Birefringence in gradient-index rod lenses: a direct measurement method and interferometric polarization effects

Gradient-index (GRIN) media can contain stress birefringence resulting from the variation in material composition. Anisotropy in a GRIN rod lens affects ray propagation and can degrade image quality. A technique, believed to be new, for measuring birefringence in GRIN rod lenses has been developed. The change in optical path difference (OPD) for orthogonal polarizations is measured directly. With this method, effects on OPD from standard imaging aberrations are excluded. Birefringence measurements for various GRIN rod samples are presented. The data are compared with results obtained previously by use of a Twyman-Green measurement method. Also, the polarization effects on tilt fringes observed with the direct measurement method and the Twyman-Green method are presented and modeled theoretically. Tilt fringes for large birefringence test cases are also modeled.     

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.     

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.     

An optical fiber sensor for remote pH sensing and imaging

A fiber-optical probe for pH sensing and real-time imaging is successfully fabricated by connecting a polymer imaging fiber and a gradient index (GRIN) lens rod which was modified with a sensing film. By employing an improved metallographic microscope, an optical system is designed to cooperate with the probe. This novel technique has high-quality imaging capabilities for observing remote samples while measuring pH. The linear range of the probe is pH 1.2-3.5. This technique overcomes the difficulty that high-quality images cannot be obtained when directly using conventional imaging bundles for pH sensing and imaging. As preliminary applications, the corrosion behavior of an iron screw and the reaction process of rust were investigated in buffer solutions of pH 2.0 and 2.9, respectively. The experiment demonstrated that the pH values of the analytes' surface were higher than that of buffer solutions due to the chemical reaction. It provides great potential for applications in optical multifunctional detection, especially in chemical sensing and biosensing.     

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.     

Characterization of gradient-index lens-fiber spacing toward applications in two-photon fluorescence endoscopy

We report on the experimental investigation into the characterization of two-photon fluorescence microscopy based on the separation distance of a single-mode optical fiber coupler and a gradient-index (GRIN) rod lens. The collected two-photon fluorescence signal exhibits a maximum intensity at a defined separation distance (gap length) where the increasing effective excitation numerical aperture is balanced by the decreasing confocal emission collection. A maximum signal is found at gap lengths of approximately 2, 1.25, and 1.75 mm for GRIN lenses with pitches of 0.23, 0.25, and 0.29 wavelength at 830 nm. The maximum two-photon fluorescence signal collected corresponds to a threefold reduction of axial resolution (38.5 microm at 1.25 mm), compared with the maximum resolution (11.6 microm at 5.5 mm), as shown by the three-dimensional imaging of 10 microm beads. These results demonstrate an intrinsic trade-off between signal collection and axial resolution.     

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.     

Studies on the light-focusing plastic rod. 15: GRIN rod prepared by photocopolymerization of a ternary monomer system

Plastic GRIN rod and fiber lenses have been fabricated by photocopolymerization of a ternary monomer system, methyl methacrylate-N-vinyl carbazole-vinyl acetate. We now propose the general mechanism for forming radial GRIN in the ternary monomer system using computer simulation. The relationship between the preparation condition and the optical characteristics was clarified. The region having quadratic-index distribution and the numerical aperture were remarkably improved by the ternary monomer system.     

Use of scanned detection in optical position encoders

The use of scanning detection in optical noncontact position sensing is proposed, and a prototype is implemented, using optical scanning of pseudorandom binary sequences printed in bar-code format. Light from a vibrating fiber tip is imaged onto the printed code using a GRIN (graded index) lens, and the reflected light detected via the same lens, resulting in a single scanner module. Improved flexibility and signal processing possibilities are obtained compared to conventional diode array optical code readers. Performance limitations of scanning position encoders are analyzed and discussed. Suggestions for implementation using microoptoelectromechanical systems are presented.     

Study of process parameters on optical qualities for injection-molded plastic lenses

Numerical simulations for mold-flow analysis and experimental measurements of injection-molded plastic lenses have been conducted for investigation of optical qualities, residual birefringence, and form accuracy resulting from various pertinent process conditions. First, residual birefringence distributions on the lens have been predicted and verified experimentally. Furthermore, full-scale factorial design of experiments was conducted to comprehend the influences of qualities, such as shear stresses, form accuracy, and volumetric deviation, on the measured primary or Seidel aberrations. In conclusion, residual birefringence induced by stresses represented by photoelasticity measurements agrees well with the numerical predictions and the experimental results indicate that the residual birefringence is mainly generated during the mold-filling stage. In addition, spherical aberration of the injection-molded plastic lenses is more sensitive to the pertinent qualities as compared to coma and astigmatism.     

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。     

The effect of pressure on GRIN lenses

The changes of the optical power of Gradient Index (GRIN) lenses occurring in hydrostatic pressures of the range of 0-2 GPa are investigated. The measurements of the position of the waist of the semiconductor laser beam revealed the increase of the optical power of the lenses with increasing pressure. The use of the special plano-concave lenses insensitive to the changes of the refractive index of the pressure medium allowed to attribute the changes to the increasing index gradient in GRIN material. The effect has been explained within the frame of Mueller’s theory of photoelasticity. The findings have been then confirmed in experiments with the plano-planar and plano-convex lenses of the same materials.     

Probability of Failure of Sylgard-Mounted Optical Lenses in Head-Up Display During Thermal Cycle Testing

Lenses made from optical glass do not have a single characteristic strength. The strength of any optical glass is highly dependent on the area under stress and its surface finish. The nominal design strength of manufactured glass is typically in the 6.9–70 MPa range. This study presents an analysis of measured strain data and an approach to quantify the failure probability of optical lenses that are used in head-up display systems for aircraft applications when these lenses are subjected to accelerated thermal cycling. The thermal cycling produces thermal stress within the elastomerically mounted optical lens of the head-up display. We used a combination of experimental methods and finite element modeling to determine the thermal strain in the optical lens. The thermal strain values that were obtained using these methods were validated and were found to be in a cumulative distribution. This cumulative strain provides a quantitative estimate of the effects of thermal stress in the optical lens. We then determined the failure probability using Weibull parameters.     

Two practical methods for improving the long-term stability of thephotoelastic optical fiber pressure sensor

The differential approach of photoelastic optical fiber pressure sensor (POFPS) has been published. However, the experimental aspects of this sensor were little involved in it. Two practical methods are described to investigate this subject. First, the discordance of expansion coefficient, between the cladding steel and the graded-index (GRIN) lens, is considered by using indium steel cladding instead of the conventional stainless steel cladding. Then an experimental setup is designed to make the infrared light intensity distribution observable by using a CCD camera. Practical tests prove that these two practical methods and the design of the differential approach have improved the long-term stability of POFPS     

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.     

Spectral properties of multiorder diffractive lenses

Diffractive lenses have been traditionally designed with the first diffracted order. The spectral characteristics of diffractive lenses operating in higher diffracted orders differ significantly from the first-order case. Multiorder diffractive lenses offer a new degree of freedom in the design of broadband and multispectral optical systems that include diffractive optical elements. It is shown that blazing the surface-relief diffractive lens for higher diffraction orders enables the design of achromatic and apochromatic singlets. The wavelength-dependent optical transfer function and the associated Strehl ratio are derived for multiorder diffractive lenses. Experiments that illustrate lens performance in two spectral bands are described, and the results show excellent agreement with the theoretical predictions.     

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.     

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.     

Analysis and fabrication of minifeature lamp lens by excimer laser micromachining

A variety of shapes of lamp lenses at the feature millimeter scale have been extensively used in lamp design. To further improve the light efficiency and to reduce the overall dimension of lamps, the lamp lens at the micrometer scale is fabricated by excimer laser cross scanning on a polycarbonate sheet. To verify the proposed method, the influence of an optical system with various shapes and sizes of lamp lenses on the light efficiency is explored in advance by ASAP optical software. The lens with a miniature feature can produce a smaller divergence angle than that with a large-size lens feature. The experiment is carried out at varying laser operating parameters, mask shape, and dimensions. The simulation shows that the desired lamp lens profile can be effectively produced by excimer laser micromachining.