Chapter 2.5 - Compensation Of Intrinsic Aberrations In The Interferometer

2.5. COMPENSATION OF INTRINSIC ABERRATIONS IN THE
INTERFEROMETER

A Twyman–Green interferometer may easily have aberrations of its own due to
defective optical components, so that the interferometric pattern is the result of the
addition of the aberrations of the optical system under test and the intrinsic interferometer
aberrations. Basically, the final aberration may be the superposition of
three sources, the reference path W_ref, the testing path W_test, and the element or
optical surface under test W_surf . A method to isolate the optical surface aberration
from the instrument aberration has been proposed by Jensen (1973). His procedure
takes three different measurements with different positions and orientations of the
surface under test. To describe it let us assume that these three measurements are as
follows.

A the normal testing position, as in Figure 2.28(a). Then, the inteferogram
aberration can be written as
At the normal testing position, but rotating the surface under test 180^o, as
shown in Figure 2.28(b), the interferogam aberration now is

where the bar on top of W_surf means that this wavefront aberration has been rotated
by 180^o.

FIGURE 2.28. Calibration of a Twyman-Green Interferometer by absolute testing a concave sphere.

The vertex of the optical surface under test is placed at the focus of the
focusing lens, as illustrated in Figure 2.28(c). Then, the surface aberrations do
not appear on the interferogram. However, The reflected wavefront is rotated.
Now we have

In any of these three equations, we can rotate all wavefronts in the same expression
and it will remain valid. This is done either by placing the bar on top of the W that
does not have it or by removing it if it is already there. By using this property, it is
possible to obtain

With this expression the intrinsic interferometer aberrations are subtracted, making
the instrument as if it did not have any aberration of its own. If a large number of
similar spherical surfaces are to be tested, the intrinsic instrumental aberration can be
expressed as

Once the interferometer is calibrated, this intrinsic aberration can be subtracted if the
surface under test has a radius of curvature close to the one of the mirror used to make
the calibration.

Unfortunately, as shown by Creath and Wyant (1992), this method is quite
sensitive to experimental errors due to misalignments, such as decentrations and
tilts in the rotation and shifting of the surface under test. In view of this, they
proposed a simpler method where both the intrinsic interferometer aberration and
the aberration of the spherical surface are almost rotationally symmetric. Then, Eq.
(2.37) reduces to

and the intrinsic aberration is just W_focus. It is important to point out that this method
works for Twyman–Green well as for Fizeau interferometers.

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Chapter 2.5 - Compensation Of Intrinsic Aberrations In The Interferometer

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