Aging of the human lens: changes in lens shape upon accommodation and with accommodative loss.

Accommodation in the human eye occurs through controlled changes in crystalline lens shape, thickness, and refractive surface placement relative to the cornea. The changes in lens curvatures, whether surface or internal, have been characterized as a function of accommodation and subject age by use of quantitative analysis of Scheimpflug slit-lamp photographic images. Radii of curvature of the major lens refractive surfaces--the external and nuclear boundaries--decrease linearly with increasing accommodation in all eyes that are capable of accommodation. The rates at which they change with accommodation are age dependent, decreasing steadily toward zero with increased age. For the curves visible in each lens half, arising from boundaries between adjacent zones of discontinuity, radius of curvature and location are linearly related over the entire accommodative range for a given lens and over the age range for the population. The slope of this relationship changes with both accommodation and age, decreasing linearly in both cases. The relationship between these geometric changes and the loss of accommodative amplitude is discussed.     

Measurement of parameters of simple lenses using digital holographic interferometry and a synthetic reference wave

The use of digital holographic intrerferometry in the testing of simple thin lenses is explored. Focal length, radius of curvature, and refractive index are the lens parameters that can be determined using this method. The digital holograms using the lens under test are recorded at various positions of the test lens using off-axis geometry. This is combined with a digitally computed plane wavefront to determine the curvature of the light beam emerging from the test lens. Focal length is the position of the test lens where a single fringe results. The radius of curvature of the test lens is also determined similarly using a long focal length lens to concentrate a collimated beam onto the test lens. The nonuniformities on the lens surface could also be found by using this method. The implementation of the method is shown by using computer simulations in the case of biconvex lenses. The method can be utilized to measure the parameters of plano-convex and concave lenses also.     

Apodizing of an achromatic lens by a gray-glass negative lens element

The apodizing performance of a plano-concave lens made of gray glass was analyzed numerically. It was found that apodizing performance depends solely on the edge transmittance of the lens (a zero center thickness is assumed here) for any reasonable ratio of radius of curvature of the concave surface and the lens radius. If a modest increase in the size of the central diffraction peak and light losses introduced by such a lens can be accepted, it is possible to reduce energy diffracted into diffraction rings approximately tenfold.     

球面投影光刻物镜的设计

针对人工晶体或隐形眼镜的面形上连续浮雕结构加工的特点,本文介绍了基于空间光调制器(DMD)曲面投影光刻物镜系统的设计方法.根据其成像面为曲面的特点,根据光学设计理论多次利用弯向物方的弯月形负透镜结构进行场曲校正,同时运用光的衍射原理优化设计物镜系统的数值孔径以消除DMD投影过程中的栅格效应. 运用ZEMAX工程光学设计软件对系统进行了模拟、优化,并对优化后的结果进行了分析.对于设计实例利用上述设计原则给出了设计结果,工作波长为g线(峰值波长λ=436nm),像面曲率r=22.5mm,视场φ6mm,数值孔径NA=0.1,分辨力为7.8 μm(64Ip/mm)时的光学调制传函值>0.8,畸变<±0.05%.     

Sound field calculations for an ultrasonic linear phased array with a spherical liquid lens

Lenses are often used to provide focusing in the elevation dimension of ultrasonic linear phased-array transducers. The use of a liquid lens in this application adds a variable geometric focusing capability, determined by the radius of curvature of the lens surface and speed of sound in the liquid, to the electronic focusing produced by the linear phased array. An efficient method to calculate the sound field radiated from the linear phased-array transducer through the liquid lens is presented. It treats the lens surface as a secondary source distribution according to Huygens's principle, and employs a modified form of the rectangular radiator method to calculate the field. The appropriate phases for the array elements to focus and steer the beam are calculated by considering the refraction on the lens surface. Comparisons of computer simulations and experimental measurements of the field intensity distribution of a prototype linear array transducer with a liquid lens demonstrate the accuracy of the proposed method.     

Design of lenses with curved Petzval image surfaces

Abstract

Design strategies have been devoted to simplify and miniaturize optical systems. In this paper, by constraining image surface to coincide with the Petzval surface, we achieve a compact f/2.8 lens system design with a curved Petzval image surface. Arc distortion is proposed to accurately measure the distortion relative to a curved image surface. The optical performance of our curved image surface lens is analysed and compared. Results show that modulation transfer function (MTF) of our curved Petzval design over 69% at 100 cycles/mm for entire fields is achievable with 100-mm effective focal length, 40º full field of view, >92.4% edge relative illumination, <0.5% arc distortion. Comparisons with a traditional lens with a planar image plane demonstrate that a curved Petzval image surface is an excellent strategy to simplify and miniaturize optical systems, compensate field curvature and benefit astigmatism correction, increase off-axis illumination and improve MTF. Furthermore, the lens with a curved Petzval image surface has a more uniform optical power distribution and greater degree of lens symmetry.     

Aging of the human lens: changes in lens shape at zero-diopter accommodation

Scheimpflug photographs of the zero-diopter-accommodated anterior segments of 100 human subjects, aged 18 to 70 yr and evenly spaced over this range, were digitized and analyzed to characterize lens and lens nucleus shape as a function of age by the Hough transform and other image analysis methods. Anterior and posterior lens surface curves exhibit a decrease in radius of curvature with increasing age, in qualitative but not quantitative agreement with the earlier observations of Brown [Exp. Eye Res. 19, 175 (1974)]. In contrast, the shape of the lens nuclear boundaries changes little with age. Overall lens volume at zero diopters increases with age, but the volume of the lens nucleus remains unchanged. The lens center of mass moves anteriorly with increasing age, as does the central clear region of the lens. Although these data sets were found to be more variable than those of Brown, the complementary variability of other factors, such as anterior chamber depth, for each subject leads to a very high statistical correlation between lens shape and lens location relative to the cornea. This supports the finding of previous work that image formation on the retina for a given individual results from the multifactorial balancing of related factors.     

Nested shell optical model of the lens of the human eye

A nested shell model of the human lens is developed based on the known anatomical construction of the lens, on the known way in which the lens grows throughout its life, on the measured characteristics of the lens surfaces as a function of the age of the lens, on the measured changes in the shape of the lens during accommodation, and on measured material characteristics of the lens materials, such as density and index of refraction throughout. The observed changes in central surface curvature and thickness force the shell thicknesses to vary in a predictable way and in turn force the shell surface asphericity to take certain values. Thus, in addition to giving the shape of each shell, the model predicts the change expected in the asphericity of the lens surfaces as the lens ages and adds cortical cell layers. Two examples are given, one for a 25-year-old lens and one for a 40-year-old lens, to show how the cortical layers change their shapes throughout the cortex and over time as the lens ages. The performance of the model of this paper is compared to that of two other nested shell models, one where the layers have constant thickness and one where the lens posterior is fixed within the eye over time, to show the superior performance of this model with respect to maintaining a constant refractive error for the eye as the lens ages and grows.     

Determination of refractive indices of biconvex lenses by use of a Michelson interferometer

Measurements of lens parameters such as focal length, radius of curvature, and refractive index are important. We describe a measurement method that utilizes a Michelson interferometer to determine parameters of thin, convex lenses. The real fringe system formed by a Michelson interferometer is used to determine the focal lengths and the radii of curvature of the lenses. The refractive index of the lens material is determined from the thin-lens formula. We were able to determine the refractive indices to an accuracy as great as 99.97%. A detailed theoretical and experimental analysis is given.     

Superresolution performance of an absorbing glass positive lens element

Superresolution performance of a plano-convex lens made of absorbing glass is analyzed numerically. It was found that a reduction of the radius of the Airy disk depends solely on the center transmittance of the lens (a zero edge thickness is assumed) for any reasonable ratio of radius of curvature of the convex surface and the lens radius. The modest decrease in the size of the central diffraction peak is followed by a large decrease of its energy content and a rapid brightening of the diffraction rings. The most that can be achieved with such a lens is a reduction of the radius of the Airy disk to 71% of the corresponding clear aperture value, followed by approximately 78% of the energy being diverted into diffraction rings.     

Characteristics of the thick,compound refractive lens

A compound refractive lens (CRL), consisting of a series of N closely spaced lens elements each of which contributes a small fraction of the total focusing, can be used to focus x rays or neutrons. The thickness of a CRL can be comparable to its focal length, whereupon a thick-lens analysis must be performed. In contrast with the conventional optical lens, where the ray inside the lens follows a straight line, the ray inside the CRL is continually changing direction because of the multiple refracting surfaces. Thus the matrix representation for the thick CRL is quite different from that for the thick optical lens. Principal planes can be defined such that the thick-lens matrix can be converted to that of a thin lens. For a thick lens the focal length is greater than for a thin lens with the same lens curvature, but this lengthening effect is less for the CRL than for the conventional optical lens.     

二元平场透镜

讨论二元平场透镜的光学特性和象差。这种透镜不引入光焦度,当物体们我限远处孔径光阑与透镜重合时,不产生初级球差、彗差、轴用和轴外色差,但是它对场曲、畸变和轴上色差有贡献。给上用于校正双胶爱镜组的场曲的二元透镜实例。计算结果表明,二元透镜在平场光学系统中具有实用价值。     

Combined Twyman-Green and Mach-Zehnder interferometer for microlens testing

A new interferometer design for microlens testing is presented. The phase-shifting system combines the advantages of a Twyman-Green and a Mach-Zehnder interferometer and permits full characterization of the aberrations of microlenses as well as radius of curvature and focal length measurements. The Twyman-Green system is applied to surface testing in reflection (single reflection), whereas the Mach-Zehnder system is used for lens testing in transmission (single pass). Both measurements are performed without removal of the test part, allowing for combination of the results without confusion of the actual lens and without an azimuthal orientation error. The interferometer setup is explained, the test procedure is described, and experimental results are given.     

Measurement of a damaged layer thickness with reflection acoustic microscope

An acoustic microscope was used for determining the frequency dependence of surface acoustic wave (SAW) velocity on a specimen whose silicon single-crystal surface was machined under various conditions. Consequently, thickness of the damaged layers could be estimated from the curvature points of frequency dispersion curves of the SAW velocity. It was revealed that thicknesses of the damaged layers can be estimated through rough approximation by about one-half the wavelength determined by the frequency at curvature points. From specimens possessing two damaged layers, frequency dispersion curves with two curvature lines can be obtained. From the curvature point at high frequencies the thickness of the top damaged layer can be determined. On the other hand, from the curvature point at low frequencies, the thickness of the inner damaged layer can also be determined. By choosing an acoustic lens as the condition for exciting SAWs, images can be observed while varying the frequency. From observation results obtained with this method, the distribution in the depth direction can be clarified.     

Optical element for generation of accelerating Airy beams

We demonstrate an optical element for generation of accelerating Airy beams. The element is conveniently constructed by combination of positive and negative cylindrical lenses of matching radii of curvature. With proper choice of lens curvatures, the resulting surface profile closely follows a cubic polynomial. Passing a gaussian beam through this element and performing optical Fourier transform yields beam profiles close to the Airy function. Our experiments demonstrate parabolic propagation, or acceleration, of the resulting focal spots.     

Simple method for improving the sampling in profile measurements by use of the Ronchi test

We present a simple method for increasing the number of data points obtained during performance of profilometric measurements with the Ronchi test. The method is based on multiple ronchigram acquisitions that are superimposed after a few very simple data-processing operations. The measurement method, experimental setup, and data processing are described in detail from the ronchigram to the measured profile, and experimental results for a concave surface of an spherical ophthalmic lens are provided. The radius of curvature values measured for that surface are compared with the ones obtained with a high-precision radioscope, showing very good agreement and demonstrating the capability of the technique to measure topographic profiles of reflective samples.     

Aspheric mirror with constant angular magnification II

Differential equations for a constant-angular-magnification aspheric-mirror surface shape are derived for a general dependence of the camera image height on the camera field angle. The explicit equations of the constant-angular-magnification mirror surface are given for some particular values of the angular magnification. For a series of odd integer values of the angular magnification, 10th-order polynomial approximations of the mirror surface are presented. The imaging performance of such a mirror with an angular magnification of 7 is analyzed and compared with a spherical mirror. The main cause of image blur in all-sky cameras at the edge of the field of view was found to be a strong image curvature. We show that increasing the camera-to-mirror distance and/or stopping down the camera lens reduces the image blur.     

在Excel中用VBA实现透镜设计软件的开发

本文首先介绍着屏的归一化处理.接着提出主透镜的曲面模型,并分析获取该曲面的条件.然后以纠正着屏偏差为目标论述如何在旧透镜的基础上获得了新的透镜曲面.扼要介绍了软件的组成和一些算法.通过实例验证本文的方法,阐述这种软件的现实意义.     

Lens design for a white-light cosine-transform achromat

We describe the lens design for a twin-imaging white-light interferometer in which the interference pattern at the exit-pupil plane is the cosine transform of the spatial-intensity distribution of the object. The achromatic condition in terms of optical power is derived. The analysis of the transform aberration shows that the even aberrations, e.g., spherical aberration and field curvature, do not degrade the cosine transform and need not be corrected. This significant simplification permits us to design systems with good performance and uncomplicated lens structures. We present a lens design with three elements and a length of 320 mm. The system is capable of resolving more than 10(6) pixels with an operating spectral bandwidth of 100 nm. The results of an experiment with an early four-element design are also presented.     

A single exposure reflection moiré interferometric technique for complete curvature analysis of bent plates

Most known moiré methods need to be repeated three times for getting curvature information in three different in plane directions, for the complete analysis. To overcome this difficulty, a new single exposure moiré interferometric technique is proposed that maps completely partial curvature contours in three different directions of laterally loaded specularly reflecting plate models. Converging HeNe laser light is diffracted by a lens plane cross grating. The 00, + 10 and the +01 diffraction orders are permitted through the Fourier transform (FT) plane and collimated to illuminate the plate model. The reflected light from the loaded model records the model with the inherent deformed interferometric cross grating superimposed on it. A posteriori Fourier filtering of the developed recording (moirégram) gives partial curvature contours pertaining to three different in plane directions from which the principal curvatures and the principal directions are obtained. Also, this technique, being a single exposure technique, has the potential for complete bending analysis of plates subjected to lateral impact loading and destructive loading applications, where the repeatability of the event may not be possible.