泽尼克各项像差对人眼光学质量的影响

基于两个人眼光学质量客观评价标准同心相对瞳孔平面(PFWc)和区域调制传递函数(Marea MTF),研究和分析了波前像差均方根值WRMS处于0.05~1.00μm较大范围内泽尼克各项像差对人眼光学质量的影响。分析结果表明,泽尼克各项在WRMS一定时,瞳孔中心区域的光学质量差距明显,离焦(C4)和球差(C12)项的MPFWc值最小,而五叶草(C15、C20)项的MPFWc值最大。五叶草项在WRMS值处于0.05~1.00μm的范围内,其Marea MTF值均大于0.94,表明该像差项对光学质量的影响可以忽略。MPFWc值和Marea MTF值随着WRMS值的增大而减小,但不是简单的线性关系,随着WRMS值的增大,它们的变化趋于平缓。各项泽尼克像差对人眼光学质量的影响存在较大差别,对人眼光学质量的影响从大到小依次为:球差、离焦、散光、彗差、三叶草、四叶草、五叶草等。     

Zernike模式像差共轭组合模型

根据Zernike模式在单位圆的同心孔径圆域内某些模式间具有一定耦合性的结论及对应Zernike模式像差在一定同心光瞳区域内的相互抵消特性,对具有相同角频率不同阶数的Zernike模式建立组合模型,同时根据同心光瞳区域内像差均方根值的降幅比参数给出了同心光瞳直径为4 mm时的Zernike模式线性共轭组合模型。最后通过共轭组合模型对光学质量影响的研究发现,共轭模型组合之后能显著提高光学质量。同时也表明Zernike模式组合对光学质量的影响不具备叠加性,而对共轭组合模型表现为补偿关系。     

Zernike模式像差共轭组合模型

根据Zernike模式在单位圆的同心孔径圆域内某些模式间具有一定耦合性的结论及对应Zernike模式像差在一定同心光瞳区域内的相互抵消特性,对具有相同角频率不同阶数的Zernike模式建立组合模型,同时根据同心光瞳区域内像差均方根值的降幅比参数给出了同心光瞳直径为4mm时的Zernike模式线性共轭组合模型。最后通过共轭组合模型对光学质量影响的研究发现,共轭模型组合之后能显著提高光学质量。同时也表明Zernike模式组合对光学质量的影响不具备叠加性,而对共轭组合模型表现为补偿关系。     

Effects of interactions among wave aberrations on optical image quality after refractive surgery

Research on wave aberrations indicates that interactions and balances among aberrations can provide better visual quality for normal eyes. In this paper, we investigate the aberration compensatory mechanism for eyes after LASIK surgery. Data of Zernike coefficients of wave-front aberrations are collected from 60 post-operative eyes through a Hartmann-Shack wave-front sensor, and then a series of Monte Carlo simulations are performed by manipulating the value of each Zernike coefficient (second order through seventh order). The modulation transfer function (MTF) ratio as a function of spatial frequency is used to evaluate the aberrations’ characteristic of independence. Finally, in a control condition, “synthetic” model eyes are produced through Monte Carlo arithmetic and the aberration independence of the synthetic eyes is analyzed. The results suggest that, for 6 and 3 mm pupil size, aberrations of the eyes after LASIK surgery are still not independent and the adaptive mechanism still exists. However, the adaptive mechanism does not hold for the “synthetic” eyes.     

Analysis and demonstration of multiplexed phase computer-generated hologram for modal wavefront sensing

We propose to implement a modal wavefront sensor (MWS) using a multiplexed phase computer-generated hologram (MPCGH). Based on general orthogonal aberration modes, the theoretical treatments of the MWS employing a MPCGH are presented with scalar diffraction approximations and Fourier analysis. Under the small aberration approximations, we give the analytical formula for characterizing the relationship between the sensor signal and the amplitude of the aberration mode. We design several MPCGHs with an effective method of modified off-axis reference beam holograms superposition, and code some common orthogonal Zernike aberration modes into the MPCGH. The numerical simulation is carried out to investigate the performance of MWS to detect particular aberration mode(s). The results exhibit the expected responses of the corresponding symmetric spot pair, and indicate that the wavefront distorted by a special Zernike aberration mode, after modulated by the MPCGH, can be transformed into beams with an intensity-normalized differential signal, which can reflect the change trend of the aberration coefficients in the test wavefront. The experimental demonstration with designed MPCGHs in conjunction with two phase-only spatial light modulators was carried out to test the performance of the MWS.     

基于近红外光谱的人眼像差校正系统中变形镜性能对比研究

对比分析了基于近红外光谱的人眼像差校正系统中两种微机械薄膜变形镜(OKO37单元和BMC140单元)的结构特征和空间特性,着重对变形镜的影响函数进行了主成分研究,建立了变形镜电压控制模型,并通过调整参数d确定变形镜最优控制模式。最后对Zernike单位模式波前像差和Thibos模式人眼波前像差进行拟合仿真实验,结果表明BMC140单元变形镜对Zernike各阶模式的拟合能力均为OKO37单元变形镜的2倍以上。对RMS均值为0.683λ(λ=0.785 μm)的Thibos模式人眼像差,BMC变形镜校正后残余像差RMS值为0.063λ,达到了光学系统的衍射极限(λ/14)。而OKO变形镜由于受相邻电极交连值大、电极分布密度小等因素的影响,其校正能力不及BMC变形镜,残余像差RMS值为0.168λ。本方法也可用于其他种类变形镜的性能评估。     

基于人眼光学质量的球差和离焦补偿关系研究

基于人眼光学质量客观评估方法,通过实测的屈光手术前后人眼波前像差数据,研究和分析了球差与离焦的补偿关系。结果表明,对于屈光手术前的近视眼患者,离焦与球差的补偿关系并不明显。对于屈光手术后的近视眼患者,离焦与球差的补偿关系明显,残余离焦可以部分补偿由于高阶像差增加引起的视功能降低。当残余离焦处于0.27D～0.74D范围内,离焦与高阶像差组合后,光学质量提高了20%以上。在屈光手术方案设计时,预留0.27D～0.74D的离焦时,可以使80%的人眼达到更好的视觉矫正效果。     

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.     

超视力人眼模型的研究

超视力人眼模型对充分发掘人眼视力达到“鹰视”具有重要意义。用Zernike多项式描述角膜前表面，用渐变折射率描述晶状体的折射率分布，同时考虑人眼视轴和光轴的夹角对成像的影响，利用光学设计软件Zemax建立了人眼超视力模型。将Zernike条纹矢高面应用到人眼模型中，能有效改变视轴方向(即5°视场)的成像质量，提高点扩散函数（PSF）值。采用晶状体渐变折射率符合人眼的实际解剖结构，可有效减小人眼像差。通过分析人眼极限分辨能力和人眼模型波像差，得出当空间频率为60周期/度时，该模型对目标高频细节感知的调制度可达到0.55。     

利用离轴三反镜光学系统确定各镜的装调公差

利用条纹泽尼克系数与赛德尔像差的关系,在三反镜光学系统的出瞳面上,用条纹泽尼克系数来表示系统的波像差。通过光学设计软件Zemax计算得到三反镜光学系统各镜的装调公差,以公差要求高的镜面作为装调基面,从而减少要调整的自由度。通过分析泽尼克(Zernike)系数在公差范围内的变化幅度来确定光学系统在出瞳面上各个像差的变化幅度,用该幅度的变化量来决定主次三镜各自由度在各个方向上的敏感度,最终确定各个自由度的优化调整级别。对一大口径无遮拦离轴三反镜光学系统进行了装调,在波长λ=632.8nm的条件下进行了检测。结果表明:整个光学系统全视场波前误差的均方根值RMS=0.108λ。     

光学窗口形变对平行光管光学性能影响分析

由于环境工况的多变性,光学窗口设计交叉了光、机、热等多种学科。在压差、轴向温差及径向温差工况下,分析光学窗口形变对某大口径、长焦距平行光管光学性能的影响,建立了光学窗口的有限元模型,与理论结果进行对比,验证了该有限元模型的有效性。以有限元分析得出的光学窗口变形数据为输入数据,带入改进了的Zernike多项式光机分析接口程序,获得了与像差对应的Zernike系数。用得到的Zernike系数表示光学窗口面型,以波像差作为光学系统成像质量评价指标,分析光学窗口变形对大口径、长焦距平行光管系统光学性能的影响。结果表明:光学窗口变形对平行光管系统光学性能的影响可以忽略不计。     

泽尼克多项式校正全息阵列光镊像差的实验研究

像差会影响光镊对粒子的捕获效果. 全息阵列光镊中, 像差不仅来自光学元件, 由特定算法设计的光阱相位片也会在光路中引入像差. 本文通过液晶空间光调制器加载泽尼克多项式相位图, 对全息阵列光镊中由光栅透镜组型算法引起的像差进行校正. 结果显示: 利用三阶泽尼克多项式可有效消除光路中由光栅透镜组型算法引 起的慧差, 使得捕获2 μm聚苯乙烯小球的阵列光阱刚度提高了约40%; 对比不同项的像差校正结果发现, 全息阵列光镊中由算法引起的慧差 与光学元件引起的像差一样, 也会对阵列光阱的捕获效果产生较大影响; 同时根据一阶像差校正结果可得光栅透镜 组型算法对于一阶泽尼克像差具有鲁棒性. 实验结果表明, 对全息阵列光镊中由 算法引起的像差进行校正, 对于提高光阱的捕获效果和深化对算法特性的认识都具有重要意义.     

The influence of the sampling dots on the analysis of the wave front aberration by using the covariance matrix method

The covariance matrix method is a simple method for solving the Zernike polynomial with the higher fitting precision. In this paper, it was used to analyze the several optical wave fronts of the fine polished aluminum disk surface captured by a Twyman-Green interferometer system. We had found that the PV (peak-to-valley) and rms (root-mean-square) values of the wave front aberration changes with changing the Zernike term and the expressions for the several optical wave fronts with the different sampling dots were wrong. By analyzing the relations among the condition number of the coefficients matrix, the Zernike term, and the number of the sampling dots, it was indicated that the number of the sampling dots had only reduced the fluctuation the PV and the rms value while the Zernike term increases, but did not change the case that the expressions for the wave front aberration were wrong when the Zernike term is larger than 14, especially when the number of the sampling dots is less. Such an analysis will be valuable in solving the Zernike polynomial for the wave front aberration analysis by using the covariance matrix method in optical testing.     

偏置模式波前传感器光强信息提取及输出信号对比分析

在小像差近似下,对偏置模式波前传感器进行了理论分析,明确了该传感器的适用条件,对比分析了3种信息提取方式和3种传感器信号输出方式的优劣。针对Zernike像差模式,数值模拟研究了传感器对单阶和多阶模式的响应特性。结果表明,畸变波前中与偏置模式相同或相关的模式之间有响应,但传感器对各阶Zernike模式的响应灵敏度不同,而且不相关模式的存在对传感器输出信号和灵敏度均有影响。     

基于主观式测量人眼波前像差的眼模型研究

通过主观式光线追踪波前像差测量方法得到用Zernike系数描述的人眼波前像差;在Gullstrand-Le Grand眼模型的基础上,引入用医用角膜地形图仪测量并用高次非球面函数拟合的实际人眼角膜形状数据,又引入角膜、前房及玻璃体厚度等个体化的眼结构参数;在光学建模软件Zemax中用所测Zernike系数建立评价函数,并对用Zernike矢高面描绘的晶状体表面进行优化.由此建立了个体化眼模型,并由此模型中可以计算得到与实际测量的波前像差值完全相同的各项Zernike系数值,从而可用于描述实际人眼的光学特性.     

Scaling pseudo-Zernike expansion coefficients to different pupil sizes

Orthogonal polynomials are routinely used to represent complex surfaces over a specified domain. In optics, Zernike polynomials have found wide application in optical testing, wavefront sensing, and aberration theory. This set is orthogonal over the continuous unit circle matching the typical shape of optical components and pupils. A variety of techniques has been developed to scale Zernike expansion coefficients to concentric circular subregions to mimic, for example, stopping down the aperture size of an optical system. Here, similar techniques are used to rescale the expansion coefficients to new pupil sizes for a related orthogonal set: the pseudo-Zernike polynomials.     

基于矢量波像差理论的两反光学系统装调研究

 为了实现对两反光学系统的精密装调,提出一种基于矢量波像差理论和波像差检测技术对失调量精确求解的装调方法。使用矢量波像差理论,将已设计的两反光学系统参数、失调量和失调光学系统的波像差之间建立方程;然后通过干涉测量法得到某一个视场的干涉图,利用条纹分析软件得到表征失调系统三阶彗差和三阶像散的泽尼克项系数,将泽尼克项系数代入方程从而求解出失调量。运用此方法对4 m口径RITCHEY-CHR-TIEN结构的天文望远镜进行模拟装调,最终求解的失调量与引入的失调量结果相互吻合,说明该装调方法正确。     

Adaptive correction of human-eye aberrations in a subjective feedback loop

An adaptive optical system with a subjective feedback loop is used to improve the visual acuity and to determine the aberrations of the human eye. Corrections of as many as 12 low-order aberration modes were made, based on the perceived sharpness of the test object observed through the adaptive optical system. The acuity of vision was improved by adjustment of the weights of the orthogonal modes produced by a deformable mirror. Objective measurements of the correcting aspherical figures, obtained in independent subjective correction cycles for one person, demonstrated good repeatability. Participants in the study with strong ocular aberrations reported moderate to significant improvement of their visual acuity, estimated with the U.S. Air Force 1951 acuity chart.     

振幅型复合计算全息模式波前传感理论及验证

全息模式波前传感器是利用复合全息元件对待测波前中像差模式进行直接测量的一种新型波前传感器,其中的复合全息元件可编码设计多阶Zernike像差模式。提出一种有效方案以编码设计振幅型复合计算全息元件,该方案通过将多个编码有某阶Zernike像差模式的透过率调制扭曲光栅叠加产生振幅型计算全息元件。在小像差近似条件下推导了传感器输出信号与Zernike像差模式系数的解析关系。编码设计了振幅型复合全息图,并研究了其对单阶和多阶Zernike像差模式的探测性能。利用液晶光阀加载复合全息图进行了验证实验。所得实验结果与数值模拟结果基本一致。     

振幅型复合计算全息模式波前传感理论及验证

全息模式波前传感器是利用复合全息元件对待测波前中像差模式进行直接测量的一种新型波前传感器,其中的复合全息元件可编码设计多阶Zernike像差模式。提出一种有效方案以编码设计振幅型复合计算全息元件,该方案通过将多个编码有某阶Zernike像差模式的透过率调制扭曲光栅叠加产生振幅型计算全息元件。在小像差近似条件下推导了传感器输出信号与Zernike像差模式系数的解析关系。编码设计了振幅型复合全息图,并研究了其对单阶和多阶Zernike像差模式的探测性能。利用液晶光阀加载复合全息图进行了验证实验。所得实验结果与数值模拟结果基本一致。