The Fabry-Perot Interferometer

4 phase shift between two successively emerging rays, and s,S amphtildes. 

We will first calculate the optical path difference A (the retardation) between two successive rays mahing use of Fig. 6.27, namely 

for the case when constructive interference occurs on the symmetry ixis (the square root is zero for m = mo), rings with m — mo 1, mo — 2,. .. vill have radii proportional to /l, /3 etc. 

We shall now study the intensity distribution in more detail. Using i ig. 6.26 we find that the total transmitted amphtude S for the case of a = 0,. e. = 1 — is given by the geometrical series 

This is called the Airy distribution, and is illustrated in Fig. 6.28. The maximum intensity 

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The diffraction grating monochromator is a specific example of mnltiple beam interference effects. Interference between multiple beams can be generated by both division of amplitude (as in the Fabry-Perot interferometer) or by division of wave front (as in the diffraction grating). (Figures 5.9 and 5.10)... 

The layout for a novel scheme that overcomes the limitations of a Michelson duplexer is shown in Figure 7. The most important element of the spectrometer in Fig. 7 is the polarization-transforming reflector (PTR), which functions as a quarter-wave plate in this configuration. We will defer a detailed discussion of PTRs for the moment and focus instead on its functionality. To that end, consider Fig. 8a, where we have unfolded the optical layout between the PTR and the Fabry-Perot interferometer (FPI) in order to see the evolution of the electric field polarization more clearly. 

Figure 10 Thermal positronium-laser beam interaction region. Positronium is formed by a bunch of positrons that is stopped by a clean A1 surface in ultrahigh vacuum. Positronium atoms thermally desorbed from the surface are ionized by the laser and the e fragments are collected by a single particle detector. The laser pulse is narrowed in frequency by the Fabry-Perot interferometer.

Fig. 6. Schematic drawing of the Fabry-Perot interferometer of the type used by Benard to obtain contour lines for the free surface of a liquid undergoing thermal convection.

The instrument most commonly used to resolve the Brillouin spectrum is the Fabry-Perot interferometer. This device consists of a pair of highly reflective, optically polished mirrors. The transmission function for a plane parallel Fabry-Perot interferometer is ... 

Because the Fabry-Perot interferometer is a comb filter, an additional narrow bandpass interference filter is necessary to isolate the Brillouin scattering and reject Raman scattering or fluorescence. 

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. 

These open resonators are, in principle, the same as the Fabry-Perot interferometers discussed in Chap. 4 we shall see that several relations derived in Sect. 4.2 apply here. However, there is an essential difference with regard to the geometrical dimensions. While in a common FPI the distance between both mirrors is small compared with their diameter, the relation is generally reversed for laser resonators. The mirror diameter 2a is small compared with the mirror separation d. This implies that diffraction losses of the wave, which... 

Determination of the velocity of a metal shim moved the explosive charge detonation using the Fabry-Perot interferometer is illustrated in Figure 4.68. 

When the target velocity is to be determined, the laser beam is sent to the moving target. The target surface is prepared to produce a diffuse reflected beam. Mirrors and lenses are used to direct the reflected beam as a parallel one to the Fabry-Perot interferometer. 

The quantities measured in light scattering spectroscopy are either the anto-correlation function of the electric field C(.t) = (E(t) E 0)) or its Fourier transform, the spectrum of the scattered hght /(tw), by using the Fabry-Perot interferometer. 

Detecting a change in /left is a problem that can be solved in various ways. An interferometer approach analogous to the Mach-Zehnder interferometer [191]. [192], the Fabry-Perot interferometer [188], or the difference interferometer [193] has often been used. The... 

J.M. Vaughan The Fabry-Perot Interferometer (HUger, Bristol 1989) ... 

In experiments of this kind it is vital that careful consideration be given to the design of the sample cell and that the liquid in it be as free from dust as possible. The reason for this is that the Fabry-Perot interferometer is an instrument of high resolution, but of limited contrast. This means that any strong elastic scatterers in the cell will produce a central peak in the spectrum which is so high and wide as to overlap the... 

We will describe four types of instruments prism and grating instruments, the Fabry-Perot interferometer and the Fourier transform spectrometer. A large number of varieties of these different types are used in spectroscopic research and various applications. Spectroscopic instruments have been discussed in [6.6,7,66]. 

Because of small imperfections and the finite size of the circular aperture the practically achievable resolution is frequently reduced. Because of its high resolution the Fabry-Perot interferometer has been much used for... 

All hyperfine components have their own Airy functions, which are shifted with respect to each other. The Fabry-Perot pattern repeats itself with a period of the free spectral range, which is used for the frequency calibration. An example of a Fabry-Perot recording is illustrated in Fig. 6.29. The Fabry-Perot interferometer was discussed in [6.70]. 

Because of small imperfections and the finite size of the circular aperture the practically achievable resolution is frequently reduced. Because of its high resolution the Fabry-Perot interferometer has been much used for measuring hyperfine structure and isotope shifts. The spectral line of interest is then first selected by a monochromator or an interference filter. First, a free spectral range of sufficient width to accomodate all the spectral components of the line is chosen to allow the correct order of components to be determined. Then the plates are moved fiurther apart, resulting in an increased resolution but also the mclusion of overlapping orders. 

Figure 4.64 illustrates a possible experimental arrangement and the corresponding transmission for a Lyot filter composed of three components with the lengths L = L, l2 = 2Z, and Z3 = 4Z. The free spectral range hv of this filter equals that of the shortest component the halfwidth Av of the transmission peaks is, however, mainly determined by the longest component. When we define, analogous to the Fabry-Perot interferometer, the finesse F of the... 

We know of many types of optical interferometer (the simple double-slit Young interferometer, the Mach-Zehnder interferometer, the Fabry-Perot interferometer, the Talbot interferometer, etc.). A similar situation occurs in atom interferometry. Artificial laboratory devices exploit various types of structure for atom interferometry both material bodies (slits and gratings) and nonmaterial light structures. All these atom interferometers will be considered very briefly we refer readers for details to the book by Berman (1997) and reviews by Baudon et al. (1999), Kasevich (2002), and Chu (2002). 

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