Four-step shear method for the absolute measurement of a flat surface based on phase measuring deflectometry.

This paper presents a short review for phase measuring deflectometry (PMD). PMD is a phase calculation based technique for three-dimensional (3D) measurement of specular surfaces. PMD can achieve nano-scale form measurement accuracy with the advantages of high dynamic range, non-contact, full field measurement which makes it a competitive method for specular surface measurement. With the development of computer science, display and imaging technology, there has been an advancement in speed for PMD in recent years. This paper discusses PMD focusing on the difference on its system configuration. Measurement principles, progress, advantages and problems are discussed for each category. The challenges and future development of PMD are also discussed.

Phase measuring deflectometry (PMD) is a competitive method for specular surface measurement that offers the advantages of a high dynamic range, non-contact process, and full field measurement; furthermore, it can also achieve high accuracy. Camera calibration is a crucial step for PMD. As a result, a method based on the calibration of the entrance pupil center is introduced in this paper. Then, our proposed approach is compared with the most popular photogrammetric method based on Zhang’s technique (PM) and Huang’s modal phase measuring deflectometry (MPMD). The calibration procedures of these three methods are described, and the measurement errors introduced by the perturbations of degrees of freedom in the PMD system are analyzed using a ray tracing technique. In the experiment, a planar window glass and an optical planar element are separately measured, and the measurement results of the use of the three methods are compared. The experimental results for the optical planar element (removing the first 6 terms of the Zernike polynomial) show that our method’s measurement accuracy reached 13.71 nm RMS and 80.50 nm PV, which is comparable to accuracy values for the interferometer.

Phase measuring deflectometry (PMD) is a robust, noncoherent technique for the characterization of specular surface. For measuring high specular reflectivity surface, PMD can deliver micron radian range local gradient. However, when the measured surface has low specular reflectivity, the accuracy of the measured gradient is low since the captured fringe pattern shows low signal to noise ratio. The phase error characteristics in PMD system when testing low reflectivity surfaces are analyzed. The analysis illustrates that the random phase error increases rapidly while the nonlinear error drops slowly with the decreasing of the tested surface reflectivity. In order to attain high precision measurement of low reflectivity specular surface, a robust error reduction method based on wavelet de-noising is proposed to reduce the phase error. This error reduction method is compared with several other normally used methods in both simulation and experiment work. The method based on the wavelet de-noising shows better performance when measuring the low reflectivity specular surface.

A null phase measuring deflectometry (PMD) is presented to measure the three-dimensional shape of aspheric mirrors with radial symmetry. Curved fringes displayed on a mobile screen are reflected by the surface under test, and a camera captures the fringe patterns. By analyzing the captured fringe patterns, the deviations along the normal of the mirror’s surface can be restored by integrating the slopes of these deviations, and then the surface under test can be reconstructed. Compared with non-null PMD, the qualitative information of surface in null PMD can be shown fast and easily for a surface with large deviations in the grinding stage. Computer simulation and experiment are presented to validate the presented method.

Phase measurement deflectometry (PMD) is an excellent method for high-precision optical surface measurement; through the simple system structure, accuracy comparable to that of interference methods can be realized. The key of PMD is to solve the ambiguity between the surface shape and normal vector. Considering all kinds of methods, the binocular PMD method is undoubtedly a method with a very simple system structure and can be easily applied to complex surfaces, such as free-form surfaces. However, this method relies on a large screen with high accuracy, which not only increases the weight of the system, but also reduces the flexibility of the system, and manufacturing errors in the large-size screen can easily become error sources. In this Letter, we have made some improvements based on the traditional binocular PMD. At first, we try to replace the large screen with two small screens to increase the flexibility and accuracy of the system. Further, we replace one small screen with a single point to simplify the system structure. Experiments show that the proposed methods not only improve the system flexibility and reduce the complexity, but can also achieve high measurement accuracy.

Phase Measuring Deflectometry (PMD) and Structured-Light Modulation Analysis Technique (SMAT) perform effectively in shape and defect measurements of specular objects, but the difficulty of giving consideration to accuracy and speed has also restricted the further development and application of them. Inspired by recent successes of deep learning techniques for computational imaging, we demonstrate for the first time that deep learning techniques can be used to recover high-precision modulation distributions of specular surfaces from a single-frame fringe pattern under SMAT, enabling fast and high-quality defect detection of specular surfaces. This method can also be applied to recover higher-precision phase distributions of specular surfaces from a single-frame fringe pattern under PMD, so as to realize the 3D shape measurement. In this paper, we combine depthwise separable convolution, residual structure and U-Net to build an improved U-Net network. The experimental results prove that the method has excellent performance in the phase and modulation retrieval of specular surfaces, which almost reach the accuracy of the results obtained by ten-step phase-shifting method.

Geometry calibration is a critical step for phase measuring deflectometry (PMD) system. Generally, a circle grid, a chessboard, or a group of fringes is used to determine the camera pose during the calibration. There are two main problems with using a circle grid or a checkerboard for geometry calibration: incomplete pattern capturing and uneven gray value distribution. For fringe patterns, the camera needs to take many images of the reflected patterns. This paper proposes a new geometry calibration method for PMD system, which combines square-based fiducial markers with a marker-less flat mirror. The proposed method can accomplish the calibration in the case the captured calibration patterns are incomplete and have uneven gray value distribution, and only require to take a minimum of three images. Experiment shows the proposed method can get accuracy calibration result simple and flexible.

Fringe projection profilometry (FPP) and phase measuring deflectometry (PMD) are the currently popular technologies for measuring diffuse and specular reflective surfaces respectively. Both methodologies demonstrate superior performance for single-type reflective surfaces. However, with the rapid development of advanced manufacturing and intelligent manufacturing technologies, products have seen significant improvements in complexity, diversity, and personalization, often exhibiting composite reflective characteristics on their surfaces. The aforementioned single technology cannot meet the measurement requirements for composite reflective surfaces. To address this challenge, this paper presents a composite reflective surfaces measurement method combining FPP with PMD techniques, and an optimized system calibration method based on binocular stereo vision is proposed to enhance the system's measurement accuracy. To improve the measurement efficiency, a strategy in which the LCD screen and projector project different colorful fringe patterns simultaneously is adopted. To mitigate stray light interference from the projector on specular surface profilometry, a partition projection method is presented. Instead of establishing the pixel mapping relationship between the projector and diffused surface aeras, the coordinate mapping relationship between the specular reflective region and the projector pixel is established according to the phase-height relationship to realize the accurate projection of the projector to the diffused surface. Experiments have been performed to validate the proposed method, and the results demonstrate that it can reconstruct the composite surfaces with higher accuracy. In particular, the reconstruction accuracy of specular surface can reach several tens of nanometres.

Interferometry is a relative measurement method for optical surface testing, and thus its testing accuracy depends on the accuracy of the reference surface. Absolute measurement is one of the most effective methods to improve the testing accuracy in interferometry. We present an efficient absolute measurement method based on Zernike polynomial fitting algorithms. With our proposed method, the profiles of both the test surface and the reference surface can be calculated simultaneously. We further carried out simulation analysis to scientifically evaluate the test accuracy of the proposed method. Finally, we conducted actual experiments to demonstrate the feasibility and practicability of our method.

Phase-measuring deflectometry is a full-field gradient technique that lends itself very well to testing reflective optical surfaces. In the past, the industry’s interest has been focussed mainly on the detection of defects and ripples, since it is easy to achieve sensitivity in the nm range. On the other hand, attempts to reconstruct the absolute surface shape from the gradient map have been plagued by systematic errors that accumulate to unacceptable uncertainties during data integration. Recently, thanks to improved measurement and evaluation techniques, the state of the art in absolute surface measurement has reached a level of maturity that allows its practical usage in precision optical manufacturing and qualification systems. We demonstrate the techniques, and the progress, by way of results from mirrors for telescopes, solar concentrators, and precision laboratory assemblies.

Transparent element surface measurement using binary pattern in phase-measuring deflectometry

A multi-segments stitching method is proposed to obtain two-dimensional profile of large scale aspheric components during grinding process. We firstly analyze the corresponding relation between surface features of aspherics and measurement range of profilometer. According to multi-body system theory and slope difference, a mathematical model of multi-segments stitching method is constructed. Further, the multi-segments stitching errors based on 400 mm aspheric profile are simulated with different translation amounts, rotation angles, translation errors as well as rotation errors. The simulation results indicate that the translation error is the key factor for measuring accuracy of the multi-segments stitching method. In addition, the standard deviations of multi-segments stitching errors are between 0.2 μm and 0.4 μm as the four factors are set to the proper values. To verify the simulation analysis results, an experimental setup, including Talysurf PGI 1240 and fixture, is applied to detect a 150 mm profile line on the aspheric surface. The experiment results show that the standard deviations of multi-segments stitching errors are almost within 1 μm when the rotation angle is under 7° and the translation amount is under 11 mm. The multi-segments stitching method can employ a small-range profilometer to achieve measurement of large scale aspheric surfaces with submicrometer accuracy.

Compressed sensing (CS) based radar imaging requires the use of a mathematical model of the observation process. Inaccuracies in the observation model may cause defocusing in the reconstructed images. In the observation process, the observation positions are usually not known perfectly. Imperfect knowledge of the observation positions is a major source of model errors in imaging. In this paper, a method is proposed to compensate the observation position errors in CS-based radar imaging. Instead of treating the observation-position-induced model errors as phase errors in the data, the proposed method can determine the observation position errors as part of the imaging process. It uses an iterative algorithm, which cycles through steps of target reconstruction and observation position error estimation and compensation. The proposed method can estimate the observation position errors accurately, and the reconstruction quality of the target images can be improved significantly. Simulation results and experimental results from rail-mounted radar and airborne synthetic aperture radar are presented to show the effectiveness of the proposed method.

The accuracy of surface measurement determines the manufacturing quality of membrane mirrors. Thus, an efficient and accurate measuring method is critical in membrane mirror fabrication. This paper formulates this measurement issue as a surface reconstruction problem and employs two-stage trained Zernike polynomials as an inline measuring tool to solve the optical surface measurement problem in the membrane mirror manufacturing process. First, all terms of the Zernike polynomial are generated and projected to a non-circular region as the candidate model pool. The training data are calculated according to the measured values of distance sensors and the geometrical relationship between the ideal surface and the installed sensors. Then the terms are selected by minimizing the cost function each time successively. To avoid the problem of ill-conditioned matrix inversion by the least squares method, the coefficient of each model term is achieved by modified elitist teaching–learning-based optimization. Subsequently, the measurement precision is further improved by a second stage of model refinement. Finally, every point on the membrane surface can be measured according to this model, providing more the subtle feedback information needed for the precise control of membrane mirror fabrication. Experimental results confirm that the proposed method is effective in a membrane mirror manufacturing system driven by negative pressure, and the measurement accuracy can achieve 15 µm.

In recent years, low-cost and lightweight RGB and depth (RGB-D) sensors, such as Microsoft Kinect, have made available rich image and depth data, making them very popular in the field of simultaneous localization and mapping (SLAM), which has been increasingly used in robotics, self-driving vehicles, and augmented reality. The RGB-D SLAM constructs 3D environmental models of natural landscapes while simultaneously estimating camera poses. However, in highly variable illumination and motion blur environments, long-distance tracking can result in large cumulative errors and scale shifts. To address this problem in actual applications, in this study, we propose a novel multithreaded RGB-D SLAM framework that incorporates a highly accurate prior terrestrial Light Detection and Ranging (LiDAR) point cloud, which can mitigate cumulative errors and improve the system’s robustness in large-scale and challenging scenarios. First, we employed deep learning to achieve system automatic initialization and motion recovery when tracking is lost. Next, we used terrestrial LiDAR point cloud to obtain prior data of the landscape, and then we applied the point-to-surface inductively coupled plasma (ICP) iterative algorithm to realize accurate camera pose control from the previously obtained LiDAR point cloud data, and finally expanded its control range in the local map construction. Furthermore, an innovative double window segment-based map optimization method is proposed to ensure consistency, better real-time performance, and high accuracy of map construction. The proposed method was tested for long-distance tracking and closed-loop in two different large indoor scenarios. The experimental results indicated that the standard deviation of the 3D map construction is 10 cm in a mapping distance of 100 m, compared with the LiDAR ground truth. Further, the relative cumulative error of the camera in closed-loop experiments is 0.09%, which is twice less than that of the typical SLAM algorithm (3.4%). Therefore, the proposed method was demonstrated to be more robust than the ORB-SLAM2 algorithm in complex indoor environments.