
| | - Huixing Gong
- Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China
- School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China
- School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
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Hu Y, Wang Z, Hao Q. Circular Subaperture Stitching Interferometry Based on Polarization Grating and Virtual-Real Combination Interferometer. SENSORS (BASEL, SWITZERLAND) 2022; 22:9129. [PMID: 36501832 PMCID: PMC9737840 DOI: 10.3390/s22239129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/20/2022] [Revised: 11/16/2022] [Accepted: 11/21/2022] [Indexed: 06/17/2023]
Abstract
This paper presents a polarization grating based circular subaperture stitching interferometer. The system can be used for small F/# concave surface tests with a large F/# transmission sphere, where F/# is the ratio of focal length to aperture. A polarization grating was employed to deflect the incident beam for subaperture scanning by its axial rotation instead of a multi-axis motion-control system. Compared with the traditional subaperture stitching interferometric system, the system proposed in this paper is smaller in size and reduces the measurement error introduced by mechanical adjustment. Using a virtual interferometer model and a virtual-real combination algorithm to remove the retrace error, the full-aperture figure error can be directly obtained without the need for a complex stitching algorithm. The feasibility of the algorithm was verified, and the measurement error caused by the modeling error was analyzed by simulation. The capability of the polarization grating to scan subapertures was experimentally confirmed, and possible solutions to some engineering challenges were pointed out. The research in this paper has pioneering and guiding significance for the application of polarization grating in interferometry.
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Affiliation(s)
- Yao Hu
- Beijing Key Laboratory for Precision Optoelectronic Measurement Instrument and Technology, School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China
| | - Zhen Wang
- Beijing Key Laboratory for Precision Optoelectronic Measurement Instrument and Technology, School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China
| | - Qun Hao
- Beijing Key Laboratory for Precision Optoelectronic Measurement Instrument and Technology, School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China
- School of Opto-Electronic Engineering, Changchun University of Science and Technology, Changchun 130022, China
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Wu J, Hu C, Liu R, Wu S, Cao J, Cheng Z, Yu B, Zhang L. Adam SPGD algorithm in freeform surface in-process interferometry. OPTICS EXPRESS 2022; 30:32528-32539. [PMID: 36242312 DOI: 10.1364/oe.470007] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2022] [Accepted: 08/16/2022] [Indexed: 06/16/2023]
Abstract
The adaptive interferometer has been recently proposed to realize the metrology of unknown freeform surfaces with several restructured algorithms for feedback control. The adaptive moment estimation (Adam) stochastic parallel gradient descent (SPGD) algorithm is employed in this paper for fringes release. The proposed algorithm makes considerable progress in relieving conflict of the convergence rate, speed, and parameters intervention. Simulations and experiments show its 37% time saving and 99% convergence rate, with arbitrarily configured parameter increment, compared with the SPGD algorithm. It would have great potential in in-process tests in freeform surface fabrication or large-volume testing.
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Monoscopic Phase Measuring Deflectometry Simulation and Verification. ELECTRONICS 2022. [DOI: 10.3390/electronics11101634] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The three-dimensional (3D) shape of specular surfaces is important in aerospace, precision instrumentation, and automotive manufacturing. The phase measuring deflectometry (PMD) method is an efficient and highly accurate technique to measure specular surfaces. A novel simulation model with simulated fringe patterns for monoscopic PMD is developed in this study. Based on the pre-calibration and the ray-tracing model of the monoscopic PMD system, a comprehensive model from deformed pattern generation to shape reconstruction was constructed. Experimental results showed that this model achieved high levels of measuring accuracy in both planar and concave surfaces measurement. In planar surface measurement, the peak to valley (PV) value and root mean square (RMS) value of the reconstructed shape can reach 26.93 nm and 10.32 nm, respectively. In addition, the accuracy of the reconstructed concave surface can reach a micrometre scale. This work potentially fills critical gaps in monoscopic PMD simulation and provides a cost-effective method of PMD study.
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Hao Q, Tao X, Hu Y, Li T, Zhao W. Interferometric measurement of high-order aspheric surface parameter errors based on a virtual-real combination iterative algorithm. OPTICS EXPRESS 2021; 29:27014-27030. [PMID: 34615124 DOI: 10.1364/oe.435252] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2021] [Accepted: 07/26/2021] [Indexed: 06/13/2023]
Abstract
Aspheric surface parameters, including vertex radius of curvature, conic constant, and high-order aspheric coefficients, decide the optical properties of aspheric surfaces. The measurement of aspheric surface parameter errors (SPEs) is a substantial issue for the fabrication of aspheric surfaces. Interferometry is a mature high-accuracy method in aspheric surface figure error measurement, but challenges still exist in the measurement of SPEs for high-order aspheric surfaces or convex aspheric surfaces. We propose an interferometric measurement method for high-order aspheric SPEs based on a virtual-real combination iterative algorithm (VRCIA). We also propose a recommended measurement system including a partial compensation interferometer to obtain the partial compensated wavefront and a laser differential confocal system to obtain the best compensation distance for calculating SPEs through the VRCIA. A high-order convex aspheric surface is measured to demonstrate the feasibility of the method. The relative accuracy of vertex radius of curvature error, conic constant error and fourth-order aspheric coefficient error can reach 0.025%, 0.095% and 3.02%, respectively.
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Hao Q, Chang X, Hu Y, Tao X, Lv J, Ning Y, Cheng X. Description method with automatically configurable Gaussian radial basis function for complex freeform surface. OPTICS EXPRESS 2021; 29:16804-16819. [PMID: 34154234 DOI: 10.1364/oe.426130] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2021] [Accepted: 04/28/2021] [Indexed: 06/13/2023]
Abstract
The description of deformable mirror (DM) surface, which is usually a complex freeform surface, affects the measurement speed and accuracy in a real-time interferometric measurement system with a DM as the dynamic compensator. We propose an accurate and fast description method with automatically configurable Gaussian radial basis function. The distribution and shape factors of GRBFs are related to the complexity of the surface with sufficient flexibility to improve the accuracy, and the fitting results are automatically obtained using a traversal optimization algorithm, which can improve the fitting speed by reducing the number of time-consuming calculations. The feasibility is verified by numerical and practical experiment.
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Cai B, Zhang L, Wu J, Wang M, Chen X, Duan M, Wang K, Wang Y. Absolute phase measurement with four patterns based on variant shifting phases. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2020; 91:065115. [PMID: 32611060 DOI: 10.1063/1.5144928] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2020] [Accepted: 05/29/2020] [Indexed: 06/11/2023]
Abstract
Fringe projection profilometry has been proverbially utilized for measuring the shapes of objects. A common challenge in those systems is to accurately obtain a smooth absolute phase. Many new methods have been proposed to address this challenge. In this paper, we discuss a technique based on variant shifting phases. This approach embeds codewords into the shifting phase and only needs four patterns. However, reliable measurement results are difficult to achieve with a large number of codewords because of the phase errors. To address this shortcoming, we present a robust coding method that embeds a specific code sequence into the shifting phase and can generate more than 36 periods. The fringe order is determined using unique three-adjacent-codes combining the current period and its neighbors. An error correction algorithm is also proposed to optimize the codewords. The proposed method is experimentally verified using an established measurement system. The result shows that the proposed method is robust and efficient.
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Affiliation(s)
- Bolin Cai
- Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei 230026, China
| | - Lei Zhang
- Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei 230026, China
| | - Jun Wu
- School of Automation, Wuhan University of Technology, Wuhan 430070, China
| | - Mengyu Wang
- Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei 230026, China
| | - Xiangcheng Chen
- School of Automation, Wuhan University of Technology, Wuhan 430070, China
| | - Minghui Duan
- Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei 230026, China
| | - Keyi Wang
- Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei 230026, China
| | - Yuwei Wang
- College of Engineering, Anhui Agricultural University, Hefei 230036, China
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Ye L, Wang W, Zhang X, Xu M, Zhang J, Zheng L. Testing of large-aperture aspheric mirrors using a single coated lens. APPLIED OPTICS 2020; 59:4577-4582. [PMID: 32543565 DOI: 10.1364/ao.388276] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2020] [Accepted: 04/14/2020] [Indexed: 06/11/2023]
Abstract
The measurement of aspheric surfaces is very difficult and challenging. An optical system with a single coated lens is proposed for measuring large-aperture aspheric convex/concave surfaces. In this system, the first surface of the compensator is used as an auto-collimation surface, which can realize high-precision null compensation. Based on the third-order aberration theory, the initial design parameters of the system are obtained by analytical calculation, and the parameters are then optimized numerically. An oblate spheroid with an equivalent aperture of 426 mm is taken as an example, and the measuring accuracy of the proposed method can achieve 0.0063λ rms.
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Zhang L, Li C, Huang X, Zhang Y, Zhou S, Li J, Yu B. Compact adaptive interferometer for unknown freeform surfaces with large departure. OPTICS EXPRESS 2020; 28:1897-1913. [PMID: 32121892 DOI: 10.1364/oe.380889] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2019] [Accepted: 01/02/2020] [Indexed: 06/10/2023]
Abstract
The newest experimental validation report of the coverage for the rotationally non-symmetric departure of a freeform surface in adaptive interferometry is about 20 µm. A compact adaptive interferometer is introduced to test unknown freeform surfaces with larger departure. The cascaded DMs (woofer and tweeter) can effectively double the measurable rotationally non-symmetric departure, to ∼80 µm using current DM technology. With a constrained decoupling control algorithm, the woofer and tweeter can averagely share the aberrations without coupling. DM surface monitoring is addressed by a time-division-monitoring (TDM) technique, which avoids separate monitoring devices and configurations and thus makes a compact configuration. Measurements of two different surfaces are presented: a nearly flat freeform with ∼40 um departure, and an off-axis paraboloid with ∼50 um of asymmetric departure.
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Yan L, Zhu D, Zeng X, Li M, Wang X, Ma D. Experimental study on hybrid compensation testing of an off-axis convex ellipsoid surface. OPTICS EXPRESS 2019; 27:27546-27561. [PMID: 31684520 DOI: 10.1364/oe.27.027546] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2019] [Accepted: 09/03/2019] [Indexed: 06/10/2023]
Abstract
Aspherical surfaces can provide significant benefits to a wide variety of optical systems, but manufacturing high-precision aspherical surfaces has historically been limited by the ability to measure them. Null testing has always been the ideal method in aspherical measurement. However, in many cases, it is hard to realize null testing for complex surfaces, especially for convex surfaces in complicated forms. In this paper, we propose a hybrid compensation method combining a spherical mirror and a computer generated hologram (CGH) to achieve the null testing of the convex aspherical surface. Firstly, we introduce our self-developed mathematical models in the hybrid compensation method, including optics alignment model, distortion correction model and spherical surface error removing model. Then the performance of our proposed method is analyzed by a null testing experiment of an off-axis convex ellipsoid mirror. The experimental result shows that the proposed method can accomplish the hybrid compensation testing of convex aspherical surfaces effectively, and it can also bring much to the application of our method in convex aspherical surface testing.
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Wu G, Wu Y, Li L, Liu F. High-resolution few-pattern method for 3D optical measurement. OPTICS LETTERS 2019; 44:3602-3605. [PMID: 31305582 DOI: 10.1364/ol.44.003602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2019] [Accepted: 06/22/2019] [Indexed: 06/10/2023]
Abstract
Accurately and quickly obtaining the three-dimensional (3D) shape information of objects has become increasingly important in various scientific fields. However, simultaneously achieving the high-resolution and high-speed 3D shape measurement of unknown objects remains challenging in practice. In this Letter, we propose a novel variant shifting-phase method for 3D optical measurement. Based on a digital fringe projection system, the method performs a point-wise high-resolution measurement of objects by projecting only four intensity-coded patterns. We can retrieve the wrapped phases and their corresponding fringe orders simultaneously from these four patterns, and do not require any pre-acquired information of the object. The experimental results successfully demonstrate the effectiveness of the easy-to-operate method.
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Xue S, Chen S, Tie G, Tian Y, Hu H, Shi F, Peng X, Xiao X. Flexible interferometric null testing for concave free-form surfaces using a hybrid refractive and diffractive variable null. OPTICS LETTERS 2019; 44:2294-2297. [PMID: 31042206 DOI: 10.1364/ol.44.002294] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2019] [Accepted: 04/06/2019] [Indexed: 06/09/2023]
Abstract
Free-form surfaces have been applied in a wide range of modern optical systems. As a supporting technique for fabricating free-form surfaces, the interferometric null method for testing the surface figure error has very limited flexibility. In this Letter, we report a flexible interferometric null test method which can test free-form surfaces with a very broad departure varying range. In the presented flexible null method, a hybrid refractive and diffractive variable null (HRDVN) is utilized as the flexible null. The HRDVN has superb aberration types adaptability, amplitude adaptability, and moderate phase generating accuracy. A flexible interferometric null testing setup was established using the HRDVN. Its superb adaptive capacity and moderate test accuracy were successfully demonstrated by measuring a free-form surface with rotationally symmetric departure of 173.486λ (λ=632.8 nm) and non-rotationally symmetric departure of 23.786λ.
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Xue S, Deng W, Chen S. Intelligence enhancement of the adaptive wavefront interferometer. OPTICS EXPRESS 2019; 27:11084-11102. [PMID: 31052958 DOI: 10.1364/oe.27.011084] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2019] [Accepted: 03/23/2019] [Indexed: 06/09/2023]
Abstract
The adaptive wavefront interferometer (AWI) we have reported recently is utilized to test in-process surfaces with severe surface figure error which is beyond dynamic range of conventional interferometers [S. Xue, S. Chen, Z. Fan, and D. Zhai, Opt. Express26, 21910 (2018).]. However, it shows low intelligence when Monte-Carlo simulation is conducted to apply AWI on various surface figure error. In some simulation cases, the unresolvable fringes keep still or cannot be turned into completely resolvable fringes. To troubleshoot this issue, we studied AWIs in a general framework of global optimization for the first time. Under this framework, we explained that three optimization issues contribute to the poor performance of AWI. On this basis, we proposed a machine vision and genetic algorithm combined method (MV-GA) to control AWI to realize efficient and robust tests of various surface figure error. Monte-Carlo simulation and experiment verify the robustness has been greatly enhanced.
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