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.     

Broadband microwave Luneburg lens made of gradient index metamaterials

Luneburg lenses are able to form perfect focus that is free of aberration. Because of the varying refractive index throughout the lens, incoming electromagnetic waves can travel in a curved path and be guided to focus at the back of the lens. The implementation of Luneburg lenses is often difficult due to the challenges in creating a medium with varying refractive index using normal materials. This problem can be overcome with the use of gradient index metamaterials. We report a two dimensional Luneburg lens made of gradient index metamaterials. It consists of 17 concentric shells with etched patterns on a printed circuit board working in microwave X band frequency. The broad properties of the Luneburg lens are then discussed.     

Tomographic method for measurement of the gradient refractive index of the crystalline lens. II. The rotationally symmetrical lens

In the first part of this paper we presented a tomographic method to reconstruct the refractive index profile of spherically symmetrical lenses. Here we perform the generalization to lenses that are rotationally symmetrical around the optical axis, as is the ideal human lens. Analysis of the accuracy and versatility of this method is carried out by performing numerical simulations in which different magnitudes of experimental errors and two extreme case scenarios for the likely shape of the refractive index distribution of the human lens are considered. Finally, experimental results for a porcine lens are shown. Conceptually simple and computationally swift, this method could prove to be a valuable tool for the accurate retrieval of the gradient index of a broad spectrum of rotationally symmetrical crystalline lenses.     

Ophthalmic application of poly(HEMA)s containing nanoparticles and dimethylacrylamide

High functional ophthalmic lens materials, poly(HEMA-co-MMA)s were prepared by the copolymerization of HEMA, MMA, MA, EDGMA, and N,N-dimethylacrylamide in the presence of platinum nanoparticles with antimicrobial properties. The hydrophilic monomer N,N-dimethylacrylamide has excellent biocompatibility and oxygen transmissibility. The combination where platinum nanoparticles were added produced a colorless transparent lens. The water contents were in the range of 36.68-44.08% and the refractive index was measured to be in the range of 1.424-1.436. Meanwhile, the oxygen transmissibility ranged from 11.13 x 10(-11) to 17.63 x 10(-11) (cm2/sec) (mlO2/ml x mm Hg) increased with increasing the addition ratio of N,N-dimethylacrylamide. The physical properties measurements of the produced polymers showed that the nanoparticles did not show significant effect on the water content and refractive index of the hydrogel contact lens, but the materials effected to reduce oxygen permeability to a certain extent. The copolymers have excellent oxygen permeability, indicating that the material can be used to fabricate hydrogel contact lenses with high oxygen transmissibility.     

Influence of spoliation in poly(2-hydroxy ethyl methacrylate) soft contact lens on its free volume and optical transparency

The calcification in poly(2-hydroxy ethyl methacrylate) contact lens was investigated using positron annihilation spectroscopy (PLS). The two poly(2-hydroxy ethyl methacrylate) (PHEMA) lenses of different companies were calcified employing a simple mechanism of calcification in abiotic aqueous solutions. The calcium deposit was analyzed using energy dispersive X-ray spectroscopy (EDS). Calcified lenses showed decrease in ortho-positronium (o-Ps) lifetime and free volume hole size of the lens material suggesting diffusion of Ca²⁺ into these cavities. The change in optical property viz. refractive index of these calcified lenses were measured and correlated with positron results. To find a better correlation, a series of worn spoilt PHEMA lenses of the same power with mainly calcium deposits, were similarly characterized using PLS and refractive index. These results correlate well with the free volume of the material. For hydrophilic lenses this correlation is reported for the first time.     

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.     

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.     

基于矩阵方法的共轴球面系统屈光特性研究

基于眼科屈光学理论,运用矩阵方法建立了单个球镜片及多个球镜片组合的复杂共轴球面系统的精确屈光特性模型,并与简化模型进行比较,分析镜片间距及放置顺序对组合后屈光特性的影响。基于该精确屈光特性模型,对影响球镜度的各项不确定度分量进行分析。组成镜片的前、后表面曲率半径是影响屈光特性的主要不确定度分量,其次是镜片材料折射率和镜片间距引入的不确定度分量,中心厚度引入的不确定度分量最小。     

Retroreflector approximation of a generalized Eaton lens

We extended a previous study of the Eaton lens at specific refraction angles to the Eaton lens at any refraction angle. The refractive index of the Eaton lens is complicated and has no analytical form except at a few specific angles. We derived a more accessible form of the refractive index for any refraction angle with some accuracy using the retroreflector approximation. The finding of this study will be useful for a rapid estimation of the refractive index, and the the design of various Eaton lenses.     

Alternative method for measuring effective focal length of lenses using the front and back surface reflections from a reference plate

We present a simple method for measuring the effective focal length without determining the location of principle plane of the lens. The method is based on the measurement of confocal backreflection axial responses from the front and back surfaces of a reference plate with known refractive index and thickness. We proved the concept by measuring the effective focal lengths of thin singlet lenses and complex microscope objectives. The theoretical limit of measurement precision varies depending on the numerical aperture of the lens. This method can provide an alternative focal length measurement method for complex lenses or lenses that are permanently attached to other structures. Measurement errors were analyzed theoretically and improvements in measurement accuracy were discussed.     

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.     

PLD法制备高取向透明KTa0.65Nb0.35O3/SiO2(100)薄膜性能研究

用PLD技术结合后期退火,在透明石英单晶(100)上制备了高取向的纯钙钛矿相KTN薄膜.对薄膜的光学、电学性能分析表明,薄膜铁电居里温度为15℃,矫顽场7.32kV/cm,剩余极化强度9.25μC/cm²,折射率在波长1.2μm处为1.776,厚度968nm,沉积速率约为0.027nm/脉冲.I-V特性表明,低电场强度下,I-V服从欧姆定律,高电场强度下,I-V服从平方关系,可用空间电荷限制电流(SCLC)模型解释.薄膜漏电流在0-5V内低于250μA/mm²,具有良好的电学性能,C-F测试表明,低频电容色散大,高频色散小,在室温10kHz时介电常数为12600.介电损耗tanδ为0.04.     

Refractive index spectral dependence, Raman spectra, and transmission spectra of high-purity 28Si, 29Si, 30Si, and natSi single crystals

We performed precise measurement of the refractive index of stable silicon isotopes 28Si, 29Si, and 30Si single crystals with enrichments above 99.9?at.% and a silicon single-crystal natSi of natural isotopic composition with the Fourier-transform interference refractometry method from 1.06 to more than 80?μm with 0.1?cm(-1) resolution and accuracy of 2×10(-5)…1×10(-4). The oxygen and carbon concentrations in all crystals are within 5×10(15)?cm(-3), and the content of the metal impurities is 10(-5)…10(-6)?at.%. The peculiar changes of the refractive index in the phonon absorption region of all silicon single crystals are shown. The coefficients of the generalized Cauchy dispersion function approximating the experimental refractive index values all over the measuring range are given. The transmission and Raman spectra are also studied.     

Computational imaging through chromatic aberration corrected simple lenses

Modern camera lenses become increasingly more complex to optimize the light efficiency of the optical system. Recent research has combined single lens optics with complex post-capture correction methods based on computational photography. This study further improves lens design by correcting chromatic aberrations, after which a simple image deconvolution method is sufficient to produce a high-quality image. We initially estimate the point spread function with a blind image deconvolution method. We add Gaussian regularization as kernel prior to improve the accuracy of kernel estimation. A fast non-blind deconvolution method is then performed to recover a clear image. Experimental results show that the proposed method is at par with state-of-the-art deconvolution approaches. We found a better trade-off between lens design and digital image processing than previous work.     

Three-dimensional optical memory with a photorefractive crystal

We propose a three-dimensional optical-memory device in which refractive dot data are recorded directly into a photorefractive crystal. To record a single bit of datum, one focuses a laser beam with an objective lens onto a specific spot in a crystal, thereby changing its refractive index locally as a result of photorefraction. To record in three dimensions, one keeps the objective lens stationary while the crystal is translated. The beam-spot intensity is modulated with a beam shutter according to the logic state of the data point. The recorded data points are read with a phase-contrast microscope objective lens. We present experimental results of three-dimensional recording and reading with a LiNbO(3) crystal. The distribution of the refractive index formed by a focused beam is also analyzed with the charge-transport model.     

Waveguiding Fresnel Lenses: Modelling and Fabrication

Abstract

This paper examines the methods, problems and results of modelling Fresnel lenses, and the progress towards fabricating experimental devices that has resulted from these evaluations. The computer model used ray-tracing through phase-weighted two-dimensional Fresnel lenses overlaid onto optical waveguide structures. Several types of lenses were considered, digital phase shift, analogue and photolithographically optimized forms being selected for particular study. The evaluation was directed to determining the effect on performance of changes in dimensions, selected focal length and materials. Negative form lens structures were included, as were a range of fabrication methodologies, so that substrate anisotropy and overlayer refractive index were necessarily surveyed. The lens fabrication will ultimately employ three main technologies: dilute-melt proton-exchange in LiNbO₃, GaAlAs and Nb₂O₅ layers as the guiding films, with lens overlays in a range of deposited films with refractive indices up to 3·85. We report preliminary experimental results leading towards such lenses. For a typical lens, aberration and optical power transfer efficiency were measured and examined in relation to the expected coupling efficiency of the lens overlay to the optical waveguide (the ‘overlap’ integral).     

Image inversion and magnification by negative index prisms

A Dove prism and an anamorphic prism pair are investigated in negative index imaging systems. An equilateral triangular prism with refractive index of -1 operates as a negative index Dove prism that inverts as well as images the incident field. A negative index anamorphic prism pair acts as a negative index imaging system with magnification. The relationship between achievable magnification and aberrations is discussed. Both prism systems can be implemented by using negative index photonic crystals, and their performance is demonstrated numerically by the finite-difference time-domain method. These negative index prism structures enhance the functionalities of negative index flat lenses and broaden the applications of negative index materials.     

Micro gradient-index conical lenses: simulation and fabrication methods

In this paper, a micro gradient-index conical lens, which has a larger acceptance angle than a conventional microlens, is presented. Methods on how to simulate these lenses in commercial optical design software CodeV are introduced, and the effects of several index profiles and cone shapes are compared in simulation. Results show that a micro gradient-index conical lens has a four times larger acceptance angle compared with a microlens. Additionally, conical lenses with a Gaussian-index profile show a larger acceptance angle than those with a solid refractive index. Fabricated conical lenses show an acceptance angle of more than 27 degrees for a detection threshold of 50%, which agrees with the simulation result.     

Terahertz lenses made by compression molding of micropowders

We present a simple and versatile approach for fabricating terahertz lenses based on compression molding of micropowder polymer materials in a tabletop hydraulic press. To demonstrate the feasibility of this approach, a biconvex lens shape is calculated using a ray-tracing algorithm and lenses based on two different micropowders are fabricated. As the powder materials have different refractive indices, the resulting lenses share the same geometric shape but differ in their respective focal length. The focusing properties of the lenses are evaluated by transversal and sagittal beam profile measurements in a fiber-coupled terahertz time-domain spectroscopy system, confirming the excellent imaging qualities of the compression molded lenses.     

Determination of the refractive index of single crystal bulk samples and micro-structures

We present comparative studies for the exact determination of the refractive index of single crystals using spectroscopic ellipsometry and photonic-mode-structure investigations by means of spatially resolved photoluminescence spectroscopy, especially in the near band-gap spectral range. By applying such complementary methods we can overcome the uncertainties in the determination of the bulk refractive index introduced by surface properties. The physical effects used are the electromagnetic field reflection used by spectroscopic ellipsometry at large scale planar single crystals and the whispering-gallery-mode formation by total internal reflection in confined micro-structures. We demonstrate the applicability of such studies using the example of uniaxial ZnO bulk samples and micro-wires. By assuming a surface near region with electronic properties different from the bulk material, the method presented here gives the refractive index dispersion for both types of samples in an energy range from 1 to 3.4 eV.