Abstract

A new design technique is presented for designing holographic lenses based on a K-vector closure principle. The technique enables closed and open loop ray tracing for design optimization and image analysis. A set of APL computer programs has been written for implementation. They are described in detail along with experimental results from holograms constructed at 488 nm and read out at 633 nm.

© 1979 Optical Society of America

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References

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  1. G. H. Spencer, M. V. R. K. Murty, J. Opt. Soc. Am. 52, 672 (1962).
    [CrossRef]
  2. R. W. Meier, J. Opt. Soc. Am. 55, 987 (1965).
    [CrossRef]
  3. E. B. Champagne, J. Opt. Soc. Am. 57, 51 (1967).
    [CrossRef]
  4. A. Offner, J. Opt. Soc. Amer. 56, 1509 (1966).
    [CrossRef]
  5. J. N. Latta, Appl. Opt. 10, 599 (1971).
    [CrossRef] [PubMed]
  6. J. N. Latta, Appl. Opt. 10, 2698 (1971).
    [CrossRef] [PubMed]
  7. H. Kogelnik, Bell Syst. Tech. J. 48, 275 (1968).
  8. R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 244–253.

1971 (2)

1968 (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 275 (1968).

1967 (1)

1966 (1)

A. Offner, J. Opt. Soc. Amer. 56, 1509 (1966).
[CrossRef]

1965 (1)

1962 (1)

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 244–253.

Champagne, E. B.

Collier, R. J.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 244–253.

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 275 (1968).

Latta, J. N.

Lin, L. H.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 244–253.

Meier, R. W.

Murty, M. V. R. K.

Offner, A.

A. Offner, J. Opt. Soc. Amer. 56, 1509 (1966).
[CrossRef]

Spencer, G. H.

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 275 (1968).

J. Opt. Soc. Am. (3)

J. Opt. Soc. Amer. (1)

A. Offner, J. Opt. Soc. Amer. 56, 1509 (1966).
[CrossRef]

Other (1)

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 244–253.

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Figures (7)

Fig. 1
Fig. 1

Bragg relationship.

Fig. 2
Fig. 2

Ray tracing scheme.

Fig. 3
Fig. 3

General ray tracing geometry.

Fig. 4
Fig. 4

Reconstruction geometry.

Fig. 5
Fig. 5

Hologram geometry for convergent object beam.

Fig. 6
Fig. 6

APL calculated ray positions.

Fig. 7
Fig. 7

Measured oscilloscope pictures.

Equations (11)

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θ = ( K / 2 ) / k = λ / ( 2 Λ ) ,
G ( x p , y p ) = exp ( - x p 2 + y p 2 2 σ 2 ) .
η = sin 2 ( ζ 2 + ν 2 ) 1 / 2 ( 1 + ζ 2 ν 2 ) 1 / 2 ,
ζ = δ β T sin θ ,
ν = ( π / λ ) Δ n [ T / ( cos θ ) ] ,
ζ = Δ λ λ tan θ ( 2 π n λ ) T sin θ .
T 2 M = sin - 1 [ sin ( T 2 + T 3 ) n ] ,
T 1 M = sin - 1 [ sin ( T 1 - T 3 ) n ] .
ϕ = ( T 1 M + T 2 M ) / 2 ,
ζ = Δ λ λ 2 2 π n T sin ϕ tan ϕ ,
ν = π 2 cos [ ( T 2 M ) / 2 ] cos ϕ .

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