合成孔径激光成像雷达中非线性啁啾补偿算法的误差分析

可调谐激光器产生的非线性啁啾相位误差会降低合成孔径激光成像雷达(SAIL)的距离向分辨率。已有的补偿算法中使用的相移公式存在估算误差,外差脉冲补偿方法也存在补偿误差。由理论推导得到适合于实际有限数据的相移公式,对理想相移公式产生估算误差的物理原因进行了分析。建立了条带扫描模式下星载SAIL的计算机仿真模型,并对两个相移公式的估算误差、整体补偿和逐一扫描滤波补偿两种方法的补偿误差进行了模拟。仿真结果验证了理论推导结论。最后,给出了减少SAIL非线性啁啾补偿算法中估算误差和补偿误差的方法。     

投影条纹相移法中图像饱和误差抑制算法研究

针对投影条纹相移法三维形貌测量中的图像饱和误差进行了深入研究,分析了基于条纹相移技术的图像饱和误差抑制算法的适用范围,推导了基于六步相移的饱和误差抑制算法公式.理论分析表明,相移条纹图的帧数越多,饱和误差抑制算法的适用范围越广.并通过数值模拟和实验进行了验证,基于六步相移的饱和误差抑制算法可以更加有效地抑制图像饱和引起的相位误差.     

投影条纹相移法中图像饱和误差抑制算法研究

针对投影条纹相移法三维形貌测量中的图像饱和误差进行了深入研究,分析了基于条纹相移技术的图像饱和误差抑制算法的适用范围,推导了基于六步相移的饱和误差抑制算法公式.理论分析表明,相移条纹图的帧数越多,饱和误差抑制算法的适用范围越广.并通过数值模拟和实验进行了验证,基于六步相移的饱和误差抑制算法可以更加有效地抑制图像饱和引起的相位误差.     

Ronchi相移剪切干涉仪及其相位提取误差分析

在分析Ronchi相移剪切干涉仪典型系统参数的基础上,系统研究了该干涉仪相位提取精度的主要影响因素。结合传统的五步相移算法,采用所提出的八步与十步相移算法,对Ronchi相移剪切干涉仪的相位提取误差进行理论分析和仿真计算。仿真结果说明,八步和十步相移算法可以有效地消除多级衍射光寄生干涉对相位提取精度的影响,且十步相移算法比八步相移算法具有更高的相位提取精度;为了提高测量精度,要求相移误差优于2%;探测器位数大于10位;光栅周期误差小于1%;光源空间相干性低于0.1。通过采用不同的相移算法、剪切率和光源空间相干性的三组对比实验,对理论分析的正确性进行了验证。     

两步相移数字全息物光重建误差分析与校正

系统研究了两步相移数字全息干涉术中相移误差引起的波前再现误差的计算和校正方法. 基于衍射物光相位分布的随机性和振幅相位的相互独立性原理,介绍了相移数字全息中物光波前再现误差的表达形式,推导出步长为π/2的两步算法中物光重建误差的表达式. 通过进一步分析这一重建误差的结构和特点,结合物光表达式,给出了自动校正相移误差引起的波前重建误差的校正方法. 该方法无需增加测量,在未知相移误差大小的情况下,只对标准两步相移算法恢复的物光复振幅进行处理就可以实现对物光振幅和相位的同时校正. 计算机模拟结果表明,校正后可将 关键词： 相移干涉术 数字全息 物光重建 误差校正     

相移干涉仪中探测器非线性误差及其补偿

通过对多个相移算法的理论分析和数值模拟,发现探测器的非线性响应在相位中会引入2倍空间频率的系统误差。结果表明,非标准相移算法随着探测器非线性度的增加,相对误差也越来越大。提出了压电陶瓷驱动器的移相误差和光电探测器的非线性误差相互抵消的误差补偿技术,并给出了判别误差匹配有效性的实用判据。仿真表明,这种误差补偿技术可以使测量误差减小约一个量级。证明了在不考虑波前幅度信息时,标准相移算法对光电探测器的非线性为零响应,不影响仪器精度。     

提高数字全息再现像像质的两步相移迭代算法

在两步相移数字全息术中,相移误差直接影响着零级像和共轭像的消除.为了消除相移误差,获得实际相移值,提出了一种基于相位统计特性的两步相移迭代算法.首先利用全息图的相位统计特性计算出初始相移值,然后用数字全息图再现像抽样点强度偏差之和作为评价标准,通过迭代计算寻找参考光的真正相移值.该算法能对任意未知相移量进行提取,从而有效地消除零级像和共轭像,提高了再现像质量.理论分析和光学实验结果证明了该方法的可行性和有效性.     

基于迟滞非线性补偿系统的光学元件形貌检测

为了减少相移干涉仪中压电陶瓷致动器进行相移时,其迟滞非线性对相移算法中的相位计算带来的误差,设计了一套压电陶瓷致动器的控制系统.利用高精度电阻应变传感器和基于锁相放大原理的信号调理电路检测压电陶瓷致动器位移,建立多项式数学模型描述迟滞非线性,然后提出了一种前馈开环控制方法补偿其迟滞非线性.最后,基于所提出的方案对压电陶瓷致动器进行了期望轨迹的跟踪控制实验,同时将补偿控制系统与干涉仪相结合检测光学元件表面形貌.实验结果表明:补偿后,压电陶瓷致动器的跟踪误差在-0.156μm与+0.078μm之间,迟滞非线性度由10.4%降到2.4%,且干涉仪所测得的光学元件表面面形起伏高度均方根和峰谷分别改变了0.795nm和3.937nm.该系统对于高精度的光学元件形貌检测具有重要的意义.     

光强和方位角误差对光弹性五步彩色相移法的影响

为了了解相移法中的各种参数所产生的误差对最终结果的影响 ,对一些主要参数做深入的误差分析是十分必要的。针对五步彩色相移法所用的白光入射平面偏振场的特点 ,只考虑光强、起偏镜和分析镜方位角所引起的误差影响就可以了。提出一个分析和评估这些误差源对五步彩色相移法确定等倾角参数所产生影响的方法 ,这对合理设计实验装置和执行正确的实验条件将起到积极的作用     

结构光测量相位波动误差补偿方法研究

在计算机仿真分析投影仪伽马非线性特性对包裹相位波动误差影响的基础上,提出一种面向相移结构光测量的相位波动误差补偿方法.该方法采用二次多项式最小二乘拟合的方法近似输出条纹光强分布,实现包裹相位波动误差的补偿,减小投影仪非线性导致的系统测量误差.此方法简单,运算量小,不依赖环境光源及投影仪、摄像机具体参数,具有很强的通用性...     

Phase shifting algorithms for non-sinusoidal waveforms with phase shift errors

In phase shifting interferometry, phase errors due to harmonic components of a fringe signal can be minimized by applying synchronous phase shifting algorithms with more than four samples. However, when the phase shift calibration is inaccurate, these algorithms cannot eliminate the effects of a non-sinusoidal waveform. It is shown that by taking a number of samples beyond one period of the fringe pattern, phase errors due to the harmonic components of the fringe signal can be eliminated, even when there exists a constant error in the phase shift interval. A general procedure for constructing phase shifting algorithms that eliminate these errors is derived. A seven-sample phase shifting algorithm is derived as an example, in which the effect of the second harmonic component can be eliminated in the presence of a constant error in the phase shift interval.     

Characteristic polynomial theory of two-stage phase shifting algorithms

Two-stage phase shifting algorithms make possible to directly recover the sum or the difference of the optical phase of two different fringe patterns. These algorithms can be built by combining the known phase shifting algorithms in a non-linear way. In this work, we associate a two-dimensional characteristic polynomial to each two-stage phase shifting algorithm. This enables us to qualitatively compare their behaviour against the main systematic error sources, by means of an analysis protocol like that used for phase shifting algorithms. We show that this tool allows to understand the propagation of properties from precursor phase shifting algorithms to new evaluation algorithms built from them. As an experimental application, a wavefront distortion evaluation in differential phase-shifting interferometry is presented.     

Error compensation of four and five buckets wavefront extraction algorithms in phase-shifting interferometer

The phase-shifting method is all along an important wavefront extraction technique in the interferometer. Moreover, to require almost real-time measurement an algorithm with a small number of grabbed buckets is very helpful to the phase-shifting interferometer. Therefore, those algorithms within five buckets are very practical and are given more attention. In the paper, popular phase shifting algorithms within five buckets are compared and new four and five buckets algorithms are developed to compensate for two dominate error sources which are linear phase shift deviation and detector nonlinearity. Numerical simulations and wavefront extraction experiment verify that the proposed compensation algorithms are insensitive to linear phase shift deviation and detector nonlinearity compared with classical four and five bucket algorithm.     

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。     

抑制高阶谐波误差的随机相移条纹分析算法

高阶谐波和随机相移误差是影响条纹分析精度的主要因素。为了同时解决这两个问题,提出了基于频域滤波的迭代相移算法。该算法采用巴特沃斯低通滤波器,从频域上滤除条纹的高阶谐波分量,再运用最小二乘迭代方法从三帧随机相移条纹图像中提取相位信息。数值模拟和实验结果表明,该算法可有效地抑制由高阶谐波和随机相移引入的波纹误差,误差PV值和RMS值分别为0.368 8 rad和0.025 3 rad,其精度高于传统的三步相移算法和Wang算法。该方法适合于高精度干涉测量和三维物体表面轮廓测量。     

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。     

Error-compensating algorithms in phase-shifting interferometry: a comparison by error analysis

In this paper, two families of phase-shifting algorithms with π/2 phase steps are studied. In family I, three new algorithms are derived by using the averaging technique based on the Surrel six-sample algorithm with phase shifts of π/2. Family II includes four well-known algorithms derived by the averaging technique based on the conventional four-sample algorithm with π/2 phase steps. A polynomial model of phase-shift errors used to describe general expressions for calculation of the correct object phase via the Fourier spectra analysing method as a function of the harmonic order in the fringe signal is presented. The error-compensating properties of the algorithms in families I and II are investigated by the Fourier spectra analysing method. It is found that the averaging technique, when used in any of the algorithm with π/2 phase steps, can improve the phase-shifting algorithm property: it is insensitive to phase-shift error when the fringe signal contains the first harmonic, but it can't be used to enhance the phase-shifting algorithm properties when the fringe signal contains higher order harmonics (n2). P–V (peak–valley) phase errors are calculated by the computer simulation and tables and plots are presented, from which the algorithms in families I and II are compared. It is shown that the algorithms in family I are more insensitive to phase-shift errors when the fringe signal contains the second harmonic and the algorithms in family II are more insensitive to phase-shift errors when the fringe signal is a sinusoidal waveform.     

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.     

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。