Abstract

To the best of our knowledge, we propose the first motion-free laser beam propagation analyzer with a hybrid design using a digital micromirror device (DMD) and a liquid electronically controlled variable focus lens (ECVFL). Unlike prior analyzers that require profiling the beam at multiple locations along the light propagation axis, the proposed analyzer profiles the beam at the same plane for multiple values of the ECVFL focal length, thus eliminating beam profiler assembly motion. In addition to measuring standard Gaussian beam parameters, the analyzer can also be used to measure the M2 beam propagation parameter of a multimode beam. Proof-of-concept beam parameter measurements with the proposed analyzer are successfully conducted for a 633nm laser beam. Given the all-digital nature of the DMD-based profiling and all-analog motion-free nature of the ECVFL beam focus control, the proposed analyzer versus prior art promises better repeatability, speed, and reliability.

© 2010 Optical Society of America

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References

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  1. H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550-1567 (1966).
    [CrossRef] [PubMed]
  2. J. E. Sollid, C. R. Phipps, Jr., S. J. Thomas, and E. J. McLellan, “Lensless method of measuring Gaussian laser beam divergence,” Appl. Opt. 17, 3527-3529 (1978).
    [CrossRef] [PubMed]
  3. J. A. Arnaud, W. M. Hubbard, G. D. Mandeville, B. de la Claviére, E. A. Franke, and J. M. Franke, “Technique for fast measurement of Gaussian laser beam parameters,” Appl. Opt. 10, 2775-2776 (1971).
    [PubMed]
  4. Y. Suzaki and A. Tachibana, “Measurement of the Gaussian laser beam divergence,” Appl. Opt. 16, 1481-1482 (1977).
    [CrossRef] [PubMed]
  5. J. Falk, “Measurement of laser beam divergence,” Appl. Opt. 22, 1131-1132 (1983).
    [CrossRef] [PubMed]
  6. R. M. Herman, J. Pardo, and T. A. Wiggins, “Diffraction and focusing of Gaussian beams,” Appl. Opt. 24, 1346-1354 (1985).
    [CrossRef] [PubMed]
  7. S. Nemoto, “Determination of waist parameters of a Gaussian beam,” Appl. Opt. 25, 3859-3863 (1986).
    [CrossRef] [PubMed]
  8. T. F. Johnston, Jr., “Beam propagation (M2) measurement made as easy as it gets: the four-cuts method,” Appl. Opt. 37, 4840-4850 (1998).
    [CrossRef]
  9. W. Plass, R. Maestle, K. Wittig, A. Voss, and A. Giesen, “High-resolution knife-edge laser beam profiling,” Opt. Commun. 134, 21-24 (1997).
    [CrossRef]
  10. D. R. Skinner and R. E. Whitcher, “Measurement of the radius of a high-power laser beam near the focus of a lens,” J. Phys. E 5, 237-238 (1972).
    [CrossRef]
  11. P. J. Brannon, J. P. Anthes, G. L. Cano, and J. E. Powell, “Laser focal spot measurements,” J. Appl. Phys. 46, 3576-3579(1975).
    [CrossRef]
  12. P. J. Shayler, “Laser beam distribution in the focal region,” Appl. Opt. 17, 2673-2674 (1978).
    [CrossRef] [PubMed]
  13. C. P. Wang, “Measuring 2-D laser-beam phase and intensity profiles: a new technique,” Appl. Opt. 23, 1399-1402(1984).
    [CrossRef] [PubMed]
  14. H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Surface plasmon polariton-based optical beam profiler,” Opt. Lett. 29, 1408-1410 (2004).
    [CrossRef] [PubMed]
  15. M. K. Giles and E. M. Kim, “Linear systems approach to fiber characterization using beam profile measurements,” Proc. SPIE 500, 67-70 (1984).
  16. S. Sumriddetchkajorn and N. A. Riza, “Micro-electromechanical system-based digitally controlled optical beam profiler,” Appl. Opt. 41, 3506-3510 (2002).
    [CrossRef] [PubMed]
  17. N. A. Riza, “Digital optical beam profiler,” U.S. patent 6,922,233 (26 July 2005).
  18. N. A. Riza and M. J. Mughal, “Optical power independent optical beam profiler,” Opt. Eng. 43, 793-797 (2004).
    [CrossRef]
  19. N. A. Riza and F. N. Ghauri, “Super resolution hybrid analog-digital optical beam profiler using digital micro-mirror device,” IEEE Photon. Technol. Lett. 17, 1492-1494(2005).
    [CrossRef]
  20. M. Sheikh and N. A. Riza, “Demonstration of pinhole laser beam profiling using a digital micro-mirror device,” IEEE Photon. Technol. Lett. 21, 666-668 (2009).
    [CrossRef]
  21. M. Gentili and N. A. Riza, “Wide-aperture no-moving-parts optical beam profiler using liquid-crystal displays,” Appl. Opt. 46, 506-512 (2007).
    [CrossRef] [PubMed]
  22. M. W. Sasnett, “Propagation of multimode laser beams--the M2 factor,” in Physics and Technology of Laser Resonators, D. R. Hall and P. E. Jackson, eds. (Hilger, 1989), Chap. 9, pp. 132-142.
  23. A. E. Siegman, “How to (maybe) measure laser beam quality,” in Vol. 17 of OSA Trends in Optics and Photonics, pp. 184-199 (Optical Society of America, 1998).
  24. Model Arctic 320 Liquid Lens Technical Data Sheet: Optical and Opto-Mechanical Data (Varioptic, SA., Lyon, France, 2006), p. 1.
  25. P. Ruffin, “Autofocus liquid lenses target new applications,” Opt. Laser Europe Mag. , pp. 17-20 (October 2007).
  26. K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 164-168(1944).
  27. “Test methods for laser beam parameters: beam widths, divergence angle, and beam propagation factor,” ISO/TC 172/SC9/WG1, ISO/DIS 11146, available from Deutsches Institut für Normung, Pforzheim, Germany.
  28. M. W. Sasnett and T. F. Johnston, Jr., “Apparatus for measuring the mode quality of a laser beam,” U.S. patent 5,214,485 (25 May 1993).
  29. 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).
    [CrossRef]

2009 (1)

M. Sheikh and N. A. Riza, “Demonstration of pinhole laser beam profiling using a digital micro-mirror device,” IEEE Photon. Technol. Lett. 21, 666-668 (2009).
[CrossRef]

2007 (1)

2005 (1)

N. A. Riza and F. N. Ghauri, “Super resolution hybrid analog-digital optical beam profiler using digital micro-mirror device,” IEEE Photon. Technol. Lett. 17, 1492-1494(2005).
[CrossRef]

2004 (2)

2002 (1)

1998 (1)

1997 (1)

W. Plass, R. Maestle, K. Wittig, A. Voss, and A. Giesen, “High-resolution knife-edge laser beam profiling,” Opt. Commun. 134, 21-24 (1997).
[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).
[CrossRef]

1986 (1)

1985 (1)

1984 (2)

C. P. Wang, “Measuring 2-D laser-beam phase and intensity profiles: a new technique,” Appl. Opt. 23, 1399-1402(1984).
[CrossRef] [PubMed]

M. K. Giles and E. M. Kim, “Linear systems approach to fiber characterization using beam profile measurements,” Proc. SPIE 500, 67-70 (1984).

1983 (1)

1978 (2)

1977 (1)

1975 (1)

P. J. Brannon, J. P. Anthes, G. L. Cano, and J. E. Powell, “Laser focal spot measurements,” J. Appl. Phys. 46, 3576-3579(1975).
[CrossRef]

1972 (1)

D. R. Skinner and R. E. Whitcher, “Measurement of the radius of a high-power laser beam near the focus of a lens,” J. Phys. E 5, 237-238 (1972).
[CrossRef]

1971 (1)

1966 (1)

1944 (1)

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 164-168(1944).

Anthes, J. P.

P. J. Brannon, J. P. Anthes, G. L. Cano, and J. E. Powell, “Laser focal spot measurements,” J. Appl. Phys. 46, 3576-3579(1975).
[CrossRef]

Arnaud, J. A.

Aussenegg, F. R.

Brannon, P. J.

P. J. Brannon, J. P. Anthes, G. L. Cano, and J. E. Powell, “Laser focal spot measurements,” J. Appl. Phys. 46, 3576-3579(1975).
[CrossRef]

Cano, G. L.

P. J. Brannon, J. P. Anthes, G. L. Cano, and J. E. Powell, “Laser focal spot measurements,” J. Appl. Phys. 46, 3576-3579(1975).
[CrossRef]

de la Claviére, B.

Ditlbacher, H.

Falk, J.

Franke, E. A.

Franke, J. M.

Gentili, M.

Ghauri, F. N.

N. A. Riza and F. N. Ghauri, “Super resolution hybrid analog-digital optical beam profiler using digital micro-mirror device,” IEEE Photon. Technol. Lett. 17, 1492-1494(2005).
[CrossRef]

Giesen, A.

W. Plass, R. Maestle, K. Wittig, A. Voss, and A. Giesen, “High-resolution knife-edge laser beam profiling,” Opt. Commun. 134, 21-24 (1997).
[CrossRef]

Giles, M. K.

M. K. Giles and E. M. Kim, “Linear systems approach to fiber characterization using beam profile measurements,” Proc. SPIE 500, 67-70 (1984).

Herman, R. M.

Hubbard, W. M.

Johnston, T. F.

T. F. Johnston, Jr., “Beam propagation (M2) measurement made as easy as it gets: the four-cuts method,” Appl. Opt. 37, 4840-4850 (1998).
[CrossRef]

M. W. Sasnett and T. F. Johnston, Jr., “Apparatus for measuring the mode quality of a laser beam,” U.S. patent 5,214,485 (25 May 1993).

Kim, E. M.

M. K. Giles and E. M. Kim, “Linear systems approach to fiber characterization using beam profile measurements,” Proc. SPIE 500, 67-70 (1984).

Kogelnik, H.

Krenn, J. R.

Leitner, A.

Levenberg, K.

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 164-168(1944).

Li, T.

Maestle, R.

W. Plass, R. Maestle, K. Wittig, A. Voss, and A. Giesen, “High-resolution knife-edge laser beam profiling,” Opt. Commun. 134, 21-24 (1997).
[CrossRef]

Mandeville, G. D.

McLellan, E. J.

Mughal, M. J.

N. A. Riza and M. J. Mughal, “Optical power independent optical beam profiler,” Opt. Eng. 43, 793-797 (2004).
[CrossRef]

Nemoto, S.

Pardo, J.

Phipps, C. R.

Plass, W.

W. Plass, R. Maestle, K. Wittig, A. Voss, and A. Giesen, “High-resolution knife-edge laser beam profiling,” Opt. Commun. 134, 21-24 (1997).
[CrossRef]

Powell, J. E.

P. J. Brannon, J. P. Anthes, G. L. Cano, and J. E. Powell, “Laser focal spot measurements,” J. Appl. Phys. 46, 3576-3579(1975).
[CrossRef]

Riza, N. A.

M. Sheikh and N. A. Riza, “Demonstration of pinhole laser beam profiling using a digital micro-mirror device,” IEEE Photon. Technol. Lett. 21, 666-668 (2009).
[CrossRef]

M. Gentili and N. A. Riza, “Wide-aperture no-moving-parts optical beam profiler using liquid-crystal displays,” Appl. Opt. 46, 506-512 (2007).
[CrossRef] [PubMed]

N. A. Riza and F. N. Ghauri, “Super resolution hybrid analog-digital optical beam profiler using digital micro-mirror device,” IEEE Photon. Technol. Lett. 17, 1492-1494(2005).
[CrossRef]

N. A. Riza and M. J. Mughal, “Optical power independent optical beam profiler,” Opt. Eng. 43, 793-797 (2004).
[CrossRef]

S. Sumriddetchkajorn and N. A. Riza, “Micro-electromechanical system-based digitally controlled optical beam profiler,” Appl. Opt. 41, 3506-3510 (2002).
[CrossRef] [PubMed]

N. A. Riza, “Digital optical beam profiler,” U.S. patent 6,922,233 (26 July 2005).

Ruffin, P.

P. Ruffin, “Autofocus liquid lenses target new applications,” Opt. Laser Europe Mag. , pp. 17-20 (October 2007).

Sasnett, M. W.

M. W. Sasnett, “Propagation of multimode laser beams--the M2 factor,” in Physics and Technology of Laser Resonators, D. R. Hall and P. E. Jackson, eds. (Hilger, 1989), Chap. 9, pp. 132-142.

M. W. Sasnett and T. F. Johnston, Jr., “Apparatus for measuring the mode quality of a laser beam,” U.S. patent 5,214,485 (25 May 1993).

Shayler, P. J.

Sheikh, M.

M. Sheikh and N. A. Riza, “Demonstration of pinhole laser beam profiling using a digital micro-mirror device,” IEEE Photon. Technol. Lett. 21, 666-668 (2009).
[CrossRef]

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).
[CrossRef]

A. E. Siegman, “How to (maybe) measure laser beam quality,” in Vol. 17 of OSA Trends in Optics and Photonics, pp. 184-199 (Optical Society of America, 1998).

Skinner, D. R.

D. R. Skinner and R. E. Whitcher, “Measurement of the radius of a high-power laser beam near the focus of a lens,” J. Phys. E 5, 237-238 (1972).
[CrossRef]

Sollid, J. E.

Sumriddetchkajorn, S.

Suzaki, Y.

Tachibana, A.

Thomas, S. J.

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).
[CrossRef]

Voss, A.

W. Plass, R. Maestle, K. Wittig, A. Voss, and A. Giesen, “High-resolution knife-edge laser beam profiling,” Opt. Commun. 134, 21-24 (1997).
[CrossRef]

Wang, C. P.

Whitcher, R. E.

D. R. Skinner and R. E. Whitcher, “Measurement of the radius of a high-power laser beam near the focus of a lens,” J. Phys. E 5, 237-238 (1972).
[CrossRef]

Wiggins, T. A.

Wittig, K.

W. Plass, R. Maestle, K. Wittig, A. Voss, and A. Giesen, “High-resolution knife-edge laser beam profiling,” Opt. Commun. 134, 21-24 (1997).
[CrossRef]

Appl. Opt. (12)

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

J. Falk, “Measurement of laser beam divergence,” Appl. Opt. 22, 1131-1132 (1983).
[CrossRef] [PubMed]

C. P. Wang, “Measuring 2-D laser-beam phase and intensity profiles: a new technique,” Appl. Opt. 23, 1399-1402(1984).
[CrossRef] [PubMed]

R. M. Herman, J. Pardo, and T. A. Wiggins, “Diffraction and focusing of Gaussian beams,” Appl. Opt. 24, 1346-1354 (1985).
[CrossRef] [PubMed]

S. Nemoto, “Determination of waist parameters of a Gaussian beam,” Appl. Opt. 25, 3859-3863 (1986).
[CrossRef] [PubMed]

T. F. Johnston, Jr., “Beam propagation (M2) measurement made as easy as it gets: the four-cuts method,” Appl. Opt. 37, 4840-4850 (1998).
[CrossRef]

S. Sumriddetchkajorn and N. A. Riza, “Micro-electromechanical system-based digitally controlled optical beam profiler,” Appl. Opt. 41, 3506-3510 (2002).
[CrossRef] [PubMed]

M. Gentili and N. A. Riza, “Wide-aperture no-moving-parts optical beam profiler using liquid-crystal displays,” Appl. Opt. 46, 506-512 (2007).
[CrossRef] [PubMed]

J. A. Arnaud, W. M. Hubbard, G. D. Mandeville, B. de la Claviére, E. A. Franke, and J. M. Franke, “Technique for fast measurement of Gaussian laser beam parameters,” Appl. Opt. 10, 2775-2776 (1971).
[PubMed]

P. J. Shayler, “Laser beam distribution in the focal region,” Appl. Opt. 17, 2673-2674 (1978).
[CrossRef] [PubMed]

Y. Suzaki and A. Tachibana, “Measurement of the Gaussian laser beam divergence,” Appl. Opt. 16, 1481-1482 (1977).
[CrossRef] [PubMed]

J. E. Sollid, C. R. Phipps, Jr., S. J. Thomas, and E. J. McLellan, “Lensless method of measuring Gaussian laser beam divergence,” Appl. Opt. 17, 3527-3529 (1978).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (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).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

N. A. Riza and F. N. Ghauri, “Super resolution hybrid analog-digital optical beam profiler using digital micro-mirror device,” IEEE Photon. Technol. Lett. 17, 1492-1494(2005).
[CrossRef]

M. Sheikh and N. A. Riza, “Demonstration of pinhole laser beam profiling using a digital micro-mirror device,” IEEE Photon. Technol. Lett. 21, 666-668 (2009).
[CrossRef]

J. Appl. Phys. (1)

P. J. Brannon, J. P. Anthes, G. L. Cano, and J. E. Powell, “Laser focal spot measurements,” J. Appl. Phys. 46, 3576-3579(1975).
[CrossRef]

J. Phys. E (1)

D. R. Skinner and R. E. Whitcher, “Measurement of the radius of a high-power laser beam near the focus of a lens,” J. Phys. E 5, 237-238 (1972).
[CrossRef]

Opt. Commun. (1)

W. Plass, R. Maestle, K. Wittig, A. Voss, and A. Giesen, “High-resolution knife-edge laser beam profiling,” Opt. Commun. 134, 21-24 (1997).
[CrossRef]

Opt. Eng. (1)

N. A. Riza and M. J. Mughal, “Optical power independent optical beam profiler,” Opt. Eng. 43, 793-797 (2004).
[CrossRef]

Opt. Laser Europe Mag. (1)

P. Ruffin, “Autofocus liquid lenses target new applications,” Opt. Laser Europe Mag. , pp. 17-20 (October 2007).

Opt. Lett. (1)

Proc. SPIE (1)

M. K. Giles and E. M. Kim, “Linear systems approach to fiber characterization using beam profile measurements,” Proc. SPIE 500, 67-70 (1984).

Q. Appl. Math. (1)

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 164-168(1944).

Other (6)

“Test methods for laser beam parameters: beam widths, divergence angle, and beam propagation factor,” ISO/TC 172/SC9/WG1, ISO/DIS 11146, available from Deutsches Institut für Normung, Pforzheim, Germany.

M. W. Sasnett and T. F. Johnston, Jr., “Apparatus for measuring the mode quality of a laser beam,” U.S. patent 5,214,485 (25 May 1993).

M. W. Sasnett, “Propagation of multimode laser beams--the M2 factor,” in Physics and Technology of Laser Resonators, D. R. Hall and P. E. Jackson, eds. (Hilger, 1989), Chap. 9, pp. 132-142.

A. E. Siegman, “How to (maybe) measure laser beam quality,” in Vol. 17 of OSA Trends in Optics and Photonics, pp. 184-199 (Optical Society of America, 1998).

Model Arctic 320 Liquid Lens Technical Data Sheet: Optical and Opto-Mechanical Data (Varioptic, SA., Lyon, France, 2006), p. 1.

N. A. Riza, “Digital optical beam profiler,” U.S. patent 6,922,233 (26 July 2005).

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Figures (3)

Fig. 1
Fig. 1

Proposed motion-free hybrid-design laser beam propagation analyzer system using a DMD and an ECVFL: PD1/PD2, photodetectors; PC, personal computer.

Fig. 2
Fig. 2

For the 633 nm laser beam, DMD knife-edge beam profiling results for the f = 9.6 cm ECVFL. Knife-edge raw optical power data along the test beam (a) horizontal direction and (b) vertical direction. Error-function fit for (c) horizontal knife-edge data and (d) vertical knife-edge data. Two-dimensional beam profile (e) gradient view and (f) spatial view.

Fig. 3
Fig. 3

Table 1 data and Eq. (10) provided the least-squares curve fit for determining the test 633 nm laser beam (a) horizontal beam radius w H ( f ) and (b) vertical beam radius w V ( f ) .

Tables (1)

Tables Icon

Table 1 Corresponding Values of the ECVFL a

Equations (16)

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

ψ ( r , z ) exp ( j k r 2 2 q ( z ) ) ,
1 q ( z ) = 1 R ( z ) j λ π w 2 ( z ) .
1 q 0 = j λ π w 0 2 1 j z R ,
q 1 = A q 0 + B C q 0 + D = A j z R + B C j z R + D .
[ A B C D ] = [ 1 d 2 0 1 ] [ 1 0 1 / f 1 ] [ 1 d 1 0 1 ] = [ 1 d 2 / f d 1 + d 2 d 1 d 2 / f 1 / f 1 d 1 / f ] .
1 q 1 = C j z R + D A j z R + B = ( C j z R + D ) ( A j z R + B ) A 2 z R 2 + B 2 .
1 q 1 = A C z R 2 + B D A 2 z R 2 + B 2 j z R ( A D B C ) A 2 z R 2 + B 2 .
Im { 1 q 1 } = λ π w 2 ( f ) = z R ( A D B C ) A 2 z R 2 + B 2 ,
w 2 ( f ) = w 0 2 ( 1 d 2 / f ) 2 + λ 2 π 2 w 0 2 ( d 1 + d 2 d 1 d 2 / f ) 2 ,
w 2 ( f ) = w 0 2 [ ( 1 d 2 / f ) 2 + { λ ( d 1 + d 2 d 1 d 2 / f ) π w 0 2 } 2 ] .
θ = λ π w 0 .
W 0 = M w 0 , W ( f ) = M w ( f ) .
W 2 ( f ) = W 0 2 [ ( 1 d 2 / f ) 2 + { M 2 λ ( d 1 + d 2 d 1 d 2 / f ) π W 0 2 } 2 ] .
W H ( f ) = 2 x y I ( x , y ) ( x x 0 ) 2 x y I ( x , y ) ,
x 0 = x y I ( x , y ) x x y I ( x , y ) .
Θ = M 2 λ π W 0 .

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