Chapter 2.4 - Uses of a Twyman-Green Inteferometer

Many different kinds of optical components can be tested with this instrument. The
simplest one to test is a plane parallel plate of glass, as shown in Figure 2.13. The
OPD introduced by the presence of the glass plate is given by

where t is the plate thickness and n is the refractive index. If the interferometer is
adjusted so that no fringes are observed before introducing the plate into the light
beam, all the fringes that appear are due to the plate. If the field remains free of fringes,
we can say that the quantity (n - 1)t is constant over all the plate. If straight fringes
are observed, we can assume that the glass is perfectly homogeneous (nconstant) and
that the fringes are due to an angle ε between the two flat faces, given by

FIGURE 2.13. Testing a glass plate.

where α is a small angle between the two interfering wavefronts, which can be
determined from

Here m is the number of interference fringes per unit length being observed.

The fringes, however, may not be straight but quite distorted, as shown in
Figure 2.14, because of bad surfaces or inhomogeneities in the index, since the
only quantity we can determine is (N - 1)t. To measure the independent variations
of n and t, we must complement this test with another made in a Fizeau interferometer,
which measures the values of nt (Kowalik 1978). Many different kinds of

FIGURE 2.14. Interferogram of a glass plate.

FIGURE 2.15. Testing a thin and flexible opaque glass plate.

material can be tested with this basic arrangement (Adachi et al., 1961, 1962; Masuda
et al., 1962; Twyman and Dalladay, 1921–1922).

In many instruments, when using a glass window, the important requirement is
that the optical path difference introduced by its presence is a constant for the whole
aperture as in Eq. (2.30). However, sometimes the plate may not be transparent in the
visible, only in the infrared, where it is used, and an infrared interferometer is not
available. If a constant index of refraction is assumed, the important parameter is a
constant thickness. But an independent measurement of the flatness of the faces does
not permit this evaluation because the plate is frequently so thin that it may bend,
which, on the contrary, is not important in its operation. For these cases,Williamson
(2004) has described a configuration as shown in Figure 2.15. The interesting
characteristic of this configuration is that if the plate bends or curves in any way,
the change in one of its two faces is canceled out by the corresponding change in the
other.

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Chapter 2.4 - Uses of a Twyman-Green Inteferometer

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