Interferometer resolving power

In most instances the resolving power of an FT spectrometer is determined by the maximum retardation of the moveable mirror in the interferometer so that... 

Figure 12. Theoretical maximum solid angle for a standard Michelson system as a function of resolving power compared to field-widened interferometer operating point.

Next, let us consider that the finite dimensions of the source impose a limit to the resolving power of the Michdson interferometer in the same way as the finite slit width does for the grating spectrometer. The finite size of the source means that also rays enter the interferometer which are inclined by an angle d to the optical axis (see Fig. 34) hence, a displacement s/2 of the movable mirror produces the path difference s cos d instead of s. The total interferogram is the sum of the contributions from all points of the (circular ) source... 

Thus, the resolving power from the finite area of the source in the Michelson interferometer is... 

Of a number of studies of this line since the war, the best resolution was obtained by Series [122]. Reduction of therf Doppler width was again achieved by liquid hydrogen cooling of a discharge as gentle as possible. Spectroscopic analysis was by means of multiple Fabry-Perot interferometers, which allow an extension of spectral range without sacrifice of resolving power. 

Jacquinotl2,13 recognized that the light gathering capability of a Michel son interferometer is greater than that of a dispersive instrument operating that the same resolving power. The improvement offered by the Fourier transform spectrometer can be expressed asl"... 

The resolving power of an interferometer depends on the maximum path length difference between two interfering beams. In high resolution instruments which are commercially available the moving, mirror covers 1.25m and the resolution is 1/(2x125) = 0.004 cm . This resolution is more than adequate for studies in the visible and ultraviolet and is usually sufficient for studies in the infrared as... 

The spectral resolving power X/AX of the Michelson interferometer equals the maximum path difference As/X measured in units of the wavelength X. 

The optimum choice for the radius of the aperture is based on a compromise between spectral resolution and transmitted intensity. When the interferometer has the finesse F, the spectral halfwidth of the transmission peak is Sv/F, see (4.53b), and the maximum spectral resolving power becomes F A /A (4.56). For the radius b = (Px/F y of the aperture, which is just (F )1/4 iiYnes the radius p of a fringe with p = 1 in (4.77), the spectral resolving power is reduced to about 70% of its maximum value. This can be verified by inserting this value of b into (4.79) and calculating the halfwidth of the transmission peak P(X, F, 6). 

The spectral resolving power discussed for the different instruments in the previous sections can be expressed in a more general way, which applies to all devices with spectral dispersion based on interference effects. Let As be the maximum path difference between interfering waves in the instrument, e.g., between the rays from the first and the last groove of a grating (Fig. 4.62a) or between the direct beam and a beam reflected m times in a Fabry-Perot interferometer (Fig. 4.62b). Two wavelengths X and X2 = + AX can still be... 

Fig. 4.62a,b. Maximum optical path difference and spectral resolving power (a) in a grating spectrometer (b) in a Fabry-Perot interferometer... 

In Sect. 4.2.10 we saw that for a given resolving power the spherical FPI has a larger etendue for mirror separations r > /Ad. For Example 4.19 with D — 5 cm, d = 1 cm, the confocal FPI therefore gives the largest product RU of all interferometers for r > 6 cm. Because of the higher total finesse, however, the confocal FPI may be superior to all other instruments even for smaller mirror separations. 

In summary, we can say that at comparable resolving power interferometers have a larger light-gathering power than spectrometers. 

D.A. Jackson The spherical Fabry-Perot interferometer as an instrument of high resolving power for use with external or with internal atomic beams. Proc. Roy. Soc. (London) A 263, 289 (1961)... 

The resolving power of an interferometer is the product of finesse F and optical path difference As/A in units of the wavelength A. 

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