人眼不同瞳孔直径波前像差特性分析

采用Hartmann-Shack人眼像差仪,测量了人眼在3.1mm,5.2mm和6mm瞳孔直径下的波前像差。波前像差的RMS值表明,随着瞳孔直径的增大,人眼各阶波前像差均随着增大。与瞳孔直径为3.1mm时相比,瞳孔直径为6mm和5.2mm时,Zernike2-10阶波前像差的RMS值分别增大1.2-7.7倍和1.1-4.8倍。用调制传递函数(MTF)和Strehl比评价了高阶波前像差对成像质量的影响,结果表明,大瞳孔高阶波前像差对成像质量的影响大于小瞳孔;在3.1mm,5.2mm和6mm瞳孔直径下,欲达到衍射极限的Strehl比率,分别需要矫正Zernike波前像差前2-4阶、前3-6阶和前5-7阶,需矫正的像差阶数随瞳孔直径的增大而增加。     

Binocular open-view Shack-Hartmann wavefront sensor with consecutive measurements of near triad and spherical aberration

We have developed a binocular open-view Shack-Hartmann wavefront sensor for measuring time variation of binocular accommodation, vergence, pupil sizes (i.e., the binocular near triad), and monochromatic aberrations. The device measures these values16 times per second for up to 1 min. Our purpose is to introduce the new instrument. We have confirmed the accuracy of the device. Refractions for a 4 mm pupil were accurate across the range of measurements of model eyes and normal human eyes. We measured binocular dynamics of accommodation, vergence, and spherical aberrations.     

Adapting derivative free optimization methods to engineering models with discrete variables

In this paper we extend Continuous Derivative Free (CDF) algorithms that solve optimization models with continuous variables to the solution of optimization models with both continuous and discrete variables. The algorithm fits naturally to the solution of discretized models arising from continuous models. Roughly speaking, the finer the discretization, the closer the discretized solution is to its continuous counterpart. The algorithm also finds stationary points of real problems with continuous and discrete variables. Encouraging results are reported on an access point communication problem and on models solved with a Field Programmable Gate Array (FPGA) device, which generally forces a fixed point discretization of the problem.     

Determination of second-order derivatives of a skew ray with respect to the variables of its source ray in optical prism systems

The second-order derivative of a scalar function with respect to a variable vector is known as the Hessian matrix. We present a computational scheme based on the principles of differential geometry for determining the Hessian matrix of a skew ray as it travels through a prism system. A comparison of the proposed method and the conventional finite difference (FD) method is made at last. It is shown that the proposed method has a greater inherent accuracy than FD methods based on ray-tracing data. The proposed method not only provides a convenient means of investigating the wavefront shape within complex prism systems, but it also provides a potential basis for determining the higher order derivatives of a ray by further taking higher order differentiations.     

Tangential derivative of singular boundary integrals with respect to the position of collocation points

This paper investigates the evaluation of the sensitivity, with respect to tangential perturbations of the singular point, of boundary integrals having either weak or strong singularity. Both scalar potential and elastic problems are considered. A proper definition of the derivative of a strongly singular integral with respect to singular point perturbations should accommodate the concomitant perturbation of the vanishing exclusion neighbourhood involved in the limiting process used in the definition of the integral itself. This is done here by esorting to a shape sensitivity approach, considering a particular class of infinitesimal domain perturbations that ‘move’ individual points, and especially the singular point, but leave the initial domain globally unchanged. This somewhat indirect strategy provides a proper mathematical setting for the analysis. Moreover, the resulting sensitivity expressions apply to arbitrary potential-type integrals with densities only subjected to some regularity requirements at the singular point, and thus are applicable to approximate as well as exact BEM solutions. Quite remarkable is the fact that the analysis is applicable when the singular point is located on an edge and simply continuous elements are used. The hypersingular BIE residual function is found to be equal to the derivative of the strongly singular BIE residual when the same values of the boundary variables are substituted in both SBIE and HBIE formulations, with interesting consequences for some error indicator computation strategies. © 1998 John Wiley & Sons, Ltd.     

Material geometry optimization of involute structures using sensitivity derivatives with respect to global design variables

A behaviour sensitivity analysis and optimization capability for involute structures has been developed and implemented via a test version of the P/COMPOSITE Module (which includes the CPATCHES finite element code for the analysis of 3-D composites) in PATRAN. The user may obtain the sensitivity of the structural response with respect to a set of up to eight global material geometry variables that span the space of useful designs. The integrands of the sensitivity integrals are calculated in closed form and the same volume integration utilities that are employed throughout CPATCHES are used. This capability is restricted to problems in linear statics and a Cholesky equation solver is used. The behaviour sensitivity derivatives are validated by finite difference testing and through their successful application in severai involute optimization problems.     

Analysis of the optical field on the human retina from wavefront aberration data

Wave aberrations in the human eye are usually known with respect to the ideal spherical wavefront in the exit pupil. Using Kirchhoff's diffraction theory, we have derived a diffraction integral to compute the optical field on the retina from the wave aberration data. We have proposed a numerical algorithm based on the Stamnes-Spjelkavik-Pedersen (SSP) method to solve that integral. We have shown which approximations are admissible to reduce the complexity of the diffraction integral. In addition, we have compared our results with those of the conventional procedure used to compute intensities on the retina. We have found significant differences between our results and the conventional ones.     

Variable zoom system with aberration correction capability

We describe experiments conducted with two deformable mirrors (DMs) at fixed locations in an optical microscope imaging system. In this configuration, the DM shapes are controlled to provide 2.5× zoom capability, to allow dynamic focus control and to compensate for aberrations of the fixed optical components. Zoom is achieved by simultaneously adjusting focal lengths of the two DMs, which are inserted between an infinity-corrected microscope objective and a tube lens. Image quality is measured using contrast modulation, and performance of the system is quantified, demonstrating an improved point spread function in the adaptively compensated system.     

泽尼克像差组合对人眼光学质量的影响

基于人眼光学质量客观评价标准区域调制传递函数（AreaMTF）、斯特列尔比（SRX）和同心相对瞳孔平面（PFWc）,分析了波前像差RMS为0．25μm时泽尼克像差项组合对人眼光学质量的影响。C4（离焦）与C12（球差）等组合后,像差比例在1．33到4．90的范围内AreaMTF和SRX有极大值;C6（三叶草）与C7（彗差）等组合后,像差比例在0．20到1．00的范围内它们有极小值。二阶像差（离焦和像散）组合时,C4（离焦）起着主导作用。三阶像差（彗差和三叶草）组合时,SRX和PFWc值的变化范围均较大,分别为0．066到0．228和0．048到0．656。     

Image field distribution model of wavefront aberration and models of distortion and field curvature

The distribution model of wavefront aberrations, which takes on a significant role in the designs and alignments of imaging optical systems without vignetting, is newly presented. This model decomposes the complicated distributions into the characteristic components, which clarifies the alignment criteria. For the actual alignments, only small displacements (decentering, tilt, and surface distance) of rotationally symmetric surfaces in the system are assumed. Then, the model, which regards the aberration distributions of the system as the sum of the contributions of each surface, is extended for the system with surface displacements. As a result of the derivation, it is concluded that the aberration distributions in the rotationally nonsymmetric systems can be expressed as the sum of several folds of rotationally symmetric components. In addition, it is presented that, based on this model, suitable distribution models, even of the arbitrary higher order, can be constructed for any aberration coefficients in various optical systems.     

Space-resolving flat-field extreme ultraviolet spectrograph system and its aberration analysis with wave-front aberration

The Nam aberration of a flat-field extreme ultraviolet spectrograph system, composed of a varied line-spacing concave grating and a toroidal mirror, was analyzed by calculating the wave-front aberration with respect to an astigmatic reference surface. The toroidal mirror was used to compensate for the astigmatism that was due to the grazing incidence of light at the concave grating. The spectrograph system could form a space-resolved spectrum along the sagittal direction. The spectral and spatial resolutions of the spectrograph system were estimated from the root-mean-square spot size. The actual spectral resolution of the spectrograph system was measured from extreme ultraviolet spectra obtained from plasmas produced by an iodine laser having an energy of 0.5 J in a 4-ns duration, and it was compared with the calculated value.     

Imaging characteristics of a wavefront coding system with off-axis aberrations

Imaging characteristics are analyzed for a wavefront coding system suffering from off-axis aberrations such as primary astigmatism and primary coma. Some analytical expressions for the optical transfer function are obtained by using the stationary-phase method. These expressions give the relationship between the optical transfer function and the off-axis aberrations. Some cases are computed and illustrated graphically. It is shown that the wavefront coding system has a high tolerance to primary astigmatism and a low sensitivity to primary coma.     

Experimental study of the copper thiosulfate system with respect to thin-film deposition

An experimental study of the copper-thiosulfate system in mild acidic (pH 5) aqueous solutions, with respect to thin-film formation, was undertaken. Thin films of Cu_xS (1 x 2) were deposited by a simple electroless technique on glass or transparent polyester films, at 50 °C. Thin films were deposited from chemical baths in which the ratios of copper to thiosulfate were varied from 1:1 to 1:10. Thin films of different compositions (Cu₂S, Cu_1.8S, Cu_1.4S and CuS) were prepared and then characterized for morphological, optical and electrical properties. The deposited films chemically close to Cu₂S were found to be amorphous, while the CuS films were a mixture of both amorphous and polycrystalline phases. The optical spectra of the Cu₂S films exhibited high transmission both in the visible region of the spectrum (beyond 600 nm) and throughout the near-infrared region (800 to 2500 nm), while CuS films were found to be highly absorptive throughout the near-infrared region, with peaked transmission in the visible region at about 560 nm. The sheet resistances of the films, determined by the standard four-probe measurements, were between 100 and 650 Ω/square.     

Measurement of the repeatability of the prompt flashlamp-induced wavefront aberration on beamlines at the National Ignition Facility

We have undertaken a measurement campaign to determine the repeatability of the prompt flashlamp-induced wavefront aberration on beamlines at the National Ignition Facility (NIF) and determine the extent to which shot-to-shot variations in this aberration may degrade the performance of a proposed adaptive optics system for the short-pulse Advanced Radiographic Capability beamline on NIF. In this paper we will describe the unique NIF configuration that was required to make this measurement, present the results of the experiment, and discuss the implications of these results for the adaptive optics system design.     

Requirements for discrete actuator and segmented wavefront correctors for aberration compensation in two large populations of human eyes

Numerous types of wavefront correctors have been employed in adaptive optics (AO) systems for correcting the ocular wavefront aberration. While all have improved image quality, none have yielded diffraction-limited imaging for large pupils (>/=6 mm), where the aberrations are most severe and the benefit of AO the greatest. To this end, we modeled the performance of discrete actuator, segmented piston-only, and segmented piston/tip/tilt wavefront correctors in conjunction with wavefront aberrations measured on normal human eyes in two large populations. The wavefront error was found to be as large as 53 microm, depending heavily on the pupil diameter (2-7.5 mm) and the particular refractive state. The required actuator number for diffraction-limited imaging was determined for three pupil sizes (4.5, 6, and 7.5 mm), three second-order aberration states, and four imaging wavelengths (0.4, 0.6, 0.8, and 1.0 microm). The number across the pupil varied from only a few actuators in the discrete case to greater than 100 for the piston-only corrector. The results presented will help guide the development of wavefront correctors for the next generation of ophthalmic instrumentation.     

Second-order derivatives of a ray with respect to the variables of its source ray in optical systems containing spherical boundary surfaces

The second-order derivative matrix of a scalar function with respect to a variable vector is called a Hessian matrix, which is a square matrix. Our research group previously presented a method for determination of the first-order derivatives (i.e., the Jacobian matrix) of a skew ray with respect to the variable vector of an optical system. This paper extends our previous methodology to determine the second-order derivatives (i.e., the Hessian matrix) of a skew ray with respect to the variable vector of its source ray when this ray is reflected/refracted by spherical boundary surfaces. The traditional finite-difference methods using ray-tracing data to compute the Hessian matrix suffer from various cumulative rounding and truncation errors. The proposed method uses differential geometry, giving it an inherently greater accuracy. The proposed Hessian matrix methodology has potential use in optimization methods where the merit function is defined as ray aberrations. It also can be used to investigate the shape of the wavefront for a ray traveling through an optical system.     

Acousto-optic tunable filter chromatic aberration analysis and reduction with auto-focus system

An acousto-optic tunable filter (AOTF) displays optical band broadening and sidelobes as a result of the coupling between the acoustic wave and optical waves of different wavelengths. These features were analysed by wave-vector phase matching between the optical and acoustic waves. A crossed-line test board was imaged by an AOTF multi-spectral imaging system, showing image blurring in the direction of diffraction and image sharpness in the orthogonal direction produced by the greater bandwidth and sidelobes in the former direction. Applying the secondary-imaging principle and considering the wavelength-dependent refractive index, focal length varies over the broad wavelength range. An automatic focusing method is therefore proposed for use in AOTF multi-spectral imaging systems. A new method for image-sharpness evaluation, based on improved Structure Similarity Index Measurement (SSIM), is also proposed, based on the characteristics of the AOTF imaging system. Compared with the traditional gradient operator, as same as it, the new evaluation function realized the evaluation between different image quality, thus could achieve the automatic focusing for different multispectral images.