An Improvement of Spatial Carrier Phase-shifting Method

Spatial-carrier phase-shifting method (SCPM) retrieves the phase distribution from carrier interferograms by assuming that the phases of the processed pixel and its adjacent pixels are uniform,which introduces considerable theoretical error. A new method is presented in this paper to improve the SCPM accuracy: (1) A quadric curve is used to describe the phase distribution of the adjacent pixels; (2) The linear and quadric terms of the phase are considered as phase shifter errors; (3)Suitable phase shifting algorithms insensitive to these errors are selected. Two "5-step" algorithms are used and their properties are analyzed. An example ofphase retrieving by SCPM is given and the result shows that SCPM has high theoretical accuracy. With the potential high accuracy, ability of measuring dynamic phase andcomputational simplicity, SCPM will become a much more useful phase measurement method.     

基于一阶泰勒展开式的迭代最小二乘相移新算法

提出了一种新的最小二乘迭代算法 ,能有效消除因相移器存在导向误差面使相移平面倾斜从而导致的相移误差。当相移器存在的相移误差包括位移误差与倾斜误差时 ,同一幅干涉图诸像素点的相移并不同步 ,但其相移量在同一平面上。求解此平面 ,即可消除相移误差。通过求解由一阶泰勒展开式得到的线性方程组 ,避免了为求解此平面而求解非线性方程组最小二乘解的过程 ,使算法简化。利用迭代法 ,保证求解的精度。并通过数值模拟 ,验证了这种算法在消除较大的相移器倾斜及位移误差影响上具有良好的效果。     

移相干涉术的一种新算法：重叠四步平均法

提出了一种能大大地减小由于移相器的位移误差而引起相位复原误差的新方法，即重叠四步平均法（Ｏｖｅｒｌａｐｐｉｎｇ Ａｖｅｒａｇｉｎｇ ４－Ｆｒａｍｅ （ＯＡＦ） Ａｌｇｏｒｉｔｈｍ）。给出了这种方法的盯们复原精度与移相器的位移误差之间的关系式，从关系式中可见，ＯＡＦ算法大大地减小由于移相器的位移误差而引起相位复原误差，通过计算机模拟，得到了各种算法的相位复原精度与移相器的位移误差之间的关系曲线，分析     

Optical Differentiation Phase Measurement Using the Bias Shifting Method

A new optical phase measurement method using a differentiation filter is proposed. The new method uses two images obtained by shifting the filter. This method has an advantage in that non-uniformity of the wavefront intensity does not produce errors. We present herein the theory of the newly proposed method and verify the theory by computer simulation. The effects of non-uniformity of the wavefront intensity, noise, and bias shifting length for errors are discussed. The system has been demonstrated for a plane wave and a spherical wave. For the proposed method, although the number of errors due to noise increases, the number of errors due to non-uniformity decreases. Therefore, the proposed method is useful for the phase measurement of a wavefront for which the intensity is not uniform. In addition, it improves the accuracy of the phase measurement system using a differentiation filter.     

New algorithm of white-light phase shifting interferometry pursing higher repeatability by using numerical phase error correction schemes of pre-processor, main processor, and post-processor

White-light phase shifting interferometry (WLPSI) is frequently used for the precision measurement of 3D patterns in various fields. Phase error is one of the most dominant errors in WLPSI, and it is mainly generated by the scanner positioning error and mechanical vibrations. In this paper, phase error detection method by image analysis is proposed, and the numerical correction method for minimizing the phase error is also proposed. The image reconstruction method (IRM), iterative IRM (IIRM) as pre-processors, partial IRM (PIRM), least squares method (LSM) as a main processor, and surface compensation method (SCM) as a post-processor were developed for correcting phase errors. The five methods are implemented and simulated, and the pros and cons of each method are explained.Mirau type interferometry and the phase error generator using a PZT stage were used, and the measurements by WLPSI were done under various vibration conditions. The captured images were analyzed by the five correction methods, and the results were compared. Phase error was effectively minimized by the correction methods, and repeatability of 0.2 nm was obtained in the case of the specimen of 500 nm in height. Repeatability of 10 nm was obtained by conventional WLPSI algorithms for the same specimen.     

An effective method in calibrating nonlinear errors for phase-shifting interferometry

In phase measurement or digital holography for phase-shifting interferometry, the key role is the variation of reference light wave and recover algorithm based on interferograms and reference phase, so the calculation result is directly affected by phase-shift accuracy. However, because of the errors of nonlinear and other random factors, it is difficult to control the actual phase-shifting amount accurately. In this paper, we aim to propose an efficient method for phase-shifting interferometry which does not require accurate initial estimation of phase-shift amounts, only a few pixels with several randomly shifted interferograms are sufficient for accurate extraction of phase information. This method has reduced the dependence of reference phase, and can obtain phase-shifting amount directly without using complex revised algorithm for correcting phase-shifting nonlinear errors.     

高精度干涉检验移相算法对振动误差的免疫能力

对移相干涉测量中影响移相稳定性,从而产生测量误差的小幅度机械振动进行了研究,建立了振动误差模型,仿真分析了Wyant84b三步算法、Hariharan87五步算法、七步算法和十三步算法4种不同移相算法对振动的免疫能力。模拟结果显示,十三步算法对振动的免疫能力最好,与已发表文献成果吻合,说明本文的模拟具有较高的可信度,在一定程度上能够对影响干涉仪精度的振动误差进行合理预测,并能够起到评价和筛选移相算法的作用。     

基于π/4相移平均的多光束干涉相位提取算法

菲佐干涉仪中如存在多光束干涉现象,干涉光强将不再是严格的余弦分布形式.在导出菲佐干涉仪中多光束干涉光强公式的基础上,给出了将其近似为理想多光束干涉光强公式的条件.推导了对多光束相移干涉图用四幅算法求解的相位计算误差,并据此提出了基于π/4相移平均的多光束干涉相位提取算法:通过采集相移间隔π/4的两组干涉图序列,将两次计...     

The Local-Sampling Phase Shifting Technique for Precise Two-Dimensional Birefringence Measurement

A precise method for measurement of two-dimensional birefringence distribution is described and discussed. This method can determine the relative retardation and the azimuthal angle of the fast axis in an optical component. In order to detect relative retardation with high resolution, a local-sampling phase shifting technique is proposed. This method can measure 256 × 256 values of the birefringent phase difference and azimuthal angle in a short time with ± 0.02 deg (0.03 nm) of retardation accuracy.     

几种任意步距步进相移算法的误差分析与对比

介绍了到目前为止的几种任意步距步进相移算法,并针对相移干涉仪的两种主要误差———移相误差和探测器非线性误差进行了计算仿真,进而比较分析了它们对这这些误差的抑制能力,其结果可为实际应用合理地选择算法提供理论依据。     

Identification of nonlinear recording error in phase shifting interferometry

The phase shifting method for quantitative fringe pattern analysis provides high accuracy if stringent requirements on the component interferogram recording are met. In the paper the issue of detection and identification of error sources in the two-beam interferogram phase shifting experiment is discussed. The phase shift angle histogram and lattice-site representation are applied for that purpose. Special attention is paid to possible nonlinear recording of component interferograms in the presence of linear and nonlinear phase step errors. Four and five step phase shifting algorithms are considered. The superiority of the lattice-site representation is shown. In the case of phase steps equal to π/2, however, the lattice-site representation of shift angles for five frame algorithm does not allow to detect recording nonlinearity. The four frame counterpart shows to be very helpful in this respect. Its properties related to the fringe pattern profile under study, including a defocused Ronchi grating, are discussed.     

Phase Measurement Algorithm without Phase unwrapping Problem for Phase stepping interferometry

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双点干涉法位相缺陷检测中的解相算法比较

双点光源移相干涉测量是大口径光学元件位相缺陷检测的一种重要方法。为了分析双点干涉中误差对解相算法的影响,首先给出相位缺陷检测的系统结构和理论模型,在此基础上,针对测量过程中主要存在的一次移相误差、二次移相误差、光强误差和随机振动误差,研究了Hariharan 5帧移相算法、13帧移相算法和迭代随机移相算法的解相误差,并进行了仿真分析。结果表明,针对这几种误差源,13帧算法解相精度整体优于5帧法,迭代随机移相算法解相效果优于13帧法和5帧法,当这几种误差按实际指标同时作用时,迭代随机移相算法解相误差RMS小于5帧法和13帧法,PV值稳定在0.5 nm以内。由于随机振动占主要作用,说明迭代随机移相算法受误差影响很小。     

两步相移实现投影栅相位测量轮廓术

提出一种新的投影栅相位测量方法--两步相移法。该方法只需两幅相移条纹图，因此计算量小，速度快。给出了实验及计算结果，并同四步相移法进行了比较，证明了该方法具有较高的精度。     

一种基于移相误差估计的5步移相算法

移相误差是用移相法进行相位测量的主要误差。本文提出一种 5步移相算法 ,分两步进行相位计算 ,首先估计实际步进移相的线性移相误差 ,然后再利用此移相误差估计值计算相位分布。移相误差估计公式和相位计算公式简洁 ,算法简单易行 ,对线性移相误差和二次谐波的敏感度低 ,可基本消除线性移相误差对解调相位的影响。对本文提出的算法进行了仿真研究 ,同时给出了 Hariharan 5步算法、Surrel 6步最小算法的仿真结果。结果表明 :本算法明显优于以上两种算法 ,可基本消除线性移相误差引起的相位偏移。本算法适用于作等步移相的相位测量或移相的标定。     

由三个压电陶瓷堆组成的干涉仪移相器的校正与标定

根据傅里叶变换原理 ,提出了一种对由三个压电陶瓷堆 (PZT)组成的干涉仪移相器进行非线性及平行性校正与标定的方法。在对各个压电陶瓷堆进行非线性校正的基础上 ,利用干涉图像自动分析系统 ,综合分析各个压电陶瓷堆之间的牵制作用 ,从而得到对整体干涉仪移相器平行性校正的补偿依据。组建了一套卧式数字平面干涉仪 ,在干涉仪移相器承重 6kg的情况下进行实验 ,非线性误差由 12 %校正至 0 3 %。由于干涉仪相移器承重而引起的移相过程中的条纹旋转降至 2° ,条纹间距变化小于 2 %。     

分振幅型全Stokes同时偏振成像系统波片相位延迟误差分析

分振幅型全Stokes同时偏振成像仪具有实时性好、空间分辨率高、精度高等优点,有很高的应用价值.分振幅型全Stokes同时偏振成像系统利用偏振分束器、1/2波片和1/4波片将入射光Stokes矢量调制在4幅图像中,可解析入射光Stokes矢量. 1/2波片和1/4波片的相位延迟误差对Stokes矢量测量精度有着不可忽略的影响.建立了包含上述两种误差的Stokes矢量测量误差方程,分析了1/2波片和1/4波片相位延迟耦合误差对自然光、0°/45°线偏光、左旋圆偏光等典型基态入射光的Stokes矢量测量误差的影响,推导了任意偏振态的Stokes矢量测量误差的表征方法.在邦加球球面和球内选取不同偏振度的Stokes矢量作为入射光进行仿真.结果表明, Stokes矢量测量误差和偏振度测量误差均随着入射光偏振度的增大而增大.选取入射光偏振度为1时的偏振测量精度评估系统.为满足2%的偏振测量精度, 1/2波片相位延迟误差应在±1.6°内, 1/4波片相位延迟误差应在±0.5°内.这对提高系统的偏振测量精度具有重要意义,为系统设计和研制提供了重要的理论指导.     

干涉仪移相器相位移π/2标定方法的研究

干涉仪移相器的相位标定在很大程度上决定了移相干涉仪的测量精度。本文是用傅里叶变换的原理,测量出推动移相器移动的压电陶瓷堆(PZT)的微位移量,并在此基础上提出了一种用空域滤波法得到干涉因光强分布,并判断其移相误差从而校正移相器步进π/2的方法。本文组建了一套数字平面干涉仪,对干涉仪移相器进行实验,在5步法情况下其移相误差在0.5%以下。     

Volume quantification by fuzzy logic modelling in freehand ultrasound imaging

Introduction

Many algorithms exist for 3D reconstruction of data from freehand 2D ultrasound slices. These methods are based on interpolation techniques to fill the voxels from the pixels. For quantification purposes, segmentation is involved to delineate the structure of interest. However, speckle and partial volume effect errors can affect quantification.

Objective

This study aimed to assess the effect of the combination of a fuzzy model and 3D reconstruction algorithms of freehand ultrasound images on these errors.

Methods

We introduced a fuzzification step to correct the initial segmentation, by weighting the pixels by a distribution function, taking into account the local gray levels, the orientation of the local gradient, and the local contrast-to-noise ratio. We then used two of the most wide-spread reconstruction algorithms (pixel nearest neighbour (PNN) and voxel nearest neighbour (VNN)) to interpolate and create the volume of the structure. Finally, defuzzification was used to estimate the optimal volume.

Validation

B-scans were acquired using 5 MHz and 8 MHz ultrasound probes on ultrasound tissue-mimicking phantoms. Quantitative evaluation of the reconstructed structures was done by comparing the method output to the real volumes. Comparison was also done with classical PNN and VNN algorithms.

Results

With the fuzzy model quantification errors were less than 4.3%, whereas with classical algorithms, errors were larger (10.3% using PNN, 17.2% using VNN). Furthermore, for very small structures (0.5 cm³), errors reached 24.3% using the classical VNN algorithm, while they were about 9.6% with the fuzzy VNN model.

Conclusion

These experiments prove that the fuzzy model allows volumes to be determined with better accuracy and reproducibility, especially for small structures (<3 cm³).     

A theoretical comparison of three fringe analysis methods for determining the three-dimensional shape of an object in the presence of noise

Various levels of random noise have been added to simulated digital images of a spherical dome illuminated by fringes projected from an offset angle. The noisy images have then been analysed using Fourier transform profilometry, phase shifting profilometry and spatial phase detection. The theoretical dome was subtracted from the domes reconstructed using these methods to form error maps. The maximum and RMS errors for each error map were calculated and plotted against the added noise level. At low levels of added noise the phase shifting method produced the lower errors, but above around 10% noise the Fourier transform method was better. Only at very high levels of added noise did the spatial phase detection method achieve the lowest errors.