Surface Shape Measurement Research Articles

Development of a high-precision long trace profiler utilizing shear measurements.

Compensating for the pitch error in the scanning movement is a fundamental issue when conducting large-scale surface shape measurements with deflectometric profilers. This paper presents a new long trace profiler employing a shearing measurement technique. In this setup, the optical head and the mirror under test are mounted on two independent parallel movable air-bearing carriages to enable shearing and scanning movements separately. The distance between the optical head and the tested mirror remains fixed, effectively minimizing the influence of system errors resulting from imperfections in optical devices. Simulation studies show that the double shear measurement method with a low-spatial-frequency filtering process can effectively mitigate high-frequency angular measurement errors introduced by the instability of the air-bearing stage. Experimental tests conducted on flat mirrors demonstrated a precision of less than 50 nrad rms, thereby confirming the robustness of the system.

Finite Element Model Updating Method for Radio Telescope Antenna Based on Parameter Optimization with Surrogate Model

There are deviations between the radio telescope antenna finite element (FE) model, founded on the design stage, and the actual working antenna structure. The original FE model cannot accurately describe the antenna structure deformation characteristics under the environmental load, thereby compromising the accuracy of the active structural compensation. This article proposes an antenna FE model updating method founded on parameter optimization with a surrogate model. The updating method updates the modulus of elasticity parameters of different components of the antenna backup structure (BUS) to obtain finite element analysis (FEA) results consistent with the actual measurement of the antenna reflector surface shape. The surrogate model founded on the multi-quadratic radial basis function (RBF) improves the computational efficiency of FE model updating, replacing the complex and time-consuming finite element analysis and calculation process. This method is implemented on a radio telescope antenna with an aperture of 25 m. The results show a significant reduction in the mismatch between the antenna and the updated FE model. This method’s calculation time is significantly reduced compared with the updating method without using the surrogate model, with the RBF surrogate model taking 1% of the time of the finite element model in the FEA calculations. The proposed method can improve the antenna FE model calculation accuracy and significantly enhance the efficiency of FE model updating calculations. Thus, it can offer a reference for antenna engineering practice.

Comparative study of phase retrieval algorithms for surface shape measurement by optical profilometry

Recent advances in optical sensors and information processing technology have granted a rapid progress in three-dimensional (3D) optical metrology, enabling highly accurate 3D inspection of complex-shaped objects. However, the 3D object surface estimation requires a phase recovery from so-called intensity fringe patterns of the tested objects. In this work, we present a comparative study of three most highlighted phase retrieval methods (phase shifting, Fourier transform and wavelet transform) using single or multiple acquired fringe patterns. Moreover, the phase retrieval methods performance is tested on additive and multiplicative noise based degraded fringe patterns, giving some qualitative and quantitative conclusions. Some experimental data are processed using Fourier transform and wavelet transform based algorithms to confirm accuracy of these two phase retrieval techniques.

Laser-tracker-based reference measurement for geometric calibration of phase-measuring deflectometry with active display registration

Abstract. Phase-measuring deflectometry (PMD) with active display registration (ADR) is a ray-optics-based technique for the shape measurement of specular surfaces. To obtain quantitative results, the relative position of the cameras of the PMD–ADR setup needs to be determined by geometric calibration. Geometric calibration can be performed by inserting a planar mirror into the setup that brings all camera fields of view to overlap on an active pattern display. The mirror is tilted to multiple positions and each time the cameras capture the displayed images, which yields sufficient data to obtain the relative camera positions and the positions of the mirror. In this article, we give a more detailed description of PMD–ADR and its calibration. We also implement a laser-tracker-based reference method to measure the mirror positions and use its result to expose systematic errors in the geometric calibration.

Automatic measurement system for large-aperture-angle non-holonomic spherical stitching with laser differential confocal interference.

In response to the urgent need for highly precise and efficient stitching measurements of large-aperture-angle non-holonomic spherical surfaces, a differential confocal interference automatic stitching measurement system for large-aperture-angle non-holonomic spherical surfaces was developed. The system realizes precise positioning of the confocal position through differential confocal precise focusing technology. Through the stitching model, coordinate transformation and error compensation were performed on subaperture data, and the stitching measurement of the spherical surface shape was realized. The positions and postures of the tested samples were adjusted automatically using an automatic adjustment workbench. The stitching measurement accuracy of this measurement system can attain 0.0013λ, relative error can attain 1.36%, and measurement time for eight subaperture stitching is 6min. This system achieves automatic and rapid adjustment of large-aperture-angle spherical elements and high-precision, nondestructive, fast, and automatic measurement of surface stitching.

Influence of sampling on three-dimensional surface shape measurement

Influence of sampling on three-dimensional surface shape measurement

Research on the influence of sampling on three-dimensional surface shape measurement

Research on the influence of sampling on three-dimensional surface shape measurement

Three-dimensional surface-shape measurement of moving billets using phase-shifting profilometry

Three-dimensional surface-shape measurement of moving billets using phase-shifting profilometry

Robust phase demodulation algorithm for single-frame interferogram

This paper presents a robust phase demodulation algorithm (PDA) for single-frame interferogram based on preprocessing and watershed segmentation transformation. Compared to existing methods, the PDA can be applied to closed fringe or non-closed fringe patterns with low number of fringes indiscriminately. The proposed PDA includes two main parts, one is the preprocessing stage based on the empirical mode decomposition and Hilbert spiral transformation for background and noise removal, as well as normalization, and the other one is the correction of the wrapped phase obtained by arccosine through the watershed segmentation transformation. Through numerical simulations, the robustness of PDA to high noise and different kinds of fringe patterns is proved. The experimental evaluation of the proposed algorithm focuses on surface shape measurement of optical components, and the comparative analysis of the first 36 Zernike coefficients demonstrates that the PDA has high accuracy and the phase is good accordance with that obtained by phase-shifting interferometry.

An Error Estimation System for Close-Range Photogrammetric Systems and Algorithms.

Close-range photogrammetry methods are widely used for non-contact and accurate measurements of surface shapes. These methods are based on calculating the three-dimensional coordinates of an object from two-dimensional images using special digital processing algorithms. Due to the relatively complex measurement principle, the accurate estimation of the photogrammetric measurement error is a non-trivial task. Typically, theoretical estimations or computer modelling are used to solve this problem. However, these approaches cannot provide an accurate estimate because it is impossible to consider all factors that influence the measurement results. To solve this problem, we propose the use of physical modelling. The measurement results from the photogrammetric system under test were compared with the results of a more accurate reference measurement method. This comparison allowed the error to be estimated under controlled conditions. The test object was a flexible surface whose shape could vary smoothly over a wide range. The estimation of the measurement accuracy for a large number of different surface shapes allows us to obtain new results that are difficult to obtain using standard approaches. To implement the proposed approach, a laboratory system for the error estimation of close-range photogrammetric measurements was developed. The paper contains a detailed description of the developed system and the proposed technique for a comparison of the measurement results. The error in the reference method, which was chosen to be phasogrammetry, was evaluated experimentally. Experimental testing of the stereo photogrammetric system was performed according to the proposed technique. The obtained results show that the proposed technique can reveal dependencies that may not be detected by standard approaches.

Complementary double pulse-width-modulation for 3D shape measurement of complex surfaces

Complementary double pulse-width-modulation for 3D shape measurement of complex surfaces

A Phase Retrieval Method for 3D Shape Measurement of High-Reflectivity Surface Based on π Phase-Shifting Fringes.

Fringe projection profilometry (FPP) has been widely used for 3D reconstruction, surface measurement, and reverse engineering. However, if the surface of an object has a high reflectivity, overexposure can easily occur. Image saturation caused by overexposure can lead to an incorrect intensity of the captured pattern images, resulting in phase and measurement errors of FPP. To address this issue, we propose a phase retrieval method for the 3D shape measurement of high-reflectivity surfaces based on π phase-shifting fringes. Our method only requires eight images to be projected, including three single-frequency three-step phase-shifting patterns and one pattern used to provide phase unwrapping constraints, called conventional patterns, as well as the π phase-shifting patterns corresponding to the four conventional patterns, called supplemental patterns. Saturated pixels of conventional fringes are replaced by unsaturated pixels in supplemental fringes to suppress phase retrieval errors. We analyzed all 16 replacement cases of fringe patterns and provided calculation methods for unwrapped phases. The main advantages of our method are as follows: (1) By combining the advantages of the stereo phase unwrapping (SPU) algorithm, the number of projected fringes is reduced. (2) By utilizing the phase unwrapping constraint provided by the fourth fringe pattern, the accuracy of SPU is improved. For highly reflective surfaces, the experimental results demonstrate the performance of the proposed method.

Establishment and analysis of feasibility evaluation system and ultra-precision manufacturing technology for small aperture free-form surface optical element

Free-form optical elements are more and more broadly used in modern optical systems due to their distinctive characteristics. In order to realize the high-precision manufacturing of free-form optical element, the constraints on parameters of manufacture and measurement were established based on the designing parameters of free-form optical element. Meanwhile, the evaluation system for the machinability and detectability of free-form optical element was obtained by means of the corresponding mathematical model. Furthermore, the White Light Interference (WLI) stitching detection technology, coupled with the least square multi-parameter optimization algorithm, was used to solve shape-error measurement of free-form optical element. Additionally, a free-form surface compensation manufacturing mechanism of asymmetric shape error was established. Based on the above methods, the polynomial free-form optics were processed and measured. According to the surface shape measurement results, the same element was processed with compensation manufacturing twice. The surface shape precision was obviously improved from PV = 2553 nm and RMS = 481 nm to PV = 214 nm and RMS = 19.9 nm, which verified the effectiveness of the method. A significant value was unfolded in the engineering application of this method.

High-precision dynamic three-dimensional shape measurement of specular surfaces based on deep learning.

In order to solve the difficulty of traditional phase measuring deflectometry (PMD) in considering precision and speed, an orthogonal encoding PMD method based on deep learning is presented in this paper. We demonstrate for, what we believe to be, the first time that deep learning techniques can be combined with dynamic-PMD and can be used to reconstruct high-precision 3D shapes of specular surfaces from single-frame distorted orthogonal fringe patterns, enabling high-quality dynamic measurement of specular objects. The experimental results prove that the phase and shape information measured by the proposed method has high accuracy, almost reaching the results obtained by the ten-step phase-shifting method. And the proposed method also has excellent performance in dynamic experiments, which is of great significance to the development of optical measurement and fabrication areas.

Research on surface shape measurement of highly reflective surfaces based on stripe projection

Metal workpieces with highly reflective surfaces are particularly common in modern industrial manufacturing systems, and their three-dimensional dimensional measurement has great applications and needs in various fields. Among the various three-dimensional dimensional measurement technologies, projection three-dimensional measurement technology is adopted for its non-contact, low-cost, high-precision, and fast data processing characteristics. However, because of the high reflectance of the highly reflective surface, the structured light photos taken by the camera will be overexposed and underexposed, which will lead to the lack of three-dimensional information obtained. Due to the large range of changes in surface reflectance and the limited grayscale range of the camera, the traditional stripe projection method cannot correctly measure the three-dimensional morphology of highly reflective surfaces [1]. This paper introduces an adaptive sinusoidal stripe grating based on the reflectance of the surface of an object, which is used to compensate for the overexposure of the camera when shooting on a highly reflective surface. Finally, the generated adaptive stripes are projected onto the measured object, and the phase solution and three-dimensional surface shape reconstruction are carried out by the heterodyne multi-frequency phase shift method.

Angular phase-shifting interferometry for surface shapes measurement using vortex beam

We proposed a novel optical surface shapes measurement method based on conformal mapping-angular phase-shifting interferometry (APSI). This method rotates a Q-plate in the reference light path to introduce a 90-degree phase shift. The mathematical tool of conformal mapping is used for surface shape demodulation. After removing the helical phase in the compound phase, high-precision surface shape measurement results are obtained, and the measurement surface shape deviations are 3.33 nm (PV) and 0.26 nm (RMS). This work paves the way for surface shape measurement and compound phase demodulation using vortex beams.

Specular Surface Shape Measurement with Orthogonal Dual-Frequency Fourier Transform Deflectometry

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.

Screen-monitored stitching deflectometry based on binocular stereo vision

The measurement accuracy of the current phase measuring deflectometry (PMD) methods for in-situ measurement of the surface shape of large-aperture optics, which are placed at different inclination angles, is affected by the varied pose and deformed shape of screen due to manufacturing, external force and temperature variation, etc. This paper proposes a novel PMD method, the screen-monitored stitching deflectometry (SMSD), by combining binocular stereo vision with stitching deflectometry. And a four-camera PMD measurement system is constructed accordingly. The coordinates of the point source are determined using binocular stereo vision technology; based on the acquired coordinates, the stereo-iterative reconstruction and stitching algorithm are used to achieve the surface shape measurement. Simulations and experiments are accomplished to validate the advantages of the proposed method in reducing measurement errors caused by the varied pose and deformed shape of screen.

3D surface shape measurement of high dynamic range object based on monochrome fringe projection

3D surface shape measurement of high dynamic range object based on monochrome fringe projection

Highly Reflective Surface Shape Measurement Technology Based on Multiple Viewpoints and Fringes

Highly Reflective Surface Shape Measurement Technology Based on Multiple Viewpoints and Fringes