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.     

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.     

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.     

高效非成像聚光光学系统设计与性能分析

针对菲涅尔透镜存在实际光学效率偏低的问题,本文设计了一种由非球面透镜和棒锥镜组成的高效非成像聚光光学系统。在光学设计软件Zemax的序列模式下对非球面透镜进行了优化设计,通过最大程度地减小球差,像面光斑的几何半径从42 mm降到了1.7 mm。基于此,在Zemax的非序列模式下,完成了非球面透镜和棒锥镜的建模和优化,通过蒙特卡罗光线追迹分析实现了光学效率为87%、接收角为0.9°的非成像聚光光学系统。最后,基于非球面透镜阵列和棒锥镜样品,实现了高倍聚光型光伏模组的封装与测试。测试结果表明,该模组的光电转换效率达30.03%,与菲涅尔透镜构成的高倍聚光型光伏模组相比有显著提升。     

Axial intensity distribution of partially coherent light focused by a lens with spherical aberration

Abstract

The focusing of partially coherent light by a lens with spherical aberration (SA) is studied. The numerical calculation results are given, showing that the axial intensity distribution not only depends on the SA, but also on the coherence of partially coherent light and the Fresnel number of the lens. As the coherence decreases, the influence of the SA on the axial intensity distribution decreases, and the positions of maximum axial intensity shift towards the 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.     

平顶多高斯光束通过球差透镜的聚焦特性

利用广义惠更斯-菲涅耳衍射积分公式,研究了平顶多高斯光束通过球差透镜的聚焦特性。推导出轴上光强分布的表达式,并对轴上光强进行大量的数值计算及分析。研究结果表明,当平顶多高斯光束的阶数N一定时,透镜的球差将在很大程度上影响光束的聚焦特性;当透镜的球差一定时,N值的改变将影响轴上最佳聚焦点的位置;当无球差时,轴上最佳聚焦点并不在几何焦点处,轴上最佳聚焦点位置随着N值增加向几何焦点靠近,例如当阶数N由0增大为1时,则归一化最佳聚焦点由0.91增大到0.98。     

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.     

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。     

Interferometric measurement of near-cylindrical surfaces with high amplitude resolution

Subaperture interferometric measurements of highly curved surfaces with a shape close to a cylinder have been performed in a normal-incident setup that consists of a Fizeau interferometer in combination with a plano-concave cylindrical lens. Since the field of view in the circumferential direction is limited by spherical aberration, the optical components were designed to minimize spherical aberration. For reference measurements a second plano-convex cylindrical lens was used. The subaperture setup leads to three-dimensional surface maps of the objects under test. To eliminate the influence of residual geometric aberrations, rectangular polynomials have been fitted and subtracted from the raw data. For deformations with spatial wavelengths below 30 mm, a rms amplitude resolution of 1 nm and a rms amplitude accuracy of 3 nm were achieved. Measurements on Wolter-type-I mirror shells are discussed in detail.     

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.     

Model eyes for evaluation of intraocular lenses

In accordance with the present international standard for intraocular lenses (IOLs), their imaging performance should be measured in a model eye having an aberration-free cornea. This was an acceptable setup when IOLs had all surfaces spherical and hence the measured result reflected the spherical aberration of the IOL. With newer IOLs designed to compensate for the spherical aberration of the cornea there is a need for a model eye with a physiological level of spherical aberration in the cornea. A literature review of recent studies indicated a fairly high amount of spherical aberration in human corneas. Two model eyes are proposed. One is a modification of the present ISO standard, replacing the current achromat doublet with an aspheric singlet cut in poly(methyl methacrylate) (PMMA). The other also has an aspheric singlet cut in PMMA, but the dimensions of it and the entire model eye are close to the physiological dimensions of the eye. They give equivalent results when the object is at infinity, but for finite object distances only the latter is correct. The two models are analyzed by calculation assuming IOLs with different degrees of asphericity to elucidate their sensitivity to variation and propose tolerances. Measured results in a variant of the modified ISO model eye are presented.     

The Use of Perturbed Aspherics in Multi-wavelength Focusing Optics

The design and underlying theory is given for an aspheric singlet lens capable of operating, with minimum sphero-chromatic aberration, over a range of pre-selected wavelengths. The performance of the lens is compared with a conventional aspheric (based on Fermat's principle) using finite ray-tracing techniques. The use of the lens as a focusing element in a multi-wavelength high-power laser is evaluated.     

Simple lens axicon

We present the design of a cemented doublet-lens axicon made from spherical surfaces only. Compared with diffractive axicons, refractive cone axicons, and earlier lens axicons with aspheric surfaces, this element is inexpensive and easy to manufacture even with large apertures. The lens axicon is based on the deliberate use of the spherical aberration of the surfaces. The design principles of the element and its characterization, numerically and experimentally, are presented in detail. Although performance was traded for simplicity and robustness, the results show that the lens axicon has the main axicon properties: a narrow, extended line focus of relatively constant width.     

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.     

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.     

Well-corrected Two-element Telescope with a Flat Image

The three element Schmidt-Cassegrain telescope is a well-known catadioptric system that can be corrected for spherical aberration, coma, astigmatism and Petzval curvature. This paper describes a version with the same aberration correction, but with only two elements. There are just three optical surfaces that need to be made, two of which are aspheric. Because of the simplicity of this two-element design, alignment and environmental stability should be better than that of more conventional systems. It is also a very compact system, with a length that is only 45 per cent of the system focal length. Performance numbers for a typical design are given, as well as an explanation of the theory behind this new system.     

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.