Page 157 - Modern Optical Engineering The Design of Optical Systems

140 Chapter Seven

Figure 7.22 Amici prism (a) showing a single ray path
through the prism and indicating the image orientation,
(b) with truncated corners to reduce weight without
sacrifice of useful aperture.

in Fig. 7.22a. This can be understood by tracing the path of the dashed
ray in Fig. 7.22a which connects the circles in the arrow and crossbar
figures before and after passing through the prism.
The angle of incidence (at the roof surface) of the ray shown in
Fig. 7.22a is about 60° instead of the 45° it would be for the same ray
in the right-angle prism. Even a ray perpendicular to the roof edge has
an angle of incidence of 45°. The result is that a roof surface allows
total internal reflection for beam angles which would be transmitted
through the hypotenuse face of a right-angle prism.
In practice, the Amici prism is usually fabricated with the corners
cut off, as shown in Fig. 7.22b, in order to reduce the size and weight
of the prism. The 90° roof angle must be made to a high order of accu-
racy. If there is an error in the roof angle, the beam is split into two
beams which diverge at an angle which is six times the error. Thus, to
avoid any apparent doubling of the image, the roof angle is usually
made accurate to one or two seconds of arc.
The introduction of a roof degrades the diffraction-limited resolution
by a factor approaching 2 in the direction perpendicular to the roof
edge (due to a polarization/phase shift on reflection) no matter how
perfectly the prism is made*. Multilayer coatings have been developed
which will reduce this effect.

*A. Mahan, “Focal plane anomalies in roof prisms,” J. Opt. Soc. Am., vol. 35, 1945, p. 623.
A. Mahan, “Further studies of focal plane anomalies in roof prisms,” J. Opt. Soc. Am.,
vol. 36, 1946, p. 715A.
A. Mahan, “Focal plane diffraction anomalies in telescopic systems,” J. Opt. Soc. Am.,
vol. 37, 1947, p. 852.
A. Mahan and E. Price, “Diffraction pattern deterioration by roof prisms,” J. Opt. Soc.
Am., vol. 40, 1950, p. 664.