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。     

Age-dependent variation of the Gradient Index profile in human crystalline lenses

PURPOSE: To reconstruct the gradient index (GRIN) profile of human crystalline lenses ex-vivo using Optical Coherence Tomography (OCT) imaging with an optimization technique and to study the dependence of the GRIN profile with age. METHODS: Cross-sectional images of nine isolated human crystalline lenses with ages ranging from 6 to 72 (post mortem time 1 to 4 days) were obtained using a custom-made OCT system. Lenses were extracted from whole cadaver globes and placed in a measurement chamber filled with preservation medium (DMEM). Lenses were imaged with the anterior surface up and then flipped over and imaged again, to obtain posterior lens surface profiles both undistorted and distorted by the refraction through the anterior crystalline lens and GRIN. The GRIN distribution of the lens was described with three variables by means of power function, with variables being the nucleus and surface index, and a power coefficient that describes the decay of the refractive index from the nucleus to the surface. An optimization method was used to search for the parameters that produced the best match of the distorted posterior surface. RESULTS: The distorted surface was simulated with accuracy around the resolution of the OCT system (under 15 μm). The reconstructed refractive index values ranged from 1.356 to 1.388 for the surface, and from 1.396 to 1.434 for the nucleus. The power coefficient ranged between 3 and 18. The power coefficient increased significantly with age, at a rate of 0.24 per year. CONCLUSION: Optical Coherence Tomography allowed optical, non-invasive measurement of the 2-D gradient index profile of the isolated human crystalline lens ex vivo. The age-dependent variation of the changes is consistent with previous data using magnetic resonance imaging, and the progressive formation of a refractive index plateau.     

Adaptive model of the gradient index of the human lens. II. Optics of the accommodating aging lens

A simple, parametric model of the gradient refractive index distribution (GRIN) of the human lens with conicoid surfaces able to adapt to individual distributions as well as to the changes of the lens shape and structure with age and accommodation is presented. The first part of this work was published in a companion paper [J. Opt. Soc. Am. A24, 2175 (2007)]. It included the development of the mathematical formulation of the adaptive model; the validation of its customization capability by fitting, sample by sample, a set of in vitro refractive index distributions of lenses of different ages, ranging from 7 to 82 years, from the recent literature; and an average model of the (in vitro) aging crystalline lens. Here we extrapolate that in vitro GRIN model by assuming that the same structural parameters are valid for the living lens. Then, recent data of the changes of the shape of the aging lens with accommodation from the literature are used to build an aging and accommodating lens model. This is straightforward since the GRIN model adapts automatically to the chosen external lens geometry. A strong coupling was found between the adaptive GRIN distributions and the conic constants affecting the refractive power. To account for the lens paradox and the reported changes in lens spherical aberration with age and accommodation, age- and accommodation-dependent functions for the anterior and posterior internal conic constants were derived through optimization.     

Spherical gradient-index polymer lens with low spherical aberration

A sphere lens with a spherical gradient index (GRIN) was prepared by the modified suspension polymerization technique. GRIN spheres with quadratic- and linear-index distributions were obtained by two different methods to confirm the effect of the GRIN profile on the focusing property of the sphere lens. It was confirmed in both theory and experiment that the spherical aberration of such GRIN spheres was remarkably decreased compared with that of a homogeneous sphere.     

Gradient-index contact lens

A gradient-index (GRIN) contact lens (CL) is proposed to decrease spherical aberration and to increase the diopter. A plastic radial GRIN rod was successfully obtained by using the vapor-phase diffusion copolymerization technique. The resulting index distribution of the GRIN rod was almost parabolic against the distance from the center axis, and the Δn value was -0.030. The GRIN CL was prepared by grinding and polishing the rod. It is theoretically and experimentally concluded that using the radial GRIN material can significantly improve the optical properties of CL's.     

Graded-index fiber lens proposed for ultrasmall probes used in biomedical imaging

The quality and parameters of probing optical beams are extremely important in biomedical imaging systems both for image quality and light coupling efficiency considerations. For example, the shape, size, focal position, and focal range of such beams could have a great impact on the lateral resolution, penetration depth, and signal-to-noise ratio of the image in optical coherence tomography. We present a beam profile characterization of different variations of graded-index (GRIN) fiber lenses, which were recently proposed for biomedical imaging probes. Those GRIN lens modules are made of a single mode fiber and a GRIN fiber lens with or without a fiber spacer between them. We discuss theoretical analysis methods, fabrication techniques, and measured performance compared with theory.     

Foundations for low-loss fiber gradient-index lens pair coupling with the self-imaging mechanism

A fiber-optic collimator that emits a Gaussian beam with its beam waist at a certain distance after the exit face of the lens is labeled a self-imaging collimator. For such a collimator, the waist of the emitted Gaussian beam and its location are partly dependent on the properties of the gradient-index (GRIN) lens. Parameters for the self-imaging collimator are formulated in terms of the parameters of a GRIN lens (e.g., pitch, core refractive index, gradient index, length) and the optical wavelength. Next, by use of the Gaussian beam approximation, a general expression for the coupling power loss between two self-imaging-type single-mode fiber (SMF) collimators is, for the first time to our knowledge, derived as a function of three types of misalignment, namely, separation, lateral offset, and angular tilt misalignment. A coupling experiment between two self-imaging collimators with changing separation distance is successfully performed and matches the proposed self-imaging mechanism coupling loss theory. In addition, using a prism, lateral offset, as well as angular tilt, misalignments are experimentally simulated for a two self-imaging collimator coupling condition by a single collimator reflective test geometry. Experimental results agree well with the proposed loss formulas for self-imaging GRIN lenses. Hence, for the first time to our knowledge, the mathematical foundations are laid for employing self-imaging-type fiber collimators in SMF-based free-space systems allowing optimal design for ultra-low-loss coupling.     

Theoretical considerations for anticipating of function analysis on a gradient index-lens fabrication through double ion-exchange process

Based on precise and detailed theoretical examination of diffusion equation analysis, two-step Ag⁺-Na⁺ and Na⁺-Ag⁺ ion-exchange parameters were optimized in order to fabricate a gradient index (GRIN) lens in the BK7 glass rod. Using the diffusion equation, the impact of the concentration ratio of the exchanged ion during the first and second steps was examined in detail. Then, based on the calculated effective parameters such as concentration ratio and immersion time, a fabrication process was proposed. We managed to get the optimum parameters (the bath stop time, temperature, and length) to make a quarter pitch lens. As a result, some samples of the GRIN lens were fabricated and tested successfully. Theoretical considerations and experimental results are presented.     

眼球系统中关键屈光元件的光学模型研究

角膜和晶状体是人眼光学系统中两个关键的屈光元件,为了理解眼内各介质和整个眼球的屈光状态以及视网膜上的成像,有利于眼科临床方面的应用,需要分别对二者进行光学特性模型的分析与研究。根据角膜和晶状体的光学特性,应用光学设计软件Zemax和有关的数学工具,从光学成像角度,分别对角膜和晶状体模型进行研究:基于结合人眼光学模型的角膜双二次曲面模型的建立方法,统计分析了我国人眼实测角膜参数的数据;通过对晶状体折射率分布特点的分析,分别在轴向和径向上进行了综合分析。最后给出了符合我国人眼特点的角膜面型的统计数值,完善了我国人眼角膜光学模型的建立;获得了形式简单且能够表示晶状体折射率分布一般特征的梯度渐变模型表达式。基于收集的我国人眼实测数据的角膜面型模型和晶状体梯度渐变形式的折射率模型,为解决人眼光学系统研究中的关键问题提供了新的方案和思路。     

ABCD matrix of the human lens gradient-index profile: applicability of the calculation methods

The applicability of different approximate methods proposed to determine the paraxial properties of the gradient-index (GRIN) distribution resembling that of the human lens, by means of the system ABCD matrix, is tested. Thus, the parabolic-ray-path approximation has been extended to provide the ABCD matrix of a slab lens comprised of a rotationally GRIN medium. The results show that this method has good numerical stability, and it is also the easiest one in determining the Gaussian constants of the human lens GRIN profile.     

Correction of chromatic aberrations in GRIN endoscopes

A gradient-index (GRIN) endoscope can be constructed by substituting for the usual objective and relay sections suitable cylindrical index-distribution rod lenses. Currently available GRIN lenses exhibit large amounts of chromatic aberration. Axial color arises mostly from the relay lens, while lateral color is due to the objective lens. A negative lens cemented to a shortened GRIN relay lens can simultaneously correct axial and lateral chromatic aberrations with commercially available components. This correction system reduces the requirements for mechanical centration better than do color correctors that are incorporated into the ocular design. Monochromatic aberrations are also considered.     

Birefringent properties of diametrically loaded gradient-index lenses

Gradient-index (GRIN) lenses have been widely used as collimators in various fiber-optic sensors and as optical coupling devices in components designed for optical communication systems. However, relatively little attention has been paid to the birefringent properties of GRIN lenses and the potential for using them as photoelastic sensing elements in optical transducers. Analytical and experimental results are described that were obtained for the intensity distribution produced by studying a GRIN lens by using a polariscope. The residual birefringence inherent in an unloaded lens is initially studied. The lens is then assumed to be diametrically loaded and the superposition is studied by the method of ray tracing. When the results obtained from the simulation for a Selfoc, 0.25-pitch lens are compared with experimental data, an excellent agreement is obtained. Intensity increases monotonically with load, confirming that the lens would be a good choice for the sensing element of an optical transducer designed as part of a strain or acceleration measurement system. The numerical simulation is then used to study the influence of residual stress on sensitivity.     

Gradient-index human lens as a quadratic phase transformer

The correspondence between the linear integral transform and the ray-transfer matrix of a first-order optical system is used to evaluate the transmittance function of gradient-index (GRIN) human lens regarded as a quadratic phase transformer. The size of the GRIN crystalline lens has been considered for redefining the effective transmittance function by the pupil function. The role that the GRIN nature of the human lens plays in the retinal image quality using the point spread function (PSF) is commented on. The simulation results show that the effective radius of the output face of the lens decreases with increasing thickness and that it is higher for flat end surfaces than for curved end faces. On the other hand, the simulation results also show, for small pupil sizes, that the GRIN nature of the human lens is a retinal image degradation source producing the spread of the PSF and that the curved end surfaces of the lens constitute a retinal image quality improve factor contributing to the narrowing of the PSF.     

Making fast cylindrical gradient-index lenses diffraction limited by using a wave-front-correction element

A wave-front-correction element (WFCE) is produced to make a cylindrical Ag-ion-exchanged gradient-index (GRIN) lens with a high numerical aperture (0.53) diffraction limited (wave-front error, 0.02lambda rms). The wave-front aberrations of the cylindrical GRIN lens are measured by a phase-shifting shearing interferometer, with a conventional microscope objective used as a compensation lens. The continuous surface relief of the WFCE is produced by a lithographic process. The wave-front-corrected GRIN lens is applied to collimate the strongly divergent light (57 degrees full diverging angle measured at 1/e(2) of maximum intensity) emitted by a high-power diode laser. The power irradiated into a full angle of 2 mrad can be enhanced by a factor of 1.8 with the WFCE.     

Hybrid refractive-diffractive-gradient-index superresolving focusing device

The focusing properties and resolving power of a device consisting of a tapered gradient-index (GRIN) lens with spherical input and output faces are investigated through the use of the ABCD formalism to achieve minimization of the Airy radius for the device. Diffractive elements, such as zone plates, can, with an appropriate choice of their parameters, increase the resolution of an imaging system compared with a conventional lens. We demonstrate that by combining both elements a hybrid refractive-diffractive-GRIN device can be designed that exhibits improved superresolution characteristics.     

Performance consideration of three-dimensional optoelectronic interconnection for intra-multichip-module clock signal distribution

The structure, fabrication, and theory of a three-dimensional planarized optoelectronic clock signal distribution device, based on a thin light-guiding substrate in conjunction with a two-dimensional polymer holographic grating array, are described. We have demonstrated previously a 25-GHz 1-to-42 (6 x 7) highly parallel fan-out interconnect with a signal-to-noise ratio of 10 dB. We present theoretical research that focuses on generating a globally uniform fan-out distribution. An objective function aimed at equalizing the intensities among the fan-out beams is established. For an arbitrary M x N fan-out distribution, there are M + N + 1 sets of holograms needed to be recorded independently to provide the required equal fan-outs. The efficiency of each hologram is determined precisely. The angular misalignment, wavelength dispersion, and spot-size problems are discussed further, together with their tolerance requirements on the size of the photoreceivers integrated on the multichip modules. Employment of 0.25-pitch gradient index (GRIN) lenses as a collimator and as a focusing element is demonstrated experimentally. Optical beam profile manipulation and packaging tolerance are enhanced greatly with GRIN lenses. Finally, clock skew problems associated with the proposed system are discussed, and schemes to minimize the skew are proposed.     

激光起爆器光学窗口的研究

文章设计了平面透镜、单凸透镜、双凸透镜组及格林透镜等几种光学窗口,并通过发火试验详细讨论了几种窗口的优劣。研究结果表明,自聚焦透镜发火阈值要远低于其它光学透镜结构发火能量,是目前最为理想的窗口透镜。     

Fabrication method of ultra-small gradient-index fiber probe

Fabrication method and device of ultra-small gradient-index(GRIN) fiber probe were investigated in order to explore the development of ultra-small probes for optical coherence tomography(OCT) imaging.The beamexpanding effect of no-core fiber(NCF) and the focusing properties of the GRIN fiber lens were analyzed based on the model of GRIN fiber probe consisting of single-mode fiber(SMF),NCF and GRIN fiber lens.A stereo microscope based system was developed to fabricate the GRIN fiber probe.A fiber fusion splicer and an ultrasonic cleaver were used to weld and cut the fiber respectively.A confocal microscopy was used to measure the dimensions of probe components.The results show that the sizes of probe components developed are at the level of millimeter.Therefore,the proposed experimental system meets the fabrication requirements of an ultra-small self-focusing GRIN fiber probe.This shows that this fabrication device and method can be employed in the fabrication of ultrasmall self-focusing GRIN fiber probe and applied in the study of miniaturized optical probes and OCT systems.     

Manipulating the focal shift in a medium with electromagnetically induced transparency

By approximating the index distribution of a medium with electromagnetically induced transparency (EIT) as a gradient index (GRIN), propagation laws in the medium with EIT can be obtained. Transmission properties in an optical system with an EIT medium are analyzed. The results show that, unlike the case in the ordinary GRIN medium, the refractive index of EIT medium has the better controllability. Consequently, discussions are focused on how to conveniently manipulate the focal shift of the input in the EIT by means of controlling the index of the medium. Additionally, the speckle radius on the location of the actual focus can be diminished by adjusting some parameters in the EIT medium.