Multiple-step triangular-pattern phase shifting and the influence of number of steps and pitch on measurement accuracy

We present new extensions of the two-step, triangular-pattern phase-shifting method for different numbers of phase-shifting steps to increase measurement accuracy and to analyze the influence of the number of phase-shifting steps and pitch of the projected triangular intensity-profile pattern on the measurement accuracy. Phase-shifting algorithms to generate the intensity ratio, essential for surface reconstruction, were developed for each measurement method. Experiments determined that higher measurement accuracy can be obtained with a greater number of phase-shifting steps and a lower value of pitch, as long as the pitch is appropriately selected to be divisible by the number of phase-shifting steps and not below an optimal value, where intensity-ratio unwrapping failure would occur.     

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.     

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.     

Generic nonsinusoidal fringe model and gamma calibration in phase measuring profilometry

Gamma distortion is a dominant error source of phase measuring profilometry. It makes a single frequency for the ideal sinusoidal waveform an infinite width of spectrum. Besides, the defocus of the projector-camera system, like a spatial low-pass filter, attenuates the amplitudes of the high-frequency harmonics. In this paper, a generic distorted fringe model is proposed, which is expressed as a Fourier series. The mathematical model of the harmonic coefficients is derived. Based on the proposed model, a robust gamma calibration method is introduced. It employs the multifrequency phase-shifting method to eliminate the effect of defocus and preserve the influence of gamma distortion. Then, a gamma correction method is proposed to correct the gamma distortion with the calibrated gamma value. The proposed correction method has the advantage of high signal-to-noise ratio. The proposed model is verified through experiments. The results confirm that the phase error is dependent on the defocus and the pitch. The proposed gamma calibration method is compared with the state of the art and proves to be more robust to pitch and defocus variations. After adopting the proposed gamma correction method, the phase precision is much enhanced with higher quality in the measured surfaces.     

伺服电机转子位置检测的误差分析与补偿

针对伺服电机转子位置检测中存在安装不方便、成本高等问题,提出了基于隧道磁阻效应和时栅技术相结合的转子位置检测单元的设计方案。将空间正交的一对TMR传感单元嵌入在电机的前端盖上,实现嵌入式位置精密检测。根据检测单元转子位置解算原理,分析了检测单元的安装误差、电气误差、电磁噪声误差等引起的误差成分。提出了基于超限学习机的误差补偿方法,通过对真实值和测量值样本的训练得到模型最优参数,根据模型参数建立转子位置的误差模型。利用所得到误差模型实现对转子位置的误差补偿。实验结果表明,在2000r/min匀速工况下,补偿前转子位置最大测量误差为4.64°,补偿后转子位置误差为0.315°,精度提升了93.2%,为伺服电机转子位置检测提供了新的方法。     

离轴非球面的条纹反射检测技术

条纹反射测量技术具有动态范围大、灵敏度高的特点,通过高精度的系统标定可以获得很高的测量精度。本文研究将条纹反射测量技术应用于离轴非球面反射镜粗抛光阶段的面形检测,使用激光跟踪仪建立检测系统坐标系,然后将相机和显示屏的实测标定数据代入坐标系并在Zemax软件中建立测量装置的理想模型,通过光线追迹得到理想的屏幕像素点位置,采用相移技术可以得到实测时屏幕像素点位置,从而计算得到被测镜面形的斜率误差,最后积分得到检测结果。文中采用该方法对一块SiC离轴非球面镜进行了实测,并与三坐标测量机的结果进行对比,验证了方法的可行性,可用于指导离轴非球面镜粗抛光阶段的加工。     

Full-field phase error compensation method based on relationship between unwrapped phase and phase error

The three-dimensional reconstruction in phase-measuring profilometry (PMP) usually involves the phase error caused by the gamma effect of the projector. In this study, the relationship between the unwrapped phase and the phase error of every pixel is analysed, and an effective full-field phase error compensation method based on this relationship is proposed for the reduction of every pixel error. In our optimized PMP system, the full-field phase error can be detected by directly fitting the unwrapped phase of the reference plane. In addition, the relationship between the unwrapped phase and the phase error can be established by creating a phase-error lookup table for the phase error compensation of every pixel. The experimental results demonstrate the effectiveness of the proposed method in practical PMP, and the measurement errors can be reduced by a factor of least 10.     

Double three-step phase-shifting algorithm

We describe what we believe is a new phase-shifting algorithm called a double three-step algorithm developed to reduce the measurement error of a three-dimensional shape-measurement system, which is based on digital fringe-projection and phase-shifting techniques. After comparing the performance of different existing phase-shifting algorithms, we present the new double three-step algorithm based on the error analysis of the standard three-step algorithm. In this algorithm, three-step phase shifting is done twice with an initial phase offset of 60 degrees between them, and the two obtained phase maps are averaged to generate the final phase map. Both theoretical and experimental results showed that this new algorithm worked well in significantly reducing the measurement error.     

Vibration-induced phase errors in high-speed phase-shifting speckle-pattern interferometry

We present results from numerical simulations of a dynamic phase-shifting speckle interferometer used in the presence of mechanical vibrations. The simulation is based on a detailed mathematical model of the system, which is used to predict the expected frequency response of the rms measurement error, in the time-varying phase difference maps, as a result of vibration. The performance of different phase-shifting algorithms is studied over a range of vibrational frequencies. Phase-difference evaluation is performed by means of temporal phase shifting and temporal phase unwrapping. It is demonstrated that longer sampling windows and higher framing rates are preferred in order to reduce the phase-change error that is due to vibration. A numerical criterion for an upper limit on the length of time window for the phase-shifting algorithm is also proposed. The numerical results are finally compared with experimental data, acquired with a phase-shifting speckle interferometer of 1000 frames/s.     

Compression of interference patterns with application to phase-shifting digital holography

A compression method of phase-shifting digital holographic data is presented. Three interference patterns are recorded, and holographic information is extracted from them by phase-shifting interferometry. The scheme uses standard baseline Joint Photographic Experts Group (JPEG) or standard JPEG-2000 image compression techniques on the recorded interference patterns to reduce the amount of data to be stored. High compression rates are achieved for good reconstructed object image quality. The utility of the proposed method is experimentally verified with real holographic data. Results for compression rates using JPEG-2000 and JPEG of approximately 27 and 20, respectively, for a normalized root-mean-square error of approximately 0.7 are demonstrated.     

相移干涉显微镜中移相误差分析

本文具体分析了影响移相误差的多种因素，比较了在不同移相术中移相误差量对检测精度的影响，从而论证了五步移相术的合理性和利用压电陶瓷微位移传感器的现有定位精度实现０．１ｎｍ级检测精度的可行性。文中还给出了有关的数值计算结果和测试结果，并就有关问题进行了讨论。     

Grating-based real-time polarization phase-shifting interferometry: error analysis

A phase Ronchi grating-based real-time polarization phase-shifting method can be efficiently used for dynamic phase measurement in optical interferometry. A thorough error analysis is required for exhibiting how error sources influence phase-measurement results. We analyze the phase-measurement errors that are induced by the retardation error and azimuth angle error of the quarter-wave plate, the azimuth angle error of polarizers, the phase and intensity aberrations of diffractive wave fronts, and pixel mismatch of the interferometric patterns. The results will also be useful for evaluating the phase-measurement accuracy of other similar systems.     

光纤直流大电流传感器非线性机理及校准技术

非线性误差是干涉型数字闭环光纤电流传感器超大电流测量的主要误差源之一.借助琼斯矩阵方法,推导了光纤1/4波片不理想条件下传感器输出与被测电流的理论关系,确定了1/4波片的方位角和相位延迟误差是造成光纤电流传感器超大电流测量非线性的主要原因之一.仿真结果表明:在5 ～ 300 kA范围内,方位角误差小于4.53°,相位延...     

回转体测量机的双向法在线温度误差补偿

回转体测量机以其效率高、精度高,在回转类零件测量中得到了广泛的应用。但是由于其自身的特点,测量精度受温度影响引起的漂移误差可达120μm。针对这一问题提出了一种在线温度误差补偿技术,通过双向法测量获得内外测量架的平移量和倾斜量,然后再对各高度的内外径值进行补偿。该方法计算简单,使用方便,并大幅度提高了测量精度。实验证明,这种补偿方法可以使尺寸测量结果的稳定性误差从136μm降低到15μm左右,大大提高了测量的稳定性。     

基于BP神经网络的传感器非线性补偿

由于传感器本身的非线性特性以及传感器在测量过程中外界环境因素的影响,使得传感器的输入输出特性呈现出非线性.讨论了BP神经网络模型在传感器非线性补偿中的应用.给出了相应的补偿方法,即采用两个相同的传感器对同一被测量进行测量,其测量结果作为神经网络模型的输入,经过补偿后的传感器具有线性的输入输出关系.采用递推预报误差算法训练神经网络,具有收敛速度快、收敛精度高的特点.试验结果表明,应用神经网络对传感器的非线性进行动态补偿是一种行之有效的方法.     

Nonlinearity Compensation of the Fiber Bragg Grating Interrogation System Based on an Arrayed Waveguide Grating

In this paper, we report on nonlinearity compensation for a solid-state fiber bragg grating (FBG) sensor interrogation system based on an arrayed waveguide grating (AWG) device. A lookup table with calibration data is used to improve system linearity. A reduction in the absolute value of the measurement error from 120 mustrain or 15degC to 4.8 mustrain or 0.6degC, respectively, is experimentally demonstrated.     

Performance analysis and compensation of M/T-type digitaltachometers

New analyses are presented of the widely used M/T-type digital tachometer. This device incorporates accurate time measurement with pulse counting. It is shown that the accuracy of velocity measurement in real implementations is significantly poorer than indicated previously. Encoder nonidealities are found to introduce a bias in the measured velocity output. A significant rms output error can also result. The insensitivity of the error to the form of the encoder noise model is demonstrated, and two analyses of differing complexity are presented. These permit calculation of the tachometer error measures, based on a knowledge of the magnitude of the error characteristics of the encoder. This facilitates the implementation of a compensation function that will reduce the influence of the bias. Experimental results are presented which demonstrate the existence of the bias, verify the validity of the derived formulae, and show the benefit to be gained by compensation     

Parallel two-step phase-shifting digital holography

We propose a parallel two-step phase-shifting digital holography technique capable of instantaneous measurement of three-dimensional objects, with a view toward measurement of dynamically moving objects. The technique is based on phase-shifting interferometry. The proposed technique carries out the two-step phase-shifting method at one time and can be optically implemented by using a phase-shifting array device located in the reference beam. The array device has a periodic two-step phase distribution, and its configuration is simplified compared with that required for three-step and four-step parallel phase-shifting digital holographies. Therefore the optical system of the proposed technique is more suitable for the realization of a parallel phase-shifting digital holography system. We conduct both a numerical simulation and a preliminary experiment in the proposed technique. The results of the simulation and the experiment agree well with those of sequential phase-shifting digital holography, and results are superior to those obtained by conventional digital holography using the Fresnel transform alone. Thus the effectiveness of the proposed technique is verified.     

收发分体式四自由度激光测量系统耦合误差建模与补偿

线性导轨广泛应用于精密机床和仪器,其运动精度直接影响所在设备的空间定位精度。针对团队前期研制的收发分体式四自由度激光测量系统可以测量导轨直线度、俯仰角和偏摆角,但其直线度与角度测量结果间存在耦合干扰问题,提出了一种误差建模与补偿方法。根据激光测量系统的原理和结构,分析并确定了耦合误差的主要来源,利用矩阵光学及齐次坐标变换的方法建立了耦合误差的补偿模型。以雷尼绍XL-80型激光干涉仪为基准,对所建立的误差补偿模型进行了实验验证,结果表明:利用所建模型补偿后的直线度和角度测量误差均降低了75%以上。所提出的误差建模与补偿方法不但有助于提高四自由度激光测量系统的精度,同时也有助于降低其成本。     

Two-step phase-shifting fringe projection profilometry: intensity derivative approach

A new two-step phase-shifting fringe projection profilometry is proposed. The slowly variable background intensity of fringe patterns is removed by the use of an intensity differential algorithm. The high-resolution differential algorithm is achieved based on global interpolation of fringe gray level on a subpixel scale. Compared with the traditional three- or four-step phase-shifting method, the profile measurement is sped up with this approach. Computer simulation and experimental performance are evaluated to demonstrate the validity of the proposed measurement method. The experimental results compared with those of the four-step phase-shifting method are presented.