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Optical Shop Testing

Chapter 2 - Twyman–Green Interferometer

2.1.   INTRODUCTION

The Twyman–Green interferometer is a modification of the Michelson interferometer
used to test optical components. It was invented and patented by Twyman and
Green (1916) for the testing of prisms and microscope objectives and was later
adapted and applied to the testing of camera lenses (Twyman, 1919). The first
publications on this instrument were those of Twyman (1918a, 1918b, 1920,
1920–1921, 1923). The instrument has been very useful and so popular that many
review papers (Briers, 1972) and books (Candler, 1951; Twyman, 1957; U.S.
Department of Defense, 1963; Cook, 1971; Horne, 1972) describe it in detail. One
of the basic Twyman–Green configurations is illustrated in Figure 2.1. After the
system has been illuminated with a quasi-monochromatic point light source, the light
is collimated by means of lens L1 in order to form a flat wavefront. The wavefront is
divided in amplitude by means of a beam-splitter plate. After reflection, light from
both mirrors M1 and M2 impinges again on the beam splitter. Two interference
patterns are then formed, one going to lens L2 and the other going back to the light
source. Lens L2 permits all of the light from the aperture to enter the eye so that the
entire field can be seen. The observed fringes are of equal thickness type.

It is easy to see that if the beam splitter is all dielectric, the main interference
pattern is complementary to the one returning to the source; in other words, a bright
fringe in one pattern corresponds to a dark fringe in the other. This has to be so
because of the conservation of energy principle, even though the optical path
difference is the same for both patterns. Phase shifts upon reflection account for
this complementarity. The case of a absorbing beam splitter has been treated by
Parmigiani (1981).

It is interesting that Michelson (1918) did not consider the instrument applicable
to the testing of large optics, pointing out at the same time that the arrangement we
now know as an unequal-path interferometer was impractical because of the lack of
sufficiently coherent light sources. To answer Michelson’s comments, Twyman

FIGURE 2.1. Basic Twyman–Green interferometer configuration.

(1918) pointed out that the arrangement shown in Figure 2.2 had been suggested in
his patent (Twyman and Green, 1916) for the testing of large mirrors or lenses. This
procedure eliminates the need for a large collimator and beam splitter but unfortunately
requires (for sources of limited coherence) a concave spherical mirror as large
as the optical element under test. This kind of arrangement is often referred to as a
Williams interferometer (De Vany, 1965; Grigull and Rottenkolber, 1967) because
Burch (1940) attributed it to Williams. A Twyman–Green interferometer for general
laboratory usage is shown in Figure 2.3.

FIGURE 2.2. Twyman–Green interferometer (Williams type).


FIGURE 2.3. A general purpose Twyman–Green interferometer.

 

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