Page 212 - Modern Optical Engineering The Design of Optical Systems

Stops, Apertures, Pupils and Diffraction 195

Figure 9.17 (Upper) Prism spectrometer. (Lower) Grating
spectrometer.

it is also diffracted. As with the slit aperture discussed above, at certain
angles the diffracted wavelets reinforce, and maxima are produced when
m
sin sin I (9.20)
S
where is the wavelength, I is the angle of incidence, S is the spacing
of the grating lines, m is an integer, called the order of the maxima,
and the positive sign is used for a transmission grating, the negative
for a reflecting. (Note that a sinusoidal grating has only a first order.)
Since depends on the wavelength , such a device can be used to sep-
arate the diffracted light into its component wavelengths. When used
as indicated in Fig. 9.17, the resolution of a grating is given by

mN (9.21)
d
where m is the order and N is the total number of lines in the grating
(assuming the size of the grating to be the limiting aperture of the
system).

9.11 Diffraction of a Gaussian (Laser) Beam
The illumination distribution in the image of a point as described in
Secs. 9.9 and 9.10 was based on the assumptions that the optical
system was perfect and that both the transmission and the wave-front