Abstract

The original spectrum measured in the interferometric spectrometer with selection by amplitude modulation (SISAM) has been reconstructed, we believe for the first time, by solving the integral equation associated with the irradiance distribution in the receiving plane, using the theory of Hilbert and Schmidt. The number of sampling points is reduced greatly by dividing the larger range of wavenumber into several smaller ones and choosing the appropriate parameter. The instrumental function we obtain has a very small width and does not show noticeable sidelobes. A pure rotational spectrum of ¹⁴N₂¹⁶O is reconstructed with a high resolution in our computer experiment. It is also shown from our calculation that the recovery is good even if the order of random noise reaches 10⁻². In addition, because the kernel of the integral equation is decided by the spectrometer and is independent of the spectrum, the calculated results can be stored as memory and used for any spectrum. Therefore it is possible to finish the recovery procedure within a very short time.

© 1989 Optical Society of America