Abstract

A spectrum can be considered as a signal composed of a superposition of randomly spaced Cauchy lines of the form δ2/(δ2+x2). This signal is passed through a spectroscope which acts as a noisy channel causing distortion due to finite aperture, slits, prism absorption, and electrical band width. The loss of information in the Hartley sense can be described by the increase in width of lines in the output signal. Several definitions of line widths are compared for ease in experimental measurement and calculation as functions of δ and the instrument characteristics. The different widths do not vary in the same manner over the range of experimental conditions. In particular the resolution width departs markedly from the others. Because the intensity distribution is very complicated, the width at half-height and the median width are difficult to calculate. The latter is approximately the same as the root-mean-square width which can be more readily calculated. The most satisfactory width for both experimental and theoretical determination seems to be that of the equivalent Cauchy line shape. This is easy to measure from the observed area, which is merely a product of elementary functions and the filter characteristic.

© 1953 Optical Society of America

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