Page 217 - Modern Optical Engineering The Design of Optical Systems

200 Chapter Nine

FOURIER
OBJECT LENS A PLANE LENS B IMAGE

COLLIMATED/
COHERENT
ILLUMINATION

ƒ ƒ ƒ ƒ
Figure 9.19 An illustration with a transparent object located at the first focal point
of a lens.

sinusoidal grating has but a single diffraction order, the first. Now, if
the object is illuminated by collimated/coherent light, that diffracted
light will be focused as two points in the second focal plane of lens A
(which is indicated as the Fourier plane, midway between the lenses
in Fig. 9.19). The points will be laterally displaced by f tan from
the nominal focus. Thus, if an annular zone in the Fourier plane is
obstructed, all the spatial information of the frequency corresponding
to the radius of the obstruction will be removed (filtered) from the final
image. Thus it can be seen that the Fourier plane constitutes a sort of
map of the spatial frequency content of the object and that this content
can be analyzed or modified in this plane.

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