二元伪随机光栅与台阶校准检测系统传递函数的影响分析

采用高质量的标准位相结构是实现光学干涉检测系统的系统传递函数精确校准及保证光学元件波前/表面中高频段信息准确检测的前提。通过对二元伪随机光栅结构和台阶位相结构两类典型表面进行模拟,分析了空间周期误差及跃变边缘陡度等制造误差对于检测系统传递函数校准的影响,并分析了检测系统CCD对二元伪随机光栅欠采样和过采样时功率谱密度(PSD)的变化。结果表明：存在同等制造误差时,二元伪随机光栅结构比台阶位相结构对检测系统传递函数中高频能够实现更高精度的校准;当对二元伪随机光栅存在欠采样或过采样时,均会造成PSD随频率的下降,可通过对理想二元伪随机光栅的高度分布进行相应的采样修正消除因采样对传递函数校准的影响。     

大口径干涉仪系统传递函数的修正和校准

 采用子孔径拼接法对传统系统传递函数校准方法进行修正。将大口径干涉仪视场分成若干个等晕区,采用标准台阶相位比较法分别测得每个等晕区的传递函数,然后将大口径干涉仪系统传递函数修正为每个等晕区传递函数的加权平均,其权重因子由对应等晕区内测试面的功率谱决定。实验结果表明:中心视场对应传递函数和修正后的系统传递函数在3 mm^-1附近处差值大于0.2;修正后的系统传递函数校准方法能更准确地得到波前功率谱密度。     

大口径干涉仪系统传递函数校准

 波前功率谱密度(PSD)被用于评价ICF激光驱动器光学元件在中频区域的波前误差。目前主要采用大口径相移干涉仪检测ICF光学元件的波前畸变,通过付立叶变换获得波前的PSD分布。相移干涉仪在较高空间频率分量的测量上存在失真效应,因此需对干涉仪的空间频率传递函数进行校准。本文采用位相比较法测量大口径相移干涉仪的系统传递函数。我们采用衍射光学元件的制造工艺,设计、制作了标准的透射和反射位相元件,比较理论计算值与实测PSD值,分别获得了大口径相移干涉仪透射、反射测量模式的系统传递函数。     

大口径干涉仪系统传递函数校准

波前功率谱密度(PSD)被用于评价ICF激光驱动器光学元件在中频区域的波前误差。目前主要采用大口径相移干涉仪检测ICF光学元件的波前畸变,通过付立叶变换获得波前的PSD分布。相移干涉仪在较高空间频率分量的测量上存在失真效应,因此需对干涉仪的空间频率传递函数进行校准。本文采用位相比较法测量大口径相移干涉仪的系统传递函数。我们采用衍射光学元件的制造工艺,设计、制作了标准的透射和反射位相元件,比较理论计算值与实测PSD值,分别获得了大口径相移干涉仪透射、反射测量模式的系统传递函数。     

干涉成像系统传递函数的数值分析

干涉仪系统传递函数能有效地表征系统相位成像的性能。通过假设干涉成像系统是复振幅的线性平移不变系统,模拟计算正弦相位光栅和相位台阶这两类标准相位物体的成像,确定干涉仪系统传递函数。数值分析结果表明：系统传递函数随着波像差的增加而减小;干涉成像系统对小幅度相位（远小于1 rad）成像是近似线性的,而对大幅度相位(大于0.5 rad）成像则是明显非线性的。当正弦相位的幅度为1时,系统传递函数在1/2和1/3截止频率处出现明显的急剧下降。高度为/2的相位台阶成像时,系统传递函数随着空间频率的增加而缓慢地降低。 The performance of phase imaging in interferometric imaging system is well characterized by the system transfer function (STF). The STF of the interferometric imaging system is analyzed numerically by assuming that the system is linear and shift-invariant for the complex field. Two standard phase objects, sinusoidal phase grating and phase step, are employed and simulated to determine the STF. Numerical simulation results show that the STF decreases as the wavefront aberration of interferometric imaging system increases. It also shows that the interferometric imaging system is approximately linear for small phase (far less than 1 rad) but explicitly nonlinear for large phase (larger than 0.5 rad). The STF has a visible drop at one half or one third of the cut-off frequency of the imaging system when the amplitude of sinusoidal phase is 1 rad. For a phase step with a height of /2 rad, the STF has no visible drop but decreases slowly with the increasing of spatial frequency. The results provide a useful guidance to the design of interferometer and the measurement of STF and power spectrum density in experiment.     

干涉成像系统传递函数的数值分析

干涉仪系统传递函数能有效地表征系统相位成像的性能。通过假设干涉成像系统是复振幅的线性平移不变系统,模拟计算正弦相位光栅和相位台阶这两类标准相位物体的成像,确定干涉仪系统传递函数。数值分析结果表明:系统传递函数随着波像差的增加而减小;干涉成像系统对小幅度相位（远小于1 rad）成像是近似线性的,而对大幅度相位(大于0.5 rad）成像则是明显非线性的。当正弦相位的幅度为1时,系统传递函数在1/2和1/3截止频率处出现明显的急剧下降。高度为/2的相位台阶成像时,系统传递函数随着空间频率的增加而缓慢地降低。 The performance of phase imaging in interferometric imaging system is well characterized by the system transfer function (STF). The STF of the interferometric imaging system is analyzed numerically by assuming that the system is linear and shift-invariant for the complex field. Two standard phase objects, sinusoidal phase grating and phase step, are employed and simulated to determine the STF. Numerical simulation results show that the STF decreases as the wavefront aberration of interferometric imaging system increases. It also shows that the interferometric imaging system is approximately linear for small phase (far less than 1 rad) but explicitly nonlinear for large phase (larger than 0.5 rad). The STF has a visible drop at one half or one third of the cut-off frequency of the imaging system when the amplitude of sinusoidal phase is 1 rad. For a phase step with a height of /2 rad, the STF has no visible drop but decreases slowly with the increasing of spatial frequency. The results provide a useful guidance to the design of interferometer and the measurement of STF and power spectrum density in experiment.     

干涉仪系统传递函数测量及影响因素的分析

波前功率谱密度(PSD)被用于评价惯性约束聚变(ICF)激光驱动器光学元件中频段的波前误差。干涉仪对PSD较高空间频率分量的测量存在失真效应,可通过干涉仪系统传递函数(STF)的检测标定来获得真实的波前PSD分布。采用台阶板位相比较法测得大口径菲索相移干涉仪检测系统在透射和反射检测情形下的传递函数。对传递函数测试算法进行了比较分析,明确了干涉仪系统zoom倍率的改变等因素对传递函数测量的影响,为波前PSD的准确检测奠定了基础。     

CCD对高空间分辨率波前干涉检测的影响

推导并用实验验证了光强与入射波前在单位像元面积里成近似线性关系,从而得到入射波前经CCD采样后的功率谱密度（PSD）公式.根据该公式,模拟分析了影响CCD采集系统的系统传递函数的各个因素：入射波前、CCD的填充因子及CCD的曝光时间,得出了他们与系统传递函数的定性关系,并且通过实验明确CCD曝光时间对高空间分辨率波前检测不确定度的影响,为高空间分辨率干涉设计提供了理论依据.     

二维调制传递函数及其在波前差检测方面的应用

光学系统像质分析在光学系统设计、加工和装调过程中具有重要意义.像质分析常用的方法有调制传递函数法和波前差法.对于高分辨率光学系统,传统的一维调制传递函数由于只提供了一维空间频率信息,因此在像质检测时有一定的局限性.本文基于随机数图像的傅里叶功率谱密度理论,提出了一种利用随机数图像作为目标物来测量成像光学系统二维调制传递函数的方法;通过利用NewtonCotes求积公式,对有像差系统的光学传递函数计算公式做进一步推导,提出了利用实际成像光学系统的二维调制传递函数值直接计算系统波前差的算法.实验结果表明,二维调制传递函数较之一维调制传递函数更能真实地反应成像光学系统的成像性能;利用二维调制传递函数计算得到的波前差与理论波前差在轮廓上有较好的一致性,可以作为实际系统波前差分析的一条新途径.     

布拉格光栅应变测试系统的动态标定

为了能够简单精确地标定出Bragg光栅应变测试系统的应变拉伸系数,通过分析测试系统的解调原理,提出了运用陶瓷制动器的逆压电效应标定该系统的方法。对系统的8路应变测试通道进行了标定实验,将每路通道的实验数据进行线性拟合,分别得到了Bragg光栅应变拉伸量与解调信号相位差的关系曲线,从而确定了每路通道的应变拉伸系数,分析表明系数的标定相对误差在0.002 m/（）以内,标定结果具有较高的精度。     

Remote and high precision step height measurement with an optical fiber multiplexing interferometric system

An optical fiber multiplexing low coherence and high coherence interferometric system, which includes a Fizeau interferometer as the sensing element and a Michelson interferometer as the demodulating element, is designed for remote and high precision step height measurement. The Fizeau interferometer is placed in the remote field for sensing the measurand, while the Michelson interferometer which works in both modes of low coherence interferometry and high coherence interferometry is employed for demodulating the measurand. The range of the step height is determined by the low coherence interferometry and the value of it is measured precisely by the high coherence interferometry. High precision has been obtained by searching precisely the peak of the low coherence interferogram symmetrically from two sides of the low coherence interferogram and stabilizing the Michelson interferometer with a feedback loop. The maximum step height that could be measured is 6 mm while the measurement resolution is less than 1 nm. The standard deviation of 10 times measurement results of a step height of 1 mm configurated with two gauge blocks is 0.5 nm.     

干涉测量系统中杂散条纹影响的抑制

 为了抑制杂散条纹的影响，提出了一种简单实用的单幅三表面干涉条纹傅里叶分析法，它根据三表面干涉时各个表面干涉的条纹调制度不同，从三表面干涉图的频谱中提取测试面的频谱，从而准确地恢复测试面的面形。模拟结果证明了该方法的有效性，准确度可以达到l/1 000。实验表明：单幅三表面干涉条纹傅里叶分析法得到的面形形状与波长调谐时域傅里叶变化法和涂消光漆法得到的结果基本一致，PV值和RMS值与波长调谐时域傅里叶变化法相差分别为0.001l和0.004l，与涂消光漆法相差分别为0.042l和0.019l。通过7次单幅三表面干涉条纹傅里叶分析法测量，得到PV和RMS值的重复性分别为0.007 8l和0.002 6l。     

Monitoring/measurement of out-of-plane vibrations using shearing interferometry and interferometric grating

In this paper, an application of shear plate interferometry combined with moiré readout to monitor/measure out-of-plane vibrations is presented. Moiré fringes are produced between the fringe pattern from the shear plate and interferometric grating recorded by photographing the interference pattern generated from the shear plate. It is demonstrated that the method can be used to study periodic and non-periodic vibrations.     

Shifted-phase calibration for a 3-D shape measurement system based on orthogonal composite grating projection

This paper proposes a novel method for reducing measurement error caused by spectrum overlapping in orthogonal-composite-grating-based 3-D measurement method. For 3-D measurement systems based on orthogonal composite grating projection, spectrum overlapping causes phase of each deformed phase-shifting fringe changed differently, which violates the principle that the shifted phases between adjacent deformed fringes must be equivalent to 2π/3, and therefore results in phase measurement error. The proposed shifted-phase calibration method is based on that phase variation of each deformed fringe is independent of height and reflectivity of the measured object. Three composite gratings are projected on the reference plane, and each carrier channel includes three phase-shifting gratings needed in phase measuring profilometry (PMP). Because the adjacent phase-shifting fringes demodulated from the same carrier channel have the phase difference of 2π/3, we can respectively calculate the reference plane's phases of three carrier channels by the phase algorithm of PMP method, and the shifted phases between them are obtained. When an object is measured, the shifted phases between deformed phase-shifting fringes can be calibrated. A new 3-D measurement mathematical model is set to reconstruct object. Our experiments prove that the proposed method can effectively restrain the effect of spectrum overlapping and improve measurement accuracy almost one times.