Modified Brewster telescopes

Adolf W. Lohmann and Wilhelm Stork

The perfect shuffle permutation is an important interconnection scheme in digital optical computing.Various methods suggested for the optical implementation of the perfect shuffle need an anamorphic imagingsystem. Instead of cylinder lenses Brewster prism telescopes can be used to achieve the desired ratio of 2:1 forhorizontal and vertical magnifications. To reduce the rather large distortion of prism telescopes the Brewsterconcept can be combined with the Amici concept of a straight view dispersion prism.

Fig. 1. Concept of a Brewster telescope.

Fig. 2. Brewster telescope without a lateral shift.

The authors are with University of Erlangen-Nuremberg, PhysicsInstitute, D-8520 Erlangen, Federal Republic of Germany.

Received 2 November 1988.0003-6935/89/071318-02$02.00/0.© 1989 Optical Society of America.

For optical implementation of the perfect shuffleinterconnection in the context of digital optical com-puting we need an anamorphic telescope with a 2:1ratio for horizontal and vertical magnifications.1 ,2 De-sirable features are: simplicity, a straight optical axis,and compactness. Lateral beam compression (accord-ing to Brewster, 1781-1868) with a prism is a simplealternative (Fig. 1) to the use of cylinder lenses.3

We modify the basic Brewster telescope by combin-ing it with concepts due to Amici (1786-1863) andWadsworth. These modified Brewster telescopesmight also be useful for the temporal compression oflaser pulses.

A Brewster telescope typically consists of two prisms(Fig. 1). The lateral shift of the beam may be compen-sated by two additional prisms (Fig. 2). The Brewstertelescope by itself compresses the width of parallelbundles of rays. Compression of parallel bundles isalways connected with angular magnification (La-grange invariance). The angular magnification maybe converted into a lateral magnification by insertingthe Brewster telescope into an image forming lenssystem, such that parallel bundles between the lensescorrespond to points in the object and image planes(Fig. 3).

The Brewster telescope when used in this configura-tion will not cause aberrations because all the bound-aries are flat planes. However, rather large distortionsare to be expected.

The Brewster telescope of Fig. 2 is longer and widerthan desirable. It has eight glass-air surfaces whichmay cause spurious reflections. Therefore, we pro-pose to replace the ordinary prisms by a pair of straightview prisms as invented by Amici (Fig. 4). We com-puted the lateral magnifications of the ordinary Brew-

1318 APPLIED OPTICS / Vol. 28, No. 7 1 April 1989

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Fig. 4. Brewster telescope with two straight view prisms due toAmici.

Fig. 6. Wadsworth spectral prism (straight view).

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Fig. 7. Brewster-Wadsworth telescope with a mirror.

Fig. 8. Brewster-Wadsworth telescope with total internal reflec-tion.

ster telescope and of the Brewster-Amici telescope, inboth cases for prism pairs in tandem. The Brewster-Amici telescope has a wider usable range of entranceangles, or expressed in another way, the distortion isreduced (Fig. 5).

Amici requires at least two different types of glass.In our example (Figs. 4 and 5) three types of glass wereassumed with indices of 1.8, 1.4, and 1.3. Such a prismis not simple. As an alternative we now propose tocombine the concept of a Wadsworth spectral prism(Fig. 6) with the Brewster concept. The inner reflec-

tion may be achieved by a mirror (Fig. 7) or by totalreflection (Fig. 8). A prism angle of -30° and a refrac-tive index of 1.6 (crown glass) is suited for a magnifica-tion ratio of 2:1 for a setup as in Fig. 7 or Fig. 8.

References1. A. W. Lohmann, W. Stork, and G. Stucke, "Optical Perfect Shuf-

fle," Appl. Opt. 25,1530 (1986).2. K.-H.- Brenner and A. Huang, "Optical Implementations of the

Perfect Shuffle Interconnection," Appl. Opt. 27, 135 (1988).3. J. R. M. Barr, "Achromatic Prism Beam Expanders," Opt. Com-

mun. 51, 41 (1984).

1 April 1989 / Vol. 28, No. 7 / APPLIED OPTICS 1319

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