Abstract
The apparatus function of prism or grating spectroscopes with finite slits is derived for the general case of partially coherent illumination of the slit. Numerical results are presented for the border cases of coherent and incoherent slit illumination, as well as for full and partial illumination of the spectroscope aperture.The dependence of line intensity and line width on slit width, as well as the optimum slit width, are determined for each of these cases. It is shown that the performance of the spectroscope reaches an optimum when the aperture is at least fully illuminated.
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