Interferometer Michelson

The basic principle of the Michelson interferometer (MI) is illustrated in Fig. 4.25. The incident plane wave 

After being reflected at the plane mirrors Mi and M2, the two waves are superimposed in the plane of observation B. In order to compensate for the dispersion that beam 1 suffers by passing twice through the glass plate of beam splitter S, often an appropriate compensation plate P is placed in one side arm of the interferometer. The amplitudes of the two waves in the plane B are Vt Aq, because each wave has been transmitted and reflected once at the beam splitter surface S. The phase difference 0 between the two waves is 

The detector in B cannot follow the rapid oscillations with frequency a but measures the time-averaged intensity /, which is, according to (2.30c), 

This illustrates that the MI can be regarded either as a wavelength-dependent filter for the transmitted light, or as a wavelength-selective reflector. In the latter function it is often used for mode selection in lasers (Fox-Smith selector, Sect. 5.4.3). 

The MI can be used for absolute wavelength measurements by counting the number N of maxima in B when the mirror M2 is moved along a known distance Ay. The wavelength A is then obtained from 

Intensity transmitted through the Michelson interferometer in dependence on the phase difference between the two partial beams for T = R = 0.5 

Examples of devices in which only two partial beams interfere are the Michelson interferometer and the Mach-Zehnder interferometer. Multiple-beam interference is used, for instance, in the grating spectrometer, the Fabry-Perot interferometer, and in multilayer dielectric coatings of highly reflecting mirrors. 

Some interferometers utilize the optical birefringence of specific crystals to produce two partial waves with mutually orthogonal polarization. The phase difference between the two waves is generated by the different refractive index for the two polarizations. An example of such a polarization interferometer is the Lyot filter [4.23] used in dye lasers to narrow the spectral linewidth (Sect. 4.2.9). 

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Figure Bl.2.6. Schematic representation of a Michelson interferometer. From Griffiths P R and de Flaseth J A 1986 Fourier transfonn infrared spectroscopy Chemical Analysis ed P J Hiving and J D Winefordner (New York Wiley). Reprinted by pemiission of Jolm Wiley and Sons Inc.

A typical noisy light based CRS experiment involves the splitting of a noisy beam (short autocorrelation time, broadband) into identical twin beams, B and B, tlnough the use of a Michelson interferometer. One ami of the interferometer is computer controlled to introduce a relative delay, x, between B and B. The twin beams exit the interferometer and are joined by a narrowband field, M, to produce the CRS-type third order polarization in the sample ([Pg.1209]

Figure B2.1.2 Modified Michelson interferometer for non-collinear intensity autocorrelation. Symbols used rl, r2, retroreflecting mirror pair mounted on a translation stage bs, beamsplitter x, nonlinear crystal pint, photomultiplier Pibe.

Abstract This tutorial shows how fundamental is the role plaid by interferences in many of the physical processes involved in astrophysical signal formating and consequently instmmentation. It is obvious in interferometry. Grating spectroscopy is explained within the same framework as Young experiment, and Fabry-Perot filters are explained as Michelson interferometers.Polarization interferences, used in Lyot filters, are discussed, emphasizing the analogy with echelle gratings. 

Figure 1. Monochromatic two source interference (a) Young s points, (b) Michelson interferometer, (c) 3D representation of far-held interference fringes over all viewing angles showing both Michelson fringes at the poles and Young s fringes at the equator .

The superposition principle is illustrated further with the Michelson interferometer. Light is divided between two arms at a beamsphtter, recombined and the resulting intensity is observed. For a monochromatic source, the on-axis intensity is a superposition of the two recombined beams, and varies cosinu-soidally with the difference in path lengths Az... 

It is the self-coherence function that is measured in Fourier transform spectroscopy. Writing the measured on-axis intensity at the output of the Michelson interferometer as... 

The external geometric differential delay (see below) of an off axis source is exactly balanced within a Fizeau interferometer, resulting in fringes with the same phase on top of each source in the field. The position of a source may differ from the position of zero OPD in a Michelson interferometer depending on how dissimilar entrance and exit pupils are. The fringe contrast of off-axis sources also depend on the temporal degree of coherence of the detected light. 

A simple Michelson interferometer. If we place two mirrors at the end of two orthogonal arms of length L oriented along the x and y directions, a beamsplitter plate at the origin of our coordinate system and send photons in both arms trough the beamsplitter. Photons that were sent simultaneously will return on the beamsplitter with a time delay which will depend on which arm they propagated in. The round trip time difference, measured at the beamsplitter location, between photons that went in the a -arm (a -beam) and photons that went in the y arm (y-beam) is... 

Figure 5.5 Michelson interferometer. Reproduced by permission of Thermo Electron, B.V.

In the mid-IR, routine infrared spectroscopy nowadays almost exclusively uses Fourier-transform (FT) spectrometers. This principle is a standard method in modem analytical chemistry45. Although some efforts have been made to design ultra-compact FT-IR spectrometers for use under real-world conditions, standard systems are still too bulky for many applications. A new approach is the use of micro-fabrication techniques. As an example for this technology, a miniature single-pass Fourier transform spectrometer integrated on a 10 x 5 cm optical bench has been demonstrated to be feasible. Based upon a classical Michelson interferometer design, all... 

A Michelson interferometer (MI) can be considered as a Young-interferometer with perfect reflectors at the ends of both branches. Compared to the MZI and YI the MI has the advantage that the sensing region is passed twice. Because for monitoring the reflected light a second Y- junction is... 

This interferometric dilatometer consists of a rather simple and small Michelson interferometer, in which the two arms are parallel, and of a 4He cryostat, in which the sample to be measured is hold. The sample is cooled to 4 K, and data are taken during the warm up of the cryostat. The optical path difference between the two arms depends on the sample length hence a variation of the sample length determines an interference signal. The Michelson interferometer consists of a He-Ne stabilized laser (A = 0.6328 xm), two cube corner prisms, a beam splitter, three mirrors and a silicon photodiode detector placed in the focal plane of a 25 mm focal length biconvex lens (see Fig. 13.1). 

Fig. 2.6. Schematic illustration of the experimental setup for pump-probe anisotropic reflectivity measurements with fast scan method. PBS denotes polarizing beam splitter, PD1 and PD2, a pair of matched photodiodes to detect p- and s-polarized components of the reflected probe beam, PD3 another photodiode to detect the interference pattern of He-Ne laser in a Michelson interferometer to calibrate the scanning of the pump path length...

Based on the way the interferometer is configured, CCMI sensors can be categorized into two groups, namely the Mach-Zehnder interferometer (MZI) type and the Michelson interferometer (MI) type. The MZI sensor works in transmission mode, i.e., the transmitted interference signal is detected. The MI sensor works in reflection mode, where the light passes the interferometer twice and the reflected interference signal is detected. 

Tian, Z. Yam, S. S. Loock, H., Refractive index sensor based on an abrupt taper Michelson interferometer in a single mode fiber, Opt. Lett. 2008, 33, 1105 1107... 

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