Analysis of time-domain and spectral-domain two-beam interference including the effect of a variable spectral bandpass of a detecting system

Abstract

The effect of a variable Gaussian response function of a monochromator in a detecting system with a broadband detector is included in the theoretical and experimental analysis of time-domain and spectral-domain interference of two light beams from a source of a multimode Gaussian spectrum. The time-domain theoretical analysis gives the analytic expressions for the measured complex degree of temporal coherence of the light with and without the effect of variable spectral bandpass of the detecting system. The spectral-domain theoretical analysis of the two-beam interference gives the spectral interference law from which the visibility of the spectral interference fringes resolved for a given delay in the interferometer by a spectrometer is expressed as a function of the bandpass of the spectrometer. The theoretical conclusions are confirmed experimentally in the Michelson interferometer configuration using a laser diode operated below the threshold, a prism monochromator and a p-i-n photodetector. From the width of the central peak in the measured visibility dependence that narrows with increasing slit width of the monochromator, the spectral bandpass of the monochromator is evaluated. It is also shown how the visibility of the spectral interference fringes decreases as the slit width of the prism spectrometer increases.     

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 fibre-optic 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.     

Measuring intermodal dispersion in optical fibres using white-light spectral interferometry with the compensated michelson interferometer

Abstract

Employing a low-resolution miniature fibre-optic spectrometer, it is demonstrated that the spectral interference fringes are resolved at the output of a tandem configuration of the compensated (non-dispersive) Michelson interferometer and a two-mode optical fibre only in the vicinity of two different equalization wavelengths. Namely, the overall equalization wavelength at which the optical path difference (OPD) in the interferometer is the same as the group OPD between modes, and the fibre equalization wavelength at which the group OPD between modes is zero. Moreover it is shown that the OPD adjusted in the interferometer and measured as a function of the overall equalization wavelength gives directly the spectral dependence of the intermodal group OPD in an optical fibre. Thus the new technique of white-light spectral interferometry is used to measure intermodal dispersion in two different two-mode optical fibres in the spectral range approximately from 620 to 850 nm.     

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.     

Interferometric measurement of the modulation transfer function of a spectrometer by using spectral modulations

We present our results on measurement of the modulation transfer function (MTF) of a given spectrometer by using the sinusoidally modulated spectrum from a Michelson interferometer with white light. We studied the MTF by varying the periodicity of the spectral fringes produced by the interferometer. Experimental data are fitted to a theoretical model to derive the spectral slit width from the measured MTF of the spectrometer.     

Determination of the instrument function of a grating spectrometer by using white-light interferometry

We determined the instrument function or the response function of a grating spectrometer with finite slit widths in conditions of partial coherent illumination, by using a spectral-interference technique with white light. A Michelson interferometer of variable path delay is used to produce the spectral-interference fringes of required spacing. By deconvolution of the spectral visibility data for various exit and entrance slit widths, we have determined the exact form and frequency width of the instrument function for the spectrometer as well as the working region of the spectrometer for the least distorted output spectrum.     

White-light spectral interferometric technique to measure the wavelength dependence of the spectral bqandpass of a fibre-optic spectrometer

Abstract

A spectral-domain white-light interferometric technique with channelled spectrum detection is used to measure the wavelength dependence of the spectral bandpass of a fibre-optic spectrometer. In an experimental setup comprising a halogen lamp, a non-dispersive Michelson interferometer and the spectrometer to be measured, spectral interferograms are recorded for different optical path differences (OPDs) between interfering beams. By processing the recorded spectral interferograms using discrete filtering and a fringe amplitude demodulation method, spectral fringe visibilities, first, as a function of the wavelength for given OPDs, and second, as a function of the OPD at given wavelengths, are obtained. It is confirmed, in accordance with theory, that the latter spectral fringe visibility functions are Gaussian functions with maxima and widths dependent on the wavelength. From the widths of the Gaussian spectral fringe visibility functions the wavelength dependence of the spectrometer bandpass is determined over a wide spectral range.     

Integrated optical Young interferometer

The integrated optical configuration of a Young interferometer is proposed for refractometry and chemical sensing. We coupled light into an integrated optical Ybranch by fixing a laser diode directly at the input of the optical device. We solved the problem of ambiguity in the interference order by operating the laser diode at currents below threshold, resulting in visibility modulation of the interference fringes caused by the low coherence length of the emitted light. A very compact device results that measures the refractive index of liquids or gases. An electronic scanning technique by means of a CCD array provides a fast readout without the need for moving parts.     

Measuring dispersion between two modes of an optical fibre using time-domain and spectral-domain low-coherence interferometry

Abstract

Group optical path difference (OPD) between two modes of an optical fibre excited by a low-coherence source characterized by a multimode spectrum is evaluated measuring both the visibility dependence in the Michelson interferometer configuration and the spectral modulation at the output of the optical fibre. Using the Fourier-transform method in processing the measured spectral modulations, a slight wavelength dependence in the group OPD between two modes of the optical fibre is resolved. Comparing the group OPD corresponding to a central wavelength of the measured spectral region with the group OPD obtained from the measured visibility dependence, good agreement between results of the measurements in the spectral domain and in the time domain is achieved.     

Multipass Michelson interferometer with the use of a wavelength-modulated laser diode

An improved multipass Michelson interferometer is implemented. This technique uses the fact that the wavelength of a laser diode varies in proportion to the diode's injection current. With this method the sensitivity augmentation is accomplished by inserting a beam splitter into one arm of the interferometer, resulting in multiple reflections between the end mirror and the beam splitter. In addition, the interference of laser beams reflected from two arms can be accomplished with unequal arms in the condition of a short coherence length. The sensitivity increase of interference fringes and the compensation of the short coherence length have been demonstrated in experiments.     

Time-domain intermodal interference including higherorder dispersion effects

Abstract

The intermodal interference is analysed theoretically at the output of both a few-mode optical fibre alone and a tandem configuration of a Michelson interferometer with an optical fibre when higher-order intermodal dispersion effects are taken into account. It is revealed theoretically that in a special case of a two-mode optical fibre with a quadratic spectral dependence of the difference of propagation constants, which includes the equalization frequency with zero intermodal group delay, and fibre excitation by a broad-band light source, the time-domain visibility functions differ substantially from those corresponding to fibre excitation by a low-coherence light source. Moreover, measuring a two-mode optical fibre using time-domain and spectral-domain white-light interferometric techniques, some theoretical results are confirmed experimentally.     

Stability improvements for an interferometer through study of spectral interference patterns

Conventional Mach-Zehnder interferometer configuration is modified to enhance its stability from the vibrations. To study the effects of vibrations on the Mach-Zehnder interferometer, we used spectral interference fringes from a broadband nanosecond dye laser source. We observed an improvement in the stability of the interferometer by a factor of 3.     

Grating interferometry with a semiconductor light source

The properties of a fiber-optic-based grating interferometer with a laser diode as the light source are described. The influence of effects such as wavelength shift, line broadening, and mode hopping on the quality of an interference pattern is investigated both theoretically and experimentally. Introduction of carrier fringes in the interference pattern through the injection-current-induced modulation of a laser diode is shown. The requirements for temporal coherence properties of a light source in grating interferometry are given.     

Field widening a Michelson interferometer in convergent light

The theory of and experimental results associated with field widening a Michelson interferometer in convergent light are described. The consequence of this configuration is a relatively compact optical system with improved system étendue and reduced system transmission loss. Although the convergence of light introduces significant wave aberration, adequate visibility of interference can still be obtained at a path difference sufficiently large for high-resolution Doppler imaging. Experimentally, a full-angle field of view of 9 degrees with a minimum visibility of 0.5 was achieved. The particular advantages of the new configuration in the application of two-dimensional interferometric Doppler imaging in the ultraviolet spectral region are also discussed.     

Differential wavelength-scanning heterodyne interferometer for measuring large step height

An interferometer based on the differential heterodyne configuration and wavelength-scanning interferometry for measuring large step heights is presented. The proposed interferometer is less sensitive to environmental disturbances than other interferometers and can accurately measure interference phases. A tunable diode laser is utilized to illuminate the interferometer and thus solve the phase ambiguity problem. Counting the interference fringes as the wavelength is scanned through a known change in wavelength directly determines the step height. Three gauge blocks of different lengths, 5, 10, and 50 mm, are individually wrung on a steel plate to simulate large step heights. Comparing the results measured by the proposed interferometer with those by the gauge block interferometer reveals that the accuracy is approximately 100 nm.     

Fringe visibility of multimode laser light scattered through turbid water

Several years ago Swanson [Proc. SPIE 1750, 397 (1992)] performed a simple Michelson interferometric determination of the coherence length of a multimode argon-ion laser after the light passed through a tank of water. As colloidal particles were added to the water the observed coherence length (as measured by twice the distance the mirror moved for fringes to disappear) decreased. Subsequently, a series of careful experiments were performed with a single-mode laser to more accurately measure this change. In these experiments it was found that the 1.5-MHz width of the 514.5-nm line of a single-mode argon-ion laser broadened by as much as 1.3 +/- 0.2 MHz when small colloidal particles were added. At first glance such a broadening should not have resulted in any discernible change in the original Michelson experiment because the gain curve for the multimode laser is of the order of a few gigahertz. The zeros in the fringe visibility function depend on the spectral characteristics of the modes. Upon scattering, the spectral characteristics of the individual laser modes change from Voigt functions, containing both Lorentzian and Gaussian components, to primarily Gaussian. It is this change in the statistical properties of the modes, not the broadening, that accounts for the change in the fringe visibility for a multimode source.     

基于VC++的光谱分析软件设计与实现

 为了对红外干涉型光谱分析仪采集得到的干涉条纹进行分析,准确地反演相应的光谱分布函数,设计了基于迈克尔逊干涉结构的光谱分析算法,并通过VC++完成了对应的光谱分析软件．实验对830,940,1 064 nm三个常用近红外波长进行测试,分别与FTIR500型光谱仪的检测数据和MATLAB仿真数据进行对比．实验结果显示,本算法获得的光谱数据在主波长位置选择以及幅值探测上与FTIR500型光谱仪相近,而在噪声、杂波抑制方面优于FTIR500型光谱仪．数据处理速度略低于MATLAB,但光谱分布函数信噪比要高于MATLAB的数据处理结果,证明本系统具有一定的优越性．     

Multiple reflections in a wide-angle Michelson interferometer

The effect of multiple reflections from a semireflecting surface such as an interference filter located in front of or behind a wide-angle Michelson interferometer (WAMI) is examined. By considering the instrument as a complex operator on the incident electric field, theoretical results are obtained which describe a large variety of configurations. Experimental results are presented which are consistent with these results. It is concluded that since the presence of these reflections changes the form of the observed fringes and affects measurements of the phase and visibility of the fringes, care must be taken to avoid such reflections in designing WAMIs.     

Experiments with active phase matching of parallel-amplified Multiline HF laser beams by a phase-locked Mach-Zehnder interferometer

Active phase matching of multiline HF laser beams by means of a phase-locked Mach-Zehnder interferometer was demonstrated by locking the interferometer to the central interference fringe at zero optical path length difference. The central fringe could be found by varying the spectral content of the input beam. Laser amplification in one leg of the interferometer decreased fringe visibility without adversely affecting locking. Single-line fringe patterns produced by an array spectrometer (while the interferometer was operated in its scanning mode) were analyzed to show that no significant dispersion occurred in the amplifier. The techniques developed have potential for measuring dispersion mismatch between larger parallel amplifiers. These experiments demonstrated in principle that a number of multiline HF amplified beams can be recombined and phase-matched to produce a high beam quality output beam.     

Probing of a random phase object by a focused spatially modulated laser beam. Integral scanning method

A telescope system incorporating an illuminating spatially modulated laser beam, a diffuser in the entry plane, and a random phase screen in the spatial frequency plane was used to analyze the formation of average-intensity interference fringes in the image plane of the diffuser. It is shown that the system can operate as a shift interferometer where the contrast of the fringes is independent of the diffuser characteristics. Analytic expressions are obtained for the contrast of the fringes as a function of the parameters of the screen and the illuminating beam and it is established that the statistical anisotropy of the screen influences the contrast of the fringes. Pis’ma Zh. Tekh. Fiz. 25, 5–10 (December 26, 1999)