Abstract

The Fresnel zone of optical gratings—the region behind the grating where secondary interference between the light coming through the different openings produces real images of the grating—can be understood by comparison with other types of wave phenomena. In the Fresnel zone of light diffracted by an optical grating, different types of amplitude modulation of the wave front are observable. Gratings of stationary ultrasonic waves, being phase gratings to the light passing through them, produce similar, though not identical Fresnel patterns. Between the planes in which the secondary interference patterns are true images of the gratings, the modulation changes from amplitude to phase modulation. This change can be demonstrated by an ultrasonic wave analog. Patterns formed by the diffraction of ultrasonic waves by an amplitude grating are given. Similar patterns in surface waves are given for both the phase grating and the amplitude grating analog.

© 1959 Optical Society of America

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References

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  2. H. Talbot, Phil. Mag. 9, 401 (1836).
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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  12. E. Menzel and C. Menzel, Optik 4, 22 (1948).
  13. E. Hiedemann, Ergeb. exakt. Naturw. 14, 219 (1935).
  14. O. Nomoto, Proc. Phys.-Math. Soc. Japan 18, 402 (1936).
  15. O. Nomoto, Proc. Phys.-Math. Soc. Japan 19, 337 (1937).
  16. H. Falkenhagen and Ch. Bachem, Z. Elektrochem. 41, 570 (1935).
  17. S. Parthasarathy, Proc. Indian Acad. Sci. 4, 55 (1936).
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    [Crossref]
  19. N. Nath, Proc. Indian Acad. Sci. 4, 262 (1936).
  20. C. Raman and N. Nath, Proc. Indian Acad. Sci. 3, 119 (1936).
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  24. O. Nomoto, J. Phys. Soc. Japan 2, 41 (1947).
    [Crossref]

1948 (2)

E. Menzel and C. Menzel, Optik 3, 247 (1948).

E. Menzel and C. Menzel, Optik 4, 22 (1948).

1947 (1)

O. Nomoto, J. Phys. Soc. Japan 2, 41 (1947).
[Crossref]

1938 (1)

E. Hiedemann and K. Osterhammel, Proc. Indian Acad. Sci. 8, 275 (1938).

1937 (2)

E. Hiedemann and E. Schreuer, Z. Physik 107, 463 (1937).
[Crossref]

O. Nomoto, Proc. Phys.-Math. Soc. Japan 19, 337 (1937).

1936 (5)

O. Nomoto, Proc. Phys.-Math. Soc. Japan 18, 402 (1936).

S. Parthasarathy, Proc. Indian Acad. Sci. 4, 55 (1936).

N. Nath, Proc. Indian Acad. Sci. 4, 262 (1936).

C. Raman and N. Nath, Proc. Indian Acad. Sci. 3, 119 (1936).

P. Pisharoty, Proc. Indian Acad. Sci. 4, 27 (1936).

1935 (4)

R. Bär, Helv. Phys. Acta 8, 591 (1935).

H. Falkenhagen and Ch. Bachem, Z. Elektrochem. 41, 570 (1935).

E. Hiedemann, Ergeb. exakt. Naturw. 14, 219 (1935).

F. Zernike, Physik. Z. 36, 848 (1935).

1934 (1)

F. Zernike, Physica 1, 689 (1934).
[Crossref]

1913 (1)

M. Wolfke, Ann. Physik 40, 194 (1913).
[Crossref]

1912 (4)

M. Wolfke, Ann. Physik 37, 96 (1912).
[Crossref]

M. Wolfke, Ann. Physik 37, 797 (1912).
[Crossref]

M. Wolfke, Ann. Physik 38, 385 (1912).
[Crossref]

M. Wolfke, Ann. Physik 39, 569 (1912).
[Crossref]

1911 (1)

M. Wolfke, Ann. Physik 34, 277 (1911).
[Crossref]

1881 (1)

Rayleigh, Phil. Mag. 11, 196 (1881).

1836 (1)

H. Talbot, Phil. Mag. 9, 401 (1836).

Bachem, Ch.

H. Falkenhagen and Ch. Bachem, Z. Elektrochem. 41, 570 (1935).

Bär, R.

R. Bär, Helv. Phys. Acta 8, 591 (1935).

Falkenhagen, H.

H. Falkenhagen and Ch. Bachem, Z. Elektrochem. 41, 570 (1935).

Hiedemann, E.

E. Hiedemann and K. Osterhammel, Proc. Indian Acad. Sci. 8, 275 (1938).

E. Hiedemann and E. Schreuer, Z. Physik 107, 463 (1937).
[Crossref]

E. Hiedemann, Ergeb. exakt. Naturw. 14, 219 (1935).

Menzel, C.

E. Menzel and C. Menzel, Optik 4, 22 (1948).

E. Menzel and C. Menzel, Optik 3, 247 (1948).

Menzel, E.

E. Menzel and C. Menzel, Optik 4, 22 (1948).

E. Menzel and C. Menzel, Optik 3, 247 (1948).

Nath, N.

N. Nath, Proc. Indian Acad. Sci. 4, 262 (1936).

C. Raman and N. Nath, Proc. Indian Acad. Sci. 3, 119 (1936).

Nomoto, O.

O. Nomoto, J. Phys. Soc. Japan 2, 41 (1947).
[Crossref]

O. Nomoto, Proc. Phys.-Math. Soc. Japan 19, 337 (1937).

O. Nomoto, Proc. Phys.-Math. Soc. Japan 18, 402 (1936).

Osterhammel, K.

E. Hiedemann and K. Osterhammel, Proc. Indian Acad. Sci. 8, 275 (1938).

Parthasarathy, S.

S. Parthasarathy, Proc. Indian Acad. Sci. 4, 55 (1936).

Pisharoty, P.

P. Pisharoty, Proc. Indian Acad. Sci. 4, 27 (1936).

Raman, C.

C. Raman and N. Nath, Proc. Indian Acad. Sci. 3, 119 (1936).

Rayleigh,

Rayleigh, Phil. Mag. 11, 196 (1881).

Schreuer, E.

E. Hiedemann and E. Schreuer, Z. Physik 107, 463 (1937).
[Crossref]

Talbot, H.

H. Talbot, Phil. Mag. 9, 401 (1836).

Wolfke, M.

M. Wolfke, Ann. Physik 40, 194 (1913).
[Crossref]

M. Wolfke, Ann. Physik 37, 96 (1912).
[Crossref]

M. Wolfke, Ann. Physik 37, 797 (1912).
[Crossref]

M. Wolfke, Ann. Physik 38, 385 (1912).
[Crossref]

M. Wolfke, Ann. Physik 39, 569 (1912).
[Crossref]

M. Wolfke, Ann. Physik 34, 277 (1911).
[Crossref]

Zernike, F.

F. Zernike, Physik. Z. 36, 848 (1935).

F. Zernike, Physica 1, 689 (1934).
[Crossref]

Ann. Physik (6)

M. Wolfke, Ann. Physik 34, 277 (1911).
[Crossref]

M. Wolfke, Ann. Physik 37, 96 (1912).
[Crossref]

M. Wolfke, Ann. Physik 37, 797 (1912).
[Crossref]

M. Wolfke, Ann. Physik 38, 385 (1912).
[Crossref]

M. Wolfke, Ann. Physik 39, 569 (1912).
[Crossref]

M. Wolfke, Ann. Physik 40, 194 (1913).
[Crossref]

Ergeb. exakt. Naturw. (1)

E. Hiedemann, Ergeb. exakt. Naturw. 14, 219 (1935).

Helv. Phys. Acta (1)

R. Bär, Helv. Phys. Acta 8, 591 (1935).

J. Phys. Soc. Japan (1)

O. Nomoto, J. Phys. Soc. Japan 2, 41 (1947).
[Crossref]

Optik (2)

E. Menzel and C. Menzel, Optik 3, 247 (1948).

E. Menzel and C. Menzel, Optik 4, 22 (1948).

Phil. Mag. (2)

Rayleigh, Phil. Mag. 11, 196 (1881).

H. Talbot, Phil. Mag. 9, 401 (1836).

Physica (1)

F. Zernike, Physica 1, 689 (1934).
[Crossref]

Physik. Z. (1)

F. Zernike, Physik. Z. 36, 848 (1935).

Proc. Indian Acad. Sci. (5)

E. Hiedemann and K. Osterhammel, Proc. Indian Acad. Sci. 8, 275 (1938).

S. Parthasarathy, Proc. Indian Acad. Sci. 4, 55 (1936).

N. Nath, Proc. Indian Acad. Sci. 4, 262 (1936).

C. Raman and N. Nath, Proc. Indian Acad. Sci. 3, 119 (1936).

P. Pisharoty, Proc. Indian Acad. Sci. 4, 27 (1936).

Proc. Phys.-Math. Soc. Japan (2)

O. Nomoto, Proc. Phys.-Math. Soc. Japan 18, 402 (1936).

O. Nomoto, Proc. Phys.-Math. Soc. Japan 19, 337 (1937).

Z. Elektrochem. (1)

H. Falkenhagen and Ch. Bachem, Z. Elektrochem. 41, 570 (1935).

Z. Physik (1)

E. Hiedemann and E. Schreuer, Z. Physik 107, 463 (1937).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1

Secondary interference patterns in the Fresnel zone of a photographic grating.

Fig. 2
Fig. 2

Secondary interference patterns in the Fresnel zone of a standing ultrasonic wave grating.

Fig. 3
Fig. 3

Schematic diagram of secondary interference in the Fresnel zone of a grating.

Fig. 4
Fig. 4

Optical arrangement for observing diffraction of ultrasonic waves.

Fig. 5
Fig. 5

Schlieren picture of ultrasonic waves diffracted by an amplitude grating.

Fig. 6
Fig. 6

Stroboscopic picture of ultrasonic waves diffracted by an amplitude grating.

Fig. 7
Fig. 7

Stroboscopic picture of capillary waves by (a) corrugated dipper (phase grating analog), (b) comb dipper (amplitude grating analog), and (c) saw-tooth dipper (echelette grating analog).