Interferometer maximum transmission

The high contrast of the spectrometer is achieved either by triple passing each FP or the whole tandem setup. It results theoretically in an elevation of the apparatus function of each interferometer to the cube, which strongly enhances the contrast defined as the ratio of the maximum transmission over its minimum value. In order to achieve this high contrast, the tandem sits in a highly collimated beam between spatial filters, which also allows the stray light at the entrance to be diminished and the bandwidth at the exit pinhole in front of a photomultiplier or an avalanche diode to be selected (Fig. 2). 

The condition (4.33) for maximum transmission of the interferometer applies not only to a single wavelength X but to all Xm for which... 

Taking into account absorption and reflection losses, the maximum transmission Ij/Io = To < 1 becomes less than 100%. Within a small wavelength interval, the difference An = no — n can be regarded as constant. Therefore (4.92) gives the wavelength-dependent transmission function, cos cp, typical of a two-beam interferometer (Fig. 4.26). For extended spectral ranges the different dispersion of no(k) and e( ) has to be considered, which causes a wavelength dependence, An(k). 

The dielectric coatings of each plate of a Fabry-Perot interferometer have the following specifications R = 0.98, A = 0.3 %. The flatness of the surfaces is A/lOO at A = 500nm. Estimate the finesse, the maximum transmission, and the spectral resolution of the FPI for a plate separation of 5 mm. 

If a small fraction of the laser output is sent through a long Fabry-Perot interferometer with a separation d of the mirrors (Fig. 1.1b), the photodetector PD3 receives intensity peaks each time the laser frequency is tuned to a transmission maximum at v = mcjd (Vol. 1, Sects. 4.2-4.4). These peaks serve as accurate wavelength markers, which allow one to calibrate the separation of adjacent absorption lines. With a = 1 m the frequency separation Avp between successive transmission peaks is Avp = cjld = 150 MHz, corresponding to a wavelength separation of 10 nm at A. = 550 nm. With a semiconfocal FPI the free spectral range is cfM, which gives Av = 75 MHz for d = 0.5 m. 

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). 

A single-mode laser is frequency stabilized onto the slope of the transmission maximum of an external reference Fabry-Perot interferometer made of invar with a free spectral range of 8 GHz. Estimate the frequency stability of the laser... 

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