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A repetitive array of diffracting elements, either apertures or
obstacles, that has the effect of producing periodic alterations
in the phase, amplitude, or both, of an emergent wave is said to
be a diffraction grating [1]. One of the simplest of such
arrangements is the multipleslit configuration.
Figure 3:
A transmission grating [1]

Figure 4:
A reflection grating [1]

If one looks perpendicularly through a transmission grating at a
distant parallel line source, the eye would serve as a focusing
lens for the diffraction pattern. Recall the analysis of
Section 1.3 and the expression

(12) 
which is formally the same as equation 11 but now
describes angular location of maxima and is known as the
grating equation for normal incidence. The values of
specify the order of the various principal maxima. Notice
that the smaller becomes in Equation 12, the
fewer will be the number of visible orders.
It should be no surprise that the grating equation is in fact the
equation which describes the location of the maxima in Young´s
doubleslit setup. The interference maxima, all located at the
same angles, are now simply sharper. In the doubleslit case where
the point of observation is somewhat off from the exact center of
an irradiance maximum, the two waves, one from each slit, will
still be more or less in phase, and the irradiance, though
reduced, will still be appreciable. Thus the bright regions are
fairly broad. By contrast, with multiplebeam systems, although
all the waves interfere constructively at the centers of the
maxima, even a small displacement will cause certain waves to
arrive out of phase by with respect to others. For
example, suppose is slightly off from so that
instead of Each of the
waves from successive slits will arrive at shifted by
with respect to the previous one. Then 50 slits down
from the first, the path length will have shifted by
and the light from slit 1 and slit 51 will essentially cancel. The
same would be true for slitpairs 2 and 52, 3 and 53, and so
forth. The result is a rapid fall off in irradiance beyond the
centers of the maxima.
Consider next the somewhat more general situation of oblique
incidence, as depicted in Figs 3 and
4 The grating equation, for both transmission
and reflection, becomes

(13) 
This expression applies equally well, regardless of the refractive
index of the transmission grating itself.
Figure 5:
Part of reflection blazed phase grating [1]

In an article in the Encyclopaedia Britannica of 1888 Lord
Rayleigh suggested that it was at least theoretically possible to
shift energy out of the useless zeroth order into one of the
higherorder spectra. So motivated, Robert Williams Wood
(18681955) succeeded in 1910 to rule grooves with a controlled
shape, as shown in Fig. 5. Most modern gratings
are of this specially shaped or so called blazed
variety [1].
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