Abstract

Design principles of holographic optical elements are discussed. It is shown that a phase hologram with a high efficiency can be produced that transforms the input wavefront into an output of the required directivity. Such holograms can be used in laser systems instead of complex multilens objectives. Holograms have been obtained experimentally with a diffraction efficiency of 70%.

© 1972 Optical Society of America

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References

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  1. A. Erdélyi, Asymptotic Expansions (Dover, New York, 1956).
  2. J. Upatnieks, C. Leonard, Appl. Opt. 8, 85 (1969).
    [CrossRef] [PubMed]
  3. K. S. Pennington, J. S. Harper, Appl. Opt. 9, 1643 (1970).
    [CrossRef] [PubMed]
  4. V. I. Bobrinev, V. K. Kozlova, M. A. Majorchyk, Kvantovaia Elektronika, in press (1971).
  5. A. L. Mikaeliane, V. I. Bobrinev, Opto-Electron. 2, 193 (1970).
    [CrossRef]
  6. J. A. Raichman, Appl. Opt. 9, 2269 (1970).
    [CrossRef]

1970

1969

Bobrinev, V. I.

A. L. Mikaeliane, V. I. Bobrinev, Opto-Electron. 2, 193 (1970).
[CrossRef]

V. I. Bobrinev, V. K. Kozlova, M. A. Majorchyk, Kvantovaia Elektronika, in press (1971).

Erdélyi, A.

A. Erdélyi, Asymptotic Expansions (Dover, New York, 1956).

Harper, J. S.

Kozlova, V. K.

V. I. Bobrinev, V. K. Kozlova, M. A. Majorchyk, Kvantovaia Elektronika, in press (1971).

Leonard, C.

Majorchyk, M. A.

V. I. Bobrinev, V. K. Kozlova, M. A. Majorchyk, Kvantovaia Elektronika, in press (1971).

Mikaeliane, A. L.

A. L. Mikaeliane, V. I. Bobrinev, Opto-Electron. 2, 193 (1970).
[CrossRef]

Pennington, K. S.

Raichman, J. A.

Upatnieks, J.

Appl. Opt.

Opto-Electron.

A. L. Mikaeliane, V. I. Bobrinev, Opto-Electron. 2, 193 (1970).
[CrossRef]

Other

A. Erdélyi, Asymptotic Expansions (Dover, New York, 1956).

V. I. Bobrinev, V. K. Kozlova, M. A. Majorchyk, Kvantovaia Elektronika, in press (1971).

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Figures (3)

Fig. 1
Fig. 1

The recording setup.

Fig. 2
Fig. 2

Reconstruction of the beam with great, divergence.

Fig. 3
Fig. 3

(a) Transmitted and diffracted beams in the setup shown on Fig. 2. (b) The transmitted and diffracted diverging beams after a hologram.

Equations (12)

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F ( θ ) = - a a f ( x ) exp { i [ φ ( x ) - k x sin θ ] } d x ,
max [ φ ( x ) - k x sin θ ] - min [ φ ( x ) - k x sin θ ] 2 π
F ( θ 0 ) = [ 2 π / φ ( x 0 ) ] 1 2 · f ( x 0 ) ,
k sin θ 0 - φ ( x 0 ) = 0.
f ( x ) = A · exp [ - ( x 2 / b 2 ) ] ,
F ( θ ) = { C if θ 1 θ θ 2 , 0 if θ > θ 2 , θ < θ 1 .
C = { A · ( 2 π ) 1 2 / [ φ ( x 0 ) ] 1 2 } exp [ - ( x 0 2 / b 2 ) ] .
φ ( x 0 ) = k · cos θ 0 · ( d θ 0 / d x 0 ) k · ( d θ / d x 0 ) ,
d θ 0 / d x 0 = λ · ( A 2 / C 2 ) exp [ - ( 2 x 0 2 / b 2 ) ] ,
θ 0 ( x 0 ) = λ A 2 b C 2 · π 2 2 [ erf ( x 0 2 b ) + erf ( a 2 b ) ] + θ 1 .
C 2 = λ A 2 b ( π / 2 ) 1 2 · [ erf ( a 2 / b ) / ( θ 2 - θ 1 ) ] .
ν ( x 0 ) = ( sin θ 0 / λ ) [ θ 0 ( x 0 ) / λ ] .

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