Rayleigh (Strutt) method of making an approximate correction to spectra for finite slit widths

Abstract

An expression is derived for the distortion of spectral band contours resulting from use of finite slit widths. The leading term is in agreement with a correction proposed by Rayleigh in 1871 and derived from curvature arguments. It is shown that this correction, which is proportional to the second derivative of the observed spectrum, d²ƒ/dν², allows the true band contour to be recovered to a good approximation provided that the slit width is not greater than the half band width. Loss of resolution due to finite slit widths may also be recovered. Higher power correction terms are also given, but due to the sensitivity of the higher power gradients, dⁿƒ/dνⁿ, to noise, n even and greater than two, the terms appear to be of little practical importance at the present time.