Abstract

Precision photometric measurements of the optical Fresnel diffraction pattern produced by a straight edge were made on eight edges of various materials and with various edge cross sections to ascertain the effect of these parameters on the pattern. For unpolarized light at a wavelength of 5461 Å, approximately 600 fringes were detected and measured in each pattern, and 800 fringes were detected in some of the patterns. The theoretical position of the geometric shadow (I/I0 = 0.25) is verified to an angular accuracy of 1 × 10−4 deg. The light intensity distribution was scanned at a constant speed and detected by a 1P21 photomultiplier tube cooled to dry-ice temperature. The distance between the light source and the photometer was 52 m, and the edge was placed 20 m from the source. A simple technique for automatic compensation for fluctuations of the primary light source is also described. Accuracy of approximately 0.2% in the intensity measurements and of 0.03% in fringe position far from the shadow boundary is claimed. To within the accuracy of the experiment, the intensity distribution for all eight edges agreed throughout the complete pattern, but there is a slight variation in fringe position from the simple scalar theory.

© 1962 Optical Society of America

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References

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  1. B. N. Harden, Proc. Inst. Elect. Engrs. Pt. III 99, 229 (1952).
  2. R. D. Kodis, J. Appl. Phys. 23, 249 (1952).
    [Crossref]
  3. J. Savornin, Ann. phys. 11, 129 (1939).
  4. H. S. Carslaw, Proc. London Math. Soc. 18, 291 (1899).
  5. K. M. McDonald, Electric Waves (Cambridge University Press, New York, 1902), pp. 186–198.
  6. D. S. Jones and F. B. Pidduck, Quart. J. Math. 1, 229 (1950).
    [Crossref]
  7. P. S. Epstein, dissertation, Munich, Germany (1914).
  8. K. Artmann, Z. Physik 127, 468 (1950).
    [Crossref]
  9. S. O. Rice, Bell System Tech. J. 33, 417–504 (1954).
    [Crossref]
  10. B. B. Baker and E. T. Copson, The Mathematical Theory of Huygens’ Principle (Oxford University Press, New York, 1950), 2nd ed.
  11. C. J. Bouwkamp, Repts. on Progr. in Phys. 17, 35 (1954).
    [Crossref]
  12. W. Franz, Theorie der Beugung elektromagnetischer Wellen (Springer-Verlag, Berlin, 1957).
    [Crossref]
  13. A. Rubinowicz, Die Beugungswelle in der Kirchhoffschen Theorie der Beugung (Polska Academie Nauk, Warsaw, 1957).
  14. K. L. McDonald and F. S. Harris, J. Opt. Soc. Am. 42, 321 (1952).
    [Crossref]
  15. M. E. Hufford, J. Opt. Soc. Am. 27, 408–410 (1937).
    [Crossref]
  16. As in much of the literature on diffraction, intensity of an element of a diffraction pattern means here the flux passing through unit area of the element. It should not be confused with intensity in its specialized photometric sense of flux per unit solid angle from a source essentially confined to a point.
  17. P. Fellgett, J. Sci. Instr. 31, 217 (1954).
    [Crossref]
  18. A. Sommerfeld, Optics (Academic Press Inc., New York, 1954), p. 259.
  19. M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959), p. 433.
  20. J. D. Barnett, “Effect of edge parameters on Fresnel diffraction of light at a straight edge,” dissertation, University of Utah (1959).

1954 (3)

S. O. Rice, Bell System Tech. J. 33, 417–504 (1954).
[Crossref]

C. J. Bouwkamp, Repts. on Progr. in Phys. 17, 35 (1954).
[Crossref]

P. Fellgett, J. Sci. Instr. 31, 217 (1954).
[Crossref]

1952 (3)

B. N. Harden, Proc. Inst. Elect. Engrs. Pt. III 99, 229 (1952).

R. D. Kodis, J. Appl. Phys. 23, 249 (1952).
[Crossref]

K. L. McDonald and F. S. Harris, J. Opt. Soc. Am. 42, 321 (1952).
[Crossref]

1950 (2)

D. S. Jones and F. B. Pidduck, Quart. J. Math. 1, 229 (1950).
[Crossref]

K. Artmann, Z. Physik 127, 468 (1950).
[Crossref]

1939 (1)

J. Savornin, Ann. phys. 11, 129 (1939).

1937 (1)

1899 (1)

H. S. Carslaw, Proc. London Math. Soc. 18, 291 (1899).

Artmann, K.

K. Artmann, Z. Physik 127, 468 (1950).
[Crossref]

Baker, B. B.

B. B. Baker and E. T. Copson, The Mathematical Theory of Huygens’ Principle (Oxford University Press, New York, 1950), 2nd ed.

Barnett, J. D.

J. D. Barnett, “Effect of edge parameters on Fresnel diffraction of light at a straight edge,” dissertation, University of Utah (1959).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959), p. 433.

Bouwkamp, C. J.

C. J. Bouwkamp, Repts. on Progr. in Phys. 17, 35 (1954).
[Crossref]

Carslaw, H. S.

H. S. Carslaw, Proc. London Math. Soc. 18, 291 (1899).

Copson, E. T.

B. B. Baker and E. T. Copson, The Mathematical Theory of Huygens’ Principle (Oxford University Press, New York, 1950), 2nd ed.

Epstein, P. S.

P. S. Epstein, dissertation, Munich, Germany (1914).

Fellgett, P.

P. Fellgett, J. Sci. Instr. 31, 217 (1954).
[Crossref]

Franz, W.

W. Franz, Theorie der Beugung elektromagnetischer Wellen (Springer-Verlag, Berlin, 1957).
[Crossref]

Harden, B. N.

B. N. Harden, Proc. Inst. Elect. Engrs. Pt. III 99, 229 (1952).

Harris, F. S.

Hufford, M. E.

Jones, D. S.

D. S. Jones and F. B. Pidduck, Quart. J. Math. 1, 229 (1950).
[Crossref]

Kodis, R. D.

R. D. Kodis, J. Appl. Phys. 23, 249 (1952).
[Crossref]

McDonald, K. L.

McDonald, K. M.

K. M. McDonald, Electric Waves (Cambridge University Press, New York, 1902), pp. 186–198.

Pidduck, F. B.

D. S. Jones and F. B. Pidduck, Quart. J. Math. 1, 229 (1950).
[Crossref]

Rice, S. O.

S. O. Rice, Bell System Tech. J. 33, 417–504 (1954).
[Crossref]

Rubinowicz, A.

A. Rubinowicz, Die Beugungswelle in der Kirchhoffschen Theorie der Beugung (Polska Academie Nauk, Warsaw, 1957).

Savornin, J.

J. Savornin, Ann. phys. 11, 129 (1939).

Sommerfeld, A.

A. Sommerfeld, Optics (Academic Press Inc., New York, 1954), p. 259.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959), p. 433.

Ann. phys. (1)

J. Savornin, Ann. phys. 11, 129 (1939).

Bell System Tech. J. (1)

S. O. Rice, Bell System Tech. J. 33, 417–504 (1954).
[Crossref]

J. Appl. Phys. (1)

R. D. Kodis, J. Appl. Phys. 23, 249 (1952).
[Crossref]

J. Opt. Soc. Am. (2)

J. Sci. Instr. (1)

P. Fellgett, J. Sci. Instr. 31, 217 (1954).
[Crossref]

Proc. Inst. Elect. Engrs. Pt. III (1)

B. N. Harden, Proc. Inst. Elect. Engrs. Pt. III 99, 229 (1952).

Proc. London Math. Soc. (1)

H. S. Carslaw, Proc. London Math. Soc. 18, 291 (1899).

Quart. J. Math. (1)

D. S. Jones and F. B. Pidduck, Quart. J. Math. 1, 229 (1950).
[Crossref]

Repts. on Progr. in Phys. (1)

C. J. Bouwkamp, Repts. on Progr. in Phys. 17, 35 (1954).
[Crossref]

Z. Physik (1)

K. Artmann, Z. Physik 127, 468 (1950).
[Crossref]

Other (9)

W. Franz, Theorie der Beugung elektromagnetischer Wellen (Springer-Verlag, Berlin, 1957).
[Crossref]

A. Rubinowicz, Die Beugungswelle in der Kirchhoffschen Theorie der Beugung (Polska Academie Nauk, Warsaw, 1957).

As in much of the literature on diffraction, intensity of an element of a diffraction pattern means here the flux passing through unit area of the element. It should not be confused with intensity in its specialized photometric sense of flux per unit solid angle from a source essentially confined to a point.

A. Sommerfeld, Optics (Academic Press Inc., New York, 1954), p. 259.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959), p. 433.

J. D. Barnett, “Effect of edge parameters on Fresnel diffraction of light at a straight edge,” dissertation, University of Utah (1959).

P. S. Epstein, dissertation, Munich, Germany (1914).

B. B. Baker and E. T. Copson, The Mathematical Theory of Huygens’ Principle (Oxford University Press, New York, 1950), 2nd ed.

K. M. McDonald, Electric Waves (Cambridge University Press, New York, 1902), pp. 186–198.

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Figures (5)

Fig. 1
Fig. 1

Precise determination of geometric shadow. A pattern was measured with the diffracting edge in two positions indicated. These two patterns were later aligned on the same scale, and this intersection designates the geometric shadow.

Fig. 2
Fig. 2

Instrumental layout of light-tight hallway.

Fig. 3
Fig. 3

Analog dividing circuit. (a) Note that all components within the dashed box are precisely the components found in the strip-chart recorder. The dotted lines represent mechanical connections.

Fig. 4
Fig. 4

Cross section of the eight-edges studies. The edges are shown mounted with respect to the incident light.

Fig. 5
Fig. 5

Typical experimental straight-edge diffraction pattern trace compared with Fresnel theory. The enlarged detailed sections indicate the quality of the strip-chart recording in three regions of the pattern.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

A / Z = ( A I 0 ) / B , B + I = Z ,
Z = A ( I / I 0 ) .
| U U 0 | 2 = I I 0 = | 1 i 2 υ e 1 2 i π τ 2 | 2 .
υ = [ 2 λ ( 1 a + 1 b ) ] 1 2 S ,
I / I 0 = 1 2 [ 1 2 + S ( υ ) ] 2 + 1 2 [ 1 2 + C ( υ ) ] 2 .
I / I 0 = 1 + ( 2 / π υ ) sin ( 1 2 π υ 2 + 1 4 π ) .