利用白光干涉技术测量块状材料的群折射率

对群折射率的精确而快速测量是光学工程领域一个基础而又亟需解决的难题,本文提出了一套光谱型迈克尔逊白光干涉系统的解决方案.该系统充分利用了微型光纤光谱仪一次测量便可获得所有干涉信息的特点,无需机械扫描装置,具有结构简单和测量快速的优点.与传统的窗口傅里叶变换算法相比,本文采用小波变换直接从干涉信号的小波脊中提取群延迟,减小了由相位求导得到群延迟过程中引入的误差放大效应,进而提高了群折射率的测量精度.基于此迈克尔逊白光干涉系统,在不同干涉位置处对两块不同厚度的石英和BK7玻璃进行了测量,实验结果表明此方法在宽 关键词： 白光干涉 群折射率 小波变换 傅里叶变换     

Broadband near-infrared fibers dispersion measurement using white-light spectral interferometry

A new technique for an experimental determination of the effective refractive index, group refractive index and dispersion of fibers in a broad near-infrared spectral range is presented. The method is based on a white-light spectral interference which utilizes an unbalanced Michelson interferometer. The effective refractive index is obtained by a direct fitting the cosine function to the spectral interference pattern recorded by a low resolution spectrometer. The method has been tested in the spectral range of 1000-1700 nm both with standard telecommunication fibers and a sample of a photonic fiber. The accuracy of dispersion measurement () exceeds those from the previously reported near-infrared white-light spectral interference methods.     

Compensation of phase change on reflection in white-light interferometry for step height measurement

We present a method for compensating for the phase change on reflection in scanning white-light inteferometry that practically permits precise three-dimensional profile mapping of composite target surfaces that comprise multiple, dissimilar materials. The compensation method estimates the variation of phase change with the spectral distribution of the light source through a first-order approximation and then directly compensates for the measurement errors by performing two additional quasi-monochromatic phase-measuring interferometric measurements. Experimental results prove that the proposed compensation method is capable of reducing the measurement error in step height gauging to +/-5 nm or less.     

High-precision index measurement in anisotropic crystals using white-light spectral interferometry

White-light spectral interferometry appears an excellent tool for precise determination of indices, and has already been successfully applied to different isotropic or weakly dispersive materials such as glass or rhodamine films. In this paper, we extend the spectral method to the measurement of anisotropic media with strong dispersion. The method is discussed below and allows an accuracy of the order of 10^-5 on the principal indices of a birefringent silver thiogallate (AgGaS₂) crystal.     

Thickness of SiO2 thin film on silicon wafer measured by dispersive white-light spectral interferometry

We present a white-light spectral interferometric technique for measuring the thickness of SiO₂ thin film on a silicon wafer. The technique utilizes a slightly dispersive Michelson interferometer with a cube beam splitter and a fibre-optic spectrometer to record channelled spectra in two configurations. In the first, a standard configuration with two identical metallic mirrors, the recorded channelled spectrum is fitted to the theoretical one to determine the effective thickness of the beam splitter made of BK7 optical glass. In the second configuration one of the mirrors is replaced by SiO₂ thin film on the silicon wafer and the recorded channelled spectrum is fitted to the theoretical one to determine the thin-film thickness. We consider multiple reflection within the thin-film structure, use the optical constants for all the materials involved in the set-up, and confirm very good agreement between theory and experiment. The technique is applied to four samples with various SiO₂ film thicknesses. PACS 07.60.Ly; 68.55.Jk; 78.20     

Direct measurement of group dispersion of optical components using white-light spectral interferometry

We present a simple white-light spectral interferometric technique employing a low-resolution spectrometer for a direct measurement of the group dispersion of optical components over a wide wavelength range. The technique utilizes an unbalanced Mach-Zehnder interferometer with a component under test inserted in one arm and the other arm with adjustable path length. We record a series of spectral interferograms to measure the equalization wavelength as a function of the path length difference. We measure the absolute group refractive index as a function of wavelength for a quartz crystal of known thickness and the relative one for optical fiber. In the latter case we use a microscope objective in front and a lens behind the fiber and subtract their group dispersion, which is measured by a technique of tandem interferometry including also a Michelson interferometer.     

Evaluation of spectral phase in spectrally resolved white-light interferometry: Comparative study of single-frame techniques

Spectral phase in a white-light interferogram contains information about the absolute optical path difference (OPD) in the interferometer. Evaluation of spectral phase is therefore important in applications such as profilometry with white light. In spectrally resolved white-light interferometry (SRWLI) the white-light interferogram is spectrally decomposed by a spectrometer in order to determine this phase. Several single-frame techniques in SRWLI have been proposed for the evaluation of the phase including Fourier transform, Hilbert transform, spatial phase shifting, windowed Fourier transform and wavelet transform. In this paper we present a comparative study of these techniques in this application in relation to the temporal phase-shifting technique which is a multi- frame method. Further, we also propose a modified method to remove the influence of source spectrum modulation in Hilbert transform procedure.     

Measurement of optical constants of thin polymer films using spectrally resolved white light interferometry

Using the spectrally resolved white light interferometry we present our experimental results on the measurement of the optical constants of thin polymer films coated on a transparent substrate. As an extension to our previous work (J. Opt. Soc. Am. B12, 1559 (1995)) on thick glass plates, we have shown here that this technique can be effectively applied to very thin polymer films also. We have improved the accuracy of our results by using the Sellmeier dispersion formula for fitting the data. From the width and position of the zero-order fringe and the frequency of modulations in the white light spectrum, the refractive indexn(λ) and thicknesst of the thin polymer films are calculated. To study the accuracies involved in the technique, PVA, PMMA and PS films of varied thicknesses are coated on glass plates and the measured values are compared with ellipsometer studies.     

一种基于电光调制光频梳光谱干涉的绝对测距方法

提出了一种基于电光调制光学频率梳的光谱干涉测距方法.理论分析了电光调制光学频率梳的数学模型和光谱扩展原理,并分析得出了光谱干涉测距方法的非模糊范围和分辨力的影响因素.在实验中,使用三只级联的电光相位调制器调制单频连续波激光生成了40多阶高功率梳齿状边带,并通过单模光纤和高非线性光纤对电光调制器输出的激光进行光谱扩展,得到重复频率为10 GHz,光谱宽度达30 nm的光学频率梳.将该光频梳作为光谱干涉测距装置的光源,可以实现无"死区"的绝对距离测量.另外,使用等频率间隔重采样和二次方程脉冲峰值拟合算法对测量结果进行数据处理,可以修正系统误差,提升测距精度.实验结果表明,在1 m的测量范围内,使用该装置可以在任意位置达到±15μm以内的绝对测距精度.     

Slightly dispersive white-light spectral interferometry to measure distances and displacements

A new spectral-domain interferometric technique of measuring distances and displacements is realized when the effect of low dispersion in a Michelson interferometer, which comprises two coated plates of a beam splitter and a compensator, is known and the spectral interference fringes are resolved over a wide wavelength range. First, processing the recorded spectral interferograms by an adequate method, the unmodulated spectrum, the spectral fringe visibility function and the unwrapped phase function are obtained. Then, knowing the dispersion relation for the fused-silica plates, the ambiguity of the unwrapped phase function is removed and the thickness of fused silica and the nonlinear phase function due to the effect of the coatings are determined by using a new procedure. It is based on the linear dependence of the overall optical path difference between interferometer beams on the refractive index of fused silica. Once the thickness and the nonlinear phase function are known, the positions of the interferometer mirror are determined precisely by a least-squares fitting of the theoretical spectral interferograms to the recorded ones.     

Dispersion error of a beam splitter cube in white-light spectral interferometry

We revealed that the phase function of a thin-film structure measured by a white-light spectral interferometric technique depends on the path length difference adjusted in a Michelson interferometer. This phenomenon is due to a dispersion error of a beam splitter cube, the effective thickness of which varies with the adjusted path length difference. A technique for eliminating the effect in measurement of the phase function is described. In a first step, the Michelson interferometer with same metallic mirrors is used to measure the effective thickness of the beam splitter cube as a function of the path length difference. In a second step, one of the mirrors of the interferometer is replaced by a thin-film structure and its phase function is measured for the same path length differences as those adjusted in the first step. In both steps, the phase is retrieved from the recorded spectral interferograms by using a windowed Fourier transform applied in the wavelength domain.     

Dynamic interferometry and differential holography of irregular phase objects using phase conjugate reflection

By using phase conjugate reflection it should be possible to perform high-speed differential interferometry, that is, the measurement of small rapid changes in optical phase shift with time, as well as dynamic and/or differential holography, Schlieren, and other optical measurements of phase perturbations even on highly irregular transparent phase objects.     

Dispersive white-light spectral interferometry including the effect of thin-film for distance measurement

A spectral-domain white-light interferometric technique is used for measuring distances in a Michelson interferometer with a mirror represented by a thin-film structure (TFS) on a substrate. A fibre-optic spectrometer is employed for recording spectral interferograms that include wide wavelength range effects of dispersion in a cube beam splitter and multiple reflection within the TFS. Knowing the effective thickness of the beam splitter, its dispersion and parameters of the TFS and substrate, the positions of the second interferometer mirror are determined precisely by a least-squares fitting of the theoretical spectral interferograms to the recorded ones. We apply the technique to the beam splitter made of BK7 optical glass and to a uniform SiO₂ thin film on a silicon wafer. We compare the results of the processing that include and do not include the effect of the TFS.     

Multiplexed fiber Fabry-Perot temperature sensor system using white-light interferometry

A novel monitoring system for a fiber Fabry-Perot interferometer (FFPI) temperature sensor has yielded a resolution of 0.013 degrees C (0.0025 fringe). Light from a broadband source passes through a scanned Michelson interferometer and is reflected from a FFPI to produce a fringe pattern, the temporal position of which is proportional to a change in the optical length of the fiber interferometer. A second Michelson interferometer with a distributed-feedback laser source is used to correct for variations in the translation rate of the motor-driven scanning mirror. Coherence multiplexing of three such sensors has also been demonstrated.     

Phase-shift algorithm for white-light interferometry insensitive to linear errors in phase shift

White-light interference has changes in fringe contrast. When phase-shift techniques are applied to white-light interference, the phase-shift algorithm which can extract the phase accurately under the contrast changes is required. There is often another requirement that the phase shift between frames should not be restricted to π/2. Computer simulations show that the well-known algorithms have non-negligible errors under both requirements. To find an algorithm which will satisfy the requirements, I extract individual terms (I _j ∓ I _k ) in an algorithmic equation by considering symmetry of light intensity against phase, where I _j is light intensity just after the j-th phase shift. Using computer simulations, I search for appropriate coefficients by which the terms are multiplied in the equation, finally finding an algorithm which satisfies both the requirements with the phase shift used.     

Measurement of geometric phase for mixed states using single photon interferometry

Geometric phase may enable inherently fault-tolerant quantum computation. However, due to potential decoherence effects, it is important to understand how such phases arise for mixed input states. We report the first experiment to measure mixed-state geometric phases in optics, using a Mach-Zehnder interferometer, and polarization mixed states that are produced in two different ways: decohering pure states with birefringent elements; and producing a nonmaximally entangled state of two photons and tracing over one of them, a form of remote state preparation.     

Measurement of Carrier-Envelope-Phase shifts using spectral interferometry with a broad frequency laser source

We investigate and analyze in detail an approach to measure Carrier Envelope Phase shifts by using spectral interferometry. The method which uses a broadband laser source is applied to the characterization of an Electro Optic Carrier Envelope Phase shifter and leads to quick and accurate measurements on a large frequency domain. The shifter is inserted in one arm of a Mach–Zehnder interferometer illuminated by a wide frequency spectrum coherent source. By carefully analyzing the observed fringes, we successfully derived, with a very good accuracy, the main useful parameters of the CEP shifter on the whole investigated wavelength spectrum. The laser source which delivers pulses with a Gaussian spatial distribution and a nearly flat spatial phase does not need to be CEP stabilized and no control of the spectral phase of the pulses is necessary. This has specific advantages compared to other methods.     

扫描白光干涉测量技术的算法比较

干涉条纹零光程差位置的确定是扫描白光干涉测量的关键技术之一。介绍了扫描白光干涉法测量物体轮廓的原理,讨论了确定白光干涉条纹零级条纹位置的几种方法,并对随机生成的表面进行了大量的数字模拟测量和分析比较,得出了各种算法对测量准确度的影响。研究结果对白光干涉的应用研究提供了可靠的理论根据。     

无干涉条纹的光谱位相相干直接电场重构法

提出一种新的诊断飞秒脉冲振幅与位相的高精度测量方法.该方法发展了传统的SPIDER方法，保留了原方法对脉冲信息可以实时、有效和全面地测取的优点，并能克服其不能测量脉宽较大或位相信息复杂的脉冲的缺点.在新方法中和频后的脉冲对没有相对延时，形成无干涉条纹的剪切干涉图.在调节一个小量延时于某些特定值，可去掉剪切干涉图的歧义性.给出数值模拟结果，证明此方法无需经过傅里叶变换滤波，可直接由干涉图唯一地提取出脉冲的振幅与位相信息. 关键词： 光谱位相相干直接电场重构法 飞秒脉冲测量 超快信息光学     

Measurement of fiber chromatic dispersion using spectral interferometry with modulation of dispersed laser pulses

We propose and experimentally demonstrate a method for fiber dispersion measurement based on the modulation of laser pulses stretched by the fiber under test. The measured spectrum of the modulated pulses is the result of the interference between the stretched pulse spectra shifted by the modulation harmonics. The interference pattern is processed as in Fourier transform spectral interferometry. Unlike to conventional spectral interferometry, environmental conditions do not affect the interferogram due to the lack of any interferometer; additionally, large dispersions can be characterized by the method proposed. Its high accuracy is demonstrated in experimental comparison with the widely used phase shift technique.