Abstract

A convenient expression describing the location of Fresnel diffraction patterns when a diffracted spherical wave is focused by a lens is given. Experimental results confirm the predicted positions of 26 axial extrema corresponding to integer numbers of Fresnel half-period zones. Experimental radial intensity profiles are presented for some of these positions.

© 1986 Optical Society of America

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References

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  1. F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).
  2. J. M. Stone, Radiation and Optics (McGraw-Hill, New York, 1963).
  3. J. Terrell, Los Alamos National Laboratory, ESS-9 D436, Los Alamos, New Mexico 87545 (personal communication).
  4. M. E. Hufford, “Some new diffraction photographs,” Phys. Rev. 3, 241–243 (1914).
    [CrossRef]
  5. M. E. Hufford, H. T. Davis, “The diffraction of light by a circular opening and the Lommel wave theory,” Phys. Rev. 33, 589–597 (1929).
    [CrossRef]
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975).
  7. C. A. Taylor, B. J. Thompson, “Attempt to investigate experimentally the intensity distribution near the focus in the error-free diffraction patterns of circular and annular apertures,”J. Opt. Soc. Am. 48, 844–850 (1958).
    [CrossRef]
  8. Y. Li, H. Platzer, “An experimental investigation of diffraction pattens in low-Fresnel-number focusing systems,” Opt. Acta 30, 1621–1643 (1983).
    [CrossRef]
  9. Y. Li, E. Wolf, “Three-dimensional intensity distribution near the focus in systems of different Fresnel numbers,” J. Opt. Soc. Am. A 1, 801–808 (1984).
    [CrossRef]
  10. A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971).
  11. R. G. Wenzel, G. P. Arnold, “Parametric oscillator: HF oscillator–amplifier pump CdSe parametric oscillator tunable from 14.1 μ m to 16.4 μ m,” Appl. Opt. 15, 1322–1326 (1976).
    [CrossRef] [PubMed]
  12. M. V. R. K. Murty, “Lateral shearing interferometers” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978).
  13. R. G. Wenzel, “Effect of the lens aperture separation on the focal shift in large-f-number systems,” J. Opt. Soc. Am. A (to be published).

1984 (1)

1983 (1)

Y. Li, H. Platzer, “An experimental investigation of diffraction pattens in low-Fresnel-number focusing systems,” Opt. Acta 30, 1621–1643 (1983).
[CrossRef]

1976 (1)

1958 (1)

1929 (1)

M. E. Hufford, H. T. Davis, “The diffraction of light by a circular opening and the Lommel wave theory,” Phys. Rev. 33, 589–597 (1929).
[CrossRef]

1914 (1)

M. E. Hufford, “Some new diffraction photographs,” Phys. Rev. 3, 241–243 (1914).
[CrossRef]

Arnold, G. P.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975).

Davis, H. T.

M. E. Hufford, H. T. Davis, “The diffraction of light by a circular opening and the Lommel wave theory,” Phys. Rev. 33, 589–597 (1929).
[CrossRef]

Hufford, M. E.

M. E. Hufford, H. T. Davis, “The diffraction of light by a circular opening and the Lommel wave theory,” Phys. Rev. 33, 589–597 (1929).
[CrossRef]

M. E. Hufford, “Some new diffraction photographs,” Phys. Rev. 3, 241–243 (1914).
[CrossRef]

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).

Li, Y.

Y. Li, E. Wolf, “Three-dimensional intensity distribution near the focus in systems of different Fresnel numbers,” J. Opt. Soc. Am. A 1, 801–808 (1984).
[CrossRef]

Y. Li, H. Platzer, “An experimental investigation of diffraction pattens in low-Fresnel-number focusing systems,” Opt. Acta 30, 1621–1643 (1983).
[CrossRef]

Murty, M. V. R. K.

M. V. R. K. Murty, “Lateral shearing interferometers” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978).

Platzer, H.

Y. Li, H. Platzer, “An experimental investigation of diffraction pattens in low-Fresnel-number focusing systems,” Opt. Acta 30, 1621–1643 (1983).
[CrossRef]

Siegman, A. E.

A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971).

Stone, J. M.

J. M. Stone, Radiation and Optics (McGraw-Hill, New York, 1963).

Taylor, C. A.

Terrell, J.

J. Terrell, Los Alamos National Laboratory, ESS-9 D436, Los Alamos, New Mexico 87545 (personal communication).

Thompson, B. J.

Wenzel, R. G.

R. G. Wenzel, G. P. Arnold, “Parametric oscillator: HF oscillator–amplifier pump CdSe parametric oscillator tunable from 14.1 μ m to 16.4 μ m,” Appl. Opt. 15, 1322–1326 (1976).
[CrossRef] [PubMed]

R. G. Wenzel, “Effect of the lens aperture separation on the focal shift in large-f-number systems,” J. Opt. Soc. Am. A (to be published).

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).

Wolf, E.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Acta (1)

Y. Li, H. Platzer, “An experimental investigation of diffraction pattens in low-Fresnel-number focusing systems,” Opt. Acta 30, 1621–1643 (1983).
[CrossRef]

Phys. Rev. (2)

M. E. Hufford, “Some new diffraction photographs,” Phys. Rev. 3, 241–243 (1914).
[CrossRef]

M. E. Hufford, H. T. Davis, “The diffraction of light by a circular opening and the Lommel wave theory,” Phys. Rev. 33, 589–597 (1929).
[CrossRef]

Other (7)

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975).

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).

J. M. Stone, Radiation and Optics (McGraw-Hill, New York, 1963).

J. Terrell, Los Alamos National Laboratory, ESS-9 D436, Los Alamos, New Mexico 87545 (personal communication).

A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971).

M. V. R. K. Murty, “Lateral shearing interferometers” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978).

R. G. Wenzel, “Effect of the lens aperture separation on the focal shift in large-f-number systems,” J. Opt. Soc. Am. A (to be published).

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Figures (5)

Fig. 1
Fig. 1

Fresnel diffraction of a coherent monochromatic plane wave by a circular aperture.

Fig. 2
Fig. 2

Diffraction of a spherical wave, with subsequent focusing by a lens.

Fig. 3
Fig. 3

Fresnel diffraction patterns. Values of the Fresnel number are given at the left. The plane-wave patterns are in the column labeled F, while F+ and F refer to positive and negative Fresnel numbers from Eq. (2) for the spherical patterns.

Fig. 4
Fig. 4

Setup used to obtain the spherical diffraction patterns of Fig. 3 and to test Eq. (2).

Fig. 5
Fig. 5

Fresnel number versus distance from lens. The dots are experimental points, and the curve is a plot of Eq. (2). The experimental parameters are given in Table 1.

Tables (1)

Tables Icon

Table 1 Parameters of Eq. (2) Used in This Work

Equations (7)

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F = a 2 / λ l .
Δ = s P Q m - s O m ,
s P Q m = s x + P Q m
P Q m = w O m . Δ = s x + w O m - s O m = w x .
Δ = a 2 2 R 0 - a 2 2 ( L 2 - L 0 ) .
F = a 2 λ [ 1 L 0 - L 1 f L 1 - f + 1 R 0 ] .
F a 2 λ [ 1 L 0 - f + 1 R 0 ] .

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