Reconstruction and Deconvolution of Spectrum in Grating Spectroscopy

The spectrum measured in the grating spectroscopy is doubly smeared by diffraction and convolution. The original spectrum can be recovered by solving two types of integral equations successively. The theory of Hilbert and Schmidt is applied to those solutions. The resolution attained with this method approaches to the theoretical one. The recovered spectrum well corresponds to the original one even in the presence of noise of the order of 10-2. It was verified that when the number of calculating points is small (-100), the recovery can be done by a personal computer in the laboratory. Some results by a computer simulation show that this mathematically rigorous method is useful in practice.