Comparison Between Spectrometers and Interferometers

1 Spectral Resolving Power and Light-Gathering Power 

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 

ASj 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.4.59a) or between the direct beam and a beam reflected m times in a Fabry-Perot interferometer. Two wavelengths and + AX can still 

With the maximum time difference aT = As /c for the traversing times on two paths with the path difference As, we obtain with v = c/x from (4.104) 

The product of the minimum resolvable frequency interval Av and the maximum difference of traversing times through the spectral apparatus is equal to one. 

The Upper limit for the resolving power is therefore, according to (4.102), 

For m = 2 and N = 10 this gives 7 = 2 x 10, or AA = 5 x 10 A. Be-canse of diffraction, which depends on the size of the grating (Sect. 4.1.3), the realizable resolving power is 2-3 times lower. This means that at A = 500 nm, two lines with A A 10 nm can still be resolved. 

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The Martin Puplett polarizing interferometer lends itself readily to the implementation of a balanced two input - two output beam interferometer where the difference between the two beams is only the axis of polarization. This highly balanced system allows a direct interferometric ratio determination between the two inputs at both output beams separately. In the far I.R. this feature is currently exploited by Mather et al. and separately bu Gush in an attempt to measure the residual cosmic background radiation in outer space. This is believed to follow approximately a 3° K blackbody radiation distribution. The balanced dual beam eliminates the radiation contributed by the spectrometer and the actual measurement consists of a direct comparison of the space field of view with a calibrated 3°K blackbody source in the second input beam. 

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