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 linear velocity using a resonant ring interferometer with a low-coherence light source

It is demonstrated theoretically and experimentally that linear velocities of reflecting objects may be measured using a resonant ring interferometer with a low-frequency light source. The limiting sensitivity of this interferometer is estimated. It is shown that a resonant ring interferometer can be used to measure extremely low linear velocities corresponding to subhertz Doppler frequency shifts of light, which cannot be measured by conventional Doppler techniques based on direct measurements of the frequency difference between the initial and reflected waves. Pis’ma Zh. Tekh. Fiz. 25, 34–42 (December 12, 1999)     

Measurement of the nonlinear refractive index of fibers with a rotating nonlinear Sagnac interferometer

We developed a method to measure the nonlinear refractive-index coefficient of fibers using a nonlinear Sagnac interferometer. To enhance the measurement accuracy, we employed a phase-sensitive detection technique using a rotational sensitive property of the Sagnac interferometer. The measured values were reproducible to within 10 % accuracy.     

Measurement of the induced refractive index in a photothermorefractive glass by a liquid-cell shearing interferometer

A liquid-cell shearing interferometer was developed to measure refractive-index variations (delta n) in transparent materials. The cell was filled with a liquid having a matched refractive index. The achieved resolution was better than 1/1000 of a fringe shift and resulted in a delta n measurement sensitivity down to 10(-7) for 1-mm-thick samples. A refractive-index increment in photothermorefractive glass of up to 5 x 10(-6) was observed after UV exposure at 325 nm. A refractive-index decrement of up to 1 x 10(-3) was observed after thermal development of the exposed sample. It was proved that photothermorefractive glass obeys the reciprocity law; i.e., delta n depends on the UV dosage but does not depend on the irradiance.     

Determination of the refractive index of a lens using the Murty shearing interferometer

An innovative nondestructive technique for measuring the refractive index of a simple lens is described. The proposed method is superior to existing ones because the focusing error and the spherical aberrations are reduced. Apart from this, the strength parameters (i.e., r1 and r2) of a lens are not required at all since the derived lens-index formula is independent of the lens's physical parameters. The shearing interferometric technique is a sensitive aid for detecting the focal plane of the test lens. A modified criterion for determining the focal length has been used. In this case two miscible liquids or compounds are not necessary. The well-known liquid immersion method is the particular case of this technique. The Murty shearing interferometer has been used as an optical device to observe the defocusing defect in the form of fringes. The amount of defocusing is easily calculated. An equation for this error has been theoretically deduced and experimentally verified. The technique described is quick to perform and easy in handling. The various effects due to the lens's aperture and aberrations, thickness of the glass cell, liquid column, etc. are also discussed. For N liquids, there are N(N - 1)/2 ways of calculating the lens's index. Owing to its nature this is termed the nondestructive nonmiscible-liquid immersion technique for index measurement of a lens.     

Simultaneous determination of the refractive index and wedge angle of an optical wedge plate using a photorefractive holographic interferometer

Abstract

A simple and effective method for simultaneously determining the refractive index and the wedge angle of an optical wedge plate is described. The method is based on a real-time holographic interferometer which uses a photorefractive crystal as the recording and reconstruction medium. The wedge sample under test is inserted into a rectangular cell that is placed in the object light beam of the holographic interferometer. The interference patterns produced before and after a reference liquid is poured into the cell are received by a CCD camera and stored in a computer, respectively. The refractive index and the wedge angle of the wedge sample are determined by measuring the number of fringes falling inside a fixed aperture. The principle of the method is analysed and some experimental results with adequate accuracy are given.     

Measuring dispersion between two modes of an optical fibre using low-coherence spectral interferometry with a Michelson interferometer

Abstract

It is demonstrated experimentally that even if the spectral interference between two modes of an optical fibre excited by a low-coherence source is not resolved at its output by a spectrometer of a given resolving power, it is resolved in the Michelson interferometer configuration. In a tandem configuration of a dispersive Michelson interferometer and a two-mode optical fibre, the optical path difference (OPD) in the interferometer is adjusted close to the group OPD between modes to produce a low-frequency spectral modulation that can be processed. Thus, using the Fourier-transform method in processing the measured spectral modulations and subtracting the effect of the dispersive Michelson interferometer, the wavelength dependence of the group OPD between two modes of the optical fibre over a limited spectral region is obtained.     

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.     

Extrinsic fiber-optic Fabry-Perot interferometer sensor for refractive index measurement of optical glass

A simple fiber-optic sensor based on Fabry-Perot interference for refractive index measurement of optical glass is investigated both theoretically and experimentally. A broadband light source is coupled into an extrinsic fiber Fabry-Perot cavity formed by the surfaces of a sensing fiber end and the measured sample. The interference signals from the cavity are reflected back into the same fiber. The refractive index of the sample can be obtained by measuring the contrast of the interference fringes. The experimental data meet with the theoretical values very well. The proposed technique is a new method for glass refractive index measurement with a simple, solid, and compact structure.     

Frequency dependence in a liquid's complex refractive index measured with infrared spectroradiometry

A laboratory measurement of wavelength dependence in the real n(lambda) and the imaginary k(lambda) parts of a liquid's complex refractive index is presented. A known heat flow through the liquid-gas interface is generated while a high-resolution infrared radiance spectrum is taken simultaneously. Wavelength variations of the absorption coefficient allow the emerging radiation to sense subsurface temperature gradients. This technique is valid only at intervals at which the absorption coefficient is sufficiently low to allow subsurface temperatures to be measured. Knowledge of a liquid's thermal conductivity, specific heat, and light transmission speed is required. Measurement error depends on radiance measurement error and the minimization of atmospheric parameters.     

Thickness dependence of refractive index for anodic aluminium oxide films

Abstracts are not published in this journal     

High sensitivity of taper-based Mach-Zehnder interferometer embedded in a thinned optical fiber for refractive index sensing

A taper-based Mach-Zehnder interferometer (MZI) embedded in a thinned optical fiber is demonstrated as a highly sensitive refractive index (RI) sensor. A RI sensitivity of 2210.84 nm/RIU (refractive index unit) is obtained at the external RI of 1.40, which is ten times higher than that of normal taper- and long-period fiber grating (LPFG)-based sensors. The sensitivity can be further improved by decreasing the diameter of the thinned fiber and increasing the interferometer length of the MZI. The proposed MZIs have lower temperature sensitivities compared with normal fiber sensors, which is a desirable merit for RI sensors to reduce the cross sensitivity caused by thermal drift.     

Accurate measurement of interferometer group delay using field-compensated scanning white light interferometer

Interferometers are key elements in radial velocity (RV) experiments in astronomy observations, and accurate calibration of the group delay of an interferometer is required for high precision measurements. A novel field-compensated white light scanning Michelson interferometer is introduced as an interferometer calibration tool. The optical path difference (OPD) scanning was achieved by translating a compensation prism, such that even if the light source were in low spatial coherence, the interference stays spatially phase coherent over a large interferometer scanning range. In the wavelength region of 500-560 nm, a multimode fiber-coupled LED was used as the light source, and high optical efficiency was essential in elevating the signal-to-noise ratio of the interferogram signal. The achromatic OPD scanning required a one-time calibration, and two methods using dual-laser wavelength references and an iodine absorption spectrum reference were employed and cross-verified. In an experiment measuring the group delay of a fixed Michelson interferometer, Fourier analysis was employed to process the interferogram data. The group delay was determined at an accuracy of 1×10(-5), and the phase angle precision was typically 2.5×10(-6) over the wide wavelength region.     

Simultaneous measurement for liquid level and refractive index based on all-fiber modal interferometer

A simple fiber sensor capable of simultaneous measurement of liquid level and refractive index (RI) is proposed and experimentally demonstrated. The sensing head is an all-fiber modal interferometer manufactured by splicing an uncoated single-mode fiber with two short sections of multimode fiber. The interference pattern experiences blue shift along with an increase of axial strain and surrounding RI. Owing to the participation of multiple cladding modes with different sensitivities, the height and RI of the liquid could be simultaneously measured by monitoring two dips of the transmission spectrum. Experimental results show that the liquid level and RI sensitivities of the two dips are 245.7 pm/mm, ?38 nm/RI unit (RIU), and 223.7 pm/mm, ?62 nm/RIU, respectively. The approach has distinctive advantages of easy fabrication, low cost, and high sensitivity for liquid level detection with the capability of distinguishing the RI variation simultaneously.     

Measurement of the wavelength dependence of birefringence for optical disk substrates

The in-plane and vertical birefringence of polycarbonate plastic substrates of optical disks are measured for wavelengths between 360 and 860 nm, which covers the full range of interest for blue as well as for the current red and infrared recording. It is found that the birefringence generally decreases as the measurement wavelength is increased. In a typical case, the in-plane birefringence, Δn‖ goes from 1.7 × 10(-5) to 1.2 × 10(-5), and the vertical birefringence, Δn⊥, drops from 7.5 δ 10(4-) to 5.7 × 10(4-) in the wavelength range from 360 to 860 nm.