Abstract

Experimental work at the University of Utah has produced high-resolution optical diffraction patterns by slit apertures, 20 m from source and 30 m from photomultiplier receiver slit. The slit widths varied in 26 values from 0.5 to 32 mm with 4358- and 5461-Å light, corresponding to a Fresnel-variable difference ranging from 0.271 to 19.396. The receiver-slit width was 0.2 mm. A versatile program developed at The Aerospace Corporation for calculation of Fresnel integrals has been used for comparison with experiment, including averaging to give the effect of integration by the photomultiplier slit. Experimental and theoretical diffraction curves are compared for various slit widths. One double-slit-pattern comparison is also given. A high degree of symmetry is found in the measured curves. Even the very fine fluctuations of irradiance in the experimental and theoretical curves match. Three-dimensional theoretical projections of diffraction patterns show the continuous change of pattern from near-Fraunhofer to Fresnel diffraction.

© 1969 Optical Society of America

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References

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  1. Franklin S. Harris, Michael S. Tavenner, and Gordon R. Orme, J. Opt. Soc. Am. 50, 1131A (1960).
  2. J. Dean Barnett and Franklin S. Harris, J. Opt. Soc. Am. 48, 872 (1958).
  3. Francis A. Jenkins and Harvey E. White, Fundamentals of Optics (McGraw–Hill Book Co., New York, 1957), 3rd ed., Ch. 18.
  4. Tablitsii Integralov Frenelya, Izd. Akad. Nauk USSR, Moscow (1953).
  5. M. P. Bachynski and G. Bekefi, J. Opt. Soc. Am. 47, 428 (1957).
    [Crossref]
  6. J. Picht, Optik 15, 83 (1958).
  7. John W. Sherman, IRE Trans. Antennas Propagation AP10, 399 (1962).
    [Crossref]
  8. M. Cagnet, M. Françon, and J. C. Thrierer, Atlas of Optical Phenomena (Julius Springer-VerlagBerlin/Vienna and Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962), pp. 23–24.
  9. Arthur C. Lind and J. Mayo Greenberg, J. Appl. Phys. 37, 3195 (1966).
    [Crossref]
  10. Leo Beiser, Appl. Opt. 5, 869 (1966).
    [Crossref] [PubMed]
  11. R. L. Mitchell in Proceedings of the Seminar on Computerized Imaging Techniques, Washingotn, D. C., 26 June 1967 (Society Photo-optical Instrumentation Engineers, Redondo Beach, Calif., 1967).

1966 (2)

Arthur C. Lind and J. Mayo Greenberg, J. Appl. Phys. 37, 3195 (1966).
[Crossref]

Leo Beiser, Appl. Opt. 5, 869 (1966).
[Crossref] [PubMed]

1962 (1)

John W. Sherman, IRE Trans. Antennas Propagation AP10, 399 (1962).
[Crossref]

1960 (1)

Franklin S. Harris, Michael S. Tavenner, and Gordon R. Orme, J. Opt. Soc. Am. 50, 1131A (1960).

1958 (2)

J. Dean Barnett and Franklin S. Harris, J. Opt. Soc. Am. 48, 872 (1958).

J. Picht, Optik 15, 83 (1958).

1957 (1)

Bachynski, M. P.

Beiser, Leo

Bekefi, G.

Cagnet, M.

M. Cagnet, M. Françon, and J. C. Thrierer, Atlas of Optical Phenomena (Julius Springer-VerlagBerlin/Vienna and Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962), pp. 23–24.

Dean Barnett, J.

J. Dean Barnett and Franklin S. Harris, J. Opt. Soc. Am. 48, 872 (1958).

Françon, M.

M. Cagnet, M. Françon, and J. C. Thrierer, Atlas of Optical Phenomena (Julius Springer-VerlagBerlin/Vienna and Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962), pp. 23–24.

Harris, Franklin S.

Franklin S. Harris, Michael S. Tavenner, and Gordon R. Orme, J. Opt. Soc. Am. 50, 1131A (1960).

J. Dean Barnett and Franklin S. Harris, J. Opt. Soc. Am. 48, 872 (1958).

Jenkins, Francis A.

Francis A. Jenkins and Harvey E. White, Fundamentals of Optics (McGraw–Hill Book Co., New York, 1957), 3rd ed., Ch. 18.

Lind, Arthur C.

Arthur C. Lind and J. Mayo Greenberg, J. Appl. Phys. 37, 3195 (1966).
[Crossref]

Mayo Greenberg, J.

Arthur C. Lind and J. Mayo Greenberg, J. Appl. Phys. 37, 3195 (1966).
[Crossref]

Mitchell, R. L.

R. L. Mitchell in Proceedings of the Seminar on Computerized Imaging Techniques, Washingotn, D. C., 26 June 1967 (Society Photo-optical Instrumentation Engineers, Redondo Beach, Calif., 1967).

Orme, Gordon R.

Franklin S. Harris, Michael S. Tavenner, and Gordon R. Orme, J. Opt. Soc. Am. 50, 1131A (1960).

Picht, J.

J. Picht, Optik 15, 83 (1958).

Sherman, John W.

John W. Sherman, IRE Trans. Antennas Propagation AP10, 399 (1962).
[Crossref]

Tavenner, Michael S.

Franklin S. Harris, Michael S. Tavenner, and Gordon R. Orme, J. Opt. Soc. Am. 50, 1131A (1960).

Thrierer, J. C.

M. Cagnet, M. Françon, and J. C. Thrierer, Atlas of Optical Phenomena (Julius Springer-VerlagBerlin/Vienna and Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962), pp. 23–24.

White, Harvey E.

Francis A. Jenkins and Harvey E. White, Fundamentals of Optics (McGraw–Hill Book Co., New York, 1957), 3rd ed., Ch. 18.

Appl. Opt. (1)

IRE Trans. Antennas Propagation (1)

John W. Sherman, IRE Trans. Antennas Propagation AP10, 399 (1962).
[Crossref]

J. Appl. Phys. (1)

Arthur C. Lind and J. Mayo Greenberg, J. Appl. Phys. 37, 3195 (1966).
[Crossref]

J. Opt. Soc. Am. (3)

M. P. Bachynski and G. Bekefi, J. Opt. Soc. Am. 47, 428 (1957).
[Crossref]

Franklin S. Harris, Michael S. Tavenner, and Gordon R. Orme, J. Opt. Soc. Am. 50, 1131A (1960).

J. Dean Barnett and Franklin S. Harris, J. Opt. Soc. Am. 48, 872 (1958).

Optik (1)

J. Picht, Optik 15, 83 (1958).

Other (4)

M. Cagnet, M. Françon, and J. C. Thrierer, Atlas of Optical Phenomena (Julius Springer-VerlagBerlin/Vienna and Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962), pp. 23–24.

Francis A. Jenkins and Harvey E. White, Fundamentals of Optics (McGraw–Hill Book Co., New York, 1957), 3rd ed., Ch. 18.

Tablitsii Integralov Frenelya, Izd. Akad. Nauk USSR, Moscow (1953).

R. L. Mitchell in Proceedings of the Seminar on Computerized Imaging Techniques, Washingotn, D. C., 26 June 1967 (Society Photo-optical Instrumentation Engineers, Redondo Beach, Calif., 1967).

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Figures (9)

Fig. 1
Fig. 1

Geometry of experiment. (The source, diffracting mount, and photometer are shown schematically but not to scale.)

Fig. 2
Fig. 2

Experimental irradiance diffraction patterns for varying slit widths ΔV = 0.271 to 4.331.

Fig. 3
Fig. 3

Experimental irradiance diffraction patterns for varying slit widths ΔV = 4.873 to 17.325.

Fig. 4
Fig. 4

Three-dimensional plot of single-slit pattern 0.500 to 0.100 of far-field condition.

Fig. 5
Fig. 5

Three-dimensional plot of single-slit pattern 0.250 to 0.050 of far-field condition.

Fig. 6
Fig. 6

Three-dimensional plot of single-slit pattern 0.125 to 0.025 of far-field condition.

Fig. 7
Fig. 7

Comparison of experimental diffraction pattern for 3.2-cm-wide slit with calculated averages, to simulate various receiver-slit widths.

Fig. 8
Fig. 8

Diffraction pattern of double slit recorded directly on film.

Fig. 9
Fig. 9

Double-slit pattern measured by photomultiplier scanning compared with calculated pattern.

Equations (1)

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Δ V = S [ 2 ( A + R ) / A R λ ] 1 2