Mechanism of compensation of aberrations in the human eye

We studied the mechanism of compensation of aberrations within the young human eye by using experimental data and advanced ray-tracing modeling. Corneal and ocular aberrations along with the alignment properties (angle kappa, lens tilt, and decentration) were measured in eyes with different refractive errors. Predictions from individualized ray-tracing optical models were compared with the actual measurements. Ocular spherical aberration was, in general, smaller than corneal spherical aberration without relation to refractive error. However, horizontal coma compensation was found to be significantly larger for hyperopic eyes where angle kappa tended to also be larger. We propose a simple analytical model of the relationship between the corneal coma compensation effect with the field angle and corneal and crystalline shape factors. The actual shape factors corresponded approximately to the optimum shapes that automatically provide this coma compensation. We showed that the eye behaves as an aplanatic optical system, an optimized design solution rendering stable retinal image quality for different ocular geometries.     

Imaging performance of widefield solid immersion lens microscopy

We investigate the performance of a widefield imaging system employing an aplanatic solid immersion lens. Off-axis imaging quality is examined theoretically at different radii and thicknesses of the aplanatic solid immersion lens. It is found that field curvature is the major aberration affecting the imaging quality. Aberrations are measured experimentally, and the results are in very good agreement with those obtained from simulations and demonstrate the situations where high quality images can be obtained with the aplanatic solid immersion lens.     

The design of a triplet with a shape-dependent third-order aberration optimization technique

Abstract

We have derived a series of shape-dependent third-order aberration equations involving lens thickness. These equations are used in a simple and direct method to correct real aberrations and to find the minimum aberration for triple design that has been proposed. These calculated third-order aberrations can exactly meet the target values for each stage by means of the damped least-squares method. The shape of the three elements permits the control of three third-order aberrations: spherical aberration, coma and astigmatism. The spherical aberration is targeted first. The minimal value of the real on-axis aberration is obtained. Similarly, the coma and astigmatism target values are adjusted so as to force the full field angle real off-axis aberrations down to a minimum. Finally, the manual adjustment of the lens thickness and air spacing is used to attain the minimum aberration at the 0.7 field angle. To verify the method, two triplet design examples are presented.     

The Fabry-Perot Interferometer. History,Theory, Practice and Applications

Abstract

A simple algebraic algorithm is proposed as a computational tool for the thin-lens design of a triplet which consists of a singlet and a cemented doublet. The triplet is required to yield specified amounts of lens power, primary spherical aberration, central coma, longitudinal chromatic aberration and secondary spectrum. The three element powers of the triplet are first obtained by solving the simultaneous linear equations of the total lens power, longitudinal chromatic aberration and secondary spectrum. A quadratic equation is obtained by combining the equations of spherical aberration and central coma, and the lens shapes are then obtained by solving this quadratic equation. The solving process is purely algebraic and is therefore easy to calculate and guarantees that all the solutions can be found.     

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.     

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。     

Correcting ocular spherical aberration with soft contact lenses

Following aberroscopy, aspheric front surface soft contact lenses (SCLs) were custom-made to correct spherical refractive error and ocular spherical aberration (SA) of 18 myopic and five hypermetropic subjects (age, 20.5 +/- 5 yr). On-eye residual aberrations, logMAR visual acuity, and contrast sensitivity were compared with the best-correcting spectacle lens, an equally powered standard SCL, and an SCL designed to be aberration free in air. Custom-made and spherical SCLs reduced SA (p < 0.001; p < 0.05) but did not change total root-mean-square (rms) wave-front aberration (WFA). Aberration-free SCLs increased SA (p < 0.05), coma (p < 0.05), and total rms WFA. Visual acuity remained unchanged with any of the SCL types compared with the spectacle lens correction. Contrast sensitivity at 6 cycles/degree improved with the custom-made SCLs (p < 0.05). Increased coma with aspheric lens designs and uncorrected astigmatism limit the small possible visual benefit from correcting ocular SA with SCLs.     

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.     

Finite conjugate spherical aberration compensation in high numerical-aperture optical disc readout

Spherical aberration arising from deviations of the thickness of an optical disc substrate from a nominal value can be compensated to a great extent by illuminating the scanning objective lens with a slightly convergent or divergent beam. The optimum conjugate change and the amount and type of residual aberration are calculated analytically for an objective lens that satisfies Abbe's sine condition. The aberration sensitivity is decreased by a factor of 25 for numerical aperture values of approximately 0.85, and the residual aberrations consist mainly of the first higher-order Zernike spherical aberration term A60. The Wasserman-Wolf-Vaskas method is used to design biaspheric objective lenses that satisfy a ray condition that interpolates between the Abbe and the Herschel conditions. Requirements for coma by field use allow for only small deviations from the Abbe condition, making the analytical theory a good approximation for any objective lens used in practice.     

Compact description of substrate-related aberrations in high numerical-aperture optical disk readout

Optical disks are read out by focusing a beam of high numerical aperture (NA) through the substrate. Deviations of the thickness from the nominal value result in spherical aberration; tilting the substrate results in coma. Exact analytical expressions for the rms aberration per micrometer thickness mismatch (for spherical aberration) and per degree tilt (for coma) are derived. The paraxial estimates for these sensitivities proportional to NA4 (spherical aberration) and NA3 (coma) underestimate the exact values by a factor of approximately 2 for the value NA = 0.85, corresponding to the new Blu-ray disk format. Expansion of the aberration function in Zernike aberrations shows that the exact aberration functions are well described by the lowest-order Zernike spherical aberration (A40) and coma (A31) term for all but the very highest NA values.     

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.     

集成光学非球面消球差双凸波导透镜的研制

针对微透镜制作采用的球透镜研磨,多组分玻璃基板离子交换,结晶化玻璃基板光热法,本文提出非球匠消球差双凸波导透镜设计、制备及参数测试方法.该方法根据集成光学原理,研制了一种非球面消球差双凸波哥透镜.该透镜数值孔径大,放大倍数高,接近衍射极限,采用光刻、复制工艺,结构简单,一致性好.实验结幂表明,NA=0.35,β=6.932,光强分布与理论值一致,达到设计要求.     

Effect of polarization on a solid immersion lens of arbitrary thickness

A solid immersion lens can be applied for high-resolution subsurface analysis of integrated circuits and other physical systems. We present a thorough analysis of the focal field distribution of a solid immersion lens system of arbitrary thickness. Cases of linearly and radially polarized illumination are examined and accurate expressions derived for the electric field in the image space. The effect of the spherical interface on both transverse and axial intensity profiles is analyzed. The performance and practicality of configurations deviating from the hemispherical and aplanatic cases are studied. The results show that optimal resolution is obtained at focal positions between the hemispherical and aplanatic points when radially polarized illumination is applied.     

Interferometric testing of high-numerical-aperture convex surfaces

Interferometric tests of convex surfaces for large-N.A. lens systems often present problems. We show how such surfaces can be tested with a reference surface having a much smaller N.A. by making use of the aplanatic imaging properties of a spherical surface.     

The Systematic Design of Two-component Objectives

A self-contained account is given of systematic methods for the preliminary design of corrected two-component objectives, employing design parameters which remain valid in all cases. Explicit formulae given the necessary values of spherical aberration and central coma for each component in useful forms. A simple algorithm is described with which glass types and lens shapes may be determined to give the desired primary aberrations; and a second algorithm is used which permits zero-thickness elements to be replaced by ones of finite thickness, and other design changes to be made to a given component, without disturbing the detailed Gaussian optics of the complete system and also leaving exactly unchanged the primary aberrations of the remaining components. The methods are suitable for use with electronic desk computers having limited storage and programming capabilities. The two algorithms described are applicable to the whole range of optical design problems, and are of particular advantage in the preliminary design stages of zoom lenses.     

Variable power phase lenses

A method is given to construct a phase lens capable of creating an optical aberration of variable power that is described by a single Zernike polynomial function whose meridional index is 1 or greater. The phase lens is created from two identical phase elements, each creating a single Zernike aberration, that can be rotated with respect to each other, thereby increasing the aberration effect from zero to twice the value of either. This is possible because these aberrations are vectorlike. Results are given from the testing of an example that was manufactured and designed to produce coma (Zernike term Z(3,1)).     

Alteration of imaging properties of an optical pickup's objective lens by a nonrotationally symmetric coating

One can control the aberrations of an optical readout system by varying the width of a strip of antireflection coatings deposited upon plastic objective lenses. It is found that one can control the magnitude of the third-order astigmatism of the system by changing the coating width. This process has the advantage that it does not significantly cause other kinds of aberration such as coma and spherical aberrations to deteriorate. When these nonrotational symmetrically (NRS) coated lenses are used for off-axis operations such as tracking movements in optical drives, the change in the magnitude of the astigmatism (DAS) that is generated can be made smaller than those of symmetrically coated or noncoated lenses. As much as a 73% decrease in DAS was observed experimentally with a NRS-coated lens. Including the birefringence of the plastic material in the analysis yields a low and constant level of astigmatism generated by shifting of the objective lens.     

Application of the see-saw method to all refracting optical systems

The optical see-saw diagram is a method that describes image correction to third-order approximation over a finite field of view in rotationally symmetric systems that employ aspheric surfaces. The aim of this paper is to describe the correction of aberrations caused by plane surfaces in all refracting optical systems in terms of the see-saw diagram. A lens correction algorithm based on the see-saw method is described to correct analytically the Seidel aberrations, primary spherical aberration, coma, astigmatism, and distortion, in such systems. We then apply this lens correction algorithm to the design of equivalent configurations by aspherizing different surfaces of the system, and the high-order aberrations of the equivalent configurations are evaluated by means of transverse-ray-aberration plots. Results indicate that this method gives information on what the contribution must be to the third-order aberrations that each component should provide to the system to give a better balance of high-order aberrations. Examples of the lens correction algorithm applied to lenses with six refracting surfaces and working for both finite and infinite object conjugates are given.     

光谱共焦位移传感器的色散物镜设计

光谱共焦位移传感器具有精度高、适应性强等特点,传感器的关健部件是产生轴向色散的物镜.本文对传感器的工作原理进行了分析,推导了计算物镜光学参数的公式,并依据此公式计算结果设计物镜,得到了满足设计指标的物镜,且与理论计算相符.传感器的工作波长范围是500～700 nm,设计的色散物镜利用高色散玻璃和双胶合透镜达到了1 mm...