Experimental validation of closed-loop adaptive optics based on a self-referencing interferometer wavefront sensor and a liquid-crystal spatial light modulator

A closed-loop adaptive optics system based on a self-referencing interferometer wavefront sensor (SRI WFS) using phase-shifting point-diffraction technique and an electrically addressed phase-only liquid-crystal spatial light modulator (LC SLM) is built and validated experimentally. The wavefront aberration of incoming beam is directly measured by analyzing four frames phase-shifted interferograms captured by a single CCD camera in two camera shots, and then by loading the conjugate function onto the SLM the wavefront aberration is corrected. The proposed scheme does not rely on any complicated control algorithm or wavefront-reconstruction algorithm and can achieve high-resolution and high-accuracy correction. Closed-loop correction results of single order Zernike aberrations and a Kolmogorov turbulence phase screen show that considerable improvements in the Strehl ratio (of greater than 0.94) is achieved.     

Wavefront aberrations in the accommodated human eye based on individual eye model

In this research, we firstly construct individual eye models based on the wavefront and the measured cornea structure of the eyes. Then we analyze the influence of accommodation on the wavefront aberrations based on individual eye model. The individual eye model has the same wavefront aberration as that measured from Hartmann–Shack wavefront sensor. The optical design software ZEMAX is used to construct the individual eye models for 20 normal eyes. Accommodative conditions are from 0 to –4 diopter in steps of one diopter. The variations of the total, the spherical, the coma and the higher-order root-mean-square wavefront aberrations, as accommodations, are illustrated. Influence of accommodation on wavefront aberration varies from individual to individual, and the variation magnitude is independent of the magnitude of the wavefront aberration of the eye.     

Phase diversity for calibrating noncommon path aberrations of adaptive optics system under nonideal measurement environment

When the defocus cannot be measured and the wavefront solution set is restricted by a multi-channel, some practical problems exist in the calibration of the noncommon path aberrations of the adaptive optics system. To solve these problems, an evaluation function of phase diversity algorithm is constructed in this paper. We use the method that the estimated aberration and the modulated deformable mirror iterate each other to make up the nonideal measurement environment. Then the ill-pose problem of the solution by phase diversity, produced as relaxing constraints of the diversity defocus on the wavefront solution set, is solved. We have adopted the proposed method to measure the noncommon path aberrations of the adaptive optics system on a 1.23 m telescope. Experimental results demonstrate that wavefront solution is more accurate and the whole imaging quality is improved effectively by using the deformable mirror to compensate the aberration measured.     

Individual eye model based on wavefront aberration

Based on the widely used Gullstrand-Le Grand eye model, the individual human eye model has been established here, which has individual corneal data, anterior chamber depth and the eyeball depth. Furthermore, the foremost thing is that the wavefront aberration calculated from the individual eye model is equal to the eye's wavefront aberration measured with the Hartmann-shack wavefront sensor. There are four main steps to build the model. Firstly, the corneal topography instrument was used to measure the corneal surfaces and depth. And in order to input cornea into the optical model, high-order aspheric surface-Zernike Fringe Sag surface was chosen to fit the corneal surfaces. Secondly, the Hartmann-shack wavefront sensor, which can offer the Zernike polynomials to describe the wavefront aberration, was built to measure the wavefront aberration of the eye. Thirdly, the eye's axial lengths among every part were measured with A-ultrasonic technology. Then the data were input into the optical design software–ZEMAX and the crystalline lens's shapes were optimized with the aberration as the merit function. The individual eye model, which has the same wavefront aberrations with the real eye, is established.     

模拟合成孔径雷达数据片波差的测量和胶片、波差的容限

本文介绍一种用马赫-陈德干涉系统测量模拟合成孔径雷达数据片波差的方法.该法能把两种原因产生的波差区分开来,即把通过胶片变形的波面与平面参考波面比较,求出胶片厚度不平产生的波差;把合成孔径雷达数据片的一级衍射波面与两个半径不等的参考球面波比较,分别求出由模拟装置产生的方位维和斜距维波差.本文给出一些实验结果和分析.这种方法还可以用于测量真实合成孔径雷达数据片的波差.由胶片厚度变化产生的波差可以用液体门补偿.但是,在实际中使用液体门是很繁复的,有时也没有必要.因此,我们认瑞利准则出发导出合成孔径雷达数据片胶片厚度变化产生的波差的容限,以此作为判断是否要用液体门的依据.     

基于位相变更的非相干数字全息自适应成像

菲涅耳非相干数字全息作为一种非扫描的三维成像技术具有其独特的优势,但其成像过程中会受到各种像差的影响,导致成像分辨率、再现像的质量降低.为了解决这一问题,可以结合适当的自适应光学技术对波前像差进行探测和校正.位相变更是一种基于两幅具有已知位相差的强度图像实现波前探测和像差校正的技术.本文发展了基于位相变更的非相干数字全息自适应成像技术,不需要引入引导星,利用全息记录过程中的两幅相移全息图,实现波前像差的探测.本文给出了所发展技术的数值仿真和实验结果,结合位相变更算法求解出系统像差的位相分布,将像差的共轭位相加载到光瞳面上,在全息图记录的同时校正像差,从而提高重建像的质量.     

Effect of transition zone on wavefront aberration with treatment decentration after conventional refractive surgery

Based on the ablation profile of conventional refractive surgery, the influence of transition zone on induced wavefront aberrations with decentration, as well as laser oblique incidence, was studied. The results indicated that transition zone played a significantly important role in the influence of decentration on the postoperative aberrations. The induced coma increased rapidly with the increase of lateral translation of the centre of ablation. Furthermore, the induced spherical aberration increased theoretically as the translation increase and the sign of spherical aberration was usually positive for myopic correction. And yet it changed from positive to negative for hyperopic correction. In addition, the induced spherical aberration was related with the corrected refraction. As an important goal for refractive surgery, the optimal postoperative visual performance may be smoothly achieved by minimizing treatment decentration and optimizing transition zone in refractive surgery.     

Wavefront and ray-density plots using seventh-order matrices

The optimization of an optical system benefits greatly from a study of its aberrations and an identification of each of its elements’ contribution to the overall aberration figures. The matrix formalism developed by the author was the object of a previous paper and allows the expression of image-space coordinates as high-order polynomials of object-space coordinates. In this paper we approach the question of aberrations, both through the evaluation of the wavefront evolution along the system and its departure from the ideal spherical shape and the use of ray density plots. Using seventh-order matrix modelling, we can calculate the optical path between any two points of a ray as it travels along the optical system and we define the wavefront as the locus of the points with common optical path length; the results are presented on the form of traces of the wavefront on the tangential plane, although the formalism would also permit sagittal plane plots. Ray density plots are obtained by actual derivation of the seventh-order polynomials.     

扩大人眼波前像差仪测量范围方法的研究

提出了一种扩大人眼波前像差仪测量范围的方法,该法综合了波前重建展开算法和波前探测的模板技术,大幅度扩大了波前测量范围.在待测波前像差超出展开算法测量范围的情况下,此方法仍能对像差正常测量.与模板技术相比,该法大幅扩大了可测的曲率范围.以球面波前入射的实验数据表明,所提出的新方法所能测量的最小曲率半径由模板法的75 mm降低到10 mm,并且由于本方法突破了展开算法的极限,实际上对局部曲率更高的波前仍可测量.     

The study of wavelength-dependent wavefront aberrations based on individual eye model

Theoretical calculations of the wavelength dependence of the ocular wavefront aberrations are performed with individual eye model. Individual eye model, based on the traditional Gullstrand-Le Grand eye model, has been established with measured individual cornea data, eyeball depth and wavefront aberrations. We analyze the wavelength-dependent wavefront aberrations at 12 different visible wavelengths (between 400 and 750 nm) for eight eyes. The change of defocus with wavelength (longitudinal chromatic aberration, LCA) is noticeable, and in good agreement with the results from references. In most cases, the primary spherical aberration changes significantly with wavelength. In comparison with the primary spherical aberration, the other higher-order wavefront aberrations have a smaller change with wavelength. These results have potential applications in those situations where defocus or higher-order wavefront aberrations information in arbitrary wavelength is required.     

Aberration theory of plane‐symmetric grating systems

Aberration theory of plane‐symmetric optical systems of mirror and grating has been developed based on the wavefront aberration method. A toroidal reference wavefront surface is used to define the wavefront aberration. Based on the ray geometry, the coordinate mapping relationships of the ray between the optical element and the incident and aberrated wavefronts are derived using a polynomial‐fit method; this enables the resultant coefficients of the wavefront and the transverse aberration to be kept to the fourth‐order accuracy of the aperture‐ray coordinates. By setting up the transfer equations of the field and aperture rays, the contribution to wavefront aberrations from each mirror and grating can be added to make the aberration calculation of multi‐element systems feasible. The theory is validated by the analytic formulae of the spot diagram.     

利用相位差法测量望远镜像差

大气湍流引起的动态波前畸变和望远镜的像差是限制望远镜分辨力的主要因素,如何准确地测量望远镜的像差是进一步提高望远镜分辨能力的关键问题。相位差法利用在焦面和离焦面上同时采集到的短曝光图像,恢复出瞬时波前相位分布,然后根据大气湍流的统计特性进行平均,可以实现对望远镜像差的估计。通过计算机模拟实验,对利用相位差法恢复光瞳上的波前相位和测量望远镜像差进行了研究。模拟研究结果表明,利用相位差法能有效地估计出望远镜像差,估计均方根误差约为0.08个波长。     

Wavefront sensorless adaptive optics for large aberrations

In some adaptive optics systems the aberration is determined not by using a wavefront sensor but by sequential optimization of the adaptive correction element. Efficient schemes for the control of such systems are essential if they are to be effective. A scheme is introduced that permits the efficient measurement of large amplitude wavefront aberrations that are represented by an appropriate series of modes. This scheme uses an optimization metric based on the root-mean-square spot radius (or focal spot second moment) and an aberration expansion using polynomials suited to the representation of lateral aberrations. Experimental correction of N aberration modes is demonstrated with a minimum of N+1 photodetector measurements. The geometrical optics basis means that the scheme can be extended to arbitrarily large aberrations.     

无调制两面锥波前传感器的衍射理论分析和数值仿真

两面锥波前传感器(two-sided pyramid wavefront Sensor,TSPWFS)是一种高空间采样率和高光能利用率的波前传感器.为了深入研究它的波前复原原理,采用波动光学理论详细推导了无调制TSPWFS的衍射理论,给出了无调制TSPWFS波前复原时线性重构矩阵的解析解,并且通过数值仿真确定出最佳的光瞳像中心间距,并对静态像差的波前复原及闭环校正进行数值仿真.分析结果表明,无调制TSPWFS具有波前复原时不需要现场测量响应矩阵,可以校正系统像差,闭环校正结果稳定等优点,可以在实际自适应光学系统中进行波前探测. 关键词： 自适应光学 两面锥波前传感器 波前复原     

A qualitative approach to aberrations of optical elements

A qualitative method to analyze wavefront aberrations is presented.Aberrations of the primary type,expressed in their matrix forms,are used to write the generalized ray transfer matrix of an optical component.The aberrations were treated collectively by examining the pseudospectra of an augmented matrix constructed from the aberration matrices.Results show that aberrations can be distinguished and relative strengths pronounced using this qualitative method.     

Method of reconstructing wavefront aberrations by use of Zernike polynomials in radial shearing interferometers

A novel method of reconstructing wavefront aberrations by use of Zernike polynomials for radial shearing interferometers is discussed. This method uses matrix formalism to calculate the Zernike coefficients of a wavefront under test and shows the validity of reconstructing an arbitrary wavefront aberration from an interferogram taken by a radial shearing interferometer. We also propose a new interferometer setup to determine the shape and the direction (concave or convex) of wavefront aberration in a single measurement.     

透镜初级球差的横向剪切干涉条纹研究

利用玻璃平行平板构成简单的横向剪切干涉仪可以观察到单薄透镜形成的准直光束的剪切干涉条纹,由干涉条纹分布求出对应的几何像差和离焦量.用焦距为190 mm的单薄透镜做实验,实验结果与计算机模拟结果符合,说明可以从剪切干涉条纹的分布求出透镜的轴向调整误差和初级球差.     

A wavefront sensor-less adaptive optical system for a solid-state laser

A wavefront sensor-less adaptive optical system has been set up. It consists of a deformable mirror, a high-voltage amplifier, a set of solid-state laser system, a CCD camera, control software and a genetic algorithm. This adaptive optical system does not employ a wavefront sensor to detect the wavefront information, but optimizes the light intensity within a fixed aperture in the focal plane by a 19-element piezoelectricity deformable mirror. A genetic algorithm is introduced to search the optimum surface profile of the deformable mirror for correcting the phase aberrations in a solid-state laser system. The far-field light intensity signal, which is measured by a CCD, is taken as the fitness function of the genetic algorithm. In this paper, the performance and the efficiency of this wavefront sensor-less adaptive optical system are presented. Both simulative results and experimental results are given and discussed.     

直接液体冷却薄片激光器中抽运光均匀性对光束波前畸变的影响

近年来,直接液体冷却薄片激光器因其体积功率比小,热管理能力强等优势而成为研究热点.本文建立了一套直接液体冷却薄片激光器波前畸变的分析方法.应用该方法研究了直接液体冷却薄片激光器中抽运光均匀性对光束波前畸变的影响.计算分析了均匀性为92%, 80%和70%,且总的抽运功率不变时,激光器高阶像差分布情况.随着均匀性逐渐减弱,激光器中高阶像差逐渐增强,低阶像差量基本保持不变.实验中,设计加入波导和未加入波导结构,构建了均匀性为92%和70%的抽运光分布,分别测量了两种情况下的波前抖动情况以及波前畸变分布,抽运功率为5 k W时,测量获得了整个增益模块的光程差高阶分量(OPD_H),其畸变量均方根(RMS)值为0.66μm和0.79μm,实验结果和理论分析结果基本趋势一致.     

基于波像差检测的大口径RC光学系统装调分析

通过对520 mm口径RC系统进行面形波像差检测,并将其主、次镜各光学零件实际面形的干涉检测结果输入Code V软件进行了系统成像质量的波像差分析.分析结果与实际系统装调完成后的系统成像质量波像差检测结果对比,具有高度的一致性,说明在计算机辅助装调工艺中应用该仿真工具仿真度高,可以用于实际光学装调的仿真分析、指导光学装调.