Research on micro-optical lenses fabrication technology

We present a detail investigation on the development of a series of gradient index (GRIN) optical glass microlens and polymer microlens and microlens arrays in our laboratory in recent years. The special glass material GRIN lenses have been fabricated mainly by using ion-exchange technology, which are applied to construct micro-optic devices and other applications. On one hand, we demonstrated the light propagation and imaging properties of GRIN lenses and the results analyzed. On the other hand, we have explored a drop-on-demand ink-jet printing method to produce microlens array using nano-scale polymer droplets involved with a uniform ultraviolet light and heat solidifying process. The experimental setup for manufacturing polymer microlens array and the performance of refractive microlens elements are also given in this paper.     

梯度折射率球透镜的制备及其光线轨迹测试

自麦克斯韦鱼眼透镜理论模型提出后,长期以来学术界一直以为它只是一种绝对光学仪器,在实践中并没有应用的可能。但通过对麦克斯韦鱼眼微球透镜的理论研究表明,在一定条件下,它具有良好的成像性能和耦合效率。根据菲克定律推导出梯度折射率球透镜的折射率分布函数。并且熔制了含Li+硅酸盐玻璃和采用槽沉法以及Na+/Li+离子交换法制备直径为0.3—3.0mm的梯度折射率球透镜。通过干涉法测得了梯度折射率球透镜的折射率分布曲线,并研究了光线通过梯度折射率球透镜的轨迹。研究结果表明:在590℃,离子扩散系数为3.07×10-6mm2/s;所制备的梯度折射率球透镜的折射率分布是抛物线分布,并且和理论分析相吻合;梯度折射率球透镜的光线轨迹满足椭圆方程。     

层状GRIN板折射率分布的自动测量

采用溶液 凝胶扩散共聚法成功地合成了二元体系的甲基烯酸苄酯 甲基烯酸甲酯 (BZMA MMA)层状梯度折射率板 ,折射率分布是其主要性能指标。给出了一种测量该制品折射率分布的简便实验装置和自动实现方法。该测量方法基于激光干涉的原理 ,由计算机自动跟踪干涉条纹的移动来计算梯度折射率材料的折射率分布。实验表明 ,该方法简单易行 ,具有较高的折射率测量精度 ,为科学评价自研制梯度折射率材料的性能提供了保证     

Fabrication of gradient refractive index ball lenses

The theoretical model of the Maxwell fish eye sphere lens has long been regarded as an absolute optical instrument without practical application since it was proposed. But the study on the theory of Maxwell fish eye micro-spherical lens shows that at certain condition it has fine image formation ability and coupling efficiency. Based on the Fick's diffusion equations, the distribution function of refractive index of gradient refractive index (GRIN) ball lenses is derived. Lithium-containing silicate glass is fabricated and GRIN ball lenses whose diameters are from 0.3 to 3.0 mm are made by ion exchange and the sagging method in sodium nitrate. Radial refractive index profiles of these GRIN ball lens are measured by interferometer. Results show that the distribution of the index of refraction is a parabolic curve and in concordance with the computational consequence and its Δn is 0.0002.     

Aberration improvement of gradient index rod lens

The aberration of gradient index (GRIN) rod lenses induced by deviation from the ideal refractive index distribution is decreased by optimized thermal diffusion. The index distribution coefficients are estimated by a novel method. The lenses' heat treatment process and aberration testing system are described.     

Design,fabrication and evaluation of a photographic objective that uses a radial GRIN lens

Some technical issues in the design, fabrication and evaluation process of the photographic objective lens are treated. In the design process, a unique design technique called the quasi-equivalent glass method is applied. Also, a convenient method is described for the determination of tolerances of the refractive index profile. Performance evaluation showed that the GRIN material made by sol-gel method is usable for photographic lenses.     

Fabrication of gradient refractive index ball lenses using the method of combination of ion exchanging and sagging

Based on the Fick’s diffusion equations, the distribution function of refractive index of a gradient refractive index ball lens (GRIN ball lens/GBL) is derived. Lithium containing silicate glass is fabricated and GRIN ball lenses (GBLs) which diameters are from 0.3 mm to 3.0 mm are made by the method of combination of Ion exchanging and sagging in sodium nitrate. Refractive index profiles of these GBLs are measured by interferometer, and the performances such as effective focal length (EFL), back focal length (BFL) and numerical aperture (NA) between GBLs and homogeneous ball lenses (HBLs) are compared. Results show that the distribution of the index of refraction is parabolic curve and its Δn is about 0.0002, the performances of the former are super to the latter.     

Full-field measurement of surface reflectivity using a microscopy for refractive index profiling of GRIN lenses

This paper outlines an improved technique for profiling the refractive index of Graded-index (GRIN) lenses based on the measurements obtained from a reflectivity image. Reflective cross-sectional image of the GRIN lens were compared with a reflectance reference target under illumination at small incidence angles to obtain the full-field refractive index distribution of the GRIN lens quickly and easily.     

离子交换引起的GRIN棒透镜大折射率差值分析

利用两次离子交换法制作了GRIN棒透镜样品，并采用雅明干涉法对样品的折射率分布进行了测试.结果表明，样品获得了较大的折射率差值.讨论了两次离子交换增大折射率差的原因.研究结果在制作生产梯度折射率材料方面有一定的参考价值和指导意义.     

Multistep ion exchange processes of gradient refractive index rod lens

A mathematical model for research on the refractive index profile (RIP) of multistep ion exchange processes (IEPs) of gradient refractive index rod lenses (GRINs) is established by the different initial condition and boundary condition, based on the Fickian diffusion equation. GRIN rod lenses have been fabricated using the three-step IEPs. Research results indicate that the experimental deviations of refractive index (DRI) are in good agreement with the theoretical data. The DRI of three-step IEPs is superior to the one- and two-step IEPs and smaller than 10(-5).     

低色差GRIN棒透镜制备工艺的研究

熔制了含Li+硅酸盐玻璃,玻璃的棒料在NaNO3熔盐中进行离子交换后得到了梯度折射率(GRIN)棒。采用干涉法测得了GRIN棒的折射率分布曲线。实验结果表明:通过所述的工艺,可以获得直径达5mm的GRIN棒,其折射率分布曲线与双曲正割曲线接近。分析表明GRIN棒的轴向色差评价函数值约为0 6～0 7%。     

Pupil-segmentation-based adaptive optical correction of a high-numerical-aperture gradient refractive index lens for two-photon fluorescence endoscopy

The intrinsic aberrations of high-NA gradient refractive index (GRIN) lenses limit their image quality as well as field of view. Here we used a pupil-segmentation-based adaptive optical approach to correct the inherent aberrations in a two-photon fluorescence endoscope utilizing a 0.8 NA GRIN lens. By correcting the field-dependent aberrations, we recovered diffraction-limited performance across a large imaging field. The consequent improvements in imaging signal and resolution allowed us to detect fine structures that were otherwise invisible inside mouse brain slices.     

Reliability in reconstruction of the axisymmetric refractive index profiles from transverse interferograms. Accurate versus approximate methods: A comparative study

A mathematical formalism related to the approximate as well as the accurate interferometric data reduction schemes is briefly outlined and subsequently applied in the reconstruction of the assumed (Luneburg) axisymmetric refractive index distribution. The presented comparative analysis confirms the generally held opinion that the approximate methods (“straight-line” and Kokubun-Iga approaches) may provide quite reasonable results in the examination of refractively inhomogeneous disturbances characterized by weak gradient and moderate index variation. On the other hand, the accurate scheme for transverse interferometric data interpretation and reduction, based on the close-form correlation between the fringe shift and the deflection function, [1] remains the only method for reliable reconstruction of strongly refracting index profiles, independently of magnitude of refraction and ambiguity of the fringes. This fact is of considerable importance for transverse interferometry of fibers (preform rods) and/or GRIN-rod lenses characterized by high numerical apertures.     

方形自聚焦透镜折射率分析

利用MATLAB 偏微分方程工具箱(PDE)实现方形玻璃纤维边界条件下离子扩散的有限元解法,给出一般步骤,对离子交换制备方形自聚焦透镜过程进行计算机模拟.运用分离变量法求解方形玻璃纤维中Tl+离子浓度定解方程,由离子浓度与折射率的线性关系,得到了方形自聚焦透镜折射率分布的数学表达式,计算出折射率分布图以及理论值.与实验值校验表明,相对误差小于0.33%.     

层状梯度折射率板浑浊层机理研究

采用溶液 凝胶扩散共聚法可以成功地合成二元体系的甲基丙烯酸苄酯 甲基丙烯酸甲酯层状梯度折射率板。但采用此法合成的板,在其中部会产生浑浊层,减小了梯度折射率变化范围及梯度折射率指数差Δｎ。通过对层状梯度折射率板浑浊层进行光谱分析、差热分析及其共聚实验,得出了浑浊层产生的两种可能机理。     

Preparations on Several GRIN Lenses

Gradient index materials have been developed from glass melting process to GRIN lenses. Two kinds of GRIN lenses have been fabricated by ion-exchange and glass fusion/diffusion. The main applications to GRIN lenses are demonstrated.     

Thermal emission characteristics of a graded index semitransparent medium

This paper develops a numerical model for thermal radiative transfer in a two-dimensional semitransparent graded index medium. A piecewise continuous refractive index model, the linear refractive index bar model, is presented. This model is established based on three hypotheses, and has a higher precision than the bar model used previously. This paper also studies the thermal emission from a two-dimensional graded index medium, which is scattering or non-scattering. We find that it can present an obvious pattern of directional distribution at times. The refractive index distribution and absorption coefficient are the two main influential factors. This finding differs from the common belief that thermal sources, such as the incandescent filament of a light bulb, emit a quasi-isotropic light. The finding also suggests that there maybe other important applications of artificial GRIN materials.     

Measuring optical properties of an eye lens using magnetic resonance imaging

We compare the focal lengths of porcine lenses measured optically and by using a novel MRI technique. The geometric properties of the lenses were also measured and compared. The MRI technique exploits the dependence of both the lens refractive index and relaxation rates on the local protein concentration. By measuring the refractive index and corresponding values of R2 (=1/T2) for samples of lens homogenates with different protein concentrations, the dependence of refractive index on R2 was determined empirically. R2 maps, constructed from monoexponential fits to multiecho images of a slice through the lens containing the optical axis, were converted to refractive index maps using this relationship. A simulated ray trace through the refractive index map provided an estimate of lens focal length that was compared to a direct optical measurement of focal length using a laser ray-tracing method. It was found that the mean focal lengths estimated from the two techniques agreed within experimental uncertainty. The refractive index profile along the optical axis was found to be well described by a simple function of the form n=n0 + n1 x ra where r is the (normalized) lens radius.     

Multiple-beam interference fringes applied to investigate the index profile of the optical fiber dip

A numerical-based phase shift method is presented to study optical fibers having a dip in the refractive index profile at the center of the core. Mathematical expressions for the shape of multiple-beam Fizeau fringes crossing a graded-index optical fiber (GRIN) comprising a central graded-index dip or GRIN fiber with a constant refractive index dip, immersed in a silvered liquid wedge, are derived. The index profile parameters of the central dip are determined by comparing the theoretical fringe shape across the fiber cross-section and the experimental fringe shape obtained from micro-interferograms of the wedge interferometer.