A straightforward method of evaluating the imaging properties of a spectrometer at a given wavelength is to measure the tangential and sagittal extent of an image (often called the width w' and height h' of the image, respectively).
Geometric raytracing provides spot diagrams in good agreement with observed spectrometer images, except for well-focused images, in which the wave nature of light dictates a minimum size for the image. Even if the image of a point object is completely without aberrations, it is not a point image, due to the diffraction effects of the pupil (which is usually the perimeter of the grating). The minimal image size, called the diffraction limit, can be estimated for a given wavelength by the diameter a of the Airy disk for a mirror in the same geometry:
α = 2.44λƒ/noOUTPUT = 2.44λ (r'λ/Wcosβ) (8-1)
Here ƒ/noOUTPUT is the output focal ratio, r'(λ) is the focal distance for this wavelength, and W is the width of the grating. Results from raytrace analyses that use the laws of geometrical optics only should not be considered valid if the dimensions of the image are found to be near or below the diffraction limit calculated from Eq. (8-1).
A fundamental problem with geometric raytracing procedures (other than that they ignore the variations in energy density throughout a crosssection of the diffracted beam and the diffraction efficiency of the grating) is its ignorance of the effect that the size and shape of the exit aperture has on the measured resolution of the instrument.
An alternative to merely measuring the extent of a spectral image is to compute its linespread function, which is the convolution of the (monochromatic) image of the entrance slit with the exit aperture (the exit slit in a monochromator, or a detector element in a spectrograph). A close physical equivalent is obtained by scanning the monochromatic image by moving the exit aperture past it in the image plane and recording the light intensity passing through the slit as a function of position in this plane.
The linespread calculation thus described accounts for the effect that the entrance and exit slit dimensions have on the resolution of the grating system.