Caustics in a meridional plane produced by plano-convex conic lenses

We study the formation of caustic surfaces formed in both convex-plano and plano-convex conic lenses by considering a plane wave incident on the lens along the optical axis. By using the caustic formulas and a paraxial approximation, we derive analytic expressions to evaluate the spherical aberration to the third order, and a formula to reduce this aberration is provided. Furthermore, we apply the formulas to evaluate the circle of least confusion for a positive lens as a function of all parameters involved in the process of refraction through the conic lenses.     

Examination of the effect of the fibrous structure of a lens on the optical characteristics of the human eye: a computer-simulated model

We introduce a model of the human eye for which we take into consideration the laminated nature of lens fibers. The thickness of each lamina is 5.6 μm; thus the lens comprises 300 eccentric lenses of minute dimensions. The index gradient of the lens is such that the index of refraction increases exponentially from the lens core to its peripheral zone. A vector ray-tracing technique is employed to study the optical haracteristics of the system. Both paraxial and marginal rays are simulated, and the angles of incidence vary from 0° to ±20°. Special attention is given to the meridional caustic surfaces as well as the wave-front distortion of the refracted rays. A quasi-Newton optimization technique is employed to obtain the best parameters for the system. A computer modeling program, written in FORTRAN 77, is used to simulate a ray's refraction through the multisurfaces of the eye. The results show full agreement with previous data and that the cornea is responsible for eliminating possible spherical aberration of the system.     

Spherochromatic aberration of a single electrostatic lens of simplified design

Parameters of a single lens composed of two coaxial cylinders have been numerically calculated for the case of energy spread in a charged-particle beam. The spherical and chromatic aberration coefficients of this lens have been determined. It is shown that the focus-spot size calculated from the classical formulas taking into account the coefficients found is in good agreement with the results of numerical calculations.     

Wavefront and caustics of a plane wave refracted by an arbitrary surface

A simple expression is given for the k-function associated with the general solution of Stavroudis to the eikonal equation for refraction or reflection of a plane wave from an arbitrary surface. Using this result, we specialize the solution to derive analytic expressions for the wavefront and caustic surfaces after refraction of a plane wave from any rotationally symmetric surface. The method is applied to evaluating and comparing the wavefront and caustic surfaces formed both by a planospherical lens and a planoaspheric lens used for laser beam shaping, which provides understanding of how the irradiance is redistributed over a beam as the wavefront folds back on itself within the focal region.     

Improved solution for the cemented doublet

A method is described that permits the calculation of a cemented doublet with a given spherical aberration and coma at the edge of the lens. In particular the aberrations can be set to zero. Given one glass, the equations reported in this paper permit the determination of a second matching glass that minimizes the spherochromatism and coma of the lens. This result is obtained by the introduction, into the third-order thin-lens formulas, the third-order values of the aberration coefficients, as derived from the equation developed by Mossotti which yields zero finite aberrations for the same lens with added thickness. After a brief historical introduction, the third-order equations are developed and tables for the color-correcting glasses and SI and SII (the Seidel third-order coefficients) are given for objects at infinity and at a magnification of - 1, both for flint- and crown-leading cases. The paper closes with a table of corrected doublets.     

Effects of the peripheral layers on the optical properties of spherical fish lenses

We created a computational optical model of spherical fish lenses that takes into account the effects of the peripheral layers, which differ in cellular composition from the bulk of the lens. A constant refractive index, except for the lens capsule, in the outer about 6% of lens radius made it possible to uniquely infer the refractive index gradient in more central layers from a known or desired longitudinal spherical aberration curve using the inverse Abel transform. Since the zone of constant refractive index is wider than necessary to make the solution unique and for optimal optical performance of the lens, we propose that its width be set by the metabolic needs of the lens.     

Optical aberrations of intraocular lenses measured in vivo and in vitro

Corneal and ocular aberrations were measured in a group of eyes before and after cataract surgery with spherical intraocular lens (IOL) implantation by use of well-tested techniques developed in our laboratory. By subtraction of corneal from total aberration maps, we also estimated the optical quality of the intraocular lens in vivo. We found that aberrations in pseudophakic eyes are not significantly different from aberrations in eyes before cataract surgery or from previously reported aberrations in healthy eyes of the same age. However, aberrations in pseudophakic eyes are significantly higher than in young eyes. We found a slight increase of corneal aberrations after surgery. The aberrations of the IOL and the lack of balance of the corneal spherical aberrations by the spherical aberrations of the intraocular lens also degraded the optical quality in pseudophakic eyes. We also measured the aberrations of the IOL in vitro, using an eye cell model, and simulated the aberrations of the IOL on the basis of the IOL's physical parameters. We found a good agreement among in vivo, in vitro, and simulated measures of spherical aberration: Unlike the spherical aberration of the young crystalline lens, which tends to be negative, the spherical aberration of the IOL is positive and increases with lens power. Computer simulations and in vitro measurements show that tilts and decentrations might be contributors to the increased third-order aberrations in vivo in comparison with in vitro measurements.     

Effects of primary spherical aberration, coma, astigmatism and field curvature on the focusing of ultrashort pulses: homogenous illumination

We analyze the spatiotemporal intensity of pulses with durations of 20 fs and shorter and a carrier wavelength of 810 nm at the paraxial focal plane of an achromatic doublet lens. The incident pulse is well-collimated, and we use the Seidel aberration theory for thin lenses to evaluate the phase change due to the aberrations of the lens. In a set of cemented thin lenses with the stop at the lens, there is only spherical aberration, coma, astigmatism and field curvature, whereas the distortion aberration in the phase front is zero. We analyze the effect of these aberrations in the focusing of ultrashort pulses for homogenous illumination. We will show that the temporal spreading introduced by these aberrations in pulses shorter than 20 fs at 810 nm is very small but the spatial spreading is not, which reduces the intensity of the pulse considerably.     

Observation of a stronger focus due to spherical aberration

Abstract

Recently it was predicted that addition of spherical aberration to a focusing system with a small Fresnel number can increase the value of the maximum intensity on the optical axis. In this paper we report experiments which confirm this prediction. To this end we have measured the three-dimensional intensity distribution in the focal region of a lens with spherical aberration. We also show that this effect cannot be used to increase the intensity at a fixed distance from the lens.     

In situ optical testing of infrared lenses for high-performance cameras

We propose to evaluate infrared lenses with a dedicated analyzer having the same mechanical interface as the usual cameras. The proposed analysis is based on a wavefront measurement and allows a diagnostic of possible internal defects of the analyzed lens. The infrared lens analyzer described is constituted with a quadriwave lateral shearing interferometer and works with a blackbody light. We describe the response of this interferometer and an innovative method to obtain the wavefront under test. We finally present the experimental analysis of long-wavelength infrared lenses and the particular case of a modified lens that generates a large spherical aberration.     

球透镜逆反射器的反光性能

分析了逆反射球透镜的原理，从单个球透镜出发，详细讨论了光线传播过程及光通量分布，得到了其反光性能与各因素的关系。并把此结论推广到球透镜逆反射阵列，提出球透镜逆反射器的基本概念及应用的要点。     

Normalized parameter relating the spherical aberration of a thin lens to the diffraction limit and fiber coupling efficiency

In this paper, we calculate the transverse spherical aberration TA of a thin lens and defines a normalized aberration Y equal to TA divided by the theoretical resolution limit. As a rule of thumb, (a) a thin lens that suffers only from spherical aberration may be considered effectively diffraction-limited as long as Y < 1.6. Similarly, (b) the coupling efficiency of a Gaussian beam to a single-mode fiber may be high even when Y > 1.6, and, specifically, (c) the lens need be diffraction-limited only over a radius approximately equal to the radius (to the 1/e-point) of the Gaussian beam.     

Angle- and size-dependent characteristics of incoherent Raman and fluorescent scattering by microspheres. 1. General expressions

A dipole model is used to simulate incoherent Raman and fluorescent scattering by microspheres. The use of the addition theorem for spherical harmonics circumvents the need to evaluate double sums in the final formulas, thereby drastically reducing computational effort. Special attention is paid to consideration of backscattering geometry, which is important for lidar applications. The formulas derived for backscattering geometry decrease the computation time for size parameter x approdximately 100 by a factor of 200 compared with the time for calculations performed at other angles.     

轴位移法测定GRIN透镜的折射率分布系数

本文对GRIN透镜的精确光线追迹公式作了推导,介绍了轴位移法对透镜折射率分布的测量方法及相应的数据处理,并对测量误差进行了分析和计算,从而对测定GRIN透镜折射率分布提供了一种精确而且实用的方法。     

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%.     

Imaging of Extended Objects Using an Off-axis Holographic Lens

Abstract

The aim of this paper is to evaluate the performance of an off-axis holographic lens afflicted with third-order spherical aberration and coma using a numerical ray-tracing procedure. The light intensity distribution in the aberration spot observed at the Gaussian image plane has been evaluated for different amounts of coma and for a fixed value of spherical aberration. The images of both an extended coherent and an incoherent edge as well as bar objects have been computed and the results compared with the aberration-free case. All the results are illustrated in graphical form.     

Improving the accuracy of the caustic test

The caustic or Gaviola test, used for testing aspheric mirrors, has been studied with reference to the research of Schroader ["The caustic test," in Amateur Telescope Making III, A. G. Ingalls, ed. (Kingsport Press, Kingsport, Tenn., 1953), pp. 429-456]. It is shown that the two central formulas, which are used to determine the mirror quality, give significant errors for the large-diameter, short-focal-length mirrors commonly used in astronomical optics. We derive analytically two alternative equations, which are more exact, and show that they lead to significant improvement.     

Combinational system of a truncated ball lens and a hyperbolic lens for collimating a highly divergent source

We propose the use of a truncated ball lens in a collimating system to transform a spherical wave from a highly divergent source into a plane wave. The proposed scheme, which incorporates a hyperbolic lens, is discussed, and the overall system is found to have a large acceptance angle and to be free of spherical aberration. Diffraction and polarization effects are neglected, as well as skew rays.     

Aberrated lenses for generating flattened laser irradiance

Expressions for describing Gaussian beams focused by a lens with spherical aberration have been derived. Numerical results show that, when the coefficient of the spherical aberration is negative, one can obtain flattened laser irradiance at two positions along the focused field. The larger the coefficient of negative spherical aberration, the larger the flatness is. The effect of the Fresnel number of the focusing lens on the flattened laser irradiance is also investigated.