Dispersive Michelson Interferometer Research Articles

Refraction and dispersion measurement using dispersive Michelson interferometer

A new approach to a dispersive Michelson interferometer (DMI) is introduced. Rings of Equal Chromatic Order (RECO) are formed by a DMI illuminated by a white light source and crossed with an auxiliary dispersion spectrograph. The theoretical foundations are developed and then applied to different glass plates (BAK1, BK7, N-LAF35 and SK4) of thicknesses (12.101, 12.473, 9.930 and 6.602mm), respectively. The sample is introduced in one of the arms of the interferometer. The refraction and dispersion of the samples are deduced from a single RECO interferogram. The refractive index and its variation are measured across the spectral range: 0.500–0.650µm with relative errors of 10−3 and 1.6 ×10−4, respectively. A good agreement between our measurements and reference data is found.

Phase retrieval from spectral interferograms including a stationary-phase point

We report on a simple processing procedure to retrieve the phase from spectral interferograms including a stationary-phase point. First, the numerical simulations are performed to demonstrate high precision of the phase retrieval from the spectral interferogram. Second, the feasibility of the procedure is confirmed in processing the experimental data from a dispersive Michelson interferometer comprising a cube beam splitter and a plate made of BK7 optical glass. From the retrieved spectral phase, the effective thickness of the BK7 optical glass is determined precisely.

Spectral interferometry and reflectometry used for characterization of a multilayer mirror

A white-light spectral interferometric technique is used to retrieve a relative spectral phase and group delay of a multilayer mirror from the spectral interferograms recorded in a dispersive Michelson interferometer. The phase retrieval is based on the use of a windowed Fourier transform in the wavelength domain, and characterization of the multilayer mirror is completed by a three-step measurement of the reflectance spectrum of the mirror in the same interferometer.

The effect of silicon substrate on thickness of SiO2 thin film analysed by spectral reflectometry and interferometry

Techniques of spectral reflectometry and interferometry are used for measuring small changes in thickness of SiO2 thin film grown by thermal oxidation on different silicon substrates. A slightly dispersive Michelson interferometer with one of its mirrors replaced by a thin-film structure is used to measure the reflectance and interferometric phase of the thin-film structure at the same time. The experimental data are used to determine precisely the thickness of the SiO2 thin film on silicon wafers of two crystallographic orientations and different dopant concentrations. We confirmed very good agreement between the experimental data and theory and revealed that the thin-film thickness, which varies with the type of silicon substrate, depends linearly on the wavelength at which minimum in the spectral reflectance occurs. Similar behaviour was revealed for the interferometric phase.

Spectral interferometry and reflectometry used to measure thin films

A new method for a precise measurement of the oscillatory part of phase change on reflection (interferometric phase) from a thin-film structure is presented. The method, which is based on phase retrieval from the spectral interferograms recorded at the output of a slightly dispersive Michelson interferometer, is combined with reflectometry. The interferometric phase of the thin-film structure is measured precisely using a reference sample of known phase change on reflection. The spectral reflectance of the thin-film structure is also measured in the interferometer. The feasibility of the method is confirmed in processing the experimental data for SiO2 thin film on a silicon wafer of known optical constants. Four samples of the thin film are used and their thicknesses are determined. We confirm very good agreement between the thicknesses obtained from the interferometric phase and reflectance measurements.

Windowed Fourier transform applied in the wavelength domain to process the spectral interference signals

We report on processing the spectral interference signals by a new method based on a windowed Fourier transform applied in the wavelength domain. First, the numerical simulations are performed to demonstrate high precision of the phase retrieval from the spectral signal. Second, the feasibility of the method is confirmed in processing experimental data from a dispersive Michelson interferometer comprising a cube beamsplitter made of BK7 glass. From the retrieved spectral phase difference, the effective thickness of the beamsplitter is determined precisely.

Phase retrieval from the spectral interference signal used to measure thickness of SiO2 thin film on silicon wafer

A new method of phase retrieval from the spectral interference signal is presented, which is based on the use of a windowed Fourier transform in the wavelength domain. The phase retrieved by the method is utilized for measuring the thickness of SiO2 thin film on a silicon wafer. The numerical simulations are performed to demonstrate high precision of the phase retrieval. The feasibility of the method is confirmed in processing experimental data from a slightly dispersive Michelson interferometer with one of the mirrors replaced by SiO2 thin film on the silicon wafer. We determine the thin-film thickness for four samples provided that the optical constants for all the materials involved in the experiment are known. We confirm very good agreement with the previous results obtained by the fitting of the recorded channelled spectra to the theoretical ones.

Direct measurement of dispersion of the group refractive indices of quartz crystal by white-light spectral interferometry

We present a white-light spectral interferometric technique employing a low-resolution spectrometer for a direct measurement of the dispersion of the ordinary and extraordinary group refractive indices of a quartz crystal over the wavelength range approximately from 480 to 860nm. The technique utilizes a dispersive Michelson interferometer with the quartz crystal of known thickness to record a series of spectral interferograms and to measure the equalization wavelength as a function of the displacement of the interferometer mirror from the reference position, which corresponds to a balanced non-dispersive Michelson interferometer. We confirm that the measured group dispersion agrees well with that described by the dispersion equation proposed by Ghosh. We also show that the measured mirror displacement depends, in accordance with the theory, linearly on the theoretical group refractive index and that the slope of the corresponding straight line gives precisely the thickness of the quartz 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.

Dispersive white-light spectral interferometry with absolute phase retrieval to measure thin film

We present a white-light spectral interferometric technique for measuring the absolute spectral optical path difference (OPD) between the beams in a slightly dispersive Michelson interferometer with a thin-film structure as a mirror. We record two spectral interferograms to obtain the spectral interference signal and retrieve from it the spectral phase, which includes the effect of a cube beam splitter and the phase change on reflection from the thin-film structure. Knowing the effective thickness and dispersion of the beam splitter made of BK7 optical glass, we use a simple procedure to determine both the absolute spectral phase difference and OPD. The spectral OPD is measured for a uniform SiO(2) thin film on a silicon wafer and is fitted to the theoretical spectral OPD to obtain the thin-film thickness. The theoretical spectral OPD is determined provided that the optical constants of the thin-film structure are known. We measure also the nonlinear-like spectral phase and fit it to the theoretical values in order to obtain the thin-film thickness.

Dispersive white-light spectral two-beam interference under general measurement conditions

Summary Spectral-domain interference of two beams from a white-light source is analysed theoretically and experimentally when the effects of both dispersion in an interferometer and the response function of a spectrometer are taken into account. The spectral interference law is expressed analytically under the condition of a Gaussian response function of a spectrometer. The theoretical analysis is accompanied by experiments employing a dispersive Michelson interferometer and a low-resolution spectrometer. Two experiments with different amounts of dispersion in the Michelson interferometer are realized giving rise to the spectral interference fringes resolved only in the vicinity of the so-called equalization wavelength, at which the group optical path difference between interfering beams is zero. The recorded spectral interferograms are in good agreement with the theoretical ones, which are modelled knowing dispersion in the interferometer and the bandpass of the spectrometer.

Dispersive white-light spectral interferometry to measure distances and displacements

Processing of the spectral interferograms recorded at the output of a dispersive Michelson interferometer by a low-resolution spectrometer is performed with a knowledge of both dispersion and thickness of the interferometer optical element (beam splitter or optical sample). The recorded spectral interferograms, including the equalization wavelengths, are fitted by using a least-squares method to the theoretical interferograms to obtain the optical path differences (OPDs) between interfering beams. From the OPDs, which vary with both the wavelength-dependent refractive index and the thickness of fused-silica optical element, distances or displacements are determined. Within two different configurations of a dispersive Michelson interferometer we show that the range of measurable distances depends on the thickness of the optical element. We also confirm by this measurement technique that errors of manually adjusted 10 μm displacements of the interferometer mirror are below 1 μm.

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

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.

Dispersive Fourier transform measurement of an opaque solid at 6K

A helium temperature cry ostat for use with a dispersive Fourier Michelson interferometer is briefly described. The cryostat has enabled the experimental measurement of the far infra-red complex reflection coefficient and hence complex refractive index of LiTaO3 at 6K, without the need for theoretical fitting models or Kramers-Kronig analysis.