利用预失真条纹校正PMP系统投影仪畸变的研究

依据摄像机畸变模型提出了一种投影条纹相位畸变校正方法来简化相位-高度映射关系.该方法首先通过投两套互相垂直的相移正弦条纹,以相位值代替投影仪像素坐标,将投影仪当成摄像机看待,标定出投影仪的内参量.然后根据标定出的投影仪镜头畸变参量对理想相位施加反向的畸变,在投影时反向畸变的光栅通过镜头畸变,又成为理想的光栅,从而简化了相位-高度映射关系.实验中,虽然由于测量误差的影响,校正后的投影仪径向畸变系数还是比原来小了1个数量级.     

利用预失真条纹校正PMP系统投影仪畸变的研究*

依据摄像机畸变模型提出了一种投影条纹相位畸变校正方法来简化相位-高度映射关系.该方法首先通过投两套互相垂直的相移正弦条纹,以相位值代替投影仪像素坐标,将投影仪当成摄像机看待,标定出投影仪的内参量.然后根据标定出的投影仪镜头畸变参量对理想相位施加反向的畸变,在投影时反向畸变的光栅通过镜头畸变,又成为理想的光栅,从而简化了相位-高度映射关系.实验中,虽然由于测量误差的影响,校正后的投影仪径向畸变系数还是比原来小了1个数量级.     

Least-squares calibration method for fringe projection profilometry with some practical considerations

Fringe projection profilometry (FPP) is a widely used three-dimensional profile measurement technique. One vital step in this technique is calibration, which determines the system accuracy. The least-squares method, because of its flexibility and simplicity, is commonly used in system calibration for FPP. However, calibration results are affected by the nonlinear gamma of the projector and projection fringe cycle broadening. This paper proposes a new look-up table (LUT) generation method by analyzing the differences between the real and ideal unwrapped phases. The aforementioned problems could then be solved after the phase error is compensated by the LUT. Finally, the validity of the proposed method is demonstrated through experiments, and the accuracy reaches 0.02 mm.     

Removing harmonic distortion of measurements of a defocusing three-step phase-shifting digital fringe projection system

Binary defocusing method was adopted in 3D profilometry as it allows real-time measurement and does not need to handle the luminance nonlinearity of a projector. Current patch-based binary fringe patterns are periodic and carry strong harmonic distortion as compared with the ideal sinusoidal fringe patterns, which affects the measuring performance remarkably. In this paper, we propose a framework for generating aperiodic fringe patterns based on optimized patches. The produced fringe patterns can significantly lower the noise floor and suppress the harmonic distortion in the constructed phase map. Accordingly, the achieved depth measuring performance can be significantly improved. Special care is also taken during the optimization of the patches in our framework such that the depth measuring performance is robust to fringe period and defocusing extent.     

Analysis of phase distortion in phase-shifted fringe projection

This paper describes the analysis of phase distortion in phase-shifted fringe projection method. A phase distortion occurs when the phase shifting technique is applied to extract the phase values from projected fringe patterns in surface contouring. The phase distortion will induce measurement errors especially in the measurement of micro-components. The cause of such phase distortion is investigated and the influence of phase distortion on the measurement of micro-components is discussed. To eliminate the phase distortion, a continuous wavelet transform (CWT) is employed to extract phase values from object surface modulated fringe patterns. Principle of the proposed CWT phase extraction method is described and experiments are conducted to verify the proposed method. It is shown that by the use of CWT phase extraction method phase distortion induced in conventional phase-shifting technique can be completely eliminated.     

Period correction method for binary fringe defocused projection

Binary fringe defocused projection can resolve the problem caused by the nonlinear gamma of the projector. Owing to the intersecting axis measurement system, the broadening of the fringe period on the reference plane can cause measurement errors. Non-uniform periodical binary fringe defocused projection is utilized to overcome this problem. After appropriate defocused projection of non-uniform periodical binary fringe, uniform periodical sinusoidal fringe can be obtained on the reference plane. This method can prevent the nonlinear gamma effect and broadening of the fringe period, and filter high harmonics and high-frequency noise. Three-dimensional (3-D) shape measurement experiments of standard flat are performed with four-step phase-shift method. Experimental results demonstrate that the proposed method exhibits high measurement precision. Highly accurate 3-D measurements of large objects can also be performed with the proposed method.     

A novel fringe adaptation method for digital projector

Aimed to obtain high-quality sinusoidal fringe projection, a new method to correct the output fringe of digital projector is presented. The method is based on the proposed fringe transform model, which describes the relationship of the input and output fringe pattern. Firstly, a series of fringe patterns are projected and from the fringe images, the transform function is calculated by the pattern shifting method. At last, by modifying the input fringe pattern, a standard sinusoidal output fringe can be achieved. Different from the previous methods, the waveform nonlinearity is estimated by varying the intensity of the projected fringe pixel by pixel; thus the waveform nonlinearity can be estimated precisely and the time cost is considerably reduced. Experimental results show that by modification of the input projection patterns the projector can project fringe with high-quality sinusoidal waveform leading to high performance of the projection system.     

单周期条纹双四步相移投影仪的标定方法

针对投影仪标定方法中存在畸变及倾斜投影引起条纹周期、条纹级数变化的问题,提出一种单周期条纹双四步相移投影仪的标定方法.设计生成横向和纵向各两组单周期条纹图像,经投影仪投影到带有圆形标识的标定板上,相机同步采集标定板图像,叠加由双四步相移获得的两幅相位主值图,对叠加相位主值图相位展开,利用展开的绝对相位值计算投影仪像素坐标值,最终将投影仪标定转换为成熟的相机标定.实验结果表明:仿真投影仪标定实验准确度的最大重投影误差约为0.4pixel,均方根误差为0.132 96pixel;实际投影仪标定实验准确度的最大反投影误差约为0.46pixel,均方根误差为0.143 12pixel;实验结果与仿真结果的最大反投影误差相差15%,均方根误差相差7.6%.与现有的采用三频相位展开进行投影仪标定的方法相比,投影光栅图像数可减少8幅.该方法改善了现有投影仪标定方法的不足,标定准确度和标定效率均得到提高.     

Fringe contrast-based 3D profilometry using fringe projection

Quality-guided algorithm is a widely used method in phase unwrapping. This paper shows an accurate quality map based on fringe contrast for 3D shape measurement. Phase-shifted fringe patterns are projected onto an object surface by a programmable liquid crystal projector and recorded by a CCD camera. A wrapped phase map and a fringe contrast map are extracted from the deformed fringe patterns by the phase-shifting technique. Guided by the contrast map, the quality-guided unwrapping algorithm minimizes unwanted shadow and non-uniform surface reflectance effects and is able to retrieve a correct surface profile. Validity of the proposed method is tested on a fish model and a cutting tool specimen.     

Flexible digital projector calibration method based on per-pixel distortion measurement and correction

When a digital projector is applied in high precision applications, the intrinsic parameters and distortion characteristics should be calibrated precisely. In this paper, a flexible full-field projector calibration method is proposed without any approximate distortion model. With planar homography theory and fringe projection technique, the projector distortion characteristic on each pixel can be measured independently and an initial distortion map is generated. The intrinsic parameters are calibrated afterwards. Then, the initial distortion map can be refined by correcting the non-perpendicularity between the optical axis and image plane. The original pattern to be projected is corrected with the refined distortion map. Thus, the calibrated projector can be regarded as an ideal projector conforming to the pinhole model. Experimental results show a nearly ideal residual map for the corrected projection pattern. In addition, the proposed calibration method is flexible without any sophisticated ancillary equipment or complicated procedure.     

A novel three-dimensional shape measurement method based on a look-up table

Fringe projection profilometry is widely used for three-dimensional shape measurement. In an oblique-angle projection, the fringe cycle is broadened on the reference plane. Phase errors are mainly caused by the nonlinear gamma of the projector and fringe cycle broadening. This study describes a phase error compensation method to eliminate these phase errors. A look-up table that stores phase errors is constructed for phase error compensation. Based on it, a new height equation is proposed. The experimental results show that the proposed method can compensate for the phase errors of the fringe projection profilometry, thereby improving the measurement accuracy significantly.     

Rapid 3D surface profile measurement of industrial parts using two-level structured light patterns

This paper aims to present a rapid 3D shape measurement system based on novel monochromatic structured light patterns. The system consists of projectors shooting the fringe patterns onto the inspected parts and cameras recording the corresponding distorted images. Using the two-level fringe patterns, the correspondence between the projector image and camera image can be established with sub-pixel accuracy. The two-level pattern is based on three spatiotemporal binary stripes, in which the value of the stripe boundary (first-level coding) is determined by the two adjacent stripes patterns over time and the codeword of the strip boundary (second-level coding) depends on its values and neighbor boundary values in space. The proposed pattern is robust to ambience light variation and part texture. Moreover, the occlusion can be overcome and high density measurement can be achieved. Experiments with different 3D parts are conducted to evaluate the robustness and accuracy of the inspection system using the two-level patterns. The results show that the system has desired properties of high accuracy, high density, rapid acquisition, and robustness, which are essential for industrial application.     

Surface profile measurement of low-frequency vibrating objects using temporal analysis of fringe pattern

A simple and accurate algorithm (phase scanning method) is proposed for 3D surface contouring and dynamic response determination of a vibrating object. A sinusoidal fringe pattern is projected onto a low-frequency vibrating object by a programmable liquid crystal display projector. The fringe patterns are captured by a high-speed CCD camera with a telecentric gauging lens. Phase values are evaluated point by point using phase scanning method. From the phase values of each point on the object, the contour of the specimen at different instants of vibration can be retrieved. In this paper, a small vibrating coin is used to demonstrate the validity of the method and the experimental results are compared with test results on a stationary coin using four-step phase shifting and fast Fourier transform methods. The technique is especially useful in applications where the vibrating object has a complicated shape.     

Accurate calibration for a camera–projector measurement system based on structured light projection

The accurate calibration for a camera–projector measurement system based on structured light projection is important to the system measurement accuracy. This study proposes an improved systematic calibration method focusing on three key factors: calibration model, calibration artifact and calibration procedures. The calibration model better describes the camera and projector imaging process by considering higher to fourth order radial and tangential lens distortion. The calibration artifact provides a sufficient number of accurate 3D reference points uniformly distributed in a common world coordinate system. And the calibration procedures calibrate the camera and projector simultaneously based on the same reference points to eliminate the influences of the camera calibration error on the projector calibration. The experiments demonstrate that our calibration method can improve the measurement accuracy by 47%.     

Self-calibration of a fringe projection system using epipolar constraint

A new self-calibration method for a fringe-projection based 3D measurement system is proposed. To determine homologous points in the proposed camera/projector configuration, the phase map is converted to the u, v coordinates in the projected image. The projector can conceptually be regarded as camera acting in a reversed mode. Taking the epipolar constraint into account, this approach can allow self-calibration of the fringe projection system. Considering the effect of noise, we propose a nonlinear self-calibrating model. The experimental results show the effectiveness of this approach.     

Background and amplitude encoded fringe patterns for 3D surface-shape measurement

This paper presents a new fringe projection method for surface-shape measurement that uses background and amplitude encoded high-frequency fringe patterns. The background and amplitude, combined as a codeword, identify the wrapped phase fringe order to partially unwrap the phase to a low frequency. The low-frequency wrapped phase map is then directly used to reconstruct the surface based on geometry constraints without requiring additional images as in other temporal phase-unwrapping methods. Measurements performed on a double-hemisphere, mask, and manikin head, using projected fringe patterns with 48 periods, demonstrated the ability of the method to perform 3D shape measurement with only four projected patterns and captured images, using a single camera and projector.     

Three-dimensional shape measurement for an underwater object based on two-dimensional grating pattern projection

In this paper, a practical method using phase tracking and ray tracing algorithms is proposed for measuring the three-dimensional (3D) shape of an underwater object. A 2D projected sinusoidal fringe goes through the water and illuminates the tested object. Firstly, the phase tracking algorithm is employed to identify homologous points in phase distributions of the deformed fringe captured by the camera and these of the fringe pattern projected by the projector. The projector is regarded as a special camera as regards the stereovision principle. In the calibrated system, both ray directions of the homologous points can be easily figured out. Secondly, the ray tracing algorithm is used to trace the propagation path of each ray and to calculate the 3D coordinates of each point on the tested object's surface. Finally, the whole shape of the tested object can be reconstructed.     

Improved 3D displacement measurements method and calibration of a combined fringe projection and 2D-DIC system

An improved measurement method and an automatic calibration procedure are proposed for a combined 2D Digital Image Correlation and Fringe Projection system that allows measuring in- and out-of-plane displacement maps with only one image at each deformation stage of a specimen. The proposed method increases the accuracy and range of the out-of-plane displacements by taking into account the divergences of both the projected fringes (uncollimated) and the camera (with non-zero FOV). The calibration is performed automatically by acquiring a sequence of images of a reference plane by displacing perpendicular to it the camera and fringe projector with a motorized translation stage. The acquired images are then used to obtain a fringe function for each pixel and the necessary parameters required for the correction of the in-plane displacements. Furthermore, a closed form expression is obtained that relates the out-of-plane displacements with the shifted phase at each pixel for a given experimental set-up. This expression is in good agreement with the fringe function obtained by fitting a simple 2nd order polynomial to the experimental obtained calibration data. Finally, the polynomial approach is proposed as a fringe function because it avoids the errors in the determination of the required parameters of the theoretical expression as well as some small misalignment or aberration effects.     

结构光三维测量系统标定的关键算法研究

系统参数标定是结构光三维测量系统的关键问题之一,标定板特征圆圆心检测精度与投影仪、相机镜头gamma效应引起的相位误差是系统参数标定的主要误差来源。采用Sobel算子粗定位标定板特征圆的边缘点,以正交傅里叶-马林矩(OFMM)算子对边缘点进行亚像素定位,用椭圆拟合法确定特征圆圆心的方法提高标定板特征圆检测精度。同时,推导结构光三维测量系统gamma非线性数学模型,将计算得到的系统gamma值的倒数作为投影正弦光栅的指数以降低gamma效应引起的相位误差。实验结果证明了该方法的准确性,与不采用亚像素边缘检测与gamma校正相比,X、Y方向的标定精度分别提高约3.5倍与5倍。     

Microscopic surface contouring by fringe projection method

This paper describes the use of optical fringe projection method for 3D surface profile and deformation measurement of micro-components. In this method, sinusoidal linear fringes are projected on a micro-component surface by a grating phase shifting projector and a long working distance microscope (LWDM). The image of the fringe pattern is captured by a high-resolution CCD camera and another LWDM and processed by phase-shifting technique. A simple procedure is described which enables calibration of the optical set-up for subsequent quantitative measurement of micro-components of unknown shapes. This method is relatively simple and accurate, and is capable of conducting fully automated measurements. In this paper, two micro-components, a micro-mirror (0.1 mm×0.1 mm) and a micro-electrode pad are used to demonstrate deformation measurement and microscopic surface contouring.