Array of Brewster telescopes

Adolf W. Lohmann, Stefan Sinzinger, and Wilhelm Stork

Brewster telescopes are useful for anamorphic image formation or for anamorphic beam compression. Withan array of micro-Brewster telescopes a wide uniform beam can be compressed into many beams of a smallerdiameter. Thus arrays of microprisms might form an array of micro-Brewster telescopes, which can be usedas array illuminator.

A Brewster telescope consists of one or more prisms.A bundle of parallel rays will be laterally compressedor expanded if the angle at the exit differs from theentrance angle (Fig. 1). Brewster telescopes may beused for anamorphic image formation of motion pic-tures, where the horizontal magnification typically dif-fers by a factor of 2 from the vertical magnification.

Anamorphic image formation is also useful in thecontext of optical interconnection networks.1 Forthat purpose we have proposed two modified designs ofa Brewster telescope.1 In earlier designs the Brewstertelescope has always been wide enough to process animage as a whole.

We now propose an array of micro-Brewster tele-scopes. Such an array may subdivide a wide uniformbeam into many small beams without losing any light(Fig. 2). Every microbeam may serve to illuminate amicrocomponent such as a Fabry-Perot etalon, filledwith a nonlinear material. We will call such an arrayof micro-Brewster telescopes an array illuminator ofthe Brewster type.

Several other array illuminators have been suggest-ed before.2 4 Their advantages and disadvantages dif-fer widely. A systematic comparison is still missing.Some of the array illuminators consist of microimage-

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

Received 23 January 1989.0003-6535/89/183835-03$02.00/0.© 1989 Optical Society of America.

forming systems such as lenslet arrays.5 That varietymay serve to compress microimages such that interlac-ing becomes feasible (Fig. 3). This particular type ofinterlacing, where the microimages of the right halfappear in alternate order with the microimages of theleft half is called perfect shuffling.6

For obtaining a Brewster magnification of two, oneneeds at least two prisms in tandem (Fig. 4). Such atandem arrangement will restore the previous direc-tion of the rays, which is often desirable. A lateralshift may appear to be a problem at first. However, ina setup with two prismatic arrays, the shift will notbother us. Instead, crossover of adjacent rays willoccur (Fig. 5). The crossover is acceptable both for thepurpose of array illumination and also in the context ofperfect shuffling. Most likely one may want all outgo-ing rays to be parallel. A numerical calculation indi-cates that the design of Fig. 5 ought to be modified asshown in Fig. 6. Prismatic gratings of good qualityexist commercially as indicated by Figs. 7-9 Therange of available grating periods is of the order of 50-500 micrometers.

Finally the question arises whether the ray-opticalapproach we have adopted so far is valid when Fresneldiffraction is taken into account. A rule of thumb saysthat the edge at the boundary of parallel rays will beblurred laterally by JXZ, where Z is the propagationlength. Let us assume the propagation length to be Z= D, where D is the period of the grid. If the lateralblur +/D should be not more than D/4, it follows thatDshould satisfy D 16X. This tolerance formula indi-cates that arrays of Brewster telescopes are reasonablecandidates for array illuminators, especially if a com-pression by 2:1 is enough. Eventually, one will requirearray illuminators with periods of only a few wave-lengths. The Brewster telescopes would seem to betoo coarse in view of the diffraction blur tolerances.However, one may simply minify the light field behindthe Brewster array by means of a high-quality macro-

15 September 1989 / Vol. 28, No. 18 / APPLIED OPTICS 3835

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Fig. 1. Basic concept of bundle compression, due to Brewster.

Fig. 5. Two prism pairs in sequence cause a crossover of rays.

Fig. 2. Transformation of a uniform bundle into an array of highpower beams (array illuminator).

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Fig. 3. Local image compression, followed by interlacing and over-all expansion; together they equal perfect shuffling. Fig. 6. Modified design of cascaded prism pairs.

3836 APPLIED OPTICS / Vol. 28, No. 18 / 15 September 1989

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lens. The tolerance condition will scale down accord-ingly.

Fruitful discussions with N. Streibl are gratefullyacknowledged. H. J. Preuss (E. Leitz) made the pris-matic prisms available to us.

References

1. A. W. Lohmann and W. Stork, "Modified Brewster Telescopes,"Appl. Opt. 28, 1318-1319 (1989).

2. A. W. Lohmann, "An Array Illuminator Based on the TalbotEffect," Optik 79, 41-00 (1987).

0 100 200 300lateral shift [micron]

Fig. 9. Measurement of a commercial prismatic grating (E. Leitz):phase deviation from an ideal prismatic grating.

3. A. W. Lohmann, J. Schwider, N. Streibl, and J. Thomas, "ArrayIlluminator Based on Phase Contrast," Appl. Opt. 27, 2915-2921(1988).

4. J. Jahns, M. E. Prise, M. M. Downs, S. J. Walker, and N. Streibl,"Dammann Gratings as Array Generators," in Annual Meeting ofOptical Society of America Technical Digest Series 1987 (Opti-cal Society of America, Washington, DC, 1987), Vol. 22, paperWJ3.

5. A. W. Lohmann and F. Sauer, "Holographic Telescope Arrays,"Appl. Opt. 27, 3003-3007 (1988).

6. A. W. Lohmann, G. Stucke, and W. Stork, "Optical Perfect Shuf-fle," Appl. Opt. 25, 1530-1531 (1986).

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