New Method of Determining Spectral Line Profile Using the Fabry-Perot Interferometer

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Abstract
By solving an integral equation associated with the interferogram of the Fabry-Perot interferometer numerically, it is possible to reconstruct spectral lines of various profiles. The theory of Hilbert and Schmidt is applied, in which a pair of integral equations arc solved and the spectral line profile is reconstructed using their eigenfunctions and eigen values. The resolution is 0.004 cm-1 at about 20000 cm-1 when the optical path difference varies from 5×103 µm to 5×103+0.4 µm, for instance, by pressure-scanning. The range of wave number is 0.4 cm-1 and the reflectivity is 0.95. It is confirmed that this method gives satisfactory results in the presence of noise of Gaussian distribution of which standard deviation is 2.5×10-4.