Abstract

A deflecting staircase can be used like a telescope array to produce local beam compression in 1-D. Such a component may be useful for array illumination in digital optical information processing. This paper introduces the concept of staircase telescope arrays and discusses realizations with mirrors, prisms, and gratings. The addition of a macro deflecting element and the extension of the staircase concept to 2-D beam compression are further topics.

© 1989 Optical Society of America

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References

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  1. A. W. Lohmann, F. Sauer, “Holographic Telescope Arrays,” Appl. Opt. 27, 3003–3007 (1988).
    [CrossRef] [PubMed]
  2. A. W. Lohmann, W. Stork, G. Stucke, “Optical Perfect Shuffle,” Appl. Opt. 25, 1530–1531 (1986).
    [CrossRef] [PubMed]
  3. B. S. Wherrett, “Architectural Aspects of Optical Computing,” Workshop on Optical Bistability in Optical Computing, SPIE 769, 7–26 (1987).
  4. A. W. Lohmann, S. Sinzinger, W. Stork, “Array of Brewster telescopes,” Appl. Opt. 28, 3835–3837 (1989).
    [CrossRef] [PubMed]
  5. L. Solymar, D. J. Cooke, Volume Holography and Volume Gratings (Academic Press, London, 1981), Sect. 2.10.

1989 (1)

1988 (1)

1987 (1)

B. S. Wherrett, “Architectural Aspects of Optical Computing,” Workshop on Optical Bistability in Optical Computing, SPIE 769, 7–26 (1987).

1986 (1)

Appl. Opt. (3)

Workshop on Optical Bistability in Optical Computing, SPIE (1)

B. S. Wherrett, “Architectural Aspects of Optical Computing,” Workshop on Optical Bistability in Optical Computing, SPIE 769, 7–26 (1987).

Other (1)

L. Solymar, D. J. Cooke, Volume Holography and Volume Gratings (Academic Press, London, 1981), Sect. 2.10.

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Figures (13)

Fig. 1
Fig. 1

Effect of a telescope array: local compression of light beams.

Fig. 2
Fig. 2

Deflection at a plane which changes the beamwidth d. Sloc: beam scaling factor, given by the ratio of output beam width dout to input beam width din.

Fig. 3
Fig. 3

A staircase geometry introducing gaps between adjacent beamlets. Sglob: global scaling factor, given by the ratio of output field width Dout to input field width Din.

Fig. 4
Fig. 4

Mirror staircase. The steps may be of rectangular shape (dashed lines).

Fig. 5
Fig. 5

Light path with a mirror staircase. The steps are 1mm in height and 2mm in depth.

Fig. 6
Fig. 6

Prism staircase. Local beam compression occurs when light passes from the high index medium to the low index medium.

Fig. 7
Fig. 7

Grating staircase (H: holographic grating).

Fig. 8
Fig. 8

Grating staircase fabricated as a stack of (holographic) gratings (H: holographic grating).

Fig. 9
Fig. 9

Recording of a reflective holograting staircase. The staircase coated with holographic emulsion (HE) is illuminated with plane waves along the directions indicated by the two arrows. To obtain the desired uniform layer when coating the staircase with holographic emulsion a second staircase can be used as a gauge (dashed). With the index-matched gauge in place during the exposure, beam distortion by an uneven rear surface of the emulsion can be avoided.

Fig. 10
Fig. 10

Combination of macro grating and mirror staircase. The macro grating performs a global field compression, after that the mirror staircase introduces gaps between the individual beamlets. This sequence minimizes the effect of boundary diffraction if the input is uniform. If individual beamlets are arriving at the component, the order of the two operations should be exchanged.

Fig. 11
Fig. 11

Combination of macrograting and grating staircase. Shown is a design with macro grating and staircase parallel to each other; the overall field width does not change. Both grating elements, however, contribute multiplicatively to the scaling of the individual beamlets. The sequence macro grating–grating staircase is advisable for the reduction of boundary diffraction effects. If the gratings are to be realized holographically, they can be recorded in rigid coupling with a single exposure. For this, the component coated with holographic emulsion has to be illuminated with two plane waves in the directions indicated by the arrows.

Fig. 12
Fig. 12

Light path with a combination of a macro grating and a mirror staircase. The light path has been made visible by submerging the grating and the staircase into water and adding some drops of fluorescein. The original scaling factor of the grating is 0.4, reduced underwater to 0.7. The steps of the staircase are 1 mm in height and 5.5 mm in depth.

Fig. 13
Fig. 13

(a) When the height (z-position) of the deflecting step is varied the beamlet position in the output plane moves along a straight line. The orientation of this line is controlled by the (x,y)-deflection of the beamlet. (b) By shifting the beamlets along parallel lines, they can be separated only with distortion of the array. For local beam compression, however, distortion-free separation is necessary, requiring shifts in two independent directions.

Equations (3)

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S loc = d out d in = [ ( 1 n in 2 n out 2 sin 2 ϑ in ) / ( 1 sin 2 ϑ in ) ] 1 / 2 .
λ z / d d / 4 z d 2 / 4 λ .
N d / 4 λ .

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