高分辨力哈特曼传感器的快速波面重构和拼接

建立哈特曼传感器的模型,证明在高空间分辨力下,可以采用Hudgin模型进行波面重构,避免了采用Fried模型带来的复杂性。对哈特曼子孔径缺失破坏连续性的问题进行了分析,介绍了相应的边缘处理算法。完成了基于离散傅里叶变换的波面重构算法数值模拟,实现了波面的无损重构。针对实际应用中输入波面在被遮挡处不连续的问题,提出了基于最小二乘解的拼接方案,实现了非连续波面拼接。分析了影响波面重构速度的主要因素,提出了提高波面重构性能的方法。     

Harnessing caustics for wave-front sensing

Scintillation in measured wave fronts adds spurious dislocations and deformations to their reconstruction. The source of the problem is caustics formed by aberrations in intermediate planes. I propose to use intentional caustics to measure wave fronts under severe conditions such as low light level, fast scale variations, large aberrations, and discontinuities in the wave front. A simple realization is based on the Hartmann-Shack sensor, which samples the wave front with a lenslet array. Movement of the lenslets' foci is linear with slope changes. Here the lenslets are effectively formed in an acousto-optic device: Two standing waves are launched perpendicularly to the light beam and to each other. At some distance down the beam, each wave creates a comb of caustics, and the two orthogonal combs add up to an array of caustic spots. The spatial frequency of the array is linear with the temporal frequency of the standing sound waves. A simple Fourier demodulation scheme supplies the two wave-front gradients.     

Influence of wave-front aberrations on bit error rate in inter-satellite laser communications

We derive the bit error rate (BER) of inter-satellite laser communication (lasercom) links with on-off-keying systems in the presence of both wave-front aberrations and pointing error, but without considering the noise of the detector. Wave-front aberrations induced by receiver terminal have no influence on the BER, while wave-front aberrations induced by transmitter terminal will increase the BER. The BER depends on the area S which is truncated out by the threshold intensity of the detector (such as APD) on the intensity function in the receiver plane, and changes with root mean square (RMS) of wave-front aberrations. Numerical results show that the BER rises with the increasing of RMS value. The influences of Astigmatism, Coma, Curvature and Spherical aberration on the BER are compared. This work can benefit the design of lasercom system.     

Experimental validation of Fourier-transform wave-front reconstruction at the Palomar Observatory

Wave-front reconstruction with use of the Fourier transform has been validated through theory and simulation. This method provides a dramatic reduction in computational costs for large adaptive (AO) systems. Because such a reconstructor can be expressed as a matrix, it can be used as an alternative in a matrix-based AO control system. This was done with the Palomar Observatory AO system on the 200-in. Hale telescope. Results of these tests indicate that Fourier-transform wave-front reconstruction works in a real system. For both bright and dim stars, a Hudgin-geometry Fourier-transform method produced performance comparable to that of the Palomar Adaptive Optics least squares. The Fried-geometry method had a noticeable Strehl ratio performance degradation of 0.043 in the K band (165-nm rms wave-front error added in quadrature) on a dim star.     

彩色数字全息的非插值波面重建算法研究

彩色数字全息及多波长照明的数字全息检测研究中,避免插值误差的可变放大率波面重建是一个重要的研究内容.由于Fresnel衍射积分可以表示成Fourier变换及卷积两种形式,对应地存在两种波面重建算法：其一,将重建距离分为两段的衍射“接力”算法;其二,用球面波为重建波的卷积算法.文中对这两种算法进行理论分析及实验研究,讨论让重建计算满足取样定理的条件.结果表明,卷积算法较容易满足取样定理,能够获得较好的重建物光场.     

彩色数字全息的非插值波面重建算法研究

彩色数字全息及多波长照明的数字全息检测研究中,避免插值误差的可变放大率波面重建是一个重要的研究内容.由于Fresnel衍射积分可以表示成Fourier变换及卷积两种形式,对应地存在两种波面重建算法：其一,将重建距离分为两段的衍射“接力”算法;其二,用球面波为重建波的卷积算法.文中对这两种算法进行理论分析及实验研究,讨论让重建计算满足取样定理的条件.结果表明,卷积算法较容易满足取样定理,能够获得较好的重建物光场. 关键词： 彩色数字全息 波面重建 衍射计算     

Linear phase retrieval for wave-front sensing

Phase retrieval from one or more intensity measurements is a potentially powerful and appealing technique for real-time adaptive-optics wave-front sensors. Under the assumption of small wave-front phase excursions, one is able to derive an exact solution to the inverse problem given three or more intensity measurements with known phase offsets. Applications include a high-order wave-front sensor to correct for residual aberrations in an adaptive-optics system in tandem with a low-resolution Hartmann-Shack wave-front sensor. The formula can also furnish mathematical insights into the full nonlinear phase-retrieval task.     

自适应光学随机并行梯度下降算法波前整形规律仿真

本文首先介绍了基于Zernike模式的SPGD算法对大气湍流畸变波前的整形原理,通过推导得到了关于性能指标的简明表达式,使SPGD算法收敛速率得到明显提升。然后建立了自适应光学随机并行梯度下降算法波前整形系统模型,主要对SPGD算法收敛速率、整形能力和整形效果随波前畸变量和变形镜模型的变化规律作了较为详细的仿真研究,整体定性结果表明：三者的变化规律有一定的相似性,同时利用最小二乘法得到了关于整形能力和整形效果变化规律的定量表达式,若从自适应光学波前整形系统的实时性和简单性考虑,在保证一定整形效果的情况下,选择37单元变形镜对畸变波前的3~27（25）阶Zernike像差进行整形即可。     

一种大型望远系统波前检测的方法

 对传统S-H波前检测方法进行了改进的基础上，设计了一套适应于大型望远系统的波前检测方案。利用五角棱镜光束转向系统形成大型望远系统各子孔径准参考光束，实现依次扫描各子孔径；并用改进的S-H波前传感器实现依次探测各子孔径的波前。理论分析证明了由五角棱镜的制造误差和运动误差引起的波前倾斜误差在微变情况下，可通过波前修正方法予以修正，可有效地再现出望远系统自身波前误差。该方案可适用于大口径望远系统的波前检测。     

Adaptive wave-front correction by means of all-optical feedback interferometry

A novel adaptive wave-front correction system based on an all-optical feedback interferometer is described. In this system the two-dimensional output fringe intensity from a Mach-Zehnder interferometer with large radial shear is optically fed back to an optically addressed phase-only liquid-crystal spatial light modulator. Consequently, without a separate aberration-free reference wave, the modulator phase approximates the conjugate of the interferometer phase that is directly related to the phase of the input aberrated wave front, so this system is applicable in adaptive optics. We successfully achieved real-time correction of aberrated wave fronts: A diffraction pattern that was seriously distorted because of aberrations was transformed into a diffraction-limited spot immediately after the feedback loop was closed.     

高质量数字全息波面重建系统研究

基于阿贝成像理论对数字全息波面重建系统进行研究. 结果表明,利用成像系统对物光场进行变换,可以让物光场的高频角谱分量到达电荷耦合器件（CCD）探测器.为研究重建物光场质量,导出了CCD在光学系统后任意位置波面重建的计算公式,研究了物光通过傍轴光学系统到达CCD时波面重建系统的脉冲响应. 理论及实验研究表明,将CCD平面置于物光场像平面附近可以对物光场进行高质量重建. 关键词： 信息光学 数字全息 波面重建     

Closed-loop aberration correction by use of a modal Zernike wave-front sensor

We describe the practical implementation of a closed-loop adaptive-optics system incorporating a novel modal wave-front sensor. The sensor consists of a static binary-phase computer-generated holographic element, which generates a pattern of spots in a detector plane. Intensity differences between symmetric pairs of these spots give a direct measure of the Zernike mode amplitudes that are present in the input wave front. We use a ferroelectric liquid-crystal spatial light modulator in conjunction with a 4-f system and a spatial filter as a wave-front correction element. We present results showing a rapid increase in Strehl ratio and focal spot quality as the system corrects for deliberately introduced aberrations.     

Validity of wave-front reconstruction and propagation of ultrabroadband pulses measured with a Hartmann-Shack sensor

Wave-front reconstruction for ultrabroadband laser pulses is verified by use of a Hartmann-Shack sensor. We estimate the accuracy of numerical wave-front propagation by comparing numerical with experimental results and verify that wave fronts of ultrabroadband laser pulses from a hollow fiber can be propagated correctly by a single polychromatic wave-front measurement to a place where detection is not practicable, e.g., inside a vacuum chamber or laser focus.     

Generalized method for wave-front analysis

We suggest and demonstrate a new method for wave-front analysis based on common-path phase-shift interferometry. We introduce a formalism and an iterative mathematical algorithm in which the wave front is transformed, modified, and inversely transformed. The resulting intensity data are sufficient to reconstruct the entire wave front. In a more restricted case, in which the wave-front modifications are arbitrarily applied over arbitrary spatial regions of the wave front, the wave front is reconstructed semianalytically by use of a model that allows a local solution, followed by an iterative algorithm. Measurement results indicating that the suggested approach has an improved measurement accuracy with respect to existing quantitative phase measurement methods are presented.     

Refractive microlens array for wave-front analysis in the medium to hard x-ray range

We report an alternative approach to x-ray wave-front analysis that uses a refractive microlens array as a Shack-Hartmann sensor. The sensor was manufactured by self-assembly and electroplating techniques and is suitable for high-resolution wave-front analysis of medium to hard x rays. We demonstrate its effectiveness at an x-ray energy of 3 keV for analysis of x-ray wave-front perturbations caused by microscopic objects. The sensor has potential advantages over other methods for x-ray phase imaging and will also be useful for the characterization of x-ray beams and optics.     

Statistical description of wave-front aberration in the human eye

The wave aberration of the human eye has been measured by means of a Hartmann-Shack wave-front sensor in a population of normal subjects. The set of data has been used to compute the phase distribution, the power spectrum, and the structure function for the average eye to analyze the statistics of the ocular aberration considered as a phase screen. The observed statistics fits the classical Kolmogorov model of a statistically homogeneous medium. These results can be of use in understanding the average effect of aberrations on the retinal image and can serve as a tool to analyze the consequences of ocular-aberration compensation by adaptive optics, customized ophtalmic elements, or refractive surgery.     

Φ2 m平面反射镜低频轮廓非接触测量设备研制进展

口径2 m的高质量平面反射镜可用于大口径光电设备像质评价和性能检测,但受使用环境影响,平面反射镜的面形精度不易长期保持稳定,因此需要在使用前对其面形精度进行现场、快速校验,而常规的全口径或子孔径干涉检测均难以满足上述需求。由于反射镜面形在制造过程引入的中高频误差已处于稳定状态,环境扰动只引入低频像差,而选择子孔径斜率扫描再重构波面低频轮廓的方法较适于面形精度现场校验。提出双五棱镜配合双测角仪进行子孔径斜率同步差分测量的方法,可改善长测量周期内环境扰动引起的随机误差。并对测量设备光学、机械及控制系统进行设计,提出采用2台S-H传感器代替传统测角仪用于子孔径斜率测量的解决方法。验证试验结果表明,波面重构算法以及仪器测角精度可满足面形测量精度需求,其与ZYGO干涉仪测量结果的互差小于20 nm（RMS）。     

快速傅里叶算法在哈特曼夏克传感器波前重构算法中的应用

提出了一种应用快速傅里叶变换算法提高哈特曼－夏克波前传感器波前重构实时性的快速算法，在根据波前斜率值应用最小二乘法估计波前相位的过程中，应用快速傅里叶变换算法进行方程的对角化和相位值的解耗，算法精站度，稳定，空间分辨率越高，算法实时性的优越性就越显著。     

Reconstruction of the laser wave-front by stimulated scatterings in the pico-second range

The reconstruction of the exciting laser wave-front by the backward Stimulated Raman Scattering (S.R.S.) and Rayleigh Wing Scattering (S.W.R.S.) is observed in benzene and cyclohexane in the case of pico-second pulses. The characteristic properties of this reconstruction are different of those obtained in the nano-second range.     

五角棱镜的光束转向误差对波前测量的影响

从分析五角棱镜的角度制造误差产生的光学平行差入手，推导出确定入射光线和棱镜调整的表达式；利用棱镜转动定理建立了五角棱镜的光输出平面波前与其角度制造误差和导轨引起的运动误差之间的关系；并用计算机模拟试验分析了五角棱镜的角度制造误差和导轨引起的运动误差产生的扫描光束转向的波前误差。指出此研究结果有利于五角棱镜的加工和棱镜调整，还有利于大口径望远系统波前检测过程中扫描光束转向的波前误差的修正。