Image Processing Reference
Figure 3.6 Interferogram dominated by tilt.
terfere either constructively or destructively providing a uniformly illuminated pat-
tern, but the level of the illumination varies. Differences in the two beams will
appear as changes in intensity. The power of this interferometer is realized by intro-
ducing an aberrator in one of the beam legs. The effect of inserting a tilt aberrator in
one leg can be seen in the pupil plane interferogram, shown in Fig. 3.6.
Introducing the aberrator into the pupil plane of the beam introduces a phase
variation across one of the wavefronts. By recombining the aberrated beam with the
unaberrated beam in the reference leg, phase or optical-path-length differences are
converted into intensity variations that can be seen or recorded. Analyzing the
interferogram provides a measure of the amount of phase variation in the aberrated
beam over the wavefront.
The Mach-Zehnder interferometer can be modified into a direct wavefront sen-
sor suitable for use in image stabilization. In the previous examples, the interferom-
eter relied on the insertion of an aberrator into one optical leg rather than an
aberrated wavefront entering the interferometer. Figure 3.7 shows a modification
to the Mach-Zehnder interferometer that allows it to be used as a wavefront sensor
by generating a reference wavefront from the aberrated beam using a pinhole as a
An alternative approach is to introduce a beam expander in one leg and a beam
compressor in the other, so that the compressed beam is compared against the refer-
ence shape of the smoother expanded beam. In this form, the Mach-Zehnder inter-
ferometer is referred to as a radial shearing interferometer.
Smart and Steel (1975) demonstrated that a reference beam can be directly gen-
erated from an aberrated beam using a pinhole or an obstruction in a partially trans-
mitting medium such that the division of the beam in the modified Mach-Zehnder
interferometer is not needed. The resulting point diffraction interferometer has
been successfully used as a wavefront sensor for the Hubble Space Telescope and
in many other applications.