A refractive index interferometry method based on the X-ray crystallography

The absorption contrast image is very low for those weakly absorbing materials or weak phase object, such as the soft biological tissues, however, the phase item value of refractive index is a thousand larger than the absorption item, therefore the refractive index interferometry method is expected to be a new imaging tool for them. An interferometry method based on the X-ray crystallography is explored to the measurement of refractive index in this paper. The theoretical foundation, the optical design, the crystal transistor performance are the key parts to this interferometry method based on the X-ray crystallography. We give out a special refractive index detection scheme, using a laboratory hard X-ray source, and four single Si crystals. With this instrument, refractive index profile of those weak phase object can be unfolded accurately using this method. This refractive index interferometry method based on the X-ray crystallography will provide a new research tool for those special material properties or biological tissues study.     

Real-time measurement of glucose concentration and average refractive index using a laser interferometer

This study presents a non-destructive, highly precise optical metrology system for measuring the average refractive index of a liquid solution such that its glucose concentration can be derived. The metrology system is employed to measure the average refractive indices of samples with known glucose concentrations ranging from 0 to 200 g/l. By applying a regressional analysis technique to the experimental results, an analytical expression is derived to describe the relationship between the refractive index and the glucose concentration. An excellent agreement is observed between the experimentally determined values of the glucose concentration and the analytically derived results. For an assumed laser interferometer resolution of 1 nm, the measurement resolution of the proposed metrology system is found to be at least F=0.05 g/l, which is significantly better than that of F=2 g/l obtained using the polarimetric glucose sensor presented by Lo and Yu [A polarimetric glucose sensor using a liquid-crystal polarization modulator driven by a sinusoidal signal. Opt Commun, 2006; 259: 40–8].     

用迈克耳孙干涉仪测量厚透明材料折射率

使用迈克耳孙干涉仪测量了厚透明材料的折射率.在光路中一半视场平行放入待测材料,对应的条纹出现压缩,根据条纹隐入和涨出计算待测材料的折射率,并进行了相关实验和误差分析.应用Zemax软件对实验进行了模拟,验证了其可行性.     

Polynomial approximation method for tomographic reconstruction of three-dimensional refractive index fields with limited data

We propose a polynomial approximation method (PAM) for reconstruction of three-dimensional refractive index fields by interferometric tomography using limited data. Based on the assumption that the fields to be reconstructed are usually smooth and can be decomposed into a finite order of (orthogonal) polynomials, a set of linear equations can be constructed using both the measured projection data and the Radon transform of the basis functions. By solving these equations, the least-squares solutions of expansion coefficients can be obtained and then substituted back to yield the desired fields. Numerical results have demonstrated that the proposed method is fast, robust to noise and can achieve satisfactory results for refractive index fields with limited projection views and large opaque objects.     

Automatic determination of refractive index profile, sectional area, and shape of fibers having regular and/or irregular transverse sections

A new method based on a mathematical model and a computer program is suggested to determine the refractive index profile of fibers having regular and/or irregular transverse sectional shape. Microinterferogram of both multiple-beam Fizeau fringes and the duplicated image from two-beam interference microscope are used for the determination of refractive index profile, cross-sectional area and shape of three different types of fibers. To confirm the suggested model, the calculated area and the shape of the transverse section of these fibers are compared with those results obtained using conventional methods.     

Zygo interferometer for measuring refractive index of liquids and its application for heavy water analysis

The Zygo interferometer for measuring refractive index of liquids such as heavy water is presented. The accuracy of measurement in the refractive index of liquids is found to be ±0.0002 in the Zygo interferometer. An application of Zygo interferometer for heavy water analysis is also presented. The interferometer is found to be useful for determining the percentage purity of heavy water with an accuracy of ±5% in the purity range of 0–100%.     

Modified Michelson interferometer for probing refractive index of birefringent crystal CSBN50

Based on the modified Michelson interferometer and phase analysis method, a high-accuracy method for probing the refractive index (RI) of transparent medium is proposed. The validated test was performed on a birefringent crystal CSBN50 with the estimated accuracy being up to 10⁻⁴. The ordinary and extraordinary refractive indices of CSBN50 at 632.8 nm are determined as n₀=2.32853±0.00016 and n_e=2.27664±0.00016, respectively.     

利用线阵CCD测定液体折射率

采用几何光学与波动光学相结合的方法,利用CCD图像测量技术实现了透明液体折射率的自动化测量.     

Automatic determination of refractive index profile of fibers having regular and/or irregular transverse sections considering the refraction of light rays by the fiber

A new model, using non-destructive two- and/or multiple-beam interferometric techniques, is suggested for measuring the refractive index profile of fibers having regular and/or irregular cross-sectional shape taking into consideration the refraction of the light rays by the fiber. The proposed model is applied for three different fibers having different cross-sectional shapes and different refractive index profiles. These fibers are PPT, homogeneous fiber, with circular cross-section, graded index optical fiber of circular cross-sectional shape and Dralon fiber of irregular cross-section. To validate the proposed model it is used, firstly, to calculate the index profile for a standard PPT fiber. Secondly, the calculated results for the irregular Dralon fiber and GR-IN optical fiber are compared with that calculated using other conventional method. From this comparison, we recommend that the refraction must be taken into account to obtain accurate results especially for birefringent fibers and graded index optical fibers.     

迈克耳孙干涉仪测量介质板折射率的问题研究

使用迈克耳孙干涉仪测量较厚介质板的折射率时,发现迈克耳孙干涉仪中放入待测介质板后,反射镜M1的调节方向异常.针对这一实验现象,从理论上进行分析,解释了实验中出现的异常现象,并推导出反射镜M1在两次观测中移动的距离与介质板折射率的关系式.实验结果进一步证明理论与公式的正确性.     

The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method

In this article, through the linear fit of objective distance and reciprocal of magnification in different imaging locations, we use imaging method to measure the central refractive index n(0) and focusing constant α of radial gradient index (GRIN) lens and obtain 10⁻³ measurement accuracy of n(0). At the same time, under distortion, the fourth-order refractive index coefficient and aberration of GRIN lens are derived.     

Zygo interferometer for measuring refractive index of photorefractive bismuth silicon oxide (Bi12SiO20) crystal

An application of the Zygo system for measuring the refractive index of optical materials such as bismuth silicon oxide (BSO) having a higher value of the refractive index than that of glass is presented. The setting accuracy is found to be of the order of 1 μm in the Zygo phase measuring interferometer. The mean value of refractive index of BSO crystal measured by the interferometer for several samples of thickness in the range of 3–9 mm is 2.542 at a wavelength of 632.8 nm. The accuracy of measurement is ±0.002. It is possible to achieve an accuracy of ±0.0003 for a sample of thickness of 30 mm in the measurement of refractive index due to high setting accuracy of the Zygo system.     

A theorem on refractive index as a function of wavelength

A theorem upon refractive index as a function of wavelength is derived starting from the Taylor expansion around the origin of this function. Our result involves the above index, the group index, and the coefficient of material dispersion all extrapolated to zero wavelength.     

The use of defocussed position of a Ronchi grating for evaluating the refractive index of lens

This report describes a Ronchi-grating shearing interferometric collimation method for determining the refractive index of a lens. A new formula has been deduced for the refractive index of the lens, which is independent of lens parameters. This newly developed device has two lenses. One of them collimates the light from a point source while the other acts as a decollimator. The point source acting as a test target is situated in the front focal plane of the collimator. The test lens is placed inside a glass cell in the back focal plane of the collimator. The Ronchi grating is exactly placed in the back focal plane of the decollimator, and a fringe-free space is observed in the common region. When the test lens is immersed in a liquid cell, it disturbs the focal point and hence interference fringes are observed. The combined system consisting of the test lens and the decollimator is moved to bring the focal point on the Ronchi grating. Thus, the difference between the two settings gives the amount of defocusing.     

改进的油浸法测量聚硅氧烷微球的折射率

在传统的油浸法基础上,引入透光率指标来判断粉体与浸液折射率的差异,测量了聚硅氧烷微球粉体的折射率.该方法将传统油浸法的适用范围扩展至超细粉体甚至纳米粉体的折射率测量.     

Measurement of small differences in refractive indices of solutions with interferometric optical method

Based on the principles of both surface plasmon resonance (SPR) and heterodyne interferometry, an optical method for measuring small differences in refractive indices of solutions was proposed. On a specially designed probe, two light beams are incident on both reference and test solutions. The phase differences between the p- and s-polarizations of each reflected light under SPR condition are measured simultaneously with heterodyne interferometric technique. The phase values are substituted into special equations derived from Fresnel's equations. Finally, the difference between the refractive indices of these two solutions can be estimated. The feasibility of this method was demonstrated and the measurement sensitivity of refractive index can reach a value of at least 8.57×10⁻⁷. This method should bear the merits of a simple structure, easy operation, high sensitivity and rapid measurement.     

Study of in fiber Mach–Zehnder interferometer based on two spaced 3-dB long period gratings surrounded by a refractive index higher than that of silica

The paper deals with the response of a Mach–Zehnder interferometer composed by two 3-dB long period gratings (LPG) with different external refractive indices higher than that of silica (leaky configuration). A rough analysis of the cladding propagation arising in leaky configuration has allowed us to establish a model that is sufficient to describe the interferometer couplings evolution at the resonance. In particular, we have shown that the interferometer sensitivity depends strongly on its phase-shift Δ and is optimized for Δ equal to π [2π] or 3π/4 [2π]. An experimental study was undertaken and allowed us to validate our model. Finally, a comparison with a single LPG demonstrated an increased sensitivity to the external index, suggesting the conception of a new fiber sensor operating with external refractive indices higher than that of silica.     

Fabrication of an integrated optical Mach-Zehnder interferometer based on refractive index modification of polymethylmethacrylate by krypton fluoride excimer laser radiation

It is known that deep ultraviolet (UV) radiation induces a refractive index increase in the surface layer of polymethylmethacrylate (PMMA) samples. This effect can be used for the fabrication of integrated optical waveguides. PMMA is of considerable interest for bio and chemical sensing applications because it is biocompatible and can be micromachined by several methods, e.g. structuring by photolithography, ablation and hot embossing. In the presented work direct UV irradiation of a common PMMA substrate by a krypton fluoride excimer laser beam through a contact mask has been used to write integrated optical Mach-Zehnder interferometers (MZI). MZI are used as sensitive bio and chemical sensors. The aim was to determine contact mask design and laser irradiation parameters for fabricating single-mode MZI for the infrared region from 1.30 μm to 1.62 μm. Straight and curved waveguides have been generated and characterized to determine the optical losses. The generation of channel waveguide structures has been optimized by a two step irradiation process to minimize the lithographic writing time and optical loss. By flood exposure to UV laser radiation in the first step the optical absorption of PMMA can be increased in the irradiated region. The required refractive index profile is then achieved with a second lithographic irradiation. The spectral behaviour of an unbalanced, integrated optical MZI fabricated by this excimer laser based contact mask method is shown for the first time. Further the optical intensity at the output port of a MZI has been measured while the optical path length difference was tuned by creating a temperature difference between the two arms of the MZI.     

Photonic crystal refractive index sensing based on sandwich structure

An ultracompact refractive index sensing based on the sandwich structure of photonic crystal is presented and demonstrated with solutions of water, methylsilicone and silicone. The performances of the sensor are analyzed theoretically by using Fabry-Perot cavity mode, the change in opposite direction between the transmission of the refractive index sensing and its quality factor is derived. The experimental results are consistent with the results of theoretical analysis.     

Determining the refractive index of liquids using a modified Michelson interferometer

An accurate method for measuring the refractive index of liquids is proposed, modeled, and experimentally verified. The experimental setup is a modified Michelson interferometer employing a novel liquid chamber that allows the optical pathlength to be continuously varied without moving a mirror. This experiment allows determining the refractive index of a given liquid to high precision, with an accuracy limited only by the normal random variables encountered in interferometric measurements and ultimately the accuracy to which the wavelength of the laser light is known.