Refractive index profiling across a candle flame using speckle techniques

Refractive index profiles have been obtained at different heights in the region above a candle flame both theoretically and experimentally by means of double and multiple exposure speckle photography. Improved fringe visibility has been achieved in the case of the multiple exposure technique giving rise to accurate measurement of the refractive index. Theoretical analysis shows that the resulting speckle pattern is equivalent to the ordinary pattern convolved with a function representing the effect of light deflection, while the interference pattern obtained is modulated by a background representing the autocorrelation function of the diffuser.     

A comparative study of spliced optical fibers

A fusion-spliced optical fiber is examined with a laser sheet of light. A CCD camera is used to record the transverse interference pattern from the fiber. The buckling on the fiber material in one direction of the spliced point is distinct inside the transverse interference pattern. The refractive index profile inside the fiber core, obtained at different illumination directions, is calculated using a new method showing the change in the refractive index due to fusion splicing of the fiber. A simple theoretical model is introduced to simulate the anomalous behavior in the transverse interference fringes due to a slight change of the optical parameters.     

毛细管干涉仪的理论分析

从几何光学出发,推导了毛细管干涉仪的从柱面透镜到接收屏的光线的光程．对光线追迹模拟,结果表明毛细管干涉仪的干涉条纹的形成可用双光束的干涉来解释．从柱面不同位置入射的两条光线可能具有相同的光程,而且从柱面透镜不同位置出发的两条光线可能到达接收屏的同一点,当它们满足相干条件时,就会形成干涉条纹．建立了干涉条纹的计算机模拟程序, 模拟了毛细管中液体折射率、毛细管内径、外径对干涉条纹的影响. 结果表明实验中应使用薄壁毛细管, 由于干涉条纹对柱面透镜到毛细管之间的距离非常敏感, 为提高精度, 建议在实验中用已知折射率的标样来确定这一距离.     

Features of the refraction of glancing light rays from optically less dense absorbing media

A study is made of the refraction of glancing light rays at the interface of two optically homogeneous media, one of which is absorbing. Experimental data indicate an increase by several times in the flux of the refracted rays in the case of refraction of glancing rays from absorbing slabs. It is shown that the dispersion zone of deflection of the light rays partly transmits glancing rays in a transparent slab and can be opaque in weakly absorbing slabs. It is established that the increase in the intensity of the refracted beams is due to the more effective transformation of the glancing rays moving in the dispersion zone into refracted rays. Data are available on the dependence of the refracted flux on the relative refractive index.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 57–60, March, 1981.I thank V. E. Zuev, S. D. Tvorogov, and M. V. Kabanov for their interest in the work and discussion of the results.     

LFI法测量半透明油的折射率

LFI方法曾被用来测量大直径光纤的折射率.用一半盛油一半为空气的毛细管代替光纤,并用聚焦的条形光束照射毛细管,空气与油的干涉条纹同时产生.根据空气的条纹可以确定参数b,根据一组已知折射率的标准样品可确定另一参数c,同时可以建立标准液体最外条纹的偏折角与折射率的标准曲线.对于未知折射率的样品,一旦测量出其最外条纹的偏折角,从标准曲线上就可以读出其折射率.实测了一组半透明油的折射率,其结果与阿贝折射仪测量结果接近.     

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.     

Automatic refractive index profiling of fibers by phase analysis method using Fourier transform

Automatic fringe pattern analysis is a powerful and inexpensive digital image-processing technique. It is used to analyze the fringe pattern obtained by different optical techniques, such as multiple-beam Fizeau fringes. To perform accurate and fast automatic measurement of fiber refractive index profile, phase analysis method has been used with the Fourier transform technique. In this paper, the refractive index profiles of polyethylene fibers with different draw ratios are presented by two methods, fringe shift method and phase analysis method. A comparison between the results obtained is presented.     

Determination of the refractive index profile of a symmetric fiber preform by the transport of intensity equation

The refractive index profile of an axially symmetric fiber preform is determined by using the transport of intensity equation. In this method the preform is immersed in an index-matching liquid, and a collimated light beam impinges on it laterally. The intensity distributions of the transmitted light are measured on two close parallel planes inside the preform core. From the recorded intensity distributions, the deflection function is calculated by the transport of intensity equation. The refractive index profile is obtained by means of Abel inversion. Also, for comparison, the refractive index profile of the preform is measured by the focusing method and the results are in agreement with less than 3% error.     

干涉法测量掺铒光纤的非线性折射率

本文提出一种测量掺铒光纤非线性折射率的方法,该方法使氩离子激光通过一根掺铒光纤和另一根并排的普通光纤产生干涉.由掺铒光纤的非线性折射率导致的位相差变化将使干涉条纹发生位移,通过位移的测量可以得出光纤的非线性折射率.     

透射式微分干涉显微镜测量光纤折射率分布

提出一种由两组偏光棱镜组成的透射式微分干涉系统,用来测量光纤的折射率分布。系统利用旋转检偏器对测量光束进行调制,从相位分布和光程分布中计算出折射率分布。介绍了测量原理、测量公式、系统组成及典型应用。用该系统对光纤折射率进行实际测量,给出渐变折射率光纤的二维分布,及折射率沿轴向的分布图,同时还在NR 9200光纤测试仪上进行了测试。结果表明,系统原理正确,结构简捷,具有足够分辨率和测量精度,抗干扰能力强,不破坏光纤,还可测量包层和芯层的直径,发现光纤加工过程中的缺陷,特别适合加工、焊接等工艺过程中的检测。     

基于白光扫描干涉法的光纤折射率分布的测量

提出了一种光纤折射率分布的测量方法,采用白光扫描干涉技术,并在参考镜上构造与光纤样品相同的结构来克服白光相干长度短的限制,优化了光路,提高了干涉条纹间的对比度。采用与白光干涉信号的包络线呈高斯分布的Morlet小波作为小波变换的母小波进行拟合处理,得到光纤与已知折射率的匹配液之间的相对高度。通过计算获得光纤的折射率分布,并对获得的数据采用光纤折射率分布的经典函数进行拟合,得到多模光纤和单模光纤的决定系数分别为0.997 2和0.996 4。最后将实验获得的结果与官方参数进行比较,误差为0.01%,表明该种方法测量的精度较高,完全可以用来测量光纤的折射率。     

光在双轴晶体表面的反射与折射

介绍了光在双轴晶体表面反射、折射问题的求解方法.用该方法可以方便精确地计算晶体任意取向下光从任意方向入射时折射光的折射率、偏振态、波矢方向、能流方向. 推导了反射光、折射光的振幅和能量的计算公式. 并以KTP晶体为例，给出了数值计算的结果. 关键词： 双轴晶体 双折射 菲涅耳公式 布儒斯特角     

Determination of GR-IN optical fibre parameters from transverse interferograms considering the refraction of the incident ray by the fibre

The core–cladding refractive index difference Δn and the index gradient profile parameter of the graded index (GR-IN) optical fibre has been determined. The curve representing the real path, in the core region, due to refraction of the beam and the change in the exit wavefront are considered. Multiple-beam Fizeau fringes and two-beam interference Pluta polarizing microscope, are used for this investigation. A new method, based on a derived mathematical expression, is used with a prepared computer program to estimate the fringe shift inside GR-IN of the fibre core. The estimated and experimental values of the fringe shift, along the core radius, are used to obtain the refractive index profile of the optical fibre. A comparison between the new method and a previous model considering the refraction has been shown. Microinterferograms are given for illustrations.     

Simulation of the speckle pattern rotation in an absorbing optical fiber under the change of sign of the circular polarization of propagating light

The effect of rotation of a speckle pattern of circularly polarized light outgoing from a few-mode absorbing optical fiber under the change of sign of the circulation is numerically simulated on the basis of the wave approach. The theoretically predicted parabolic dependence of the value of the angle of rotation of the speckle pattern on the fiber length is discussed. Optical fibers with power-law refractive index profiles are considered.     

Influence of the volume speckle on fiber specklegram sensors based on four-wave mixing in photorefractive materials

In this work, the dependence on the speckle size in the performance of a micro displacement sensor based on fiber specklegrams stored in a photorefractive BSO (Bi₁₂SiO₂₀) crystal is experimentally demonstrated. In our experimental setup, a plastic optical fiber (POF) was used to generate a subjective speckle pattern which was recorded in the crystal by using a four-wave mixing arrangement in transmission geometry. The speckle size was controlled by modifying the diameter of a pupil aperture adjacent to a lens producing the image of the speckle. The signal speckle beam was mixed into the crystal with two counter propagating pump beams to generate a fourth beam which is proportional to the conjugate of the original speckle beam. Real time fringe patterns were obtained at the output of the system by producing micro displacements of the fiber output end. Increases of the phase conjugation reflectivity and the visibility of the fringe patterns were appreciated when the speckle length was increased by decreasing the pupil aperture diameter. This behavior allowed recovering the autocorrelation functions of fringe patterns associated to micro displacements that initially led to decorrelation, and therefore, to improve the dynamic range of the metrological system. Until the best of our knowledge this is the first report about the influence of the speckle size on fiber specklegrams sensors recorded on photorefractive materials by four-wave mixing.     

Simultaneous measurement with one-capture of the two in-plane components of displacement by electronic speckle pattern interferometry

We present the simultaneous measurement of the two in-plane displacement components by electronic speckle pattern interferometry with three object beams and without an in-line reference beam. Three interference fringe patterns, corresponding to three different sensitivity vectors, are recorded in a single interferogram and separated by means of the Fourier transform method. Then, two interference fringe patterns are selected to obtain the in-plane displacement components.     

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.     

由菲涅尔反射测量平行平面介质的折射率

一激光束投射在一平行平面介质的表面上，在此表面有一反射光束和从介质内折射出来的另一光束，只要测出这两光束的Ｐ光和Ｓ光的强度，就可计算该介质的折射率。本文介绍测量原理及方法。     

Spatial coherence of an optical turbulent beam in a biased photorefractive crystal due to the spatiotemporal modulation instability

We report the experimental observation of the dynamic pattern formation of a broad coherent light beam in a biased photorefractive crystal due to the spatiotemporal modulation instability. When the nonlinearity exceeds a specific threshold, the coherent light beam not only breaks up into light spots due to the modulation instability but also fast fluctuates both spatially and temporally, forming an optical turbulent beam, which behaves as a quasi-homogeneous speckled beam or a partially incoherent beam. We investigate the spatial coherence property of an optical turbulent beam from the visibility of the averaged double-slit interference fringe. We also numerically demonstrate the visibility variation of the instantaneous interference fringe of an optical turbulent beam.     

Improvement of the dynamic range of a fiber specklegram sensor based on volume speckle recording in photorefractive materials

In this work, the improvement of the dynamic range of a micro displacement sensor based on fiber specklegrams holographically stored in a photorefractive BSO (Bi₁₂SiO₂₀) crystal is reported. In our experimental setup, a plastic optical fiber (POF) was used to generate a subjective speckle pattern that was recorded in the crystal using a two-wave mixing arrangement. The speckle size was controlled by modifying the diameter of a pupil aperture adjacent to a lens producing the image of the speckle. Fringe patterns were obtained at the output of the system by producing micro displacements of the fiber output end. An increase in the visibility of the fringe patterns was appreciated when the pupil aperture diameter decreased even without controlling the average modulation of the intensity of the light pattern, i.e. when the speckle length increased and the average light modulation simultaneously decreased. This behavior allowed recovering the autocorrelation functions of fringe patterns associated with displacements that initially led to decorrelation, and therefore, significantly to improve the dynamic range of the metrological system. To the best of our knowledge this is the first report about the influence of speckle size on the dynamic range of fiber specklegrams sensors recorded on photorefractive materials.