Abstract

Optical diffraction offers an effective method of characterizing low-frequency liquid surface acoustic waves. We use a laser line generator to produce patterns that are amenable for computer-aided analysis. We present a segmented nonlinear regression approach to accurately determine the positions of the maxima and minima in the pattern. The robustness of this scheme is investigated through simulation. The approach is then used to analyze optical diffraction patterns obtained experimentally.

© 2009 Optical Society of America

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References

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2007 (3)

2006 (2)

J. Dong, R. Miao, J. Qi, and F. Li, “Unusual distribution of the diffraction patterns from liquid surface waves,” J. Appl. Phys. 100, 033108 (2006).
[CrossRef]

T. K. Barik, P. R. Chaudhuri, A. Roy, and S. Kar, “Probing liquid surface waves, liquid properties, and liquid films with light diffraction,” Meas. Sci. Technol. 17, 1553-1562(2006).
[CrossRef]

2002 (1)

R. Miao, Z. Yang, J. Zhu, and C. Shen, “Visualization of low-frequency liquid surface acoustic waves by means of optical diffraction,” Appl. Phys. Lett. 80, 3033-3035 (2002).
[CrossRef]

2000 (1)

M.-C. Park and S.-W. Kim, “Direct quadratic polynomial fitting for fringe peak detection of white light scanning interferograms,” Opt. Eng. 39, 952-959 (2000).
[CrossRef]

1998 (1)

1997 (1)

T. W. Ng, “Speckle reduction in the small-angle light scattering technique using sample vibration,” J. Polym. Sci. Part B Polym. Phys. 35, 937-943 (1997).
[CrossRef]

1996 (1)

T. Iwai and T. Asakura, “Speckle reduction in coherent information processing,” Proc. IEEE 84, 765-781 (1996).
[CrossRef]

1994 (1)

1987 (1)

1983 (1)

Asakura, T.

T. Iwai and T. Asakura, “Speckle reduction in coherent information processing,” Proc. IEEE 84, 765-781 (1996).
[CrossRef]

Barik, T. K.

T. K. Barik, P. R. Chaudhuri, A. Roy, and S. Kar, “Probing liquid surface waves, liquid properties, and liquid films with light diffraction,” Meas. Sci. Technol. 17, 1553-1562(2006).
[CrossRef]

Black, T. D.

Cha, S. S.

Chatterjee, M. R.

Chaudhuri, P. R.

T. K. Barik, P. R. Chaudhuri, A. Roy, and S. Kar, “Probing liquid surface waves, liquid properties, and liquid films with light diffraction,” Meas. Sci. Technol. 17, 1553-1562(2006).
[CrossRef]

Chen, S. T.

Dong, J.

J. Dong, J. Qi, and R. Miao, “Measurement of the damping of liquid surface wave by diffraction method,” Braz. J. Phys. 37, 1129-1133 (2007).
[CrossRef]

J. Dong, R. Miao, J. Qi, and F. Li, “Unusual distribution of the diffraction patterns from liquid surface waves,” J. Appl. Phys. 100, 033108 (2006).
[CrossRef]

Federico, A.

Guo, H.

Iwai, T.

T. Iwai and T. Asakura, “Speckle reduction in coherent information processing,” Proc. IEEE 84, 765-781 (1996).
[CrossRef]

Kar, S.

T. K. Barik, P. R. Chaudhuri, A. Roy, and S. Kar, “Probing liquid surface waves, liquid properties, and liquid films with light diffraction,” Meas. Sci. Technol. 17, 1553-1562(2006).
[CrossRef]

Kaufmann, G. H.

Kim, S.-W.

M.-C. Park and S.-W. Kim, “Direct quadratic polynomial fitting for fringe peak detection of white light scanning interferograms,” Opt. Eng. 39, 952-959 (2000).
[CrossRef]

Li, F.

J. Dong, R. Miao, J. Qi, and F. Li, “Unusual distribution of the diffraction patterns from liquid surface waves,” J. Appl. Phys. 100, 033108 (2006).
[CrossRef]

Liu, G.

Magnusson, R.

Miao, R.

J. Dong, J. Qi, and R. Miao, “Measurement of the damping of liquid surface wave by diffraction method,” Braz. J. Phys. 37, 1129-1133 (2007).
[CrossRef]

J. Dong, R. Miao, J. Qi, and F. Li, “Unusual distribution of the diffraction patterns from liquid surface waves,” J. Appl. Phys. 100, 033108 (2006).
[CrossRef]

R. Miao, Z. Yang, J. Zhu, and C. Shen, “Visualization of low-frequency liquid surface acoustic waves by means of optical diffraction,” Appl. Phys. Lett. 80, 3033-3035 (2002).
[CrossRef]

Ng, T. W.

T. W. Ng, “Speckle reduction in the small-angle light scattering technique using sample vibration,” J. Polym. Sci. Part B Polym. Phys. 35, 937-943 (1997).
[CrossRef]

Park, M.-C.

M.-C. Park and S.-W. Kim, “Direct quadratic polynomial fitting for fringe peak detection of white light scanning interferograms,” Opt. Eng. 39, 952-959 (2000).
[CrossRef]

Qi, J.

J. Dong, J. Qi, and R. Miao, “Measurement of the damping of liquid surface wave by diffraction method,” Braz. J. Phys. 37, 1129-1133 (2007).
[CrossRef]

J. Dong, R. Miao, J. Qi, and F. Li, “Unusual distribution of the diffraction patterns from liquid surface waves,” J. Appl. Phys. 100, 033108 (2006).
[CrossRef]

Roy, A.

T. K. Barik, P. R. Chaudhuri, A. Roy, and S. Kar, “Probing liquid surface waves, liquid properties, and liquid films with light diffraction,” Meas. Sci. Technol. 17, 1553-1562(2006).
[CrossRef]

Schemm, J. B.

Shen, C.

R. Miao, Z. Yang, J. Zhu, and C. Shen, “Visualization of low-frequency liquid surface acoustic waves by means of optical diffraction,” Appl. Phys. Lett. 80, 3033-3035 (2002).
[CrossRef]

Vest, C. M.

Yang, Z.

R. Miao, Z. Yang, J. Zhu, and C. Shen, “Visualization of low-frequency liquid surface acoustic waves by means of optical diffraction,” Appl. Phys. Lett. 80, 3033-3035 (2002).
[CrossRef]

Yu, E.

Zhu, J.

R. Miao, Z. Yang, J. Zhu, and C. Shen, “Visualization of low-frequency liquid surface acoustic waves by means of optical diffraction,” Appl. Phys. Lett. 80, 3033-3035 (2002).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

R. Miao, Z. Yang, J. Zhu, and C. Shen, “Visualization of low-frequency liquid surface acoustic waves by means of optical diffraction,” Appl. Phys. Lett. 80, 3033-3035 (2002).
[CrossRef]

Braz. J. Phys. (1)

J. Dong, J. Qi, and R. Miao, “Measurement of the damping of liquid surface wave by diffraction method,” Braz. J. Phys. 37, 1129-1133 (2007).
[CrossRef]

J. Appl. Phys. (1)

J. Dong, R. Miao, J. Qi, and F. Li, “Unusual distribution of the diffraction patterns from liquid surface waves,” J. Appl. Phys. 100, 033108 (2006).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Polym. Sci. Part B Polym. Phys. (1)

T. W. Ng, “Speckle reduction in the small-angle light scattering technique using sample vibration,” J. Polym. Sci. Part B Polym. Phys. 35, 937-943 (1997).
[CrossRef]

Meas. Sci. Technol. (1)

T. K. Barik, P. R. Chaudhuri, A. Roy, and S. Kar, “Probing liquid surface waves, liquid properties, and liquid films with light diffraction,” Meas. Sci. Technol. 17, 1553-1562(2006).
[CrossRef]

Opt. Eng. (1)

M.-C. Park and S.-W. Kim, “Direct quadratic polynomial fitting for fringe peak detection of white light scanning interferograms,” Opt. Eng. 39, 952-959 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. IEEE (1)

T. Iwai and T. Asakura, “Speckle reduction in coherent information processing,” Proc. IEEE 84, 765-781 (1996).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic description of the experimental setup used to obtain optical diffraction patterns from liquid surface waves for computer-aided processing.

Fig. 2
Fig. 2

Flow chart of the segmented nonlinear regression approach used to determine the maxima. A similar approach can be used to determine the minima.

Fig. 3
Fig. 3

(a) Simulated irradiance distribution with noise incorporated and the best-fit polynomial (dashed curve). (b) Derivative of the polynomial best fit found. The inset shows small values from the same plot which clearly indicates that the line does not pass through the origin.

Fig. 4
Fig. 4

Simulation results of the MSE in regression deter mination of the maxima position plotted against a fraction that describes the magnitude of noise R for various values of period P.

Fig. 5
Fig. 5

Diffraction pattern recorded at (a)  280 Hz and (b)  300 Hz .

Fig. 6
Fig. 6

Sample column line distributions obtained from Figs. 4(a) and 4(b).

Tables (1)

Tables Icon

Table 1 Positions of the Maxima in Figs. 4(a) and 4(b) Obtained from Eight Equally Spaced Columns from Left to Right in the Images Using the Segmented Nonlinear Regression Approach

Equations (4)

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

I ( x n ) = n J n 2 ( 4 π h cos θ / λ ) δ [ x λ z n Λ cos θ ] ,
I ( x ) = B ( x ) + E ( x ) cos [ P ( x ) ] ,
I ( x ) = M { 1 + cos ( 2 π P [ x P 2 ] ) + R δ ( x ) } ,
MSE = 1 N i = 1 N ( x j ) 2 .

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