Dispersive spectral-domain two-beam interference analysed by a fibre-optic spectrometer

Abstract

The effect of a fibre-optic spectrometer on analysed spectral interference of two beams from a white-light source is studied theoretically and experimentally, including the effect of dispersion in an interferometer. First, the spectral interference law is expressed analytically under the condition of a Gaussian response function of a fibre-optic spectrometer, and then second, the theoretical analysis is accompanied by three experiments employing a fibreoptic spectrometer and a Michelson interferometer with different amounts of dispersion. Within one experiment the interference fringes are resolved over a wide spectral range and within two experiments the interference fringes are resolved only in a narrow spectral range around a wavelength at which the group optical path difference between interfering beams is zero. Knowing dispersion in the interferometer and the bandpass of the spectrometer, the positions of the interferometer mirror in the corresponding range are determined and good agreement between the recorded spectral interferograms and the theoretical ones is found. IntroductionRecent advances in spectral-domain optical interferometry [1, 2] have attracted considerable interest in using portable miniature fibre-optic spectrometers in various fields of optics and in measuring their parameters and characteristics. Among the functions and parameters characterizing spectrometers, response functions and bandpasses are the most important. Time-domain and spectral-domain interferometric techniques [2,3], including the applications of Fabry-Perot and Michelson interferometers or prism-and grating-based spectrometers, play key roles in measuring not only the temporal coherence functions and the spectra of light sources, but also the parameters and characteristics of the spectral instruments [4][5][6][7][8][9]. Thus, instrument functions [4], modulation transfer functions [5] and spectral slit widths of a grating [5] and a prism spectrometer [6] have been measured or determined for given spectrometer slit widths. More recently, time-domain and spectral-domain low-coherence interferometry has been used to measure the spectral bandpasses of a fibre-optic spectrometer with different read optical fibres [7]. Most recently, a white-light spectral interferometric technique has been used to measure the wavelength dependence of the spectral bandpass of the spectrometer [8]. Moreover, the constant-bandwidth operation of the Czerny-Turner monochromator has been reviewed [9].

Interferometric measurement of nanoliter volume concentration of binary liquid mixtures

“…The spectrometer S2000, having an asymmetric crossed CzernyTurner design, is equipped with a 600 l=mm diffraction grating and a Sony ILX511 linear array CCD with 2048 elements (Hlubina, 2004). The maximum speed of the spectrum capturing with this spectrometer has been 3 ms, but the average of 8 measurements was used, yielding the total acquisition time of 24 ms.…”

“…We have found the zero OPD positions, for binary mixtures of different concentrations, applying the wavelet algorithm for locating the center of a low coherence interferogram (Hlubina, 2004). Using these data we have calculated the index of refraction of binary liquids and, after that, their concentration using the Lorentz-Lorenz equation.…”

<title>Applications of dispersive white-light spectral interferometry in optics</title>

“…Once the overall thickness tef t and the spectral phase 5()) are determined, it results from Eq. (19) that knowing the refractive index dispersion n(\) it is possible to fit the theoretical spectral interferograms (14) to the recorded ones and to determine precisely the mirror positions L.15 For the equalization wavelength Aeq the relation is fulfilled (20) from which it results that for the various positions L of mirror 2 in the interferometer, the different equalization wavelengths '\eq can be resolved, so that the function L = L(Aeq) can be obtained. If one of the equalization wavelengths, A0, is chosen as that corresponding to the reference position L0 of mirror 2 in the interferometer, the displacement tL = L -L0 of mirror 2 from the reference position is related to the differential group refractive index LN(Aeq) N(Aeq) _ N(Xo) of the material via the relation L&L(Aeq) I.N(Aeq)(t -tef), (21) which enables us to determine either the overall thickness t -tef of the optical material of known dispersion or the differential group refractive index dispersion LN = LN(Aeq) of the optical material of known overall thickness t -tef.…”

A simple white-light fiber-optic interferometric sensing system for absolute position measurement

“…where: o-the optical angular frequency, I WLS (o)-the optical power spectrum of the used white light source (WLS), V-the overall spectral fringe visibility [6][7][8], where VZ0 and it includes the effect of the response function of the spectrometer or equivalently the coherence length of the WLS and also the effects of the geometry of the sensing interferometer, c-the speed of light in vacuum, D-the distance between the fiber tip and the sensing mirror, and t 0 -the time delay. In Fig.…”