Abstract

A method for designing and recording holographic optical elements that have low aberrations and high efficiencies is presented. It is based on incorporating a holographic element with low aberration into a final element in order also to achieve high diffraction efficiency.

© 1988 Optical Society of America

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References

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  1. R. W. Meier, J. Opt. Soc. Am. 55, 987 (1965).
    [CrossRef]
  2. E. B. Champagne, J. Opt. Soc. Am. 57, 51 (1967).
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  3. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  4. Q. J. Withrington, Proc. Soc. Photo-Opt. Instrum. Eng. 147, 161 (1978).
  5. I. A. Mikhailov, Opt. Spektrosk. 58, 612 (1985).
  6. R. C. Fairchild, J. R. Fienup, Opt. Eng. 21, 133 (1982).
  7. K. A. Winick, J. R. Fienup, J. Opt. Soc. Am. 73, 208 (1983).
    [CrossRef]
  8. J. Kedmi, A. A. Friesem, Appl. Opt. 23, 4015 (1984).
    [CrossRef] [PubMed]
  9. J. N. Cederquist, J. R. Fienup, J. Opt. Soc. Am. A 4, 699 (1987).
    [CrossRef]
  10. Y. Amitai, A. A. Friesem, Opt. Eng. 26, 1133 (1987).
  11. Y. Amitai, A. A. Friesem, J. Opt. Soc. Am. A 5, 702 (1988).
    [CrossRef]

1988

1987

J. N. Cederquist, J. R. Fienup, J. Opt. Soc. Am. A 4, 699 (1987).
[CrossRef]

Y. Amitai, A. A. Friesem, Opt. Eng. 26, 1133 (1987).

1985

I. A. Mikhailov, Opt. Spektrosk. 58, 612 (1985).

1984

1983

1982

R. C. Fairchild, J. R. Fienup, Opt. Eng. 21, 133 (1982).

1978

Q. J. Withrington, Proc. Soc. Photo-Opt. Instrum. Eng. 147, 161 (1978).

1969

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

1967

1965

Amitai, Y.

Y. Amitai, A. A. Friesem, J. Opt. Soc. Am. A 5, 702 (1988).
[CrossRef]

Y. Amitai, A. A. Friesem, Opt. Eng. 26, 1133 (1987).

Cederquist, J. N.

Champagne, E. B.

Fairchild, R. C.

R. C. Fairchild, J. R. Fienup, Opt. Eng. 21, 133 (1982).

Fienup, J. R.

Friesem, A. A.

Kedmi, J.

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Meier, R. W.

Mikhailov, I. A.

I. A. Mikhailov, Opt. Spektrosk. 58, 612 (1985).

Winick, K. A.

Withrington, Q. J.

Q. J. Withrington, Proc. Soc. Photo-Opt. Instrum. Eng. 147, 161 (1978).

Appl. Opt.

Bell Syst. Tech. J.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng.

Y. Amitai, A. A. Friesem, Opt. Eng. 26, 1133 (1987).

R. C. Fairchild, J. R. Fienup, Opt. Eng. 21, 133 (1982).

Opt. Spektrosk.

I. A. Mikhailov, Opt. Spektrosk. 58, 612 (1985).

Proc. Soc. Photo-Opt. Instrum. Eng.

Q. J. Withrington, Proc. Soc. Photo-Opt. Instrum. Eng. 147, 161 (1978).

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Figures (3)

Fig. 1
Fig. 1

Transfer of the optimized grating function to the final element with an intermediate hologram. (a) Recording of the intermediate hologram int. (b) Recording of the final hologram ″.

Fig. 2
Fig. 2

Recording and readout geometries for a Fourier-transform holographic lens. (a) Recording geometry for the optimized ′. (b) Recording geometry for the final hologram ″. (c) Readout geometry for the final hologram ″.

Fig. 3
Fig. 3

Predicted diffraction efficiencies as functions of angular deviations for the holograms ′ and ″.

Equations (14)

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Φ H = ϕ o - ϕ r ,
1 R H = 1 R o - 1 R r ,
sin β H = sin β o - sin β r ,
ϕ i = ϕ c ± Φ H ,
1 R i = 1 R c ± μ 1 R H ,
sin β i = sin β c ± μ sin β H ,
ϕ o eff - ϕ r eff = Φ H eff .
ϕ i = - ϕ r eff - Φ H opt .
ϕ r = ϕ r eff .
Φ H = ϕ o - ϕ r = - ϕ i - ϕ r = ϕ r eff + Φ H opt - ϕ r eff = Φ H opt .
R r = R r eff ,
β r = β r eff .
1 R o = 1 R r eff + 1 R H opt = 1 R r eff + 1 R H eff = 1 R o eff ,
sin β o = sin β r eff + sin β H opt = sin β r eff + sin β H eff = sin β o eff .

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