Image Processing Reference
In-Depth Information
Chapter 3
Figure 3.1 Comparison of an aberrated wavefront to a reference sphere, showing
the optical path difference.
transform the optical-path-length variation in a wavefront into a change in intensity
that can be measured by a camera.
A plane wavefront entering a well-corrected lens results in a focused spot in the
focal plane that is described by an Airy function. Figure 3.2 shows the radially sym-
metric Airy function pattern of the spot. The diameter of the central disc, defined in
Eq. 1.1, is the distance between the Airy function minima. The location of several
minima is plotted in Fig. 3.2.
is the wavelength, f # is the f -ratio of the optical system, and x is the spatial
position of the first minima.
The shape of the Airy function shown in Fig. 3.2 is determined by diffraction at
the entrance aperture as well as the optical-path-length differences in the entering
wavefront (Hecht 2002). Changing the angle of the plane wavefront entering the
lens with respect to the optical axis displaces the location of the spot in the focal
plane; however, it does not radically change the shape of the spot on the sensor. The
presence of aberrations of higher order than tilt introduce changes in the shape of
the wavefront at the entrance pupil and result in a change in the intensity pattern in
the focal plane. Thus, a lens can be a sensitive tool in measuring phase changes by
converting the wavefront to intensity and the change in the phase to a displacement
in the focal plane.
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