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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 20, Iss. 11 — Jun. 1, 1981
  • pp: 2017–2025

Diffraction theory for an achromatic Fourier transformation

G. M. Morris  »View Author Affiliations


Applied Optics, Vol. 20, Issue 11, pp. 2017-2025 (1981)
http://dx.doi.org/10.1364/AO.20.002017


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Abstract

A three-lens achromatic Fourier transform system is analyzed in the context of paraxial Fresnel diffraction theory. From the analysis a general solution for the required wavelength dependence of the various lenses is found. A particular arrangement of the general system is then considered. Using first-order lens design principles, it is shown that each dispersive lens can be fabricated using a holographic zone lens and glass element cascade. The paraxial chromatic aberrations of the resulting system are calculated. It is found that this system design yields an achromatic transformation that is well corrected (paraxially) over the entire visible spectrum.

© 1981 Optical Society of America

History
Original Manuscript: December 20, 1980
Published: June 1, 1981

Citation
G. M. Morris, "Diffraction theory for an achromatic Fourier transformation," Appl. Opt. 20, 2017-2025 (1981)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-20-11-2017


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References

  1. E. N. Leith, J. A. Roth, Appl. Opt. 18, 2803 (1979). [CrossRef] [PubMed]
  2. P. Chavel, J. Opt. Soc. Am. 70, 935 (1980). [CrossRef]
  3. L. Mertz, Transformations in Optics (Wiley, New York, 1965), p. 94.
  4. J. M. Richardson, “Device for producing identifiable sine and cosine (Fourier) transforms of input signals by means of noncoherent optics,” U.S. Patent3,669,528 (13June1972).
  5. G. L. Rogers, Noncoherent Optical Processing (Wiley, New York, 1977), Chap. 5.
  6. G. L. Rogers, Appl. Opt. 18, 3152 (1979). [CrossRef] [PubMed]
  7. R. H. Katyl, Appl. Opt. 11, 1255 (1972). [CrossRef] [PubMed]
  8. C. G. Wynne, Opt. Commun. 28, 21 (1979). [CrossRef]
  9. G. M. Morris, N. George, Opt. Lett. 5, 446 (1980). [CrossRef] [PubMed]
  10. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 5.
  11. R. Kingslake, Lens Design Fundamentals (Academic, New York; 1978), p. 201.
  12. Schott Optical Glass, Inc., 400 York Ave., Duryea, Penn. 18642.
  13. This transform design is based on Eq. (6) and Eqs. (10)–(15) of Ref. 7. The following parameters were used to attain the lens powers in Eq. (34): N = −1; M0 = −1, f0 = a = S = 0.5 m, and z = −a.

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