Abstract

A new type of holographic optical element combines some of the flexibility of computer-generated holograms with the high light efficiency of volume phase holograms to produce optical elements capable of arbitrary illumination transformations with nearly 100% light efficiency. The optical element is recorded by subdividing a volume hologram film surface into numerous small areas (facets), each of which is individually exposed. A final optical system consisting of two dichromated gelatin holograms in series is demonstrated. The first hologram spatially redistributes the incident light, and the second hologram produces a desired phase front on the redistributed light.

© 1981 Optical Society of America

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References

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  1. M. Quintanilla, A. M. deFrutos, Appl. Opt. 20, 879 (1981).
  2. See segmented mirror from Spawr Optical Research, Inc., 1527 Pomona Rd., Corona, Calif. 91720. This method does not produce illumination with a smooth phase front.
  3. P. W. Rhodes, D. L. Shealy, Appl. Opt. 19, 3545 (1980).
  4. Stencil Marker by Lumonics, Inc., 105 Schneider Rd., Kanata, Ontario, Canada K2K 1Y3.
  5. N. C. Gallagher, D. W. Sweeney, IEEE J. Quantum Electron. QE-15, 1369 (1979).
  6. D. W. Sweeney et al., Appl. Opt. 15, 2959 (1976).
  7. A. multifacet volume hologram technique was first described by S. K. Case and V. Gerbig at the Deutsche Gesellschaft fur Angewandte Optik annual meeting in Bad Harzburg, West Germany, June, 1979.
  8. S. K. Case, V. Gerbig, Opt. Engineer. 19, 711 (1980).
  9. V. Gerbig, Opt. Commun. 36, 90 (1981).
  10. S. K. Case, V. Gerbig, Opt. Commun. 36, 94 (1981).
  11. U. Levy, A. A. Friesem, B. Sharon, Appl. Opt. 19, 1661 (1980).
  12. The work in this paper was presented at the annual meeting of the Optical Society of America, 14–17 Oct. 1980, Chicago, Ill., J. Opt. Soc. Am. 70, 1625A (1980).
  13. B. R. Brown, A. W. Lohmann, IBM J. Res. Develop. 13, 160 (1969).
  14. Light reflected from an object could be used for one of the recording waves. This standard holographic technique could work if the object were available and small. For larger complicated objects, for which we may also desire arbitrary illumination intensities, this technique would not be easy to implement. One particularly limiting factor is that the high exposure levels required by efficient hologram materials such as dichromated gelatin coupled with the relatively weak light reflected from diffuse objects would mandate excessively long exposure times. The technique also would not work if λrecording ≠ λreadout.
  15. S. K. Case, Multiple Exposure Holography in Volume Materials, Ph.D. Thesis, U. Michigan, 1976 (Xerox University Microfilms order #76-27461).
  16. B. J. Chang, C. D. Leonard, Appl. Opt. 18, 2407 (1979).
  17. S. K. Case, W. J. Dallas, Appl. Opt. 17, 2537 (1978).
  18. One could use an axicon to produce annular illumination; however, this is a special case where a conventional optical element could do our redistribution. We wish to treat the problem more generally.

1981 (3)

M. Quintanilla, A. M. deFrutos, Appl. Opt. 20, 879 (1981).

V. Gerbig, Opt. Commun. 36, 90 (1981).

S. K. Case, V. Gerbig, Opt. Commun. 36, 94 (1981).

1980 (4)

U. Levy, A. A. Friesem, B. Sharon, Appl. Opt. 19, 1661 (1980).

The work in this paper was presented at the annual meeting of the Optical Society of America, 14–17 Oct. 1980, Chicago, Ill., J. Opt. Soc. Am. 70, 1625A (1980).

P. W. Rhodes, D. L. Shealy, Appl. Opt. 19, 3545 (1980).

S. K. Case, V. Gerbig, Opt. Engineer. 19, 711 (1980).

1979 (2)

B. J. Chang, C. D. Leonard, Appl. Opt. 18, 2407 (1979).

N. C. Gallagher, D. W. Sweeney, IEEE J. Quantum Electron. QE-15, 1369 (1979).

1978 (1)

1976 (1)

1969 (1)

B. R. Brown, A. W. Lohmann, IBM J. Res. Develop. 13, 160 (1969).

Brown, B. R.

B. R. Brown, A. W. Lohmann, IBM J. Res. Develop. 13, 160 (1969).

Case, S. K.

S. K. Case, V. Gerbig, Opt. Commun. 36, 94 (1981).

S. K. Case, V. Gerbig, Opt. Engineer. 19, 711 (1980).

S. K. Case, W. J. Dallas, Appl. Opt. 17, 2537 (1978).

S. K. Case, Multiple Exposure Holography in Volume Materials, Ph.D. Thesis, U. Michigan, 1976 (Xerox University Microfilms order #76-27461).

Chang, B. J.

Dallas, W. J.

deFrutos, A. M.

Friesem, A. A.

Gallagher, N. C.

N. C. Gallagher, D. W. Sweeney, IEEE J. Quantum Electron. QE-15, 1369 (1979).

Gerbig, V.

V. Gerbig, Opt. Commun. 36, 90 (1981).

S. K. Case, V. Gerbig, Opt. Commun. 36, 94 (1981).

S. K. Case, V. Gerbig, Opt. Engineer. 19, 711 (1980).

Leonard, C. D.

Levy, U.

Lohmann, A. W.

B. R. Brown, A. W. Lohmann, IBM J. Res. Develop. 13, 160 (1969).

Quintanilla, M.

Rhodes, P. W.

Sharon, B.

Shealy, D. L.

Sweeney, D. W.

N. C. Gallagher, D. W. Sweeney, IEEE J. Quantum Electron. QE-15, 1369 (1979).

D. W. Sweeney et al., Appl. Opt. 15, 2959 (1976).

Appl. Opt. (6)

IBM J. Res. Develop. (1)

B. R. Brown, A. W. Lohmann, IBM J. Res. Develop. 13, 160 (1969).

IEEE J. Quantum Electron. (1)

N. C. Gallagher, D. W. Sweeney, IEEE J. Quantum Electron. QE-15, 1369 (1979).

J. Opt. Soc. Am. (1)

The work in this paper was presented at the annual meeting of the Optical Society of America, 14–17 Oct. 1980, Chicago, Ill., J. Opt. Soc. Am. 70, 1625A (1980).

Opt. Commun. (2)

V. Gerbig, Opt. Commun. 36, 90 (1981).

S. K. Case, V. Gerbig, Opt. Commun. 36, 94 (1981).

Opt. Engineer. (1)

S. K. Case, V. Gerbig, Opt. Engineer. 19, 711 (1980).

Other (6)

A. multifacet volume hologram technique was first described by S. K. Case and V. Gerbig at the Deutsche Gesellschaft fur Angewandte Optik annual meeting in Bad Harzburg, West Germany, June, 1979.

Stencil Marker by Lumonics, Inc., 105 Schneider Rd., Kanata, Ontario, Canada K2K 1Y3.

See segmented mirror from Spawr Optical Research, Inc., 1527 Pomona Rd., Corona, Calif. 91720. This method does not produce illumination with a smooth phase front.

Light reflected from an object could be used for one of the recording waves. This standard holographic technique could work if the object were available and small. For larger complicated objects, for which we may also desire arbitrary illumination intensities, this technique would not be easy to implement. One particularly limiting factor is that the high exposure levels required by efficient hologram materials such as dichromated gelatin coupled with the relatively weak light reflected from diffuse objects would mandate excessively long exposure times. The technique also would not work if λrecording ≠ λreadout.

S. K. Case, Multiple Exposure Holography in Volume Materials, Ph.D. Thesis, U. Michigan, 1976 (Xerox University Microfilms order #76-27461).

One could use an axicon to produce annular illumination; however, this is a special case where a conventional optical element could do our redistribution. We wish to treat the problem more generally.

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Figures (12)

Fig. 1
Fig. 1

Inefficient method for illuminating the periphery of a large hollow box.

Fig. 2
Fig. 2

Wave front transformation system for efficient illumination of the object.

Fig. 3
Fig. 3

Irradiance distributions: (a) input beam and (b) output beam.

Fig. 4
Fig. 4

Setup for recording multifacet holograms.

Fig. 5
Fig. 5

Top view of optical system showing redistributed light from hologram #1 being used as the object wave to record hologram #2.

Fig. 6
Fig. 6

Multifacet hologram recorded in absorption material (for illustration). Volume phase holograms were used for all experiments.

Fig. 7
Fig. 7

Redistribution of light between input and output planes.

Fig. 8
Fig. 8

Output light distribution.

Fig. 9
Fig. 9

Interferograms showing wave front quality: (a) output wave and (b) reference wave.

Fig. 10
Fig. 10

General object to be illuminated.

Fig. 11
Fig. 11

Light gain when using one redistribution hologram.

Fig. 12
Fig. 12

Light gain when using two redistribution holograms.

Equations (11)

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A ( r ) = A 0 exp [ ( r / ω 0 ) 2 ] .
A 1 ( r ) = A 0 ω 0 ω 1 exp [ ( r ω 1 ) 2 ] .
I 1 ( r ) = A 0 2 2 ( ω 0 r 0 ) 2 exp [ ( r r 0 ) 2 ] .
P = r min r max I 1 ( r ) 2 π rdr ,
= π A 0 2 ω 0 2 2 { exp [ ( r min r 0 ) 2 ] exp [ ( r max r 0 ) 2 ] } .
P 0 = π A 0 2 ω 0 2 2 ,
r min = r 0 ( 1 α 2 ) , r max = r 0 ( 1 + α 2 ) ,
F = P P 0 = { exp [ ( 1 α 2 ) 2 ] exp [ ( 1 + α 2 ) 2 ] } .
F = [ 1 exp ( 2 ) ] = 86 % .
G 1 = F 1 / F = 0.86 ɛ / F .
G 2 = 0.86 ɛ 2 / F .

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