Abstract

A laser beam characterization method is reported, which is applicable to arbitrary and ideal laser beam intensity profiles. This method, called the scattered light imaging method (SLIM), is based on scattered light imaging of a laser beam and provides a complete visualization of it in the region of interest. The method was applied to characterize an arbitrary pedestal-shaped beam and compared with a conventional method (camera scanning). The results we presented show that, for arbitrary beams, it seems much more meaningful to know the intensity profile evolution than to determine an M2 value. Therefore the SLIM is a powerful tool for a new and more complete type of laser beam characterization.

© 2014 Optical Society of America

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References

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  1. S. S. Kudesia, W. S. O. Rodden, D. P. Hand, and J. D. C. Jones, “Effect of beam quality on single pulse laser drilling,” in Proceedings of the 20th International Congress on Applications of Lasers and Electro-Optics, X. Chen, ed. (Laser Institute of America, 2001), pp. 1439–1448.
  2. D. D. Dlott, “Focus fluctuations in laser-materials interactions,” Opt. Photon. News 13(9), 34–37 (2002).
    [CrossRef]
  3. A. E. Siegman, “How to (maybe) measure laser beam quality,” in Diode Pumped Solid State Lasers: Applications and Issues (DLAI) (Optical Society of America, 1998), paper MQ1.
  4. A. E. Siegman, M. W. Sasnett, and T. F. Johnston, “Choice of clip levels for beam width measurements using knife-edge methods,” IEEE J. Quantum Electron. 27, 1098–1104 (1991).
  5. A. E. Siegman and S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
  6. C. Gao and H. Weber, “The problem with M2,” Opt. Laser Technol. 32, 221–224 (2000).
  7. R. D. Niederriter, J. T. Gopinath, and M. E. Siemens, “Measurement of the M2 beam propagation factor using a focus-tunable liquid lens,” Appl. Opt. 52, 1591–1598 (2013).
    [CrossRef]
  8. . Test methods for laser beam widths, divergence angles and beam propagation ratios. Part 1: Stigmatic and simple beams/ Part 2: General astigmatic beams/ Part 3: Intrinsic and geometrical classification, propagation and details of test methods (ISO, Geneva, 2005).
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    [CrossRef]
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    [CrossRef]
  11. Ophir-Spiricon, Inc., “M-200 Operator’s Manual” (2007).
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  13. P. B. Chapple, “Beam waist and M2 measurement using a finite slit,” Opt. Eng. 33, 2461–2466 (1994).
    [CrossRef]
  14. J. A. Arnaud, W. M. Hubbard, G. D. Madeville, B. de la Clavière, E. A. Franke, and J. M. Franke, “Technique for fast measurement of Gaussian laser beam parameters,” Appl. Opt. 10, 2775–2776 (1971).
    [CrossRef]
  15. B. J. Neubert, G. Huber, and W. Scharfe, “On the problem of M2 analysis using Shack-Hartmann measurements,” J. Phys. D 34, 2414–2419 (2001).
  16. B. Schäfer and K. Mann, “Determination of beam parameters and coherence properties of laser radiation by use of an extended Hartmann-Shack wave-front sensor,” Appl. Opt. 41, 2809–2817 (2002).
    [CrossRef]
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    [CrossRef]
  18. B. Eppich, G. Mann, and H. Weber, “Measurement of the four-dimensional Wigner distribution of paraxial light sources,” Proc. SPIE 5962, 59622D (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. K. C. Jorge, R. Riva, N. A. S. Rodrigues, and M. G. Destro, “Real-time measurement of laser beam quality factor (M2) by imaging transverse scattered light,” Proc. SPIE 6452, 645215 (2007).
    [CrossRef]
  24. K. C. Jorge, R. Riva, and N. A. S. Rodrigues, “Dispositivo e método para a caracterização de feixes de laser de baixa e alta potência baseado no espalhamento de luz,” PatentPI 0605596-6 A, DCTA (23November2006).
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    [CrossRef]
  27. K. Iizuka, Engineering Optics, 3rd ed. (Springer-Verlag, 1983).
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  30. R. W. Boyd, Nonlinear Optics (Academic, 2003).
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    [CrossRef]

2013 (2)

R. D. Niederriter, J. T. Gopinath, and M. E. Siemens, “Measurement of the M2 beam propagation factor using a focus-tunable liquid lens,” Appl. Opt. 52, 1591–1598 (2013).
[CrossRef]

Y.-Z. Du, G. Feng, H. Li, Z. Cai, H. Zhao, and S. Zhou, “Real-time determination of beam propagation factor by Mach-Zehnder point diffraction interferometer,” Opt. Commun. 287, 1–5 (2013).
[CrossRef]

2012 (1)

2011 (2)

2007 (1)

K. C. Jorge, R. Riva, N. A. S. Rodrigues, and M. G. Destro, “Real-time measurement of laser beam quality factor (M2) by imaging transverse scattered light,” Proc. SPIE 6452, 645215 (2007).
[CrossRef]

2005 (1)

B. Eppich, G. Mann, and H. Weber, “Measurement of the four-dimensional Wigner distribution of paraxial light sources,” Proc. SPIE 5962, 59622D (2005).
[CrossRef]

2004 (1)

2002 (2)

2001 (2)

J. Zheng, S. Zhao, Q. Wang, and L. Chen, “Measurement of beam quality factor (M2) by slit-scanning method,” Opt. Laser Technol. 33, 213–217 (2001).

B. J. Neubert, G. Huber, and W. Scharfe, “On the problem of M2 analysis using Shack-Hartmann measurements,” J. Phys. D 34, 2414–2419 (2001).

2000 (1)

C. Gao and H. Weber, “The problem with M2,” Opt. Laser Technol. 32, 221–224 (2000).

1994 (1)

P. B. Chapple, “Beam waist and M2 measurement using a finite slit,” Opt. Eng. 33, 2461–2466 (1994).
[CrossRef]

1993 (1)

A. E. Siegman and S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).

1991 (2)

A. E. Siegman, M. W. Sasnett, and T. F. Johnston, “Choice of clip levels for beam width measurements using knife-edge methods,” IEEE J. Quantum Electron. 27, 1098–1104 (1991).

M. W. Sasnett and T. F. Johnston, “Beam characterization and measurement of propagation attributes,” Proc. SPIE 1414, 21–32 (1991).
[CrossRef]

1989 (1)

1971 (1)

1966 (1)

1965 (1)

H. Kogelnik, “Imaging of optical modes—resonators with internal lenses,” Bell Syst. Tech. J. 44, 455–494 (1965).
[CrossRef]

Arnaud, J. A.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 2003).

Brüning, R.

Cai, Z.

Y.-Z. Du, G. Feng, H. Li, Z. Cai, H. Zhao, and S. Zhou, “Real-time determination of beam propagation factor by Mach-Zehnder point diffraction interferometer,” Opt. Commun. 287, 1–5 (2013).
[CrossRef]

Chapple, P. B.

P. B. Chapple, “Beam waist and M2 measurement using a finite slit,” Opt. Eng. 33, 2461–2466 (1994).
[CrossRef]

Chen, L.

J. Zheng, S. Zhao, Q. Wang, and L. Chen, “Measurement of beam quality factor (M2) by slit-scanning method,” Opt. Laser Technol. 33, 213–217 (2001).

Cortés-Martínez, R.

de la Clavière, B.

Destro, M. G.

K. C. Jorge, R. Riva, N. A. S. Rodrigues, and M. G. Destro, “Real-time measurement of laser beam quality factor (M2) by imaging transverse scattered light,” Proc. SPIE 6452, 645215 (2007).
[CrossRef]

K. C. Jorge, R. Riva, N. A. S. Rodrigues, and M. G. Destro, “M2 beam quality measurement of a single pulse of the Nd:YAG laser,” in Proceedings of Conference on Lasers in Manufacturing, Munich, 2009, pp. 323–326.

Dlott, D. D.

D. D. Dlott, “Focus fluctuations in laser-materials interactions,” Opt. Photon. News 13(9), 34–37 (2002).
[CrossRef]

Du, Y.-Z.

Y.-Z. Du, G. Feng, H. Li, Z. Cai, H. Zhao, and S. Zhou, “Real-time determination of beam propagation factor by Mach-Zehnder point diffraction interferometer,” Opt. Commun. 287, 1–5 (2013).
[CrossRef]

Duparré, M.

Eppich, B.

B. Eppich, G. Mann, and H. Weber, “Measurement of the four-dimensional Wigner distribution of paraxial light sources,” Proc. SPIE 5962, 59622D (2005).
[CrossRef]

Feng, G.

Y.-Z. Du, G. Feng, H. Li, Z. Cai, H. Zhao, and S. Zhou, “Real-time determination of beam propagation factor by Mach-Zehnder point diffraction interferometer,” Opt. Commun. 287, 1–5 (2013).
[CrossRef]

Flamm, D.

Forbes, A.

Franke, E. A.

Franke, J. M.

Gao, C.

C. Gao and H. Weber, “The problem with M2,” Opt. Laser Technol. 32, 221–224 (2000).

Gopinath, J. T.

Greenaway, A. Ha.

Haas, G.

M. Scaggs and G. Haas, “Real time laser beam analysis system for high power laser,” Proc. SPIE 7913, 791306 (2011).
[CrossRef]

Hand, D. P.

R. W. Lambert, R. Cortés-Martínez, A. J. Waddie, J. D. Shepard, M. R. Taghizadeh, A. Ha. Greenaway, and D. P. Hand, “Compact optical system for pulse-to-pulse laser beam quality measurement and applications in laser machining,” Appl. Opt. 43, 5037–5046 (2004).
[CrossRef]

S. S. Kudesia, W. S. O. Rodden, D. P. Hand, and J. D. C. Jones, “Effect of beam quality on single pulse laser drilling,” in Proceedings of the 20th International Congress on Applications of Lasers and Electro-Optics, X. Chen, ed. (Laser Institute of America, 2001), pp. 1439–1448.

Hecht, E.

E. Hecht, Optics, 3rd ed. (Addison-Wesley Longman, 1998).

Hubbard, W. M.

Huber, G.

B. J. Neubert, G. Huber, and W. Scharfe, “On the problem of M2 analysis using Shack-Hartmann measurements,” J. Phys. D 34, 2414–2419 (2001).

Iizuka, K.

K. Iizuka, Engineering Optics, 3rd ed. (Springer-Verlag, 1983).

Johnston, T. F.

M. W. Sasnett and T. F. Johnston, “Beam characterization and measurement of propagation attributes,” Proc. SPIE 1414, 21–32 (1991).
[CrossRef]

A. E. Siegman, M. W. Sasnett, and T. F. Johnston, “Choice of clip levels for beam width measurements using knife-edge methods,” IEEE J. Quantum Electron. 27, 1098–1104 (1991).

Jones, J. D. C.

S. S. Kudesia, W. S. O. Rodden, D. P. Hand, and J. D. C. Jones, “Effect of beam quality on single pulse laser drilling,” in Proceedings of the 20th International Congress on Applications of Lasers and Electro-Optics, X. Chen, ed. (Laser Institute of America, 2001), pp. 1439–1448.

Jorge, K. C.

K. C. Jorge, R. Riva, N. A. S. Rodrigues, and M. G. Destro, “Real-time measurement of laser beam quality factor (M2) by imaging transverse scattered light,” Proc. SPIE 6452, 645215 (2007).
[CrossRef]

K. C. Jorge, R. Riva, and N. A. S. Rodrigues, “Dispositivo e método para a caracterização de feixes de laser de baixa e alta potência baseado no espalhamento de luz,” PatentPI 0605596-6 A, DCTA (23November2006).

K. C. Jorge, R. Riva, N. A. S. Rodrigues, and M. G. Destro, “M2 beam quality measurement of a single pulse of the Nd:YAG laser,” in Proceedings of Conference on Lasers in Manufacturing, Munich, 2009, pp. 323–326.

Kaiser, T.

Kogelnik, H.

H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966).
[CrossRef]

H. Kogelnik, “Imaging of optical modes—resonators with internal lenses,” Bell Syst. Tech. J. 44, 455–494 (1965).
[CrossRef]

Kudesia, S. S.

S. S. Kudesia, W. S. O. Rodden, D. P. Hand, and J. D. C. Jones, “Effect of beam quality on single pulse laser drilling,” in Proceedings of the 20th International Congress on Applications of Lasers and Electro-Optics, X. Chen, ed. (Laser Institute of America, 2001), pp. 1439–1448.

Lambert, R. W.

Li, H.

Y.-Z. Du, G. Feng, H. Li, Z. Cai, H. Zhao, and S. Zhou, “Real-time determination of beam propagation factor by Mach-Zehnder point diffraction interferometer,” Opt. Commun. 287, 1–5 (2013).
[CrossRef]

Li, T.

Madeville, G. D.

Mann, G.

B. Eppich, G. Mann, and H. Weber, “Measurement of the four-dimensional Wigner distribution of paraxial light sources,” Proc. SPIE 5962, 59622D (2005).
[CrossRef]

Mann, K.

Neubert, B. J.

B. J. Neubert, G. Huber, and W. Scharfe, “On the problem of M2 analysis using Shack-Hartmann measurements,” J. Phys. D 34, 2414–2419 (2001).

Niederriter, R. D.

Riva, R.

K. C. Jorge, R. Riva, N. A. S. Rodrigues, and M. G. Destro, “Real-time measurement of laser beam quality factor (M2) by imaging transverse scattered light,” Proc. SPIE 6452, 645215 (2007).
[CrossRef]

K. C. Jorge, R. Riva, and N. A. S. Rodrigues, “Dispositivo e método para a caracterização de feixes de laser de baixa e alta potência baseado no espalhamento de luz,” PatentPI 0605596-6 A, DCTA (23November2006).

K. C. Jorge, R. Riva, N. A. S. Rodrigues, and M. G. Destro, “M2 beam quality measurement of a single pulse of the Nd:YAG laser,” in Proceedings of Conference on Lasers in Manufacturing, Munich, 2009, pp. 323–326.

Rodden, W. S. O.

S. S. Kudesia, W. S. O. Rodden, D. P. Hand, and J. D. C. Jones, “Effect of beam quality on single pulse laser drilling,” in Proceedings of the 20th International Congress on Applications of Lasers and Electro-Optics, X. Chen, ed. (Laser Institute of America, 2001), pp. 1439–1448.

Rodrigues, N. A. S.

K. C. Jorge, R. Riva, N. A. S. Rodrigues, and M. G. Destro, “Real-time measurement of laser beam quality factor (M2) by imaging transverse scattered light,” Proc. SPIE 6452, 645215 (2007).
[CrossRef]

K. C. Jorge, R. Riva, and N. A. S. Rodrigues, “Dispositivo e método para a caracterização de feixes de laser de baixa e alta potência baseado no espalhamento de luz,” PatentPI 0605596-6 A, DCTA (23November2006).

K. C. Jorge, R. Riva, N. A. S. Rodrigues, and M. G. Destro, “M2 beam quality measurement of a single pulse of the Nd:YAG laser,” in Proceedings of Conference on Lasers in Manufacturing, Munich, 2009, pp. 323–326.

Said, A. A.

Sasnett, M. W.

M. W. Sasnett and T. F. Johnston, “Beam characterization and measurement of propagation attributes,” Proc. SPIE 1414, 21–32 (1991).
[CrossRef]

A. E. Siegman, M. W. Sasnett, and T. F. Johnston, “Choice of clip levels for beam width measurements using knife-edge methods,” IEEE J. Quantum Electron. 27, 1098–1104 (1991).

Scaggs, M.

M. Scaggs and G. Haas, “Real time laser beam analysis system for high power laser,” Proc. SPIE 7913, 791306 (2011).
[CrossRef]

Schäfer, B.

Scharfe, W.

B. J. Neubert, G. Huber, and W. Scharfe, “On the problem of M2 analysis using Shack-Hartmann measurements,” J. Phys. D 34, 2414–2419 (2001).

Schmidt, O. A.

Schröter, S.

Schulze, C.

Sheik-Bahae, M.

Shepard, J. D.

Siegman, A. E.

A. E. Siegman and S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).

A. E. Siegman, M. W. Sasnett, and T. F. Johnston, “Choice of clip levels for beam width measurements using knife-edge methods,” IEEE J. Quantum Electron. 27, 1098–1104 (1991).

A. E. Siegman, “How to (maybe) measure laser beam quality,” in Diode Pumped Solid State Lasers: Applications and Issues (DLAI) (Optical Society of America, 1998), paper MQ1.

Siemens, M. E.

Taghizadeh, M. R.

Townsend, S. W.

A. E. Siegman and S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).

Van Stryland, E. W.

Waddie, A. J.

Wang, Q.

J. Zheng, S. Zhao, Q. Wang, and L. Chen, “Measurement of beam quality factor (M2) by slit-scanning method,” Opt. Laser Technol. 33, 213–217 (2001).

Weber, H.

B. Eppich, G. Mann, and H. Weber, “Measurement of the four-dimensional Wigner distribution of paraxial light sources,” Proc. SPIE 5962, 59622D (2005).
[CrossRef]

C. Gao and H. Weber, “The problem with M2,” Opt. Laser Technol. 32, 221–224 (2000).

Zhao, H.

Y.-Z. Du, G. Feng, H. Li, Z. Cai, H. Zhao, and S. Zhou, “Real-time determination of beam propagation factor by Mach-Zehnder point diffraction interferometer,” Opt. Commun. 287, 1–5 (2013).
[CrossRef]

Zhao, S.

J. Zheng, S. Zhao, Q. Wang, and L. Chen, “Measurement of beam quality factor (M2) by slit-scanning method,” Opt. Laser Technol. 33, 213–217 (2001).

Zheng, J.

J. Zheng, S. Zhao, Q. Wang, and L. Chen, “Measurement of beam quality factor (M2) by slit-scanning method,” Opt. Laser Technol. 33, 213–217 (2001).

Zhou, S.

Y.-Z. Du, G. Feng, H. Li, Z. Cai, H. Zhao, and S. Zhou, “Real-time determination of beam propagation factor by Mach-Zehnder point diffraction interferometer,” Opt. Commun. 287, 1–5 (2013).
[CrossRef]

Appl. Opt. (5)

Bell Syst. Tech. J. (1)

H. Kogelnik, “Imaging of optical modes—resonators with internal lenses,” Bell Syst. Tech. J. 44, 455–494 (1965).
[CrossRef]

IEEE J. Quantum Electron. (2)

A. E. Siegman, M. W. Sasnett, and T. F. Johnston, “Choice of clip levels for beam width measurements using knife-edge methods,” IEEE J. Quantum Electron. 27, 1098–1104 (1991).

A. E. Siegman and S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).

J. Phys. D (1)

B. J. Neubert, G. Huber, and W. Scharfe, “On the problem of M2 analysis using Shack-Hartmann measurements,” J. Phys. D 34, 2414–2419 (2001).

Opt. Commun. (1)

Y.-Z. Du, G. Feng, H. Li, Z. Cai, H. Zhao, and S. Zhou, “Real-time determination of beam propagation factor by Mach-Zehnder point diffraction interferometer,” Opt. Commun. 287, 1–5 (2013).
[CrossRef]

Opt. Eng. (1)

P. B. Chapple, “Beam waist and M2 measurement using a finite slit,” Opt. Eng. 33, 2461–2466 (1994).
[CrossRef]

Opt. Express (1)

Opt. Laser Technol. (2)

C. Gao and H. Weber, “The problem with M2,” Opt. Laser Technol. 32, 221–224 (2000).

J. Zheng, S. Zhao, Q. Wang, and L. Chen, “Measurement of beam quality factor (M2) by slit-scanning method,” Opt. Laser Technol. 33, 213–217 (2001).

Opt. Lett. (2)

Opt. Photon. News (1)

D. D. Dlott, “Focus fluctuations in laser-materials interactions,” Opt. Photon. News 13(9), 34–37 (2002).
[CrossRef]

Proc. SPIE (4)

B. Eppich, G. Mann, and H. Weber, “Measurement of the four-dimensional Wigner distribution of paraxial light sources,” Proc. SPIE 5962, 59622D (2005).
[CrossRef]

M. Scaggs and G. Haas, “Real time laser beam analysis system for high power laser,” Proc. SPIE 7913, 791306 (2011).
[CrossRef]

K. C. Jorge, R. Riva, N. A. S. Rodrigues, and M. G. Destro, “Real-time measurement of laser beam quality factor (M2) by imaging transverse scattered light,” Proc. SPIE 6452, 645215 (2007).
[CrossRef]

M. W. Sasnett and T. F. Johnston, “Beam characterization and measurement of propagation attributes,” Proc. SPIE 1414, 21–32 (1991).
[CrossRef]

Other (10)

K. Iizuka, Engineering Optics, 3rd ed. (Springer-Verlag, 1983).

Coherent Inc., Coherent Corona Laser System Operator’s Manual, 1/2001. P/N: 0176-654-00, Rev. B.

E. Hecht, Optics, 3rd ed. (Addison-Wesley Longman, 1998).

R. W. Boyd, Nonlinear Optics (Academic, 2003).

K. C. Jorge, R. Riva, and N. A. S. Rodrigues, “Dispositivo e método para a caracterização de feixes de laser de baixa e alta potência baseado no espalhamento de luz,” PatentPI 0605596-6 A, DCTA (23November2006).

K. C. Jorge, R. Riva, N. A. S. Rodrigues, and M. G. Destro, “M2 beam quality measurement of a single pulse of the Nd:YAG laser,” in Proceedings of Conference on Lasers in Manufacturing, Munich, 2009, pp. 323–326.

. Test methods for laser beam widths, divergence angles and beam propagation ratios. Part 1: Stigmatic and simple beams/ Part 2: General astigmatic beams/ Part 3: Intrinsic and geometrical classification, propagation and details of test methods (ISO, Geneva, 2005).

A. E. Siegman, “How to (maybe) measure laser beam quality,” in Diode Pumped Solid State Lasers: Applications and Issues (DLAI) (Optical Society of America, 1998), paper MQ1.

S. S. Kudesia, W. S. O. Rodden, D. P. Hand, and J. D. C. Jones, “Effect of beam quality on single pulse laser drilling,” in Proceedings of the 20th International Congress on Applications of Lasers and Electro-Optics, X. Chen, ed. (Laser Institute of America, 2001), pp. 1439–1448.

Ophir-Spiricon, Inc., “M-200 Operator’s Manual” (2007).

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Figures (13)

Fig. 1.
Fig. 1.

Schematic diagram of the SLIM.

Fig. 2.
Fig. 2.

(a) Simple imaging optical system using lens of focal length f and aperture size D. (b) Frontal laser beam intensity profile given by ICSM(xo,yo,zo). (c) Image of scattered laser beam propagating in medium formed by many laser beam intensity profiles ISLIM(yi,zi).

Fig. 3.
Fig. 3.

Experimental setup for characterizing Nd:YAG laser using SLIM. (a) Spatial filter system. (b) Imaging optical system for SLIM. (c) Image of laser beam acquired by SLIM.

Fig. 4.
Fig. 4.

(a) Setup for alignment and calibration of imaging optical system. (b) Image of illuminated grid plate (on focus).

Fig. 5.
Fig. 5.

Waveforms used to determine the magnification and spatial resolution: (a) Horizontal plane. (b) Vertical plane.

Fig. 6.
Fig. 6.

SLIM image of Nd:YAG laser beam propagation. (a)–(c) Arbitrary beam. (d)–(f) Almost-ideal beam.

Fig. 7.
Fig. 7.

Laser beam intensity profiles in the y direction obtained by the CSM at (a) 250.2 mm and (d) 255.5 mm from the lens. Frontal profiles for (b), (e) arbitrary and (c), (f) almost-ideal beams.

Fig. 8.
Fig. 8.

Comparison of laser beam intensity profiles obtained by both methods at (a) 249.0 mm and (b) 241.0 mm from the lens.

Fig. 9.
Fig. 9.

Laser beam propagation curves for almost-ideal beam obtained by SLIM and CSM.

Fig. 10.
Fig. 10.

Laser beam intensity profiles obtained by SLIM and CSM at (a) 240.1 mm and (b) 254.3 mm from the lens.

Fig. 11.
Fig. 11.

Comparison of the integration on y direction of the laser beam intensity profiles of Fig. 10(b) for both methods.

Fig. 12.
Fig. 12.

Nonsaturated and saturated laser beam intensity profiles centered at xo obtained by CSM at z=240.1mm.

Fig. 13.
Fig. 13.

Comparison of laser beam intensity profile obtained by SLIM and composed laser beam intensity profile obtained by CSM.

Tables (2)

Tables Icon

Table 1. Nominal Specifications of the Corona Nd:YAG Laser

Tables Icon

Table 2. Propagation Parameters of Almost-Ideal Laser Beam Obtained by Both Methods

Equations (7)

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1do+1di=1f.
I(xi,yi,zi)=Io(xi,yi,zi)*|h(xi,yi)|2.
Icon(yi,zi)=diNΔdi+NΔI(xi,yi,zi)dxi=diNΔdi+NΔIo(xi,yi,zi)*|h(xi,yi)|2dxi,
Iint(yi,zi)diNΔdi+NΔIo(xi,yi,zi)dxi,
ISLIM={Icon,for2wthe depth of focus;Iint,for2w<the depth of focusand resolution2w.
wy(z)2=4σy(z)2=4(yy0)2ISLIM(y,z)dyISLIM(y,z)dy.
wy(z)2=w0y2+My4θy2(zz0y)2=w0y2[1+zz0yzRy]2,

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