Abstract

Schlieren imaging of acoustic waves has been used routinely for at least half a century. The nature of the image has conventionally been analyzed by various ray tracing techniques or wavefront corrugation calculations. These are restricted to low sound frequencies or thin sound fields. We present a novel method, based on acoustooptic plane wave interaction theory, that not only is applicable to high frequencies but reveals some unexpected features of schlieren imaging.

© 1990 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Toepler, “Optische Studien nach der Methode der Schlieren Beobachtung,” Poggendorff’s Ann. 131, 33, 180 (1867).
  2. R. Lucas, P. Biquard, “Propriétés optiques des milieux solides et liquides soumis aux vibrations élastiques ultra sonores,” J. Phys. Paris 71, 464–477 (1932).
  3. C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part I,” Proc. Ind. Acad. Sci. 2, 406–412 (1935).
  4. M. V. Berry, The Diffraction of Light by Ultrasound (Academic, New York, 1966).
  5. A. Korpel, H. H. Lin, D. J. Mehrl, “Use of Angular Plane-Wave Spectra in the Analysis of Three-Dimensional Weak Acousto-Optic Interaction,” J. Opt. Soc. Am. A 4, 2260–2265 (1987).
    [CrossRef]
  6. G. Bickel, G. Häusler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975–977 (1985).
  7. J. H. McLeod, “The Axicon: a New Type of Optical Element,” J. Opt. Soc. Am. 44, 592–597 (1954).
    [CrossRef]
  8. A. Korpel, D. Mehrl, H. H. Lin, “Schlieren Imaging of Sound Fields,” in Conference Proceedings, IEEE International 87 Ultrasonics (1987), pp. 515–518.

1987 (1)

1985 (1)

G. Bickel, G. Häusler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975–977 (1985).

1954 (1)

1935 (1)

C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part I,” Proc. Ind. Acad. Sci. 2, 406–412 (1935).

1932 (1)

R. Lucas, P. Biquard, “Propriétés optiques des milieux solides et liquides soumis aux vibrations élastiques ultra sonores,” J. Phys. Paris 71, 464–477 (1932).

1867 (1)

A. Toepler, “Optische Studien nach der Methode der Schlieren Beobachtung,” Poggendorff’s Ann. 131, 33, 180 (1867).

Berry, M. V.

M. V. Berry, The Diffraction of Light by Ultrasound (Academic, New York, 1966).

Bickel, G.

G. Bickel, G. Häusler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975–977 (1985).

Biquard, P.

R. Lucas, P. Biquard, “Propriétés optiques des milieux solides et liquides soumis aux vibrations élastiques ultra sonores,” J. Phys. Paris 71, 464–477 (1932).

Häusler, G.

G. Bickel, G. Häusler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975–977 (1985).

Korpel, A.

A. Korpel, H. H. Lin, D. J. Mehrl, “Use of Angular Plane-Wave Spectra in the Analysis of Three-Dimensional Weak Acousto-Optic Interaction,” J. Opt. Soc. Am. A 4, 2260–2265 (1987).
[CrossRef]

A. Korpel, D. Mehrl, H. H. Lin, “Schlieren Imaging of Sound Fields,” in Conference Proceedings, IEEE International 87 Ultrasonics (1987), pp. 515–518.

Lin, H. H.

A. Korpel, H. H. Lin, D. J. Mehrl, “Use of Angular Plane-Wave Spectra in the Analysis of Three-Dimensional Weak Acousto-Optic Interaction,” J. Opt. Soc. Am. A 4, 2260–2265 (1987).
[CrossRef]

A. Korpel, D. Mehrl, H. H. Lin, “Schlieren Imaging of Sound Fields,” in Conference Proceedings, IEEE International 87 Ultrasonics (1987), pp. 515–518.

Lucas, R.

R. Lucas, P. Biquard, “Propriétés optiques des milieux solides et liquides soumis aux vibrations élastiques ultra sonores,” J. Phys. Paris 71, 464–477 (1932).

Maul, M.

G. Bickel, G. Häusler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975–977 (1985).

McLeod, J. H.

Mehrl, D.

A. Korpel, D. Mehrl, H. H. Lin, “Schlieren Imaging of Sound Fields,” in Conference Proceedings, IEEE International 87 Ultrasonics (1987), pp. 515–518.

Mehrl, D. J.

Nath, N. S. N.

C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part I,” Proc. Ind. Acad. Sci. 2, 406–412 (1935).

Raman, C. V.

C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part I,” Proc. Ind. Acad. Sci. 2, 406–412 (1935).

Toepler, A.

A. Toepler, “Optische Studien nach der Methode der Schlieren Beobachtung,” Poggendorff’s Ann. 131, 33, 180 (1867).

J. Opt. Soc. Am. (1)

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

J. Phys. Paris (1)

R. Lucas, P. Biquard, “Propriétés optiques des milieux solides et liquides soumis aux vibrations élastiques ultra sonores,” J. Phys. Paris 71, 464–477 (1932).

Opt. Eng. (1)

G. Bickel, G. Häusler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975–977 (1985).

Poggendorff’s Ann. 131 (1)

A. Toepler, “Optische Studien nach der Methode der Schlieren Beobachtung,” Poggendorff’s Ann. 131, 33, 180 (1867).

Proc. Ind. Acad. Sci. (1)

C. V. Raman, N. S. N. Nath, “The Diffraction of Light by High Frequency Sound Waves: Part I,” Proc. Ind. Acad. Sci. 2, 406–412 (1935).

Other (2)

M. V. Berry, The Diffraction of Light by Ultrasound (Academic, New York, 1966).

A. Korpel, D. Mehrl, H. H. Lin, “Schlieren Imaging of Sound Fields,” in Conference Proceedings, IEEE International 87 Ultrasonics (1987), pp. 515–518.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Schlieren imaging setup.

Fig. 2
Fig. 2

Definition of elevation and azimuth angles for the (a) light field and (b) sound field.

Fig. 3
Fig. 3

Locus of interacting sound wave vectors.

Fig. 4
Fig. 4

Sound column.

Fig. 5
Fig. 5

Illustration of the z-dependent time delay effect.

Fig. 6
Fig. 6

Axial far field profile of the sound at 40 MHz.

Fig. 7
Fig. 7

Axial far field profile of the sound at 20 MHz.

Equations (42)

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

Q = K 2 L k 1 ,
E ˜ i ( ϕ , ϕ ) = F - 1 [ E i ( x , y , 0 ) ] ; f x = ϕ / λ , f y = ϕ / λ ;
S ˜ ( γ , γ ) = F - 1 [ S ( 0 , y , z ) ] ; F z = γ / Λ , F y = γ / Λ .
E 1 ( v ) ( x , y ) = F [ E ˜ 1 ( ϕ , ϕ ) ] ;             ϕ = f x λ ,             ϕ = f y λ .
E ˜ 1 ( ϕ , ϕ ) = - 1 4 j k C - + E ˜ i ( ϕ - 2 ϕ B + K k γ 2 2 , ϕ - K k γ ) × S ˜ [ - ϕ + ϕ B - γ ϕ + K k γ 2 2 , γ ] d ( γ Λ ) ,
C = - n 2 p
E ˜ i ( ϕ , ϕ ) = E 0 δ ( ϕ / λ ) δ ( ϕ / λ ) ,
E ˜ 1 ( ϕ , ϕ ) = - 1 4 j k C E 0 S ˜ [ - ϕ + ϕ B - 1 2 k K ϕ 2 , k K ϕ ] × δ [ 1 λ ( ϕ - 2 ϕ B + 1 2 k K ϕ 2 ) ] .
ϕ = 2 ϕ B - 1 2 k K ϕ 2 .
k x = K - 1 2 k y 2 K .
γ = - ϕ + ϕ B - 1 2 k K ϕ 2 .
γ = - ϕ B .
E ˜ 1 ( ϕ , ϕ ) = 1 4 j k C E 0 S ˜ ( - ϕ B , k K ϕ ) × δ [ 1 λ ( ϕ - 2 ϕ B + 1 2 k K ϕ 2 ) ] .
E 1 ( v ) ( x , y ) = - 1 4 j k C E 0 exp ( - j K x ) - + S ˜ ( - ϕ B , γ ) × exp ( - j K y γ + 1 2 j K x γ 2 ) d ( γ Λ ) .
S ˜ ( γ , γ ) = exp ( j K x - ½ j K x γ 2 - ½ j K x γ 2 ) F - 1 [ S ( x , y , z ) ] ,
E 1 ( v ) ( x , y ) = - 1 4 j k C E 0 exp ( - 1 2 j K x ϕ B 2 ) × - + S ( x , y , z ) exp ( - j K z ϕ B ) d z .
E - 1 ( v ) ( x , y ) = - 1 4 j k C E 0 exp ( + 1 2 j K x ϕ B 2 ) × - + S * ( x , y , z ) exp ( - j K z ϕ B ) d z .
K L ϕ B = ½ K 2 L / k = ½ Q 1 ,
exp ( ± ½ j K x ϕ B 2 ) ,
E + 1 ( v ) = E - 1 ( v ) = - 1 4 j k C E 0 - + S ( x , y , z ) d z .
E ˜ i ( ϕ , ϕ ) = E 0 δ [ ( ϕ + ϕ B C ) / λ ] δ ( ϕ / λ ) .
E 1 ( v ) ( x , y ) = - 1 4 j k C E 0 exp [ - j k x ( 2 ϕ B - ϕ B C ) ] × - + S ˜ ( - ϕ B + ϕ B C , γ ) exp [ - j K y γ + 1 2 j K x γ 2 ] d ( γ Λ )
E 1 ( v ) ( x , y ) = - 1 4 j k C E 0 exp [ j k x ϕ B C - 1 2 j K x ( - ϕ B + ϕ B C ) 2 ] × - + S ( x , y , z ) exp [ - j K z ( ϕ B - ϕ B C ) ] d z .
E - 1 ( v ) ( x , y ) = - 1 4 j k C E 0 exp [ + j k x ( 2 ϕ B - ϕ B C ) ] × - + S ˜ * ( ϕ B - ϕ B C , γ ) exp [ j K y γ - 1 2 j K x γ 2 ] d ( γ Λ )
E - 1 ( v ) ( x , y ) = - 1 4 j k C E 0 exp [ - j k x ϕ B C + 1 2 j K x ( ϕ B - ϕ B C ) 2 ] × - + S * ( x , y , z ) exp [ - j K z ( ϕ B - ϕ B C ) ] d z .
S ˜ ( γ , γ ) = - + T ( y , z ) exp ( j K z z + j K y y ) d y d z ,
Ω = Ω c + Ω ,
K = K c + K .
S ( y , z , t ) = Re [ g ( t ) S ( y , z ) exp ( j Ω c t ) ] ,
g ( t ) = 1 2 π - + G ( Ω ) exp ( j Ω t ) d Ω .
E 1 ( v ) ( x , y , t ) = - 1 4 j k C E 0 1 2 π - + G ( Ω ) exp ( j Ω t ) × exp [ - j k x ( 2 ϕ B - ϕ B C ) ] exp ( - j K y γ + 1 2 j K x γ 2 ) × T ( y , z ) exp [ j K ( - ϕ B + ϕ B C ) z + j K γ y ] d ( γ Λ ) d y d z d Ω .
- j k x ( 2 ϕ B - ϕ B C ) = - j k x ϕ B C - j Ω V x ,
j K z ( - ϕ B + ϕ B C ) = - j z ϕ B C Ω V - j z Ω 2 2 k V 2 ,
γ Λ = 1 2 π K γ = 1 2 π K y ,
E 1 ( v ) ( x , y , t ) = - 1 4 j k C E 0 · exp ( - j k x ϕ B C ) ( 1 2 π ) 2 × - + G ( Ω ) exp ( j Ω t - j Ω V x - j Ω V z ϕ B C - j Ω 2 V 2 · z 2 k ) × T ( y , z ) exp [ j K y ( y - y ) + j K y 2 2 K x ] d K y d y d z d Ω .
K y 2 2 K min x max 1 ,
( 2 π / h ) 2 2 ( 2 π / Λ max ) · W 1 or W h 2 π · Λ max .
Ω max 2 V 2 · L 2 k 1 or 1 2 Q 1 ,
Q = K max 2 L k .
E 1 ( v ) ( x , y , t ) = - 1 4 j k C E 0 exp ( - j k x ϕ B C ) - + T ( y , z ) g ( t - x V - z V ϕ B C ) d z .
- + E 1 ( v ) ( x , y , t ) d y .
- + E 1 ( v ) ( x , y , t ) d y = - 1 4 j k C E 0 exp ( - j k x ϕ B C ) × - + T ( y , z ) g ( t - x V - z V ϕ B C ) d y d z .

Metrics