**2.4.1. Testing of Prisms and Diffraction Rulings**

The Twyman–Green interferometer is a very useful instrument for testing prisms. Its

application for testing the accuracy of the 90^{o} angle between two of the faces of a

right angle (Porro) prism, a roof (Amici) prism, or a cube corner prism is especially

interesting. As explained before, the relative rotation or reversal of the wavefronts

should be corrected, as shown in Figure 2.16, if a gas laser is not used. The

arrangements in Figure 2.17 can be used when a gas laser source is employed.

A very good cube corner prism will give rise to an interferogram like that shown in

Figure 2.18. The fringes are straight throughout the aperture. A cube comer prism

with angular errors produces an interferogram such as that shown in Figure 2.19, in

which the straight fringes abruptly change their direction. Thomas and Wyant (1977)

made a complete study of the testing of cube corner prisms.

Figures 2.20 and 2.21 show similar situations for a right-angle prism of no error

and of some angular error, respectively. If, in addition to angle errors, the surfaces are

not flat or the glass is not homogeneous, an interferogram with curved fringes is

obtained. When a right angle or porro prism is tested in the retroreflective configuration

and the surface flatness as well as the 90^{o} angle is correct, the fringes look

straight and parallel as in Figure 2.20. If the right angle has an error, the fringes look

like those shown in Figure 2.21 and can be manipulated to look like those in

Figure 2.22. We describe here a brief method for obtaining the angular error in a

right angle prism. If 2*L* is the width of the face of the prism, π/2 ± ε is the angle of the

prism, *d *is the distance between two successive fringes, *k* is the deviation of the fringe

from the straight fringe after bending, *n* is the refractive index of the prism, and λ is

the wavelength used. As shown in Figure 2.23, the error is given by

where α is the angle between the two exiting wavefronts. For example, for a prism of

100 mm face width and *k */*d* = 0:25, the error ε of the 90^{o} angle is about 1 s of arc. In

regard to the sign of the error, the hot rod or finger procedure described before can be

used.

Luneburg (1964) showed that the angular error ε in a roof face of a prism is

where *n* is the refractive index of the material, α is the angle between the two exiting

wavefronts in a single pass through the prism, *θ* is the angle between *de *roof edge and

the incident beam, and m is the number of times the lights is reflected on the roof face.

For the arrangements shown in Figs. 2.15 and 2.16 we have the values in Table 2.1.

The angle α is determined from Eq. (2.32), but with the interferometer adjusted in

such a way that all the fringes in one of the faces are eliminated.

A dispersive prism can also be tested as shown in Figure 2.24(a). This arrangement

of smoothly changing inhomogeneities in the glass may be compensated for by

appropriately figuring the faces. An axicon may be tested in a Twyman–Green

interferometer using the method described by Fantone (1981) as well as reflaxicons

(Hayes et al., 1981).

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In 1935, Bisacre and Simeon suggested a method whereby a diffraction grating

could be tested by means of a Twyman–Green interferometer. Unfortunately, they

never published their work (Candler, 1951). They used the arrangement shown in

Figure 2.24(b). The interferometer is initially adjusted to obtain horizontal fringes in

the first order. Then the grating is rotated to pass to the third order, in which the

ghosts, if any, are stronger. If there are ghosts and a tilt about an axis along the grating

chromatic dispersion is introduced, the fringes have a sawtooth appearance. When

the spacing between the horizontal fringes is increased by removing the tilt, the teeth

become larger and larger until they form a system of vertical fringes due to the

inteference between the zero order and the ghost wavefront. Using this interferometer,

Jaroszewics (1986) has also tested the spacing error of a plane diffraction

grating.

**2.4.1. Testing of Prisms and Diffraction Rulings**

The Twyman–Green interferometer is a very useful instrument for testing prisms. Its

application for testing the accuracy of the 90^{o} angle between two of the faces of a

right angle (Porro) prism, a roof (Amici) prism, or a cube corner prism is especially

interesting. As explained before, the relative rotation or reversal of the wavefronts

should be corrected, as shown in Figure 2.16, if a gas laser is not used. The

arrangements in Figure 2.17 can be used when a gas laser source is employed.

A very good cube corner prism will give rise to an interferogram like that shown in

Figure 2.18. The fringes are straight throughout the aperture. A cube comer prism

with angular errors produces an interferogram such as that shown in Figure 2.19, in

which the straight fringes abruptly change their direction. Thomas and Wyant (1977)

made a complete study of the testing of cube corner prisms.

Figures 2.20 and 2.21 show similar situations for a right-angle prism of no error

and of some angular error, respectively. If, in addition to angle errors, the surfaces are

not flat or the glass is not homogeneous, an interferogram with...

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