基于单幅干涉图的波前重构技术研究

条纹中心法是干涉测量技术中分析单幅干涉图的一种重要处理方法,该方法主要包括图像预处理、波前重构和样品表面形貌及参数的测量等三个部分。研究了条纹中心法的关键技术,特别是应用协方差矩阵法求解泽尼克多项式以进行波前重构的过程。提出了基于单幅干涉图自动波前重构的流程方法。最后应用该流程方法处理由泰曼-格林干涉系统采集的精密抛光铝制盘基片表面形成的一幅干涉图像。实验结果表明,该方法可以实现单幅干涉图的自动波前重构,干涉波前重构的拟合精度可达1．4686×10^-6nm,还可以自动获得精密抛光铝制盘基片表面的形貌及参数。     

Stability of Zernike coefficients solved by the covariance matrix method in the analysis of the wave front aberration

The deduction of Zernike coefficients is usually influenced by the finite number of sampling dots on interferogram and their inherited measurement errors. In this paper, a simplified Gram-Schmidt method for solving the Zernike polynomial with the higher fitting precision is presented and used to analyze the wave front aberrations for the circle interference fringe of the fine polished aluminum disk surface captured by a Twyman-Green interferometer system. We find the stability of the Zernike coefficients changes with changing the Zernike term, which has lead to the wrong expression for the wave front aberration. By analyzing the condition number of the coefficients matrix and the fitting precision of the method, it is indicated that the instability can be avoided when the Zernike term is lower than 14. Such an analysis will be valuable in solving the Zernike polynomial for the wave front aberration analysis in optical testing.     

Study on an automatic processing technique of the circle interference fringe for fine interferometry

The fringe center method (FCM) is an important digital processing technique of fringe patterns analysis for interferometry. In this paper, an improved automatic processing technique based on FCM was presented, which correlated the processing link and the looped feature of the circle fringe pattern. It also integrated several techniques including noise removal, the fringe thinning, the fringe patching, assignment of the fringe orders and wavefront reconstruction and can be executed orderly and automatically. Based on the new the algorithms of the fringe patching and assignment of the fringe orders, the fringe feature information was extracted automatically and the interference wavefront was reconstructed by Zernike polynomial fitting method. With the automatic processing technique, the circle interference fringe of the fine polished aluminum disks surface captured by the Twyman-Green interferometer was processed, and the surface profile and the parameters of the disk were obtained automatically. The experiments show that the improved automatic processing technique was more accurate and fast in measurement than the conventional one. It was convenient to use it in in-situ industry inspection.     

移相器微位移旋转误差的分析及测试

以压电陶瓷(PZT)微位移器为主要研究对象, 引入一种处理静态干涉图的新方法--虚光栅移相叠栅条纹法,设计实验对一台实际使用的移相器微位移旋转误差进行测试研究,对其引起的波面旋转情况进行了定量的计算分析,并给出测试结果.用虚光栅移相叠栅条纹法处理实验中加有载频的干涉图时,不需要使用任何移相器件,可以进行动态位相的检测,整个移相过程用计算机进行控制,避免了引入额外的移相误差.     

Zernike多项式拟合干涉面方法研究

本文就专著和文献中关于Zernike多项式拟合干涉波面几乎都建设采用Gram-Schimdt正交化方法,而不采用比较简单的传统经典的最小二乘法问题进行了深入研究,从理论和实践上严格地证明了两种方法的等价性。实践中发现,用最小二乘法求解Zernike多项式拟合系数的速度比用Gram-Schimdt正交化方法提高了三倍之多。由于在精密光测技术中,Zernike多项式已被广泛采用,因此,“等价性”的证明具有重要意义,并对于其它类似问题也有着普遍的参考价值。     

Efficient background removal based on two-dimensional notch filtering for polarization interference imaging spectrometers

A background removal method based on two-dimensional notch filtering in the frequency domain for polarization interference imaging spectrometers(PIISs) is implemented. According to the relationship between the spatial domain and the frequency domain, the notch filter is designed with several parameters of PIISs, and the interferogram without a background is obtained. Both the simulated and the experimental results demonstrate that the background removal method is feasible and robust with a high processing speed. In addition, this method can reduce the noise level of the reconstructed spectrum, and it is insusceptible to a complicated background, compared with the polynomial fitting and empirical mode decomposition(EMD) methods.     

基于PMD的反射镜面检测实验分析

将相位测量偏折术应用于非球面反射镜面形检测,并对实验检测结果的中高频误差进行了分析研究。计算机产生正弦性条纹图,并且显示在薄膜场效应晶体管显示屏上。摄像机通过被测反射镜观察并拍摄显示屏上的条纹图。利用相移技术和相位展开技术计算得到相位分布。以相位信息为载体对光线进行追迹,并根据反射定律得到面形梯度分布,由数值积分重建面形分布。最后使用泽尼克多项式拟合分析了其中高频误差。     

中心遮拦干涉图的处理

介绍了一种用于中心遮拦的大口径干涉仪的干水条纹处理软件，该软件通过对干涉数据进行采集，处理而得出被检波面的波差分布和像差，由于对干涉图数据拟合过程中所使用的泽尼特（Ｚｅｒｎｉｋｅ）多项式进行了修正，因此得到的结果的准确度也有了较大的提高。     

影响条纹图形拼接法测量精度的主要误差因素

通过对计算机模拟和实验结果的分析表明，影响条纹图形拼接法测量精度的主要因素是子孔径面形测量精度，重叠区的大小，面形拟合阶次和拼接模式等。     

转镜式傅里叶变换光谱仪光程差非线性的拟合法补偿

转镜式傅里叶变换光谱仪中光程差非线性带来了干涉图周期变化和相位误差,对非线性的拟合法补偿利用采样得到的干涉图进行重构,得到不含相位和周期误差的干涉图,再按照均匀采样函数对干涉图进行二次采样,消除非线性光程差对复原光谱的影响.经过二次采样的干涉图不含周期和相位误差,可以直接使用现有的软件进行光谱复原.计算机仿真实验证明这种方法行之有效,且利用4次多项式拟合干涉图效果更好.     

A study of fringe pattern trace and analysis

In this paper,the gometric center and centroid method are suggested to tracecenter location of a close fringe pattern.The fringe pattern of the interferogram is analysed byusing the general Fourier method.The analytic accuracy is controlled by using P-test methodof statistics.The analytic accuracy and sampling speed of the fringe pattern depend on thequality of the interferogram and the numbers of the sampling points.     

Improvement of the signal-to-noise ratio in interferometry using multi-frame high-dynamic-range and normalization algorithms

Using both high dynamic range (HDR) and normalization methodologies, we show a method to improve the fringe pattern contrast in interferometric measurements normally used for phase recovering. In a simulated interferogram that mimics the main effects that can be found in an interferometric process (stray-light, photon noise, electronic noise, scattering phenomena, etc.) it was possible to improve the contrast of the fringes and to decrease the root mean square error by more than 35%. The method proposed is applied to experimental interferograms to measure wavefront error and retardance changes on liquid crystal (LC) devices. It is done by using a Mach–Zehnder set-up in which we used different polarization areas. The proposed method increases the quality of the phase recovered and decreases the root mean square error by 50%.     

环形光源在干涉仪系统中的应用

 介绍了一种新的环形光源技术来抑制干涉仪系统的本征噪声以提高信噪比。阐述了环形光源抑制干涉仪系统本征噪声的原理,根据条纹对比度和需抑制噪声空间频率的要求,推导得到了环形光源的外半径和内半径。通过与传统的点光源对比实验表明：环形光源模式系统的本征噪声峰谷值小于点光源模式,且没有明显的牛顿环噪声,本征噪声的功率谱密度在空间频率小于2.5 mm ^-1时小于点光源的1/10,系统信噪比在空间频率小于2 ^-1时大于点光源的两倍。     

Direct demodulation of closed-fringe interferograms based on active contours

We demonstrate a method to directly demodulate closed-fringe interferograms using a kind of active contour called a snake. This method can be used to demodulate a single closed-fringe interferogram when its background illumination and/or contrast terms have a spatial frequency similar to the spatial frequency of the equivalent normalized interferogram. Among other cases, this problematic usually appears in interferometry when spurious reflection appears in the interferogram. In these situations, typical Fourier-based methods are of no help. We show a set of simulations and experimental results that prove the effectiveness of the proposed method.     

一种基于傅里叶变换的分析载波条纹的新方法

针对传统傅里叶变换法处理光载波干涉条纹图时会有边缘效应产生的问题,提出了一种基于傅里叶变换法的外推延拓方法,并从理论上进行了数学推导。为了验证这种方法的正确性,分别对一维数字信号和二维空间载波条纹图进行了数值模拟,进一步分析了误差产生的原因,并与传统的傅里叶变换法对比。结果表明该法可以有效抑制传统傅里叶变换法处理光载波干涉条纹图时边缘效应所造成的较大误差,在基于空间域相位调制技术的波面干涉测量中,对空间载波条纹图进行处理,可以使相位的计算精度达到3.3 mrad。     

A subfringe integration method for multiple-beam Fizeau fringe analysis

Some aspects concerning the subfringe integration method in interferogram analysis have been investigated and modified. The modified algorithm, introduced in this paper, is capable of reconstructing the phase in the presence of noise or errors in carrier frequency. The subfringe integration method was applied to analyze two computer simulated patterns of equispaced Fizeau fringes using N bucket integration. Also, it is used to analyze the multiple-beam Fizeau fringe. The refractive index profile of polyethylene fiber is obtained by using two methods, subfringe integration method, and Fourier transform method. A comparison between the obtained results using the maintained methods is presented.     

一种用于光机热集成分析的新方法——干涉图插值法

Zernike多项式是光机热集成分析中实现光、机、热各分析软件之间数据传递的重要工具。许多光学元件表面形状并不满足Zernike多项式的正交性条件，使有限元分析不能精确拟合光学元件表面变形及变形产生的各项像差。讨论影响Zernike正交性的几个因素，详细介绍将有限元分析得到的光学表面变形数据导入光学分析软件的一种新方法——干涉图插值法。该方法避开Zernike多项式拟合，在去除镜面刚体位移后将镜面畸变精确地表示成干涉图数据，直接生成数据接口。     

GaN HEMT栅边缘电容用于缺陷的研究

本文对GaN HEMT栅漏电容的频率色散特性进行分析,认为栅边缘电容的色散是导致栅漏电容频率色散特性不同于圆肖特基二极管电容的主要原因. 通过对不同栅偏置条件下缺陷附加电容与频率关系的拟合,发现小栅压下的缺陷附加电容仅满足单能级缺陷模型,而强反向栅压下的缺陷附加电容同时满足单能级和连续能级缺陷模型. 实验中栅边缘电容的频率色散现象在钝化工艺后出现,其反映的缺陷很可能是钝化工艺引入,且位于源漏间栅金属未覆盖区域的表面. 最后通过低频噪声技术进一步验证栅边缘电容提取缺陷参数的可行性. 低频噪声技术获得的单能级 关键词： HEMT 边缘电容 缺陷 低频噪声     

An automatic processing technique for accurate surface form measurement

A single shot algorithm using a Fizeau interferometer was used to measure the form profile of a spherical smooth surface by means of fringe thinning process, which plays an important role in fringe patterns analysis. In this paper, an automatic processing technique based on the fringe thinning process is presented. The circular interference fringe pattern of the spherical smooth surface captured by the Fizeau interferometer was corrected by using the flat fielding method and then processed. Based on the fringe thinning and the assignment of the fringe orders, the information on the fringe feature was recovered automatically and the interference wavefront was reconstructed by the Zernike polynomial fitting method. The results were compared with the results measured by Bünnagel method, and the results were in good agreement. This means that the single shot algorithm is reliable, fast, and less sensitive to vibration and turbulence in surface form measurements. Simulation fringes with the ray tracing technique were obtained to match the practical fringes.     

光学综合孔径成像中的傅里叶相位研究

傅里叶相位是光学综合孔径成像的重要信息,观测目标的傅里叶相位包含于干涉条纹中。从像平面干涉条纹形成原理出发,推导出大气扰动、星光方向与基线方向不垂直和望远镜系统机械误差等因素是影响干涉条纹初始相位的主要因素。利用条纹原点值和峰值位移从条纹中提取初始相位,采用闭合相位法从条纹初始相位中去除其它因素的影响,从而最终获取目标傅里叶相位：结合计算机模拟对噪声给条纹峰值位置的影响进行分析,模拟结果表明在频域中对条纹能量谱进行阈值处理有较好的去噪效果。最后结合目标重构迭代法阐述了闭合相位在像重构中的作用。