Dispersion-insensitive measurement of thickness and group refractive index by low-coherence interferometry

We describe a low-coherence interferometric technique for simultaneous measurement of geometric thickness and group refractive index of highly dispersive samples. The technique is immune to the dispersion-induced asymmetry of the interferograms, thus overcoming limitations associated with some other low-coherence approaches to this simultaneous measurement. We use the experimental configuration of a tandem interferometer, with the samples to be characterized placed in an air gap in one arm of the measurement interferometer. Unambiguous, dispersion-insensitive measurements of critical group-delay imbalances in the measurement interferometer are determined from the optical frequency dependence of interferogram phases, by means of dispersive Fourier transform spectrometry. Sample thickness and group refractive index are calculated from these group delays. A thickness measurement precision of 0.2 mum and group index measurement accuracy of 5 parts in 10(5) across a wavelength range of 150 nm have been achieved for BK7 and fused-silica glass samples in the thickness range 2000 to 6000 mum.     

Measurement of group refractive index wavelength dependence using a low-coherence tandem interferometer

A technique for the measurement of the group refractive index wavelength dependence of optical materials using a low-coherence tandem interferometer and a spectrometer is proposed. Four channeled spectra resulting from interferences of light beams from different pairs of optical paths are used for the calculation of optical path differences. The group refractive index wavelength dependence is calculated from these optical path differences generated from the sample under measurement. No a priori information of the geometric thickness of a sample is required. The wavelength dependence of the group refractive index of the samples BK7 parallel plate of 5.200 and 10.025 mm from 675 to 850 nm is experimentally measured with an accuracy of the order of 10(-5) and a repeatability of the order of 10(-9).     

Low-coherence interferometer system for the simultaneous measurement of refractive index and thickness

We have developed a low-coherence interferometer system used for the simultaneous measurement of refractive index n and thickness t of transparent plates. Both the phase index n(p) and group index n(g) can be determined automatically in a wide thickness range of from 10 microm to a few millimeters. Two unique techniques are presented to measure n(p), n(g), and t simultaneously. One allows us to determine n(p), n(g), and t accurately by using a special sample holder, in which the measurement accuracy is 0.3% for the thickness t above 0.1 mm. In the other technique the chromatic dispersion delta n of index is approximately expressed as a function of (n(p) - 1) on the basis of measured values of n(p) and n(g) for a variety of materials, and then the simultaneous measurement is performed with a normal sample holder. In addition, a measurement accuracy of less than 1% is achieved even when the sample is as thin as 20 microm. The measurement time is also 3 min or more.     

Decoupling refractive index and geometric thickness from interferometric measurements of a quartz sample using a fourth-order polynomial

A Michelson interferometer setup was used to determine refractive index and thickness of a fused-quartz sample with no knowledge of either parameter. At small angles, < 10 degrees, the interferometer equation follows a fourth-order polynomial in the sample refractive index alone, effectively decoupling the sample thickness from the equation. The incident angle of the He-Ne laser beam versus fringe shift was fitted to the polynomial, and its coefficients obtained. These were used to determine refractive index to within 6 x 10(-4) of the known value with an accuracy of +/- 1.3%. Sample thickness was determined to an accuracy of +/-2.5%. Reproducibility of the rotating table was determined to be +/-2 x 10(-3) degrees.     

Fiber optic differential interferometer

Based on low-coherence interferometry in standard single-mode fibers, a differential interferometer has been proposed. A twin-reflective mirror demodulator was used in the differential interferometer. This interferometer can be used as a fiber optic sensor to measure the elongation of the fiber or strain substressed on the fiber and has the advantage that it can automatically compensate for temperature-induced variations in the refractive index and thermal expansion of the silica fibers     

Optical coherence tomography system with no high-precision scanning stage and stage controller

Optical coherence tomography (OCT) is a novel technique for noninvasive imaging based on the use of a low-coherence interferometer. Conventionally, obtaining high-resolution images requires the use of high-precision sample and scanning stages and a stage controller for simultaneous measurement of the refractive index and the thickness of an optical sample. However, in this study a novel optical-fiber-type OCT system is developed that does not need both a high-precision scanning stage and a stage controller. Additionally, two signal demodulation processes are described. Compared with that of conventional OCT systems, the current configuration eliminates the high-precision scanning stage and stage controller and is therefore cheaper and less complex. Also, this new technique could be applied to conventional OCTs in biotissue scanning.     

Angstrom-range optical path-length measurement with a high-speed scanning heterodyne optical interferometer

A highly accurate method of optical path-length measurement is introduced by use of a scanning heterodyne optical interferometer with no moving parts. The instrument has demonstrated the potential to measure optical path length at angstrom resolution over continuous thickness in the micrometer range. This optical path length can be used to calculate the thickness of any material if the refractive index is known or to measure the refractive index of the material if the thickness is known. The instrument uses a single acousto-optic device in an in-line ultra-stable reflective geometry to implement rapid scanning in the microsecond domain for thickness measurements of the test medium.     

Rotation angle measurement based on white-light interferometry with a standard optical flat

We propose a simple white-light interferometric method of measuring a one-dimensional rotation angle with use of an optical plane parallel plate of standard refractive index. The phase change of the interference pattern of the interferometer during the rotation of the flat plate of known refractive index and thickness placed in one of the interferometer's arms is used for determination of the rotation angle. This method has been demonstrated for an accurate angle measurement over the angle range from 0° to 40° within a maximum uncertainty of 0.057°.     

Simultaneous measurement of thickness and refractive index based on rotation incidence angle

A method for simultaneous measurement of geometric thickness and refractive index of an optical wafer is presented. By using a fiber optic Mach–Zehnder interferometer (MZI) with a free space, the transmission spectrum of a MZI for the optical wafer at different incidence angle is interrogated, and the geometric thickness and the refractive index of the optical wafer are measured simultaneously. With the transmission spectrum, we can obtain a clear interferogram with a high visibility no matter how small the measurement range of the refractive index. Therefore the proposed technique possesses a broad measurement range and low cost. The experimental results show that the maximum errors of the geometric thickness and the refractive index are only 0.007?mm and 0.008, respectively, and that a broad measurement from 1.316 to 3.503 can be achieved.     

基于Edlén公式空气折射率测量系统的校准研究

为了检验对激光干涉仪测量精度有很大影响的空气折射率测量系统的测试性能,提出一种可用于基于Edlén公式的空气折射率测量系统的校准方法,并且设计了专门的校准装置,该装置主要由温度、气压以及湿度测量系统组成。实验证明：取包含因子k=2时,温度在(5~40)℃区间,测量不确定度U优于0.02 ℃;气压在(66~105)kPa区间,U=18 Pa;湿度在(10~90)%RH区间,U=2.0%RH,等效于整个系统对应的空气折射率测量的相对不确定度优于1×10^-7     

Determination of refractive indices of biconvex lenses by use of a Michelson interferometer

Measurements of lens parameters such as focal length, radius of curvature, and refractive index are important. We describe a measurement method that utilizes a Michelson interferometer to determine parameters of thin, convex lenses. The real fringe system formed by a Michelson interferometer is used to determine the focal lengths and the radii of curvature of the lenses. The refractive index of the lens material is determined from the thin-lens formula. We were able to determine the refractive indices to an accuracy as great as 99.97%. A detailed theoretical and experimental analysis is given.     

An optical fibre sensor for dynamic deformation measurements based on the intensity modulation of a low-coherence source

Abstract

An optical fibre sensing technique for the measurement of dynamic deformations using a Michelson interferometer is reported. The method applied to interferometers with an initial path unbalance of around 1 cm is based on the rf intensity modulation of a low-coherence source. A large measurement range of 1 cm is intrinsic to the method and with an adequate demodulation process sensitivity better than 10 μm is obtained. This novel approach allows for measuring dynamic deformations with a bandwidth up to 100 Hz.     

Axial-scanning low-coherence interferometer method for noncontact thickness measurement of biological samples

We investigated a high-precision optical method for measuring the thickness of biological samples regardless of their transparency. The method is based on the precise measurement of optical path length difference of the end surfaces of objects, using a dual-arm axial-scanning low-coherence interferometer. This removes any consideration of the shape, thickness, or transparency of testing objects when performing the measurement. Scanning the reference simplifies the measurement setup, resulting in unambiguous measurement. Using a 1310?nm wavelength superluminescent diode, with a 65?nm bandwidth, the measurement accuracy was as high as 11.6?μm. We tested the method by measuring the thickness of both transparent samples and nontransparent soft biological tissues.     

Local characterization of fiber-Bragg gratings through combined use of low-coherence interferometry and a layer-peeling algorithm

The technique presented here allows us to obtain an accurate determination of the refractive index modulation amplitude, the mean effective index, and the chirp of fiber-Bragg gratings. A layer-peeling algorithm is used to extract this information from low-coherence interferometry measurements. Finally, we present a systematic study over 10 uniform and chirped gratings to proof the reliability and accuracy of this technique.     

Method for measuring the refractive index and the thickness of transparent plates with a lateral-shear,wavelength-scanning interferometer

A new method for measuring simultaneously the thickness and the refractive index of a transparent plate is proposed. The method is based on a simple, variable lateral-shear, wavelength-scanning interferometer. To achieve highly accurate measurements of both refractive index n and thickness d we use several means to determine these two quantities. We finely tune a distributed-feedback diode laser light source to introduce a phase shift into the detected signal, whereas we make the sample rotate to produce variable lateral shearing. Phase shifting permits precise determination of the optical thickness, nd, whereas refractive index n is obtained from the retrieved phase of the overall interference signal for all incidence angles.     

Simultaneous measurement of refractive index and thickness of birefringent wave plates

A nondestructive measurement system based on a position sensing detector (PSD) and a laser interferometer for determining the thickness and refractive indices of birefringent optical wave plates has been developed. Unlike previous methods presented in the literature, the proposed metrology system allows the refractive index and thickness properties of the optical plate to be measured simultaneously. The experimental results obtained for the e-light and o-light refractive indices of a commercially available birefringent optical wave plate with refractive indices of n(o)=1.542972 and n(e)=1.552033 are found to be accurate to within 0.004132 and 0.000229, respectively. Furthermore, the experimentally derived value of the wave plate thickness deviates by no more than 0.9 microm from the analytically derived value of 453.95 microm. Overall, the experimental results confirm that the proposed metrology system provides a simple yet highly accurate means of obtaining simultaneous measurements of the refractive indices and thickness of birefringent optical wave plates.     

Interferometric measurement of the refractive-index distribution in plastic lenses by use of computed tomography

A nondestructive measurement method that makes possible the measurement of a three-dimensional refractive-index distribution of any shape plastic lens is presented. In this method, a Mach-Zehnder interferometer and shearing interferometer are combined into a single optical system and are used selectively. Interference fringes of a test object that is immersed in matching liquid are detected at various rotation angles. And transmitted wave fronts are calculated with these interference fringes. Finally, the refractive-index distribution is obtained by computed tomography analysis. In addition, accurate control of the matching liquid temperature makes it possible to measure the absolute refractive index of the test object. This system has good performance with a measurement accuracy of 10(-4) or better peak to valley.     

A new refractometer by combining a variable length vacuum cell anda double-pass Michelson interferometer

A new refractometer with a variable length vacuum cell has been developed to eliminate errors caused by deformations in optical windows of the cell. The refractive index of air is determined by measuring the changes in the optical path difference between the air of interest and a vacuum as a function of the changes in the cell length. An optical phase modulation technique and a dark fringe detection method are used to obtain a high resolution in measuring the optical path difference by a double-pass Michelson interferometer. A combined standard uncertainty of 5×10^-9 in the measurement of the refractive index of air has been achieved     

Spectrum-sliced Fourier-domain low-coherence interferometry for measuring the chromatic dispersion of an optical fiber

We present a novel spectrum-slicing method for measuring the chromatic dispersion of an optical fiber in Fourier-domain low-coherence interferometry. Broadband spectral interference data obtained from a low-coherence interferometer is sliced with Gaussian window functions. Each sliced spectral datum is used to calculate a relative group delay with Fourier transformation at the peak wavelength of a narrow window function. We have demonstrated that our proposed method is very powerful and simple for measuring chromatic dispersion and second-order dispersion in optical fibers and optical devices. Comparison of the proposed method with a conventional measurement method agrees within 0.5%.     

Thermal nonlinear optical response of meso-tetraphenylporphyrin under aggregation conditions versus that in the absence of aggregation

In this work, measurement of thermally induced nonlinear refractive index of meso-tetraphenylporphyrin (H₂TPP) at different concentrations in 1,2-dicoloroethane using a double-grating interferometer set-up in a pump–probe configuration is reported. The formation of aggregates of H₂TPP at concentrations greater than ca. 5 × 10^?5 M was evident by deviation from Beer’s law. An almost focused pump beam passes through the solution. A part of the pump beam energy is absorbed by the sample and therefore a thermal lens is generated in the sample. An expanded probe beam propagates through the sample and indicates the sample refractive index changes. Just after the sample a band-pass filter cuts off the pump beam from the path but the distorted probe beam passes through a double-grating interferometer consisting of two similar diffraction gratings with a few centimetres distance. A CCD camera is installed after the interferometer in which on its sensitive area two diffraction orders of the gratings are overlying and producing interference pattern. The refractive index changes of the sample are obtained from the phase distribution of the successive interference patterns recorded at different times after turning on of the pump beam using Fourier transform method. In this study, for different concentrations of H₂TPP in 1,2-dichloroethane solution the thermal nonlinear refractive index is determined. Also, we present the measurement of the temperature changes induced by the pump beam in the solution. We found that value of nonlinear refractive index increased by increasing the concentration up to a concentration of 5 × 10^?4 M and then decreased at higher concentrations. In addition, we have investigated the stability of the observed thermal nonlinearity after a period of two weeks from the sample preparation.