Abstract

With increasingly sophisticated laser applications in industry and science, a reliable method to characterize the intensity distribution of the laser beam has become a more and more important task. However, traditional optic and electronic methods can offer only a laser beam intensity profile but, cannot separate the main mode components in the laser beam intensity distribution. Recently, independent component analysis has been a surging and developing method in which the goal is to find a linear representation of a non-Gaussian data set. Such a linear representation seems to be able to capture the essential structure of a laser beam profile. After assembling image data of a laser spot, we propose a new analytical approach to extract laser beam mode components based on the independent component analysis technique. For noise reduction and laser spot area location, wavelet thresholding, Canny edge detection, and the Hough transform are also used in this method before extracting mode components. Finally, the experimental results show that our approach can separate the principal mode components in a real laser beam efficiently.

© 2005 Optical Society of America

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References

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  1. A. B. Katrich, “Laser beam shape invariance parameters,” in Fourth International Workshop on Laser and Fiber-Optical Networks Modeling (IEEE, New York, 2002), pp. 249–251.
  2. Th. Graf, J.E. Balmer, “Laser beam quality, entropy and the limits of beam shaping,” Opt. Commun. 131, 77–83 (1996).
    [Crossref]
  3. C. B. Roundy, “Laser beam quality characterization,” presented at the Conference on Lasers and Electro-Optics Lasers and Electro-Optics Applications (CLEO LEAP), Anaheim, Calif., 6 June 1996.
  4. C. B. Roundy, “Electronic beam diagnostics evaluate laser performance,” Laser Focus World (May1996), pp. 119–125.
  5. C. B. Roundy, “Practical applications of laser beam profiling,” Lasers Optronics (April1996), pp. 21–26.
  6. J. M. Fletcher, J. M. Darchuk, “Standardizing the measurement of spatial characteristics of optical beams,” in Laser Beam Radiometry, Proc. SPIE 888, 60–64 (1988).
    [Crossref]
  7. H. Q. Shangguan, L. W. Casperon, “Estimation of scattered light on the surface of unclad optical fiber tips: a new approach,” Opt. Commun. 152, 307–312 (1998).
    [Crossref]
  8. S. U. Pandey, “Measurement of two particle resolution in silicon drift detectors,” IEEE Trans. Nucl. Sci. 45(3), 315–320 (1998).
    [Crossref]
  9. A. Hyvarinen, E. Oja, “Independent component analysis: algorithms and applications,” Neural Networks 13, 411–430 (2000).
    [Crossref] [PubMed]
  10. Y. Cheung, L. Xu, “Independent component ordering in ICA time series analysis,” Neurocomputing 41, 145–152 (2001).
    [Crossref]
  11. T. Yamaguchi, K. Itoh, “An algebraic solution to independent component analysis,” Opt. Commun. 178, 59–64 (2000).
    [Crossref]
  12. A. J. Bell, T.J. Sejnowski, “An information-maximization approach to blind separation and blind deconvolution,” Neural Comput. 7, 1129–1159 (1995).
    [Crossref] [PubMed]
  13. S. Amari, A. Cichocki, H. Yang, “A new learning algorithm for blind signal separation,” Adv. Neural Inform. Proces. Syst. 8, 757–763 (1996).
  14. S. Mallat, “A theory for multi-resolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intel. 11, 674–693 (1989).
    [Crossref]
  15. I. Daubechies, Ten Lectures on Wavelets, Vol. 61 of CBMS-NSF Regional Conference Series in Applied Mathematics (Society for Industrial and Applied Mathematics, Philadelphia, 1992).
    [Crossref]
  16. H. K. Yuen, “Comparative study of Hough transform methods for circle finding,” Image Vision Comput. 8(1), 71–77 (1990).
    [Crossref]
  17. D. J. Kerbyson, T. J. Athertson, “Circle detection using Hough transform filters,” in Proceedings of the Fifth International Conference on Image. Processing and its Applications (IEE, London, 1995).
    [Crossref]
  18. J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Mach. Intell. 8, 679–698 (1986).
    [Crossref] [PubMed]
  19. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1987).
  20. D. L. Donoho, “Denoising by soft-thresholding,” IEEE Trans. Inf. Theory 41, 613–627 (1995).
    [Crossref]

2001 (1)

Y. Cheung, L. Xu, “Independent component ordering in ICA time series analysis,” Neurocomputing 41, 145–152 (2001).
[Crossref]

2000 (2)

T. Yamaguchi, K. Itoh, “An algebraic solution to independent component analysis,” Opt. Commun. 178, 59–64 (2000).
[Crossref]

A. Hyvarinen, E. Oja, “Independent component analysis: algorithms and applications,” Neural Networks 13, 411–430 (2000).
[Crossref] [PubMed]

1998 (2)

H. Q. Shangguan, L. W. Casperon, “Estimation of scattered light on the surface of unclad optical fiber tips: a new approach,” Opt. Commun. 152, 307–312 (1998).
[Crossref]

S. U. Pandey, “Measurement of two particle resolution in silicon drift detectors,” IEEE Trans. Nucl. Sci. 45(3), 315–320 (1998).
[Crossref]

1996 (4)

Th. Graf, J.E. Balmer, “Laser beam quality, entropy and the limits of beam shaping,” Opt. Commun. 131, 77–83 (1996).
[Crossref]

C. B. Roundy, “Electronic beam diagnostics evaluate laser performance,” Laser Focus World (May1996), pp. 119–125.

C. B. Roundy, “Practical applications of laser beam profiling,” Lasers Optronics (April1996), pp. 21–26.

S. Amari, A. Cichocki, H. Yang, “A new learning algorithm for blind signal separation,” Adv. Neural Inform. Proces. Syst. 8, 757–763 (1996).

1995 (2)

D. L. Donoho, “Denoising by soft-thresholding,” IEEE Trans. Inf. Theory 41, 613–627 (1995).
[Crossref]

A. J. Bell, T.J. Sejnowski, “An information-maximization approach to blind separation and blind deconvolution,” Neural Comput. 7, 1129–1159 (1995).
[Crossref] [PubMed]

1990 (1)

H. K. Yuen, “Comparative study of Hough transform methods for circle finding,” Image Vision Comput. 8(1), 71–77 (1990).
[Crossref]

1989 (1)

S. Mallat, “A theory for multi-resolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intel. 11, 674–693 (1989).
[Crossref]

1988 (1)

J. M. Fletcher, J. M. Darchuk, “Standardizing the measurement of spatial characteristics of optical beams,” in Laser Beam Radiometry, Proc. SPIE 888, 60–64 (1988).
[Crossref]

1986 (1)

J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Mach. Intell. 8, 679–698 (1986).
[Crossref] [PubMed]

Amari, S.

S. Amari, A. Cichocki, H. Yang, “A new learning algorithm for blind signal separation,” Adv. Neural Inform. Proces. Syst. 8, 757–763 (1996).

Athertson, T. J.

D. J. Kerbyson, T. J. Athertson, “Circle detection using Hough transform filters,” in Proceedings of the Fifth International Conference on Image. Processing and its Applications (IEE, London, 1995).
[Crossref]

Balmer, J.E.

Th. Graf, J.E. Balmer, “Laser beam quality, entropy and the limits of beam shaping,” Opt. Commun. 131, 77–83 (1996).
[Crossref]

Bell, A. J.

A. J. Bell, T.J. Sejnowski, “An information-maximization approach to blind separation and blind deconvolution,” Neural Comput. 7, 1129–1159 (1995).
[Crossref] [PubMed]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1987).

Canny, J.

J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Mach. Intell. 8, 679–698 (1986).
[Crossref] [PubMed]

Casperon, L. W.

H. Q. Shangguan, L. W. Casperon, “Estimation of scattered light on the surface of unclad optical fiber tips: a new approach,” Opt. Commun. 152, 307–312 (1998).
[Crossref]

Cheung, Y.

Y. Cheung, L. Xu, “Independent component ordering in ICA time series analysis,” Neurocomputing 41, 145–152 (2001).
[Crossref]

Cichocki, A.

S. Amari, A. Cichocki, H. Yang, “A new learning algorithm for blind signal separation,” Adv. Neural Inform. Proces. Syst. 8, 757–763 (1996).

Darchuk, J. M.

J. M. Fletcher, J. M. Darchuk, “Standardizing the measurement of spatial characteristics of optical beams,” in Laser Beam Radiometry, Proc. SPIE 888, 60–64 (1988).
[Crossref]

Daubechies, I.

I. Daubechies, Ten Lectures on Wavelets, Vol. 61 of CBMS-NSF Regional Conference Series in Applied Mathematics (Society for Industrial and Applied Mathematics, Philadelphia, 1992).
[Crossref]

Donoho, D. L.

D. L. Donoho, “Denoising by soft-thresholding,” IEEE Trans. Inf. Theory 41, 613–627 (1995).
[Crossref]

Fletcher, J. M.

J. M. Fletcher, J. M. Darchuk, “Standardizing the measurement of spatial characteristics of optical beams,” in Laser Beam Radiometry, Proc. SPIE 888, 60–64 (1988).
[Crossref]

Graf, Th.

Th. Graf, J.E. Balmer, “Laser beam quality, entropy and the limits of beam shaping,” Opt. Commun. 131, 77–83 (1996).
[Crossref]

Hyvarinen, A.

A. Hyvarinen, E. Oja, “Independent component analysis: algorithms and applications,” Neural Networks 13, 411–430 (2000).
[Crossref] [PubMed]

Itoh, K.

T. Yamaguchi, K. Itoh, “An algebraic solution to independent component analysis,” Opt. Commun. 178, 59–64 (2000).
[Crossref]

Katrich, A. B.

A. B. Katrich, “Laser beam shape invariance parameters,” in Fourth International Workshop on Laser and Fiber-Optical Networks Modeling (IEEE, New York, 2002), pp. 249–251.

Kerbyson, D. J.

D. J. Kerbyson, T. J. Athertson, “Circle detection using Hough transform filters,” in Proceedings of the Fifth International Conference on Image. Processing and its Applications (IEE, London, 1995).
[Crossref]

Mallat, S.

S. Mallat, “A theory for multi-resolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intel. 11, 674–693 (1989).
[Crossref]

Oja, E.

A. Hyvarinen, E. Oja, “Independent component analysis: algorithms and applications,” Neural Networks 13, 411–430 (2000).
[Crossref] [PubMed]

Pandey, S. U.

S. U. Pandey, “Measurement of two particle resolution in silicon drift detectors,” IEEE Trans. Nucl. Sci. 45(3), 315–320 (1998).
[Crossref]

Roundy, C. B.

C. B. Roundy, “Electronic beam diagnostics evaluate laser performance,” Laser Focus World (May1996), pp. 119–125.

C. B. Roundy, “Practical applications of laser beam profiling,” Lasers Optronics (April1996), pp. 21–26.

C. B. Roundy, “Laser beam quality characterization,” presented at the Conference on Lasers and Electro-Optics Lasers and Electro-Optics Applications (CLEO LEAP), Anaheim, Calif., 6 June 1996.

Sejnowski, T.J.

A. J. Bell, T.J. Sejnowski, “An information-maximization approach to blind separation and blind deconvolution,” Neural Comput. 7, 1129–1159 (1995).
[Crossref] [PubMed]

Shangguan, H. Q.

H. Q. Shangguan, L. W. Casperon, “Estimation of scattered light on the surface of unclad optical fiber tips: a new approach,” Opt. Commun. 152, 307–312 (1998).
[Crossref]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1987).

Xu, L.

Y. Cheung, L. Xu, “Independent component ordering in ICA time series analysis,” Neurocomputing 41, 145–152 (2001).
[Crossref]

Yamaguchi, T.

T. Yamaguchi, K. Itoh, “An algebraic solution to independent component analysis,” Opt. Commun. 178, 59–64 (2000).
[Crossref]

Yang, H.

S. Amari, A. Cichocki, H. Yang, “A new learning algorithm for blind signal separation,” Adv. Neural Inform. Proces. Syst. 8, 757–763 (1996).

Yuen, H. K.

H. K. Yuen, “Comparative study of Hough transform methods for circle finding,” Image Vision Comput. 8(1), 71–77 (1990).
[Crossref]

Adv. Neural Inform. Proces. Syst. (1)

S. Amari, A. Cichocki, H. Yang, “A new learning algorithm for blind signal separation,” Adv. Neural Inform. Proces. Syst. 8, 757–763 (1996).

IEEE Trans. Inf. Theory (1)

D. L. Donoho, “Denoising by soft-thresholding,” IEEE Trans. Inf. Theory 41, 613–627 (1995).
[Crossref]

IEEE Trans. Nucl. Sci. (1)

S. U. Pandey, “Measurement of two particle resolution in silicon drift detectors,” IEEE Trans. Nucl. Sci. 45(3), 315–320 (1998).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intel. (1)

S. Mallat, “A theory for multi-resolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intel. 11, 674–693 (1989).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Mach. Intell. 8, 679–698 (1986).
[Crossref] [PubMed]

Image Vision Comput. (1)

H. K. Yuen, “Comparative study of Hough transform methods for circle finding,” Image Vision Comput. 8(1), 71–77 (1990).
[Crossref]

Laser Beam Radiometry (1)

J. M. Fletcher, J. M. Darchuk, “Standardizing the measurement of spatial characteristics of optical beams,” in Laser Beam Radiometry, Proc. SPIE 888, 60–64 (1988).
[Crossref]

Laser Focus World (1)

C. B. Roundy, “Electronic beam diagnostics evaluate laser performance,” Laser Focus World (May1996), pp. 119–125.

Lasers Optronics (1)

C. B. Roundy, “Practical applications of laser beam profiling,” Lasers Optronics (April1996), pp. 21–26.

Neural Comput. (1)

A. J. Bell, T.J. Sejnowski, “An information-maximization approach to blind separation and blind deconvolution,” Neural Comput. 7, 1129–1159 (1995).
[Crossref] [PubMed]

Neural Networks (1)

A. Hyvarinen, E. Oja, “Independent component analysis: algorithms and applications,” Neural Networks 13, 411–430 (2000).
[Crossref] [PubMed]

Neurocomputing (1)

Y. Cheung, L. Xu, “Independent component ordering in ICA time series analysis,” Neurocomputing 41, 145–152 (2001).
[Crossref]

Opt. Commun. (3)

T. Yamaguchi, K. Itoh, “An algebraic solution to independent component analysis,” Opt. Commun. 178, 59–64 (2000).
[Crossref]

Th. Graf, J.E. Balmer, “Laser beam quality, entropy and the limits of beam shaping,” Opt. Commun. 131, 77–83 (1996).
[Crossref]

H. Q. Shangguan, L. W. Casperon, “Estimation of scattered light on the surface of unclad optical fiber tips: a new approach,” Opt. Commun. 152, 307–312 (1998).
[Crossref]

Other (5)

A. B. Katrich, “Laser beam shape invariance parameters,” in Fourth International Workshop on Laser and Fiber-Optical Networks Modeling (IEEE, New York, 2002), pp. 249–251.

D. J. Kerbyson, T. J. Athertson, “Circle detection using Hough transform filters,” in Proceedings of the Fifth International Conference on Image. Processing and its Applications (IEE, London, 1995).
[Crossref]

I. Daubechies, Ten Lectures on Wavelets, Vol. 61 of CBMS-NSF Regional Conference Series in Applied Mathematics (Society for Industrial and Applied Mathematics, Philadelphia, 1992).
[Crossref]

C. B. Roundy, “Laser beam quality characterization,” presented at the Conference on Lasers and Electro-Optics Lasers and Electro-Optics Applications (CLEO LEAP), Anaheim, Calif., 6 June 1996.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1987).

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Figures (12)

Fig. 1
Fig. 1

Experimental device for acquiring laser beam images.

Fig. 2
Fig. 2

Laser spots of a He–Ne and a Nd:YAG laser.

Fig. 3
Fig. 3

OI laser spots with different optic paths.

Fig. 4
Fig. 4

Original laser spots in a 3D view.

Fig. 5
Fig. 5

Circle detection by Hough transform.

Fig. 6
Fig. 6

Laser spots in a 3D view after wavelet thresholding.

Fig. 7
Fig. 7

Edge detection and circle locating.

Fig. 8
Fig. 8

Mode component of a He–Ne laser.

Fig. 9
Fig. 9

Mode components of a Nd:YAG laser.

Fig. 10
Fig. 10

Mode components of spot A.

Fig. 11
Fig. 11

Mode components of spot B.

Fig. 12
Fig. 12

Mode components of spot C.

Equations (6)

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y = w x = w A s = P Λ s ,
kurt ( υ ) = E [ υ 4 ] 3 ( E [ υ 2 ] ) 2 ,
DWT ψ { x ( t ) m , n } = 2 m / 2 m , n x ( t ) ψ * ( t n 2 m 2 m ) ,
x ( t ) = 2 m / 2 m n DWT ψ x ( m , n ) ψ ( t n 2 m 2 m ) .
For all ( x , y ) { approximate θ ( x , y ) , θ ( 0 , π / 4 , π / 2 , 3 π / 4 ) ; if g ( x , y ) < g at neighbor in direction θ o r θ + π , g ( x , y ) = 0 ; else , g s ( x , y ) = g ( x , y ) .
( x x 0 ) 2 + ( y y 0 ) 2 = r 2 .

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