基于莫尔条纹的全周转角精密测量方法

由于将莫尔条纹图进行快速傅里叶变换时会导致频谱泄露,导致无法实现360°的全周精确测量,因此提出基于莫尔条纹的全周转角测量方法并搭建转角测量系统。以1°为步距,利用CMOS相机采集不同宽度的莫尔条纹图像,采用快速傅里叶变换（fast Fourier transform, FFT）对条纹进行处理,得到光栅频谱信息。同时采用汉宁窗能量重心校正算法（Hanning-window energy centrobaric method, HnWECM）校正频谱,得到莫尔条纹图像表征转角的真实有效信息,实现全周精确测量。实验结果表明,该系统可快速精准地实现转角的全周测量,测量范围广,最大误差率为0.243 3%。     

扭转角测量系统中焦距误差分析

针对莫尔条纹测量扭转变形方案，分析了双光栅在光学系统存在焦距误差时对扭转角测量精度的影响。通过在传统的莫尔条纹测量扭转角理论公式的基础上引入焦距对于光栅像的缩放效应，推导出含有焦距因子的扭转角测量模型。由模型可知,随着光学系统焦距差异的增大，对应的扭转角也会随之发生较大变化。特别当光栅夹角在小角度范围（1°～3°）内变化时尤为明显，最终影响到扭转变形的测量精度。在设计的实验中，利用2个已知焦距的光学系统，通过采集莫尔条纹图像进行扭转角精度分析，验证了该文提出的理论。     

基于傅里叶变换的激光数字散斑测量平板玻璃的楔角

采用基于傅里叶变换的激光数字散斑测量了平板玻璃的微小楔角.通过在光路中借助毛玻璃的散射特性,采用高分辨率CCD直接记录激光散斑图像,对散斑图像进行快速傅里叶变换获得散斑结构的高信噪比的杨氏双缝干涉条纹,分析干涉条纹获得光强分布曲线,采用移动平均法消除光强曲线噪声后计算出干涉条纹间距,从而计算出平板玻璃的微小楔角.     

双螺旋叠栅条纹检测光束准直性的两种方法

介绍双螺旋叠栅条纹检测光束准直性的基本原理,进一步就双螺旋叠栅条纹的特征参量与被测光束发散角(即光束准直精度)的关系进行分析和推导。在分析双螺旋叠栅条纹进行时,首先采用频域低通滤波提取纯叠栅条纹,然后提取纯叠栅条纹的特征参量。提出两种特征参量的提取方法,一种依次进行傅里叶变换计算相位信息的傅里叶变换方法,另一种是受传统时间相移算法启发而提出的空间相移算法,讨论了在两种方法中极坐标的重采样问题和相应的计算公式,并进行了计算机模拟。结果表明,傅里叶变换方法和空间相移算法实质都是获取叠栅条纹全场趋势的平均值,使最终光束发散角的检测具有很高的精度,对自成像条纹周期的检测误差在±2.8‰以内。     

精确自动识别莫尔条纹方向角的算法

由于常规莫尔条纹计算方法难以满足速度和精度的要求,本文提出一种快速准确求取莫尔条纹方向角的算法。该算法首先根据直线方向与莫尔条纹方向越接近则均方误差值越小的原理,初步求得莫尔方向角α,之后采用Mean-Shift算法在方向角α附近进一步精确求取莫尔条纹方向角。实验结果表明:采用误差评判指标测试对比度满足5.4%时,提出的算法所获得的莫尔条纹方向角计算精度达到29',同时计算速度相对频域处理方法大幅提高,计算时间为15 ms,满足算法处理速度对实时性的要求。     

精确自动识别莫尔条纹方向角的算法

由于常规莫尔条纹计算方法难以满足速度和精度的要求,本文提出一种快速准确求取莫尔条纹方向角的算法。该算法首先根据直线方向与莫尔条纹方向越接近则均方误差值越小的原理,初步求得莫尔方向角α,之后采用Mean-Shift算法在方向角α附近进一步精确求取莫尔条纹方向角。实验结果表明：采用误差评判指标测试对比度满足5.4%时,提出的算法所获得的莫尔条纹方向角计算精度达到29＇,同时计算速度相对频域处理方法大幅提高,计算时间为15 ms,满足算法处理速度对实时性的要求。     

用电子学全息方法测量两平行光束微小夹角

提出一种根据电子学全息原理测量两平行光束微小夹角的方法，其基本思路是，用ＣＣＤ作为记录介质经图像采集卡将双光束干涉条纹图像采集于计算机中，并通过离散傅里叶变换实现干涉条纹图像从空域到频域的变换，根据所得到的频谱分布图，获取条纹数并算出条纹间距，进而推算出两平行光束的夹角。详细地阐述了该方法的原理，通过实验验证了其测量微小光束夹角的可行性，对其测量精度、范围和角度分辨率作了定量地分析。     

基于时频波谱对易原理分析莫尔条纹谱

数值解析信号波形时频域对易演变过程,研究任意信号波形与频率组分的内在联系, 并将该对易原理应用于莫尔条纹相位分析,提取相位信息。采用矩形窗模拟冲激波形和直流波形的变换过程,通过控制矩形窗函数窗宽,获得各种宽度矩形脉冲,窗宽趋于零情况下获得冲激波形,趋于∞获得直流波形。自开发快速傅里叶变换(fast Fourier transform, FFT)系统,对矩形脉冲实施离散傅里叶变换,方便快捷获得相应频谱数值解析波形,分析波形与频谱对易关系。结果发现,矩形窗函数频谱是Sa函数,窗宽变化导致Sa函数波形变化。窗宽减小时,Sa函数波形展宽,振动舒缓,趋于零极限时,变成直流波形。窗宽增大时,Sa函数波形紧缩,振动加剧,趋于∞的极限时,演变成δ冲激波形,信号波形时频域是对易的。根据时频域波形与频谱对易关系,在分析莫尔条纹时,将莫尔条纹的一级谱滤出并归一,由波谱对易原理,时域信号将体现Sa函数,使条纹对比分明,便于提取相位信息。     

Ronchi光栅Talbot效应长焦距测量的准确度极限研究

针对基于Ronchi光栅Talbot效应的长焦距测量方法,分析了利用傅里叶变换求取莫尔条纹角度的准确度限制,提出了通过傅里叶变换的多次迭代逼近来提高角度计量准确度,从而提高长焦距测量准确度的方法,并在此基础上分析了这种方法的准确度极限.     

数字投影仪性能最大化计算莫尔轮廓术

提出一种数字投影仪性能最大化计算莫尔轮廓术。为了满足动态测量的需要,利用数字投影仪的最大化刷新帧率和最高条纹频率设计,将二元编码条纹代替传统的8 bit数值正弦条纹使投影仪刷新率由传统60 Hz提高到数千Hz以上。通过编码满足抽样定理的最小周期二元条纹,利用数字投影仪的最优投影帧率性能,即可以在数字投影仪上实现投影条纹的最小等效波长,也可以实现计算莫尔条纹的优化提纯,进而从源头上有效提高计算莫尔轮廓术（CGMP）的测量精度。通过与傅里叶变换轮廓术（FTP）和高精度计算莫尔轮廓术（HCGMP）的对比实验验证了该方法的可行性和有效性,表明所提方法具有较高的测量精度,通过在线运动“心型”物体的测量表明所提方法可以满足在线和动态三维测量需要。     

载波相移云纹干涉法研究

通过对载波技术研究,提出载波相移云纹干涉法,采用该方法可以实现云纹干涉条纹信息的自动识别,给出了灵敏度和载波频率的定量关系式;同时,对载波数字相移云纹干涉法测试的精度进行了系统分析。     

Projection-type moiré topography with frequency modulation technique using liquid crystal digital gratings

A projection-type moiré topography that uses a frequency modulation technique with two liquid crystal digital gratings (LCDGs) is proposed. In this method, moiré contours are filtered to remove the image of the original grating from the moiré contours by moving the image created by the LCDGs. The frequency modulation technique can be used to analyze the fringe of step heights or other separate areas by modulating the fringe interval. The experimental results showed the possibility of measuring three-dimensional shapes and step heights.     

Phase extraction using multi-directional moiré fringes for multi-lateral shearing interferometry

The multi-lateral shearing interferometers (multi-LSIs) are featured in the improved accuracy and noise resistance of wavefront reconstruction using phase differences in multiple directions. Nowadays the multidirectional phase differences are usually extracted from multi-LSIs’ interferogram using the fast Fourier transform (FFT) method, whose accuracy is limited by spectral leakage effect. To improve the measurement accuracy of multi-LSIs, a phase extraction method developed from moiré technique is proposed in this paper. Using virtual gratings with properly large carrier frequencies, the desired phase information in each of the multiple directions can be modulated into low-frequency domain of the corresponding moiré pattern with larger separations between unnecessary side lobes. In this way, low-pass filters with higher cut-off frequencies can be applied in moiré technique to reduce the inaccuracy induced by spectral leakage effect. Meanwhile, phase shifting method can be applied to extract phase information from a single fringe pattern with better noise resistance by easily introducing phase shifts in computer generated virtual gratings. Simulation results show that the proposed method has higher accuracy and better anti-noise performance than the FFT method when spectral leakage effect exists. To demonstrate accuracy of the proposed method, a null test experiment of the quadriwave LSI has been conducted and experimental results show that measurement accuracy of the quadriwave LSI can be significantly improved by substituting the FFT method with the proposed method in phase extraction process.     

Application of the moiré deflectometry on divergent laser beam to the measurement of the angle of arrival fluctuations and the refractive index structure constant in the turbulent atmosphere

When a slightly divergent laser beam passes through a turbulent ground level atmosphere and strikes a linear grating, fluctuating self-images are formed at Talbot distances. By superimposing a similar grating on one of the self-images, even for the case of parallel gratings' lines, fluctuating moiré fringes are formed owing to the beam divergence. Recording the successive moiré patterns by a CCD camera and feeding them to a computer, after filtering the higher spatial frequencies, produces highly magnified fluctuations of the laser beam. Using moiré fringe fluctuations we have calculated the fluctuations of the angle of arrival and the atmospheric refractive index structure constant. The implementation of the technique is straightforward, a telescope is not required, fluctuations can be magnified more than ten times, and the precision of the technique is similar to that reported in our previous work.     

纳米云纹法条纹倍增技术研究

提出了一种纳米云纹法的条纹倍增技术，可用于单晶材料纳米级变形测量.在测量中，单晶材料的晶格结构由透射电镜（TEM）采集并记录在感光胶片上作为试件栅，几何光栅作为参考栅.对纳米云纹条纹的形成原理，透射电镜放大倍数与试件栅的频率关系，条纹倍增技术，位移、应变测量方法等进行了详细讨论.该方法不仅能够测量连续力学参量，如应变和位移，而且能够表征纳观非连续参量，如位错、夹杂.     

散斑干涉相位条纹图的频域滤波处理

为了解决在数字散斑干涉技术测量时,散斑干涉相位条纹图像中大量噪声对相位解包裹结果和精度产生严重影响的问题,介绍了一种条纹正余弦分解和频域低通滤波结合的方法,实现了散斑干涉相位条纹图的高精度滤波。该方法的基本思路是在对相位图像进行滤波处理前,先将相位图通过正余弦函数进行映射转换成两幅图,分别经过频域滤波,然后再合成为相位图。这种分解频域滤波方法可以在滤波的同时,有效保留相位跳变信息。实验结果表明：与传统的图像降噪方法相比,该方法能够在保留图像“尖峰”信息的基础上,较好地滤除图像中的散斑噪声,方法简单有效,有效解决了传统滤波方法应用在相位条纹图中,相图灰度信息丢失10%~40%的问题。     

A novel raster-scanning method to fabricate ultra-fine cross-gratings for the generation of electron beam moiré fringe patterns

The resolution of the electron beam moiré method depends on the line frequency of the grating. Recently, more and more effort has been devoted to increase the frequency, and a novel method for producing high-resolution electron beam gratings is presented in this work. Cross-gratings with a frequency up to 14,832 lines/mm (67 nm pitch) were successfully fabricated using a common scanning electron microscope without a dedicated pattern generation system. The quality of the grating was high enough to produce high-quality moiré fringe patterns. In this method, the ultra-fine cross-grating can be fabricated only through one-directional scanning on the resist, which can improve the grating quality and significantly reduces the fabrication time. The number of control parameters for grating fabrication could be reduced to two compared to the six parameters required by conventional methods, which facilitates the use of the electron beam moiré method. The frequency of the fabricated grating is linearly proportional to the exposure magnification. Thus, the frequency of the grating can be accurately predetermined, and the null field can be easily obtained in the electron beam moiré method. The quality of the fabricated gratings was illustrated by the obtained micrographs and moiré fringe patterns. The full-field local strain near an induced crack was studied to verify the application potential of this method.     

Improved grid-noise removal in single-frame digital moiré 3D shape measurement

A single-frame grid-noise removal technique was developed for application in single-frame digital-moiré 3D shape measurement. The ability of the stationary wavelet transform (SWT) to prevent oscillation artifacts near discontinuities, and the ability of the Fourier transform (FFT) applied to wavelet coefficients to separate grid-noise from useful image information, were combined in a new technique, SWT-FFT, to remove grid-noise from moiré-pattern images generated by digital moiré. In comparison to previous grid-noise removal techniques in moiré, SWT-FFT avoids the requirement for mechanical translation of optical components and capture of multiple frames, to enable single-frame moiré-based measurement. Experiments using FFT, Discrete Wavelet Transform (DWT), DWT-FFT, and SWT-FFT were performed on moiré-pattern images containing grid noise, generated by digital moiré, for several test objects. SWT-FFT had the best performance in removing high-frequency grid-noise, both straight and curved lines, minimizing artifacts, and preserving the moiré pattern without blurring and degradation. SWT-FFT also had the lowest noise amplitude in the reconstructed height and lowest roughness index for all test objects, indicating best grid-noise removal in comparison to the other techniques.     

Solid-state dye laser with moiré gratings

We fabricated distributed-feedback (DFB) solid-state dye lasers with moiré gratings. We formed a moiré grating pattern by superimposing two grating patterns with a rotation angle. The moiré gratings were fabricated by an “etchless” process utilizing a two-beam interference method. The gratings were coated with solidified rhodamine-B. The five laser devices were pumped with the second harmonic generation of a Nd:YAG laser and we obtained narrow-banded laser oscillations at 590, 600, 610, 620, and 630 nm wavelength. Full widths at half maximum of laser spectra were less than 0.5 nm. The results indicated that a moiré fringe can function as a resonator of DFB solid-state dye lasers.     

云纹干涉载频调制技术及分析

在物体变形场的测量中,云纹干涉的载频调制技术有重要作用.在云纹干涉中,对称光照明产生的衍射光沿试件栅表面的法线传播并产生干涉.通过改变照明光的入射角度,可实现变形条纹场的空间调制.通过光程差的分析说明了载波条纹产生的机理,得出了载波频率与照明光入射角度变化之间的关系式.利用三点弯曲加载结合二维载频调制实验,给出了实验结果.证明了在初始条纹较少的情况下,载频调制技术能有效地测量物体的位移场.