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.     

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.     

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.     

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. 14: GRIN rod of CR-39-trifluoroethyl methacrylate copolymer by a vapor-phase transfer process

The gel rod, partially polymerized CR-39 [diethylene glycol-bis-(allyl carbonate)], is placed in the atmosphere of trifluoroethyl methacrylate (3FMA) vapor, followed by heat-treatment to yield the GRIN rod. Examining the relationship between the preparation conditions and the optical properties of the GRIN rod, the plastic GRIN rods with a quadratic-index distribution up to their periphery and with higher than 0.36 N.A. were fabricated.     

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.     

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.     

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.     

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.     

Single-mode fiber coupling efficiency with graded-index rod lenses

Losses are calculated for the single-mode graded-index- (GRIN-) lens coupler. The main advantage of this coupling system is large separation between fibers with small power loss. The excess loss of the GRIN-lens coupler is due primarily to the misalignments of the GRIN lenses and is most sensitive to angular tilt rather than lateral offset or end separation. The excess loss is calculated from the overlap of two differently sized or misaligned Gaussian beams. Experimental results show that this method is adequate for predicting losses that are due to misalignments of the GRIN lenses.     

Holographic lens recorded on photopolymers: fabrication and study of the image quality

In recent years, holographic optical elements have been introduced in different applications such as high-density data storage, interconnections, spatial and temporal filters and three-dimensional displays. Simultaneously, more sensitive, efficient and durable holographic materials have been developed. Thus it is necessary to analyze the characteristics of these elements in the holographic materials developed. In this paper a method to obtain holographic lenses in a photopolymer is presented. In order to obtain, reconstruct and analyze these lenses, an optical device was designed. Once the holographic lenses are obtained, the device allows us to capture the images provided by these lenses. The imaging quality of these lenses was evaluated by means of the modulation transfer function (MTF) and the contrast. Lenses of different focal lengths were recorded. The holographic lenses obtained had high diffraction efficiency and temporal stability. Moreover, the resolution was greater than that of other lenses with the same diaphragm number.     

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.     

Large radial graded-index polymer

A very large radial graded-index (GRIN) polymer was successfully prepared for the first time, to the best of our knowledge, by two methods: the curved mold method and the diffusion copolymerization method. Both methods gave a radial GRIN polymer with a diameter of 70 mm and a ?n value greater than 0.02. Ray tracing through these radial GRIN polymers was used to predict that such a GRIN polymer could be a promising candidate for thinner ophthalmic lenses with no spherical aberration or multifocusing characteristics.     

Birefringence and internal stress in polystyrene optical fibers

The radial variations of the birefringence of the core of polystyrene optical fibers have been observed and characterized. Variations are much more important on the edge than along the axis, and they introduce a positive radial gradient of the ordinary refractive index that essentially governs light propagation. To explain the existence of such a birefringence, the conditions of the cooling of fibers during their drawing have been simulated. The radial variations of the temperature between the axis and the edge may increase by 10° and, because of the fast variation of the viscosity of polymers in the neighborhood of their glass transition, an important molecular orientation may result in the regions in which this transition first ocurs during the drawing. Comparison is performed between the behavior of polystyrene and poly(methyl methacrylate) core fibers.     

Extensions to a lens design program for the ray-optical design of waveguide lenses and prism couplers

Abstract

The design of integrated optical lens systems requires special software because such systems contain both three-dimensional and twodimensional elements (e.g. bulk prisms and planar waveguide lenses), and the waveguides are often anisotropic. We extended the popular optical computer-aided design program OSLO SIX so that it can evaluate and optimize systems that contain coupling prisms and planar waveguide lenses. We describe our software extensions and through examples we demonstrate their usage and benefits. We confirm our computations by measurement results. Finally, we present a ray-optical interpretation of transverse image line inclination and a method for its elimination.     

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.     

Serial transform optical correlator design principles

Optical correlators such as the 4f and VanderLugt optical systems have been an active area of research for many years; we refer to these types of optical system collectively as serial transform correlators (STCs). Despite being well known, misconceptions regarding the design of STCs are not uncommon. We show, for example, that one correlator configuration reported to suffer from a phase curvature problem in fact works correctly. We present and prove a simple set of rules to follow in the selection of a STC design that does not contain unnecessary constraints and that makes it easier to identify permissible optical systems. As examples, we discuss three representative types of correlator configuration, one of which is discussed in detail to highlight its practical advantages. A novel proof of the design rules is presented that does not depend on details such as what lenses or combination of lenses are used, what their focal lengths are, or what their locations are within the optical system. We also present a conventional Fourier optics proof.     

Conoscopic evaluation of the birefringence of gradient-index lenses: infidelity sources

Gradient-index lenses are samples whose special characteristics must be taken into account to design the optical polariscopes that can be applied in the evaluation of their birefringence. We discuss the main infidelity sources that modify the conoscopic patterns when a traditional polariscopic setup is used.