Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector

A structured light system using a digital video projector is widely used for 3D shape measurement. However, the nonlinear gamma of the projector causes the projected fringe patterns to be nonsinusoidal, which results in phase error and therefore measurement error. It has been shown that, by using a small look-up table (LUT), this type of phase error can be reduced significantly for a three-step phase-shifting algorithm. We prove that this algorithm is generic for any phase-shifting algorithm. Moreover, we propose a new LUT generation method by analyzing the captured fringe image of a flat board directly. Experiments show that this error compensation algorithm can reduce the phase error to at least 13 times smaller.     

Micro-three dimensional shape measurement method based on shadow Moiré using scanning electron microscopy

A novel, precise, three-dimensional shape measurement method using scanning electron microscopy (SEM) and Moiré topography has been proposed. The possibility for measurement of wavelength order using this method is discussed based on results of experiments to confirm the principle. In these experiments, a high-resolution method based on the new measurement method is proposed, employing fringe scanning technology for the shadow Moiré. The optical system is constructed with a SEM using backscattering electrons, a grating holder that can shift the position of the grating, and a grating having a pitch of 120?µm. Measured results using a bearing ball as a sample show that high resolution measurements of around one micrometre can be performed using the fringe scanning method and the new measurement arrangement. An error analysis of the method is performed to enable improvement of the measuring accuracy.     

Model for quantifying photoelastic fringe degradation by imperfect retroreflective backings

In any automated algorithm for interpreting photoelastic fringe patterns it is necessary to understand and quantify sources of error in the measurement system. We have been considering how the various components of the coating affect the photoelastic measurement, because this source of error has received fairly little attention in the literature. Because the reflective backing is not a perfect retroreflector, it does not preserve the polarization of light and thereby introduces noise into the measurement that depends on the angle of obliqueness and roughness of the reflective surface. This is of particular concern in resolving the stress tensor through the combination of thermoelasticity and photoelasticity where the components are sensitive to errors in the principal angle and difference of the principal stresses. We have developed a physical model that accounts for this and other sources of measurement error to be introduced in a systematic way so that the individual effects on the fringe patterns can be quantified. Simulations show altered photoelastic fringes when backing roughness and oblique incident angles are incorporated into the model.     

Quasi-achromatic laser Doppler anemometry systems based on a diffractive beam splitter

We propose a new beam-splitter system that makes it possible to use nonstabilized laser diodes for laser Doppler anemometry (LDA) systems by making the system wavelength independent. The beam splitter consists of two linear diffraction gratings that produce two parallel beams with a beam spacing that is wavelength dependent. This ensures passive wavelength compensation for the fringe spacing in the measurement volume. One can choose the distance between the two parallel beams by changing the distance between the two gratings, whereas the distance to the measurement volume can be designed by choice of a condensing lens with the proper focal length. This means that the system can be designed to have a desired fringe spacing in the measurement volume. The gratings are implemented as surface-relief holograms in photoresist, which makes it possible to mass produce the beam-splitter system at low cost through replication of the structure. The method for passive wavelength compensation for the fringe spacing is demonstrated both theoretically and experimentally.     

Quantization error of CCD cameras and their influence on phase calculation in fringe pattern analysis

We present an investigation into the phase errors that occur in fringe pattern analysis that are caused by quantization effects. When acquisition devices with a limited value of camera bit depth are used, there are a limited number of quantization levels available to record the signal. This may adversely affect the recorded signal and adds a potential source of instrumental error to the measurement system. Quantization effects also determine the accuracy that may be achieved by acquisition devices in a measurement system. We used the Fourier fringe analysis measurement technique. However, the principles can be applied equally well for other phase measuring techniques to yield a phase error distribution that is caused by the camera bit depth.     

新型零差激光干涉仪测量误差因素分析

介绍了新型零差激光干涉仪的测量原理,实验和理论分析了干涉条纹宽度、激光光强、散斑效应对该激光干涉仪测量误差的影响。结果表明,干涉条纹宽度对振幅测量值影响并不明显,测量误差为0.5%;光强变化引起的振幅测量误差为0.5%,光强较弱会增大测量误差;散斑效应引起的振幅测量误差与透镜参数有关,测量误差为0.4%。该新型零差激光干涉仪可有效降低测振系统对测量环境的要求。     

Certification of specimens for checking profilographs and profilometers

Conclusions By studying the problems related to certifying specimens which have regular profiles and are intended for checking contact profilographs and profilometers of the M system it is possible to arrive at the following conclusions.In the case of the visual interference method for measuring heights, which is used for certifying specimens with a profile of a simple shape formed by straight-line segments, the measurement errors produced by superposing subjectively the sighting line of a reading device over an interference fringe are determined mainly by the interference field parameters (the visible width of an interference fringe and the luminance function in the contour-shaping area). Measurements with a minimum error correspond to visible fringe widths of 0.03–0.06 rad (under normal conditions).The angle between the profile elements can be measured by means of the interference method independently of the relative position of the reference plane when =0.Profilograms with an absolute and independent scale can be obtained for profiles of a complex shape by means of a photoelectric interference scanning system.In this system the profile elements' recording errors can be analyzed by means of the profile linear approximation method by representing the screen-emitted luminous flux in the form of a Fourier series of spatial frequencies.For the majority of the specimen's regular profiles the error which can be tolerated in practice for transmitting the shape of profile-approximating elements occurs when the ratio between the interference fringe width normal to the scanning trajectory and the size of the screen components is equal to ten. The raising of this ratio does not provide a substantial reduction of the error.Translated from Izmeritel'naya Tekhnika, No. 2, pp. 24–28, February, 1969.     

A general gamma nonlinearity compensation method for structured light measurement with off-the-shelf projector based on unique multi-step phase-shift technology

ABSTRACT

Nonlinearities in the application of fringe projection metrology make it very difficult to acquire perfect 3D data. This paper describes a six-step phase-shifting technique for a structured light measurement system with an off-the-shelf projector. First, the phase error is analysed and a gamma model is established by deriving the relative expression between the wrapped phase and input images. This is then expressed in matrix form to derive a unique solution, which is used for the gamma solver. The complex gamma calibration and projector error compensation can be removed once the gamma value of the off-the-shelf projector has been determined. The ideal model reconstruction results are obtained through simulations and experiments, and the standard deviation of the phase error is found to be only 0.0039 radians. Hence, the proposed method eliminates the nonlinear errors associated with fringe projection technology using existing projectors and improves the overall image reconstruction quality.     

Phase-shifting interferometry by a similar matrix 1-norm algorithm

Phase-shifting interferometry (PSI) is an effective technique in optical measurement. In this paper, a noniterative algorithm for retrieving the unknown phase shifts in three frame generalized PSI is proposed, in which the interference term of each frame is eliminated by the aid of a reference interferogram with the phase shift of π. With this algorithm, the phase shifts can be determined by solving a system of transcendental equations with trigonometric functions, in which this system consists of three different ratios between the similar matrix 1-norms of the intensity difference and the intensity sum. After the determination of phase shifts, a phase can be retrieved easily. The algorithm provides a possible method to solve the limitation of the fringe number existing in some common algorithms. The feasibility and accuracy of this algorithm were demonstrated by the simulation and experimental results.     

Flexible three-dimensional measurement technique based on a digital light processing projector

A new method of 3D measurement based on a digital light processing (DLP) projector is presented. The projection model of the DLP projector is analyzed, and the relationship between the fringe patterns of the DLP and the fringe strips projected into the 3D space is proposed. Then the 3D shape of the object can be obtained by this relationship. Meanwhile a calibration method for this model is presented. Using this calibration method, parameters of the model can be obtained by a calibration plate, and there is no requirement for the plate to move precisely. This new 3D shape measurement method does not require any restrictions as that in the classical methods. The camera and projector can be put in an arbitrary position, and it is unnecessary to arrange the system layout in parallel, vertical, or other stringent geometry conditions. The experiments show that this method is flexible and is easy to carry out. The system calibration can be finished quickly, and the system is applicable to many shape measurement tasks.     

Phase Error Compensation of Three-Dimensional Reconstruction Combined with Hilbert Transform

Nonlinear response is an important factor affecting the accuracy of three-dimensional image measurement based on the fringe structured light method. A phase compensation algorithm combined with a Hilbert transform is proposed to reduce the phase error caused by the nonlinear response of a digital projector in the three-dimensional measurement system of fringe structured light. According to the analysis of the influence of Gamma distortion on the phase calculation, the algorithm establishes the relationship model between phase error and harmonic coefficient, introduces phase shift to the signal, and keeps the signal amplitude constant while filtering out the DC component. The phase error is converted to the transform domain, and compared with the numeric value in the space domain. The algorithm is combined with a spiral phase function to optimize the Hilbert transform, so as to eliminate external noise, enhance the image quality, and get an accurate phase value. Experimental results show that the proposed method can effectively improve the accuracy and speed of phase measurement. By performing phase error compensation for free-form surface objects, the phase error is reduced by about 26%, and about 27% of the image reconstruction time is saved, which further demonstrates the feasibility and effectiveness of the method.     

基于复Morlet小波的相位分析

针对基于结构照明的三维面形测量中的位相展开问题,提出了基于复Morlet小波分析的直接从条纹中提取自然相位的算法,并对其进行了理论分析、计算机模拟和实验,研究证明了可行性.该方法从一幅条纹图像中不需要进行相位展开就能够得到准确的相位分布方法,并且避免了传统相位方法所必须的复杂相位展开过程.当待测物体变化率比较大的时候,用传统傅里叶方法恢复得到的误差是-3～3 rad,而采用本文方法得到的误差是-2.5～0.5 rad,且对于顶部平坦部分基本没什么误差.对比分析表明,本文方法的精度要高于传统傅里叶方法.     

Analysis of low-coherence interference fringes by the Kalman filtering method

Interferometers with low-coherence illumination allow noncontact measurement of rough-surface relief with a wide range of measurement definition by locating the visibility maxima of interference fringes. The problem is light scattering by the surface to be measured, which can cause distortion of low-coherence interferometric signals. We propose to use a stochastic fringe model and a Kalman filtering method for processing noisy low-coherence fringes dynamically. Prediction of the fringe's signal value at each discretization step is based on all the information available before this step; the prediction error is used for dynamic correction of the estimates of the fringe envelope and phase. The advantages of the Kalman filtering method consist in its immunity to noise, optimal fringe evaluation, and data-processing speed.     

Universal calculation formula and calibration method in Fourier transform profilometry

We propose a universal calculation formula of Fourier transform profilometry and give a strict theoretical analysis about the phase-height mapping relation. As the request on the experimental setup of the universal calculation formula is unconfined, the projector and the camera can be located arbitrarily to get better fringe information, which makes the operation flexible. The phase-height calibration method under the universal condition is proposed, which can avoid measuring the system parameters directly. It makes the system easy to manipulate and improves the measurement velocity. A computer simulation and experiment are conducted to verify its validity. The calculation formula and calibration method have been applied to measure an object of 22.00 mm maximal height. The relative error of the measurement result is only 0.59%. The experimental results prove that the three-dimensional shape of tested objects can be reconstructed exactly by using the calculation formula and calibration method, and the system has better universality.     

Optimized multiwavelength combination sources for interferometric use

We present the use of multiwavelength combination sources in a direct method for improved central fringe identification in a white-light interferometric system. The optimum wavelength combinations of such sources can be obtained by the use of the results of a simple analysis. We find that this multiwavelength technique can greatly reduce the minimum signal-to-noise ratio required by the systemwhen used to identify the central fringe, and thus it offers an increased signal resolution. As a result, it is suitable for high-precision measurement purposes as well as for applications in coherence multiplexed interferometric sensor systems.     

Control of phase of fringes in speckle interferometry for application of fringe scanning method

The speckle interferometry is an effective technique in the displacement measurement of a structure with a rough surface. However, when the fringe scanning technique is introduced to speckle interferometry for improving the measurement resolution, generally two speckle patterns before and after the deformation of the measurement object and another speckle pattern obtained under different conditions from these two speckle patterns are required at least. So, three speckle patterns are generally required for precise fringe analysis as a minimum condition. In this paper, a method for introducing the fringe scanning method is proposed by controlling the phase of the specklegram as a fringe image using filtering techniques. Then, the temporal fringe analysis method that uses only two speckle patterns are proposed for speckle interferometry. As the result of experiments, it is shown that high precise fringe analysis can be realized by the fringe scanning methods using only two speckle patterns for the displacement measurement with a large deformation.     

Vibration-compensated interferometry system using phase-modulating interference fringe subdivision technology

An innovative vibration-compensation method, with phase-modulating interference fringe subdivision technology, is described. It simulates fringe movement by the phase difference of signals and can detect the fringe movement with an accuracy of 1/400 fringe spacing using this subdivision technology. A closed-loop vibration-compensation system is built, and the measurement of an interference fringe movement and a vibration-compensation test are successfully demonstrated. Because of this new method and a new feedback algorithm that was introduced, interference fringes can be stabilized at any preset phase position in real time. Compared with known methods, this method is simple and inexpensive, as well as effective.     

Phase error compensation for three-dimensional shape measurement with projector defocusing

This paper analyzes the phase error for a three-dimensional (3D) shape measurement system that utilizes our recently proposed projector defocusing technique. This technique generates seemingly sinusoidal structured patterns by defocusing binary structured patterns and then uses these patterns to perform 3D shape measurement by fringe analysis. However, significant errors may still exist if an object is within a certain depth range, where the defocused fringe patterns retain binary structure. In this research, we experimentally studied a large depth range of defocused fringe patterns, from near-binary to near-sinusoidal, and analyzed the associated phase errors. We established a mathematical phase error function in terms of the wrapped phase and the depth z. Finally, we calibrated and used the mathematical function to compensate for the phase error at arbitrary depth ranges within the calibration volume. Experimental results will be presented to demonstrate the success of this proposed technique.     

相移条纹投影三维形貌测量技术综述

结构光三维形貌测量系统目前得到了越来越广泛的应用和研究,相移条纹投影三维形貌精密测量技术是其重要的发展方向。对结构光相移条纹投影三维形貌测量系统的应用发展、工作过程、不同系统构成方式、相移条纹的各种形式及特点、相位误差校正方法、不同相位解包裹算法及其优缺点和适用场合、测量系统数学模型的实现方法及其相应的优缺点、高动态范围测量技术等进行了详细的分析。对相移条纹投影系统的工作流程、实现方法、关键技术的发展及其存在问题等进行了比较全面的梳理,为三维形貌精密测量技术进一步满足先进制造中更高精度的要求指出了后续的研究方向。     

基于改进Sierra 抖动算法的微离焦投影三维轮廓测量技术研究

通过分析传统频率调制的相位轮廓测量技术,提出基于蛇形扫描改进Sierra抖动算法,结合微离焦投影,可减小正弦光栅二值化的量化误差,同时抑制非对称纹理,能较大地改善离焦后光栅的正弦性。将该抖动算法生成的离焦光栅用于三维轮廓测量技术,与Bayer有序抖动算法、Sierra抖动算法和Floyd-steinberg误差扩散抖动算法进行了比较,实验结果表明:改进Sierra抖动算法具备更好的适应性,能够较大程度地降低相位误差,运算速度快,生成光栅准确度较高,改善了相位质量,适用于高精度三维轮廓测量。