Abstract

The problem of designing a flat, aspheric, holographic optical element that images a finite set of input wave fronts into a finite set of output wave fronts is rigorously analyzed. The optimum phase transfer function of the holographic optical element is analytically determined. The optimum phase transfer function is defined as the one for which the element has minimum mean-squared wave-front error averaged over the set of input wave fronts. It is also shown that in general it may not be possible to obtain a low value for this average mean-squared wave-front error by using a single holographic element. Furthermore, the performance trade-off of spherical aberration, coma, and astigmatism versus geometric distortion is clearly indicated by example.

© 1983 Optical Society of America

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  1. D. H. Close, "Holographic optical elements," Opt. Eng. 14, 408–419 (1975).
  2. W. H. Lee, "Computer-generated holograms: techniques and applications," in Progress in Optics, E. Wolf, ed. (Wiley, New York, 1978), Vol. 16.
  3. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  4. E. B. Champagne, "Nonparaxial imaging, magnification, and aberration properties in holography," J. Opt. Soc. Am. 57, 51–55 (1967); "A qualitative and quantitative study of holographic imaging, Ph.D. dissertation, Ohio State University, Columbus, Ohio (1967).
  5. J. R. Fienup and C. D. Leonard, "Holographic optics for a matched filter optical processor," Appl. Opt. 18, 631–640 (1979).
  6. R. C. Fairchild and J. R. Fienup, "Computer-originated hologram lenses," Opt. Eng. 21, 133–140 (1982).
  7. J. N. Latta and R. C. Fairchild, "New developments in the design of holographic optics," Proc. Soc. Photo-Opt. Instrum. Eng. 39, 107–126 (1973).
  8. J. N. Latta, "Computer-based analysis of holography using ray tracing," Appl. Opt. 10, 2698–2710 (1971).
  9. D. Feder, "Automatic optical design," Appl. Opt. 2, 1209–1226 (1963).
  10. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).
  11. R. Collier, C. Burkhardt, and L. Lin, Optical Holography (Academic, New York, 1971), Chaps. 8 and 9.

1982 (1)

R. C. Fairchild and J. R. Fienup, "Computer-originated hologram lenses," Opt. Eng. 21, 133–140 (1982).

1979 (1)

1975 (1)

D. H. Close, "Holographic optical elements," Opt. Eng. 14, 408–419 (1975).

1973 (1)

J. N. Latta and R. C. Fairchild, "New developments in the design of holographic optics," Proc. Soc. Photo-Opt. Instrum. Eng. 39, 107–126 (1973).

1971 (1)

1963 (1)

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Burkhardt, C.

R. Collier, C. Burkhardt, and L. Lin, Optical Holography (Academic, New York, 1971), Chaps. 8 and 9.

Champagne, E. B.

E. B. Champagne, "Nonparaxial imaging, magnification, and aberration properties in holography," J. Opt. Soc. Am. 57, 51–55 (1967); "A qualitative and quantitative study of holographic imaging, Ph.D. dissertation, Ohio State University, Columbus, Ohio (1967).

Close, D. H.

D. H. Close, "Holographic optical elements," Opt. Eng. 14, 408–419 (1975).

Collier, R.

R. Collier, C. Burkhardt, and L. Lin, Optical Holography (Academic, New York, 1971), Chaps. 8 and 9.

Fairchild, R. C.

R. C. Fairchild and J. R. Fienup, "Computer-originated hologram lenses," Opt. Eng. 21, 133–140 (1982).

J. N. Latta and R. C. Fairchild, "New developments in the design of holographic optics," Proc. Soc. Photo-Opt. Instrum. Eng. 39, 107–126 (1973).

Feder, D.

Fienup, J. R.

R. C. Fairchild and J. R. Fienup, "Computer-originated hologram lenses," Opt. Eng. 21, 133–140 (1982).

J. R. Fienup and C. D. Leonard, "Holographic optics for a matched filter optical processor," Appl. Opt. 18, 631–640 (1979).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Latta, J. N.

J. N. Latta and R. C. Fairchild, "New developments in the design of holographic optics," Proc. Soc. Photo-Opt. Instrum. Eng. 39, 107–126 (1973).

J. N. Latta, "Computer-based analysis of holography using ray tracing," Appl. Opt. 10, 2698–2710 (1971).

Lee, W. H.

W. H. Lee, "Computer-generated holograms: techniques and applications," in Progress in Optics, E. Wolf, ed. (Wiley, New York, 1978), Vol. 16.

Leonard, C. D.

Lin, L.

R. Collier, C. Burkhardt, and L. Lin, Optical Holography (Academic, New York, 1971), Chaps. 8 and 9.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Appl. Opt. (3)

Opt. Eng. (2)

D. H. Close, "Holographic optical elements," Opt. Eng. 14, 408–419 (1975).

R. C. Fairchild and J. R. Fienup, "Computer-originated hologram lenses," Opt. Eng. 21, 133–140 (1982).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

J. N. Latta and R. C. Fairchild, "New developments in the design of holographic optics," Proc. Soc. Photo-Opt. Instrum. Eng. 39, 107–126 (1973).

Other (5)

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).

R. Collier, C. Burkhardt, and L. Lin, Optical Holography (Academic, New York, 1971), Chaps. 8 and 9.

W. H. Lee, "Computer-generated holograms: techniques and applications," in Progress in Optics, E. Wolf, ed. (Wiley, New York, 1978), Vol. 16.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

E. B. Champagne, "Nonparaxial imaging, magnification, and aberration properties in holography," J. Opt. Soc. Am. 57, 51–55 (1967); "A qualitative and quantitative study of holographic imaging, Ph.D. dissertation, Ohio State University, Columbus, Ohio (1967).

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