Fringe Locking in a Laser Diode Interferometer by Optical Feedback During Modulation of Injection Current

A fringe locking phenomenon in a two beam interferometer using a semiconductor laser subject to optical feedback was, whose injection current is modulated. When a path difference of the interferometer is sufficient, fringes taken by a charge coupled device camera are seen to be stationary and the rms fluctuations of fringe phase is reduced to as low as 0.2ϖ radians from more than 8ϖ radians without the optical feedback. The rms phase fluctuation is independent of frequency and amplitude of the current modulation. The fringe locking has also been observed in the presence of both injection current modulation and piezoelectric transducer mirror vibration.     

Analysis on the laser beam pointing instability induced fringe shift and contrast dilution from different interferometers used for writing fiber Bragg grating

This paper presents an analysis on the effect of laser beam pointing instability on the fringe shift and hence the contrast dilution of superposed fringes from two beam interferometers. The interferometers analyzed are those commonly used in writing fiber Bragg grating (FBG) such as phase mask, bi-prism and phase mask based Talbot/Holographic type. The beam pointing instability is incorporated as slight change in the angle between two interfering beams. The relative immunity of different interferometers to laser beam pointing is discussed vs location of FBG writing plane from the beam splitter. The effect of the beam pointing was minimum in proximity FBG writing by phase mask. The effect, in terms of fringes contrast dilution, was worst in case of large length interferometers e.g. phase mask based-Talbot interferometer. For intermediate length prism interferometers, the effect was moderate. For a given length interferometer, the fringe shift was directly proportional to beam pointing angle and inversely proportional to fringe separation. Theoretical analysis is verified experimentally by studying the fringe instability of interference pattern formed by a bi-prism of angle 2^o with the copper vapour laser (CVL, λ = 510 nm) beams of different beam pointing instabilities.     

Fringe Locking in a Laser Diode Interferometer under Both Mirror Vibration and Injection Current Modulation

We have found that the fringes in a laser diode interferometer can be locked even in the presence of mirror vibration and injection current modulation. A theoretical analysis explains the fringe locking phenomenon. The dependence of wavelength change on both PZT (piezoelectric transducer) mirror vibration and the injection current variation are calculated using a model of coupled resonators consisting of the laser cavity and the interferometer. The fringe phase change caused by the vibration and modulation of the current is derived from this model, and was proven to be suppressed within much less than 2ϖ in excess of an integer multiple of 2ϖ.     

Observation of Gouy phase anomaly with an interferometer

The intensity variation of bright and dark fringes in Young's double slit experiment shows that a light beam propagating through the focus of a lens experiences a phase shift (called the Gouy phase shift [Gouy CR. Acad Sci Paris 1890;110:1251]) with respect to its plane wave counterpart. The additional phase change of π introduced on focusing the light beam and then further propagating it in one arm of the interferometer changes a bright fringe into a dark fringe and vice-versa. We have, thus, made direct visualization of the Gouy phase shift by a simple experiment.     

Multi-STFT for adaptive SCPS phase determination

This paper presents a fast and reliable approach for phase modulo 2π-calculation from a single fringe pattern. It calculates correct phase values even for very complex and variable shape gradients based on a locally variable fringe period determined for the entire image. In the paper, a new two-step method for wrapped phase calculation is proposed. It is performed through the use of a method based on a multiple local fast Fourier transform for estimation of a local fringes period map and a 5-point spatial carrier phase shifting (SCPS) formula for phase modulo 2π-calculation. The described approach is verified by a correct demodulation of a real fringe pattern taken by a 3D-shape measurement system.     

Phase locked loop profilometry

An innovative technique for obtaining automatic three-dimensional shape information of a diffuse surface is presented. The technique is based on a new approach of phase measuring from a fringe pattern. The target to be studied is first modulated by projecting a linear grating onto its surface. The linear fringes are deformed according to the surface shape. Demodulation is carried out by determining the phase of these deformed fringes using a novel digital phase locked loop demodulation algorithm. The technique has the main advantage that the traditional phase unwrapping process is not required. The phase is determined continuously as the algorithm scans the two-dimensional fringe pattern. Owing to its sequential nature, this phase detection technique can be implemented using a special purpose video processor for phase determination at video rates, making it a very fast algorithm. The algorithm along with experimental results of real surface profiles are presented.     

Contrast enhanced and phase controlled stroboscopic additive fibre optic TV-holography for whole field out-of-plane vibration analysis

A new technique for real-time contrast enhancement and phase control of fringes in additive Stroboscopic TV-holography applied to out-of-plane vibration analysis and its implementation on a fibre-optic electronic speckle pattern interferometer (FOESPI) are presented. Synchronous Stroboscopic illumination, firing two pulses per object vibration period, is combined with simultaneous inter-pulse (high frequency) and inter-frame (low frequency) phase modulation in the reference arm of the ESPI yielding a sequence of frames (interferograms) that are grabbed and processed in real-time. With this technique both speckle and fringe phases are independently controlled by means of the parameters of modulation enabling speckle contrast inversion, as required to enhance the visibility of fringes by sequential subtraction, as well as dynamic fringe phase shifting to solve peakvalley ambiguities.     

Step index fibre using laser interferometer

A model is suggested to describe the fringe shift which occurs due to the phase variations of cladded glass fibre introduced between the two plates of the liquid wedge interferometer illuminated with a He–Ne laser. The fringe shift of the phase object which appears in the denominator of the Airy distribution formula of the multiple beam interference is represented in the harmonic term. An experiment is conducted using liquid wedge interferometer where the step index glass fibre of a nearly quadratic thickness variation is introduced between the two plates of the interferometer. The obtained fringe shift shows a good agreement with the proposed quadratic model. The Matlab code is written to plot the interferometer fringes comprising the shift of the step index fibre. Secondly, recognition of elliptical fibres is outlined using tomographic imaging. Finally, results and concluding remarks are given.     

地基气辉成像干涉仪探测高层大气风场的定标研究

我们研制的地基气辉成像干涉仪(ground based airglow imaging interferometer,GBAⅡ)样机成功地探测了地球上空90—100 km的大气风速和温度.为了提高GBAⅡ的探测精度,本文研究GBAⅡ所拍摄的成像干涉条纹的定标:对干涉条纹中心位置定标、电荷耦合器(CCD)暗噪声和平场定标、整个光学系统衰减系数定标、步进步长定标、光程差随入射角变化量定标、仪器响应度定标和零风速相位定标等理论和实验进行了研究.利用最小二乘法对GBAⅡ拍摄的30幅成像干涉图的圆心坐标定标在CCD(123.3,121.1)像素位置;利用632.8 nm激光获得GBAⅡ所用CCD的平场定标系数矩阵,分别得到平场前后的干涉图并检测出CCD的噪声和坏点;利用GBAⅡ获得图像的边缘亮环相位与中心亮斑相位的差值对入射角10.24°时,光程差相对0°入射角时变化了0.356个条纹;拍摄200幅成像干涉图的实验离散点进行正弦拟合后的均方根标准偏差达90.34%,该完整干涉条纹的步进间隔为4.06 nm,对应步进相位为0.0094π;针对正演公式中GBAⅡ的系统衰减系数对所拍摄的原始干涉图利用IDL编程得到光学系统衰减系数的多项式,拟合的均方根标准偏差达99.98%;采用632.8 nm激光作光源,简化了GBAⅡ的响应度表达式,通过实验得其响应度为4.97×10~(-3)counts·(Rayleigh·s)~(-1);针对GBAⅡ室外观测,给出零风速定标的矩阵表达式后,对532.0 nm和632.8 nm激光的对应零风速相位分别为-9.2442°和-68.6353°.本文提供了多种定标方法,并逐一通过实验进行验证,为国内被动遥感探测高层大气风场提供了强有力的实验支持.     

Carrier fringes in the two-aperture common-path interferometer

We present a method to introduce a linear phase into an interference pattern. This phase is introduced when a grating is placed outside of the Fourier plane of a two-aperture common-path interferometer, which is built using a 4f optical imaging system. Based on an analysis of near-field diffraction, the introduction of the carrier fringes is mathematically justified. It is important to note that no tilt between the two beams is requested to produce this effect, and it turns out to be simpler, easier, and more versatile than other existing methods. The main attributes and advantages of the setup will be discussed and illustrated in detail with experimental fringe patterns.     

Phase retrieval of non-continuous fringe patterns by a genetic data reduction algorithm

In this work we focus on the possibilities of recovering the phase from a single fringe pattern that do not have a fringe order sequence or whose fringes are broken. The phase is obtained with a polynomial fitting method whose coefficients are calculated with a genetic algorithm technique that constrains the smoothness of the solutions of a merit function. It is explained how conjugate gradient methods fail in the solution of the proposed merit function. Experimental results are presented using discontinuous fringe patterns obtained from a grazing incidence interferometer while testing a polishing tool.     

An automatic processing technique for accurate surface form measurement

A single shot algorithm using a Fizeau interferometer was used to measure the form profile of a spherical smooth surface by means of fringe thinning process, which plays an important role in fringe patterns analysis. In this paper, an automatic processing technique based on the fringe thinning process is presented. The circular interference fringe pattern of the spherical smooth surface captured by the Fizeau interferometer was corrected by using the flat fielding method and then processed. Based on the fringe thinning and the assignment of the fringe orders, the information on the fringe feature was recovered automatically and the interference wavefront was reconstructed by the Zernike polynomial fitting method. The results were compared with the results measured by Bünnagel method, and the results were in good agreement. This means that the single shot algorithm is reliable, fast, and less sensitive to vibration and turbulence in surface form measurements. Simulation fringes with the ray tracing technique were obtained to match the practical fringes.     

Composite Vibration Analysis with Modulated Electronic Speckle Shearing Interferometry

A video speckle shearing interferometer has been used to study sinusoidally vibrating objects. Theroretical and experimental results show that the shear fringe patterns obtained contour the derivatives of the vibration amplitudes only for pure classical modes and when the shear is small. For composite modes, the fringe patterns observed are more difficult to interpret because the optical phase changes that are contoured are functions of both the spatial derivatives of the vibration amplitude and of the vibration phase.Presented at 1996 International Workshop on Interferometry (IWI ‧96), August 27–29, Saitama, Japan.     

Measurement of vibration amplitude by an optical fiber-based moiré interferometer

A projected-fringe fiber-based moiré interferometer is proposed to measure the local amplitude vibration of a diffuse surface. The technique is based on an optical fiber interferometer which projects interference fringes on the object surface. The visibility of these carrier fringes is modulated by a function of local amplitude vibration. Full-field quantitative analysis is performed by analyzing the fringe pattern with a 2-D Fourier transform method. Theoretical details, and experimental results are presented.     

Perspectives of Ramsey schemes based on high-order harmonics for high-resolution XUV spectroscopy

We present an experimental and theoretical investigation of Ramsey-type interference fringes using high-order harmonic generation. The ninth harmonic (λ ≃ 88 nm) of a femtosecond Ti:sapphire laser was used to excite a pair of autoionizing states of krypton. The outcome of the ionization process, detected by an ion-mass spectrometer, shows the characteristic quantum interference pattern. The behavior of the fringe contrast was interpreted on the basis of a simple analytical model, which reproduced well the experimental results without any free parameter. Finally, we also present a proposal for a similar experiment to be performed on high-lying bound state of atomic argon, with the aim of achieving even higher resolving power.     

基于干涉条纹跟踪实现纳米级位移测量的方法研究

设计了一套干涉条纹图像实时采集处理系统。在分析迈克尔逊干涉条纹特征表象的基础上 ,给出了通过跟踪干涉条纹的移动量测量被测对象纳米级位移量的理论公式 ;提出了干涉条纹特征点的提取与跟踪算法 :分段线性变换、方形窗口中值滤波和门限化边缘提取 ,给出了基于统计学原理的通过计算多条干涉条纹移动量获得被测对象纳米级位移量的计算公式。实验结果表明了该方法的有效性和实用性     

Additive-subtractive phase-modulated speckle interferometry: Fringe visibility under partial decorrelation

Additive-subtractive phase modulated speckle interferometry (ASPMSI) is a technique that minimizes the susceptibility of speckle methods to environmental noise while providing fringes of good visibility. The method requires the acquisition of two consecutive video frames of additive-speckle images of the same two deformed states of an object at a rapid enough rate such that ambient noise is not a problem. The additive-speckle images as expected are of very poor visibility due to the presence of the self-interference term. An interframe phase-modulation is introduced and the two additive-speckle images are digitally subtracted to improve the fringe visibility by removing the self-interference term. The ASPM-SI method works with in-plane and out-of-plane deformation sensitive ESPI as well as with displacement-gradient sensitive speckle-shearing interferometry. It is shown that the ASPM-SI scheme has higher visibility than conventional additive-SI and performs consistently better than subtractive-SI schemes in the presence of partial interframe speckle decorrelating optical noise. Furthermore, it is shown that the fringe visibility of the out-of-plane displacement sensitive interferometer which uses a protected reference beam separate from the object beam can be made to be essentially unity even at complete interframe decorrelation.     

Modeling of the fringe shift in multiple beam interference for glass fibers

A quadratic model is suggested to describe the fringe shift occurred due to the phase variations of uncladded glass fiber introduced between the two plates of the liquid wedge interferometer. The fringe shift of the phase object is represented in the harmonic term which appears in the denominator of the Airy distribution formula of Fabry-Perot’s interferometer. A computer program is written to plot the computed fringe shifts of the described model. An experiment is conducted using liquid wedge interferometer where the fiber of a nearly quadratic thickness variation is introduced between the two plates of the interferometer. The obtained fringe shift shows a good agreement with the proposed quadratic model. Also, it is compared with the previous theoretical shift based on ray optics of semi-circular shape.      

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.     

Active Phase-Shifting Interferometer Using Current Modulation of a Laser Diode

An active phase-shifting interferometer using current modulation of a laser diode is proposed. Fringe movement in the instrument is detected by a spatial filtering detector whose output is fed back to the injection current of the laser diode to lock the fringes and shift them correctly for phase shifting analysis. Frequency modulation characteristics of the laser diode and frequency response of the feedback system are first investigated. We constructed a portable interferometer head set apart from a mirror under test then measured the shape of a spherical mirror 130 mm in diameter, which was placed on a wooden table subject to vibration. Measurement repeatability of λ/35 was achieved.