Determination of the refractive index of a lens using the Murty shearing interferometer

An innovative nondestructive technique for measuring the refractive index of a simple lens is described. The proposed method is superior to existing ones because the focusing error and the spherical aberrations are reduced. Apart from this, the strength parameters (i.e., r1 and r2) of a lens are not required at all since the derived lens-index formula is independent of the lens's physical parameters. The shearing interferometric technique is a sensitive aid for detecting the focal plane of the test lens. A modified criterion for determining the focal length has been used. In this case two miscible liquids or compounds are not necessary. The well-known liquid immersion method is the particular case of this technique. The Murty shearing interferometer has been used as an optical device to observe the defocusing defect in the form of fringes. The amount of defocusing is easily calculated. An equation for this error has been theoretically deduced and experimentally verified. The technique described is quick to perform and easy in handling. The various effects due to the lens's aperture and aberrations, thickness of the glass cell, liquid column, etc. are also discussed. For N liquids, there are N(N - 1)/2 ways of calculating the lens's index. Owing to its nature this is termed the nondestructive nonmiscible-liquid immersion technique for index measurement of a lens.     

Measurement of thermally induced changes in the refractive index of glass caused by laser processing

The effects of CO2 laser heating of pure fused silica are investigated. Studies show that the laser heating process causes a small volume of glass to be left in an altered microstructural state. To measure the refractive index of this altered region, a process was developed to create a thin film of altered glass. Samples were measured with a prism coupler, and a theoretical model was developed to predict the intensity values collected during the measurement. A least-squares routine was used to determine the refractive index that results in the best fit between the experimental and predicted intensity data. The refractive index in the altered glass was found to increase by approximately 0.07%.     

Measurement of group refractive index wavelength dependence using a low-coherence tandem interferometer

A technique for the measurement of the group refractive index wavelength dependence of optical materials using a low-coherence tandem interferometer and a spectrometer is proposed. Four channeled spectra resulting from interferences of light beams from different pairs of optical paths are used for the calculation of optical path differences. The group refractive index wavelength dependence is calculated from these optical path differences generated from the sample under measurement. No a priori information of the geometric thickness of a sample is required. The wavelength dependence of the group refractive index of the samples BK7 parallel plate of 5.200 and 10.025 mm from 675 to 850 nm is experimentally measured with an accuracy of the order of 10(-5) and a repeatability of the order of 10(-9).     

Testing of refractive silicon microlenses by use of a lateral shearing interferometer in transmission

Wave aberrations of refractive photoresist microlenses and silicon microlenses were measured with a lateral shearing interferometer. Because of the silicon elements, a near-infrared working wavelength (lambda = 1.32 mum) was used. The wave front was evaluated by a phase step technique with four steps. Integration of the phase distributions was performed with a computationally efficient Fourier transformation algorithm. The influence of the detector vidicon nonlinearity on the measured wave front was calculated. The defocusing behavior of the interferometer was investigated by fitting the measured wave fronts with the help of Zernike circle polynomials. It is shown that the reproducibility can be kept below lambda/100 rms. Examples for the measured wave fronts of plano-convex silicon microlenses are discussed in detail.     

Measurement of the nonlinear refractive index of fibers with a rotating nonlinear Sagnac interferometer

We developed a method to measure the nonlinear refractive-index coefficient of fibers using a nonlinear Sagnac interferometer. To enhance the measurement accuracy, we employed a phase-sensitive detection technique using a rotational sensitive property of the Sagnac interferometer. The measured values were reproducible to within 10 % accuracy.     

Extrinsic fiber-optic Fabry-Perot interferometer sensor for refractive index measurement of optical glass

A simple fiber-optic sensor based on Fabry-Perot interference for refractive index measurement of optical glass is investigated both theoretically and experimentally. A broadband light source is coupled into an extrinsic fiber Fabry-Perot cavity formed by the surfaces of a sensing fiber end and the measured sample. The interference signals from the cavity are reflected back into the same fiber. The refractive index of the sample can be obtained by measuring the contrast of the interference fringes. The experimental data meet with the theoretical values very well. The proposed technique is a new method for glass refractive index measurement with a simple, solid, and compact structure.     

Simultaneous determination of refractive index and thickness of moderately thick plane-parallel transparent glass plates using cyclic path optical configuration setup and a lateral shearing interferometer

We present a simple technique for simultaneous determination of refractive index and thickness of moderately thick plane-parallel transparent glass plates (GPs) using a cyclic path optical configuration (CPOC) setup and a wedge shear plate as lateral shearing interferometer. The CPOC setup is used to simultaneously focus the counterpropagating converging beams at a common point at its hypotenuse arm. The apparent thickness and real thickness of the test GP are determined by observing three retrocollimation positions of the GP surfaces with respect to the common focus point. The RI is obtained by dividing the real thickness with apparent thickness of the GP. Presented in this paper are the results obtained for a test GP with a thickness of 14.983 mm and a RI of 1.515.     

Measurement of nonlinear refractive index coefficient using emission spectrum of filament induced by gigawatt-femtosecond pulse in BK7 glass

A beam of 33 fs laser pulse with peak power of 15-40 GW was employed to explore a convenient method to determine the nonlinear refractive index coefficient of an optical glass. It is rare to investigate nonlinearities of optical glass with such an extreme ultrashort and powerful laser pulse. According to our method, only a single beam and a few experimental apparatuses are necessary to measure the nonlinear refractive index coefficient. The results from our method are in reasonable agreement with the others, which demonstrates that this new method works well, and the nonlinear refractive index coefficient is independent of measuring technology. Meanwhile, according to our results and those obtained by others in different laser power ranges, it seems that the nonlinear refractive index coefficient has a weak dependence on the laser peak power.     

环路剪切干涉术测量附面层密度场

在附面层测量中,需对微小尺度的高速气流变化场进行瞬态测量。数字化的干涉测量方法能定量地解算出流场的密度场,是一种重要的应用。介绍了一种共路干涉的环路剪切干涉方法,对震动不敏感,无需参考面,适合附面层测量使用。采用基于空间位相调制的快速算法,配以脉冲激光器和同步控制系统,可实时地对扰流密度场进行定量测量。该系统采集分辨率200 pixels×200 pixels,采集频率可达每秒1000帧以上。系统的波前重构方法经过计算机仿真,检测结果优于1/20λ。在0.6 m风洞对圆柱体尾部附面层进行测量试验,结果表明,在一定风速下,该系统能抑制振动干扰,显著地区分出圆柱体尾部扰流信号和振动噪声,具有良好的应用前景。     

High-efficiency bragg gratings in photothermorefractive glass

Photosensitive silicate glasses doped with silver, cerium, fluorine, and bromine were fabricated at the Center for Research and Education in Optics and Lasers. Bragg diffractive gratings were recorded in the volume of these glasses with a photothermorefractive process (exposure to UV radiation of a He-Cd laser at 325 nm is followed by thermal development at 520 degrees C). Absolute diffraction efficiency of as much as 93% was observed for 1-mm-thick gratings with spatial frequencies up to 2500 mm(-1). No decreasing of diffraction efficiency was detected at low spatial frequencies. Original glasses were transparent (absorption coefficient less than 1 cm(-1)) from 350 to 4100 nm. Induced losses in exposed and developed glass decreased from 0.3 to 0.03 cm(-1) between 400 and 700 nm, respectively, and did not exceed 0.01-0.02 cm(-1) in the IR region from 700 to 2500 nm. Additional losses caused by parasitic structures recorded in the photosensitive medium were studied.     

Measurement of the surface profile of an axicon lens with a polarization phase-shifting shearing interferometer

We present a Twyman-Green interferometer (TGI)-based polarization phase-shifting shearing interferometric technique for testing the conical surface of an axicon (AX) lens. In this technique, the annular beam generated due to the passing of an expanded collimated laser beam traveling along the axis of revolution of the transparent glass AX element is split up into its reflected and transmitted components, having the plane of polarization in the orthogonal planes, by the polarization beam splitter (PBS) cube of the TGI-based optical setup. The split-up components are made to travel unequal paths along the two arms of the TGI and are recombined by the PBS. Because of the difference in path lengths traveled by the annular conical beams, a linear shear is introduced along the radial direction between the interfering components. Thus, the resulting interference pattern gives a map of the optical path difference (OPD) between two successive close points along a radial direction on the conical surface of the AX lens. The OPD map along radial directions, and hence the slopes/profiles of the conical surface, are obtained by applying polarization phase-shifting interferometry. Results obtained for an AX lens are presented.     

Study of the refractive index of microscopic glass beads by light-refraction analysis

The refractive index of submillimeter glass beads has been measured by means of a novel, to our knowledge, procedure with reference liquids that does not require close index matching and therefore avoids the use of toxic compounds for high-index glasses (i.e., n >/= 1.8). The method is based on the analysis of the light refracted by a monolayer of beads in comparison with ray-tracing simulations. For the three different types of glass beads investigated a satisfactory fit is achieved by the assumption of a radial variation of the refractive index inside the beads. This is ascribed to the tensile and compressive stresses originating inside the beads during rapid solidification of the glass.     

Method of measuring the refractive index of glass plates

Translated from Izmeritel'naya Tekhnika, No. 8, pp. 39–41, August, 1990.     

Construction of glass waveguide refractive index profiles by the effective-index finite-difference method

A numerical method is applied to construct the refractive index profiles of optical waveguides from the measured effective indices (EI). The method is based on choosing a proper analytical function for the refractive index profile and searching its unknown parameters using the simplex search algorithm. Simultaneously, the finite-difference method (FDM) is used to solve the semi-vectorial Helmholtz equation for the guided modes effective indices. The method is applied successfully to two particular Ag⁺---Na⁺ ion-exchanged glass slab waveguides. The results are as accurate as those obtained from from commonly used IWKB-based method. The EI-FDM in principle can be applied to both slab and channel waveguides and does not require that the index profiles are monotonically decreasing, like most of IWKB-based methods. The relation between the induced refractive index and silver concentration profile, measured by SIMS, is found to be almost linear.     

Origin of crystallization-induced refractive index changes in photo-thermo-refractive glass

Photo-thermo-refractive (PTR) glass is a multi-component silicate that undergoes localized refractive index decrease after UV-exposure and thermal treatment for partial crystallization. Based on this refractive index change, high efficiency volume Bragg gratings have been developed in PTR glass and have been successfully used for laser beam control. However, despite the fact that this type of glass has been widely studied and used over the last 20 years, the origin of the refractive index change upon crystallization is poorly understood. In this paper, we introduce three possible mechanisms (the precipitation of nano-sized NaF crystals and the associated local chemical changes of the glass matrix, the volumetric changes due to relaxation, and the local residual stresses) for the refractive index decrement in PTR glass and estimate the partial refractive index change due to each mechanism. Refractive index measurements are compared with high temperature XRD experiments and a general approach for the simulation of the refractive index change in PTR glass is proposed. We show that among the studied variables the residual stresses surrounding the crystals are the main responsible for the local refractive index decrement in this glass.     

Low-coherence interferometer system for the simultaneous measurement of refractive index and thickness

We have developed a low-coherence interferometer system used for the simultaneous measurement of refractive index n and thickness t of transparent plates. Both the phase index n(p) and group index n(g) can be determined automatically in a wide thickness range of from 10 microm to a few millimeters. Two unique techniques are presented to measure n(p), n(g), and t simultaneously. One allows us to determine n(p), n(g), and t accurately by using a special sample holder, in which the measurement accuracy is 0.3% for the thickness t above 0.1 mm. In the other technique the chromatic dispersion delta n of index is approximately expressed as a function of (n(p) - 1) on the basis of measured values of n(p) and n(g) for a variety of materials, and then the simultaneous measurement is performed with a normal sample holder. In addition, a measurement accuracy of less than 1% is achieved even when the sample is as thin as 20 microm. The measurement time is also 3 min or more.