Automatic Analysis of the Phase Object Using Projection Moire Deflectometry

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Refractive index profiling of a GRIN optical fiber using a modulated speckled sheet of light

A method for calculating the refractive index of GRIN optical fiber from its transverse interference pattern is presented.In this method the transverse interference fringe pattern through an optical fiber using a sheet of light is applied to get the refractive index profile of it. The optical fiber is not immersed in a matching liquid as used in different techniques [Barakat N, El-Hennawi HA, El-Zaiat SY, Hassan R. Pure Appl Opt 1996;5:27].In this method a sheet of He–Ne laser light is allowed to illuminate the fiber. The light sheet is divided into two parts, the first is refracted through the fiber while the second is used as a reference beam. Interference pattern will be obtained between these two rays displaying the refractive index variation along the fiber radius.The fringe shift of such interference pattern has been measured and used to calculate the deflection angle of light refracted by the fiber and the cladding. An equation is derived to calculate the refractive index profile difference ratio δn at different positions across the fiber cross section in terms of the corresponding deflection angle and is verified experimentally.The optical path difference between these two rays (refracted and reference beam divided by the fiber) has been derived and the fringe shift obtained has been used to calculate the refractive index profile of the fiber.Introducing a ground glass screen on the passage of the two light beams (refracted and reference beam divided by the fiber), two superimposed identical speckle patterns are formed leading to the formation of a third speckle pattern modulated by a grid structure displaying the optical thickness of the fiber.     

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.     

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.     

Automatic fringe analysis of two-beam interference patterns for measurement of refractive index and birefringence profiles of fibres

Automatic fringe pattern analysis is a powerful and inexpensive digital image-processing technique. Two-beam polarizing interference Pluta microscope [Pluta M. Opt Acta 1971;18:661, Pluta M. J Microsc 1972;96:309] is automated by the computer-aid via CCD camera and digital frame grabber. Software program is prepared to deal with the duplicated (separated and overlapped) Microinterferograms produced by two-beam polarizing microscope. It also gives an accurate and fast automatic measurement of refractive index and birefringence profiles for fibres. In this paper, the refractive index and birefringence profiles of two different types of fibres, basalt and polypropylene (PP) fibres are presented. A new method to determine the birefringence profile of fibres from non-duplicated microinterferogram is suggested. The cold drawing process for PP fibres is studied.     

Phase deviation analysis and phase retrieval for partial intensity saturation in phase-shifting projected fringe profilometry

Intensity saturation may take place as a sinusoidal fringe pattern is projected onto an object which has a relative high reflective index on some regions of the surface. If a phase-shifting method is used, the illuming light intensities at the same point of the object may have different values for each projected phase-shifting fringe pattern. Therefore, when the intensity at a point of the object exceeds the saturation level for a certain phase step of projected fringe pattern, other intensities obtained at the same point with different phase steps of projected fringe patterns do not exceed the saturation level. This kind of saturation is defined as partial intensity saturation. In the case of partial intensity saturation, a relative larger phase error is introduced when a conventional phase reconstruction algorithm is used in the phase-shifting projected fringe profilometry (PSPFP). To get rid of such disadvantage, an improved algorithm for phase reconstruction is proposed in this paper. By using the new algorithm, the effect of partial intensity saturation for the phase reconstruction can be decreased greatly and a good quality of reconstructed phase map can be obtained. Phase deviation of the reconstructed phase is also analyzed. Finally, an experimental result with PSPFP is presented to validate the feasibility of the proposed algorithm.     

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.     

A subfringe integration method for multiple-beam Fizeau fringe analysis

Some aspects concerning the subfringe integration method in interferogram analysis have been investigated and modified. The modified algorithm, introduced in this paper, is capable of reconstructing the phase in the presence of noise or errors in carrier frequency. The subfringe integration method was applied to analyze two computer simulated patterns of equispaced Fizeau fringes using N bucket integration. Also, it is used to analyze the multiple-beam Fizeau fringe. The refractive index profile of polyethylene fiber is obtained by using two methods, subfringe integration method, and Fourier transform method. A comparison between the obtained results using the maintained methods is presented.     

Evaluation of absolute phase for 3D profile measurement using fringe projection

A new method of absolute phase evaluation for three-dimensional (3D) profile measurement using fringe projection is presented, which combines the gray code and the phase shift technique. Two kinds of fringe patterns are projected onto the object surface respectively, one is sinusoidal intensity distribution used for phase demodulation and the other is gray code fringe pattern for unwrapping. These images are acquired by camera and stored into computer. The absolute phase is obtained by analyzing these images. The validity of this method is verified experimentally. The method is superior to other phase unwrapping methods.     

Surface plasmon interferometric microscopy for three-dimensional imaging of dynamic processes

A method, which we named surface plasmon interferometric microscopy, for real-time displaying of the dynamic evolution of the refractive index (RI) of a sample in three-dimensions is demonstrated experimentally. The Fourier fringe analysis technique is employed to get the phase variations of the samples by demodulating the interference patterns captured by a CCD camera, and the 3D RI distribution can be obtained through numerical interpolation from the relation between the phase and the RI of the samples. Our method may provide an interesting way to monitor fast dynamics of physical, biological, and chemical processes in real time.     

数字全息干涉术用于微波等离子体推进器羽流场的研究

利用数字全息干涉术研究了微波等离子体推进器羽流场的分布特征,由所记录的羽流场的数字全息图,经数值再现,得到了羽流场的相位分布,进而计算出等离子体羽流场的电子数密度.通过相位倍增法增加了羽流场的干涉条纹密度,从而能够更直观地反映出羽流场的折射率分布.结果表明,数字全息干涉术是研究微波等离子体推进器羽流场的一种有效方法.     

大剪切电子散斑干涉的载频调制与位移场测量

将电子散斑干涉场的载波调制引入到大剪切电子散斑干涉中,通过对参考物的微小偏转引入载波条纹;利用傅里叶变换法,解调出了变形场的相位,从而实现了物体变形场的精确测量。讨论了大剪切载频的调制机理,理论分析表明,调制条纹的空间频率与参考面偏转的角度成正比;因此,控制参考面的偏转角度可实现不同位移量系统的调制。利用中心加载周边固定圆盘进行了典型实验,实验结果证明在大剪切电子散斑干涉技术中可以通过参考面的旋转高质量地实现电子散斑干涉条纹的调制,求解位移场。该系统具有系统简单,不需要专门引入参考光,条纹质量好等优点。该技术可扩展电子散斑干涉的应用范围,有一定的实际应用价值。     

Critical Angle Refractometry for Simultaneous Measurement of Particles in Flow: Size and Relative Refractive Index

The principle of the optical technique critical angle refractometry, used to determine the size and refractive index of spherical particles (with relative refractive index below unity) in liquid flows, was investigated. This technique is based on the observation of the particle scattering pattern around the critical angle. Similarly to the recent technique developed for rainbow scattering pattern analysis for droplet temperature and size measurements, it is shown that the relative particle refractive index (m_r<1) and size can be determined from the position of the primary diffraction fringe and from the angular spacing between two fringes. Explicit equations for refractive index and particle size measurement were derived from the first-order term of the physical optics approximation. An experimental validation test and numerical computations based on the Lorenz-Mie theory were used to validate the principle of the proposed technique and to estimate its sensitivity, which was shown to be of the same order as that of the rainbow technique. This technique is considered to be useful for various applications in liquid multiphase flows where the particles size and material are to be characterized.     

单元件干涉数字全息的光线追迹模型

基于棱镜对的单元件干涉可以获得透射物体的相位信息,即数字全息,具有结构紧凑、干涉条纹稳定、测量精度高等优点。采用光线追迹方法,综合考虑了棱镜对的方位角旋转、斜面偏心等参数,建立了光线追迹等效模型,仿真了数字全息干涉条纹,给出了条纹密度变化及倾斜的解析表达式。针对单模和多模光纤等微结构光学元件,获得了干涉数字全息图,并反演出其折射率分布。搭建了显微成像单元件干涉实验装置,获得了实际测量干涉图样,实验与仿真结果一致,证明了本模型的有效性。     

A novel 3D measuring method for discontinuous object by non-integral twin-frequency grating

A new 3D shape measurement method based on non-integral twin-frequency grating projection is proposed. In this paper, the projected composite grating is composed of two sinusoidal gratings, and the quotient of whose frequencies is not an integer. By using appropriate phase-shifting algorithms, two wrapped phases can be obtained from sixteen frames of the distorted grating patterns. In aid of appropriate phase unwrapping method, the unwrapped phase of high frequency fringe is obtained only from the relation of the two wrapped phases by a pixel-to-pixel phase unwrapping technique. Therefore the unwrapped phase of high frequency fringe pattern is independent of the low frequency fringe pattern, different from traditional integral twin-frequency grating projection methods in which the phase unwrapping error of low frequency fringe pattern may be propagated onto the unwrapped phase of high frequency fringe pattern. The new theory proves that the proposed method is applicable to measure discontinuous object, and has considerable measurement accuracy.     

Two-dimensional cell parameters measurement of nematic liquid crystal using optical interferometry and Fourier transform fringe analysis technique

We report a method for the measurement of nematic liquid crystal (NLC) cell parameters i.e., switching voltage, birefringence, retardation, dielectric anisotropy, average tilt angle and change in refractive index with applied DC voltage to LC material. The proposed method is based on optical interferometry and Fourier transform fringe analysis technique, in which we obtain 2-dimensional (2D) phase map of the interferograms as a function of applied voltage. Mach-Zehnder interferometer (MZI) was used for the study of cell parameters and interferograms were recorded at different applied DC voltages to NLC cell using CCD camera. From the phase map, 2D-refractive index distribution of the LC cell with applied voltage was reconstructed. Analytical equations are derived based on optical interferometry and then solved to obtain cell parameters. The present method is fast and can give 2D-cell parameters from only two quick interferograms.     

Formation of positive and negative anisotropic holographic gratings depending on recording energy in photoreactive liquid crystalline copolymer films

Anisotropic diffractive gratings formed by birefringent molecular alignment are fabricated by a holographic technique using a photo-cross-linkable liquid crystalline copolymer (PLCCP). Depending on the exposure energy used for holographic recording, bright or dark regions of the interference fringe can be chosen for the molecular-aligned region, analogous to positive- and negative-type photoresist processing in photolithography. In conjunction with simultaneously generated surface relief gratings, the anisotropic refractive index modulation inherent in the PLCCP film exhibits different diffraction properties depending on the incident beam polarization. The anisotropic refractive index grating profiles are quantitatively presented for two cases determined by the exposure energy, based on the Fourier analysis of diffractive optics. The selection of different grating formations selected by varying only the exposure energy could provide a strategy for the fabrication of functionalized diffractive optical elements.     

The Paul wavelet algorithm: an alternative approach to calculate the refractive index dispersion of a dielectric film from transmittance spectrum

A new application of the Paul wavelet algorithm was presented to determine the refractive index dispersion of a dielectric film from transmittance spectrum in the visible and near infrared region. The developed algorithm was tested by simulated data and experimentally applied to a sample of mica. The obtained refractive index dispersion determined by the Paul wavelet algorithm was compared with the refractive index values determined by the envelope and fringe counting methods, and also with the established result. It was shown that the degree of the Paul wavelet has a major effect on the outcome of a refractive index determination. The noise immunity of the presented method was shown by the simulation study.     

干涉仪自适应抗振的空间移相术

根据时域移相算法的概念,提出了一种空间移相术,它能够检测因外界振动导致条纹抖动而引起的干涉图样的空间相位变化.运用这种技术在TwymanGreen移相式干涉仪中建立了一套自适应抗振系统,它可以实时测量振动引起的相位变化大小,并通过反馈器件PZT实时校正干涉条纹的相位,使得干涉条纹稳定以保证光学测量的正常进行,与此同时PZT还作为移相器件.     

空间载频条纹相位分析法中的相位不确定性

分析了单频、双频空间载频光学条纹相位分析技术中的相位不确定性问题,提出采用两频率之比为无理数的双频载频条纹,相位可完全确定,并提出了基于两频率之比为无理数的空间载频条纹相位确定算法,给出了实验结果。