Optical Shop Testing

Chapter 2.6 - Unequal-Path Interferometer

2.6.   UNEQUAL-PATH INTERFEROMETER

In Section 2.3, we discussed the coherence requirements of a Twyman–Green
interferometer and pointed out that, when a laser light source is used, extremely
large OPDs can be introduced (Morokuma et al., 1963). In explaining this, let us first
consider the spectrum of the light emitted by a laser. As shown in Figure 2.29(a), the

 FIGURE 2.29. Visibility in the interferometer using a mutimode gas laser.

light emitted by a gas laser usually consists of several spectral lines (longitudinal
modes) (Sinclair and Bell, 1969) spaced equally at a frequency interval Δv given by

 

If the cavity length L of a laser changes for some reason (thermal expansion or
contractions, mechanical vibrations, etc.), the lines move in concert along the
frequency scale, preserving their relative distances Δv, but always with intensities
inside the dotted envelope (power gain curve) as shown in Figure 2.29(a).

Lasers that have only one spectral line are called single-mode or single-frequency
lasers. They produce a perfect unmodulated wavetrain, but because of instabilities in
a cavity length L the frequency is also unstable. By the use of servomechanisms,
however, single-frequency lasers with extremely stable frequencies are commercially
produced. They are the ideal source for interferometry since an OPD as long as
desired can be introduced without any loss in contrast. Unfortunately, these lasers are
very expensive and have very low power outputs (less than 1 mW). Even so, a 1-mW
laser has a higher radiance than any other type of interferometric source.

It can be shown (Collier et al., 1971) that the theoretical visibility in an interferometer,
when a laser source with several longitudinal modes is used, is as
illustrated in Figure 2.29(b). Therefore, to have good contrast, the OPD (0) has to
be near an integral multiple of 2L; thus

 

Hence lasers are very convenient for Twyman–Green interferometry provided that
the mirrors in the interferometer can be adjusted to satisfy this condition. Because of
mechanical instability, the laser cavity normally vibrates, producing a continuous
instability in the frequency of the lines. This does not represent any serious
problem for small OPDs of the order of 1 m. If, however, the OPD is very large,
of the order of 10 or more meters, an almost periodic variation of the contrast is
introduced as shown by Batishko and Shannon (1972). To overcome the inconvenience
of this effect, they recommend taking photographs with exposures of the order
of 1/250 ms. This exposure is fast enough to stop the vibration of the fringes but slow
enough so that the contrast variation is integrated out.

A laser with two longitudinal modes can be stabilized to avoid contrast changes by
a method recommended by Balhorn et al. (1972), Bennett et al. (1973), and Gordon
and Jacobs (1974).

Some suggestions for aligning and adjusting the unequal path interferometer had
been given by Zielinski (1978,1979).

 

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