Phase-measuring deflectometry (PMD) is a crucial technology for measuring the forms of specular surfaces. However, existing stereo-PMD techniques have noticeable weaknesses when it comes to measuring structured specular surfaces. This limitation arises because the optical axis of the imaging system must intersect significantly with the optical axis of the display system, following the law of reflection. In contrast, near optical coaxial phase measuring deflectometry (NCPMD) offers several advantages over conventional PMD techniques. These advantages include a compact configuration, lightweight design, and minimal measurement errors due to the shadows of surface structures. NCPMD achieves this by utilizing a plate beamsplitter. With the assistance of the plate beamsplitter, the optical axis of the display screen can be configured much closer to the optical axis of the imaging system. As a result, the system becomes more compact and significantly reduces volume compared to the conventional PMD configuration. However, the introduction of the plate beamsplitter can impact on the measurement accuracy of the system. Specifically, the refractive effect of the beamsplitter can reduce the measurement accuracy. To address this challenge, a refraction error model is proposed for the NCPMD system. This model considers the influence of the plate beamsplitter’s refraction, allowing for the determination of measurement errors caused by this effect. Additionally, a virtual simulation system is established to analyze the shape reconstruction error resulting from the plate beamsplitter’s refraction. According to the experiments and results, the measurement accuracy can be effectively improved after the refractive error compensation.
The near optical coaxial phase measuring deflectometry (NCPMD) is one of the phase measuring deflectometry (PDM) techniques which is typically used for specular surface form measurement. The NCPMD utilizing a plate beamsplitter to folding the optical axis of display screen to make it close to the optical axis of the imaging system which makes the system more compact and has significantly reduced volume compared with the traditional PMD configuration. The NCPDM can achieve compact configuration, light weight, and reduce measurement error caused by structure shadows of the off-axis configuration of traditional PDM. However, the plate beamsplitter will lead measurement errors to the NCPMD system due to the beamsplitter will inevitably inherited certain form errors on the two surfaces during manufacturing process. In this paper, a reflection error model of the NCPMD system is proposed, and the measurement error caused by the reflection effect of the plate beamsplitter is determined by considering the influence of the unevenness of the upper and lower surfaces of the plate beamsplitter. Simulation studies show that the proposed reflection model can accurately determine the measurement errors caused by the form errors of the beamsplitter, which can be effectively used for subsequent error compensation.
Iterative calculation is a necessary step in the calibration of stereo deflectometry. Inaccurate input can result in the iterative process converging in a wrong position or unconvergence. Image distortion is an important factors affecting the accuracy of the input. In order to reduce the influence of image distortion and increase the robustness of the calibration, a method based on a search algorithm is investigated for stereo deflectometry. Because there is few distortion at an image center, a search window with a certain border length is positioned at the image center to obtain a group of data for the iterative process. The size of the window is determined based on an algorithm proposed in this paper. Due to the fact that the centers of distortion and image are not coincident, the window is consecutively relocated within the image. A function is proposed to evaluate the input accuracy. Along with the window moving, the calculated data which makes the proposed function reach the minimum is selected to compute the following iterative process. Experimental results affirm the presented method can significantly enhance the robustness of the calibration accuracy of a stereo deflectometry system. By applying the proposed method, the RMS (root mean square) of calibration error can be increased from 0.31 pixels to 0.05 pixels.
Color fringe projection systems for 3D shape measurement have been widely studied in academia because of the advantages of non-contact operation, full-field, and fast data processing. A color CCD camera and a DLP (Digital Light Processing) projector are mostly used. However, crosstalk between color channels of the camera and projector changes the sinusoidal shape of the obtained fringe patterns and then reduces the measurement accuracy. Several methods have been proposed to solve this problem, but they are either too complicated for calculating the color-coupling coefficients using a series of phase-shifting fringe patterns or unstable convergence due to the iterative technique used. This paper presents a simple method to reduce crosstalk between red, green and blue channels. Crosstalk between color channels can be seen as signal aliasing, so different wavelength in color channels can be used to keep them apart. Two wrapped phase maps are obtained by processing corresponding spectrum with FTP (Fourier transform profilometry) in each color channel. The unwrapped phase is calculated based on multi-frequency heterodyne principle. Simulated and experimental results show that the proposed method can significantly reduce the influence of crosstalk on phase calculation and improve the measurement accuracy of the color fringe projection system.
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