Abstract

We demonstrate motion-free beam quality M2 measurements of stigmatic, simple astigmatic, and general astigmatic (twisted) beams using only a focus-tunable liquid lens and a CCD camera. We extend the variable-focus technique to the characterization of general astigmatic beams by measuring the 10 second-order moments of the power density distribution for the twisted beam produced by passage through multimode optical fiber. Our method measures the same M2 values as the traditional variable-distance method for a wide range of laser beam sources, including nearly TEM00 (M21) and general astigmatic multimode beams (M28). The method is simple and compact, with no moving parts or complex apparatus and measurement precision comparable to the standard variable-distance method.

© 2013 Optical Society of America

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References

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  1. ISO 11146-1:2005, “Lasers and laser related equipment test methods for laser beam widths, divergence angles and beam propagation ratios. Part 1: Stigmatic and simple astigmatic beams.”
  2. A. E. Siegman, “How to (maybe) measure laser beam quality,” in Diode Pumped Solid State Lasers: Applications and Issues (DLAI) 1998 (Optical Society of America, 1998), paper MQ1.
  3. R. Cortés, R. Villagómez, V. Coello, and R. López, “Laser beam quality factor (M2) measured by distorted fresnel zone plates,” Rev. Mex. Fis. 54, 279–283 (2008).
  4. M. Scaggs and G. Haas, “Real time laser beam analysis system for high power lasers,” Proc. SPIE 7913, 791306 (2011).
    [CrossRef]
  5. O. A. Schmidt, C. Schulze, D. Flamm, R. Brüning, T. Kaiser, S. Schröter, and M. Duparré, “Real-time determination of laser beam quality by modal decomposition,” Opt. Express 19, 6741–6748 (2011).
    [CrossRef]
  6. D. Flamm, C. Schulze, R. Brüning, O. A. Schmidt, T. Kaiser, S. Schröter, and M. Duparré, “Fast M2 measurements for fiber beams based on modal analysis,” Appl. Opt. 51, 987–993 (2012).
    [CrossRef]
  7. J. Pérez-Vizcaíno, O. Mendoza-Yero, R. Martínez-Cuenca, L. Martínez-León, E. Tajahuerce, and J. Lancis, “Free-motion beam propagation factor measurement by means of a liquid crystal spatial light modulator,” J. Disp. Technol. 8, 539–545(2012).
    [CrossRef]
  8. C. Schulze, D. Flamm, M. Duparré, and A. Forbes, “Beam-quality measurements using a spatial light modulator,” Opt. Lett. 37, 4687–4689 (2012).
  9. T. F. Johnston, “Beam propagation (M2) measurement made as easy as it gets: the four-cuts method,” Appl. Opt. 37, 4840–4850 (1998).
    [CrossRef]
  10. Ophir-Spiricon, Inc., “M-200 Operator’s Manual” (2007).
  11. Coherent, Inc., “Mode Master PC User Manual” (2011).
  12. DataRay, Inc., “WinCamD+M2DU M2 System User Manual”.
  13. M. Sheikh, and N. A. Riza, “Motion-free hybrid design laser beam propagation analyzer using a digital micromirror device and a variable focus liquid lens,” Appl. Opt. 49, D6–D11 (2010).
    [CrossRef]
  14. P. Marraccini and N. A. Riza, “Multimode laser beam analyzer instrument using electrically programmable optics,” Rev. Sci. Instrum. 82, 123107 (2011).
    [CrossRef]
  15. A. E. Siegman, Lasers (University Science, 1986), Section 17.6.
  16. M. W. Sasnett, “Propagation of multimode laser beams—the M2 factor,” in The Physics and Technology of Laser Resonators, D. R. Hall and P. E. Jackson, eds. (Hilger, 1989), Chap. 9, pp. 132–142.
  17. Optotune AG, “EL-10-30 Datasheet,” extended form of datasheet available from Optotune AG upon request.
  18. V. Daneu, A. Sanchez, T. Y. Fan, H. K. Choi, G. W. Turner, and C. C. Cook, “Spectral beam combining of a broad-stripe diode laser array in an external cavity,” Opt. Lett. 25, 405–407 (2000).
    [CrossRef]
  19. ISO 11146-2:2005, “Lasers and laser related equipment test methods for laser beam widths, divergence angles and beam propagation ratios. Part 2: general astigmatic beams”.
  20. B. Eppich, C. Gao, and H. Weber, “Determination of the ten second order intensity moments,” Opt. Laser Technol. 30, 337–340 (1998).
    [CrossRef]
  21. J. Serna, F. Encinas-Sanz, and G. Nemes, “Complete spatial characterization of a pulsed doughnut-type beam by use of spherical optics and a cylindrical lens,” J. Opt. Soc. Am. A 18, 1726–1733 (2001).
    [CrossRef]
  22. A. Letsch and A. Giesen, “Characterization of general astigmatic laser beams,” Proc. SPIE 6101, 610117 (2006).
    [CrossRef]
  23. C. Li, G. Hall, X. Zeng, D. Zhu, K. Eliceiri, and H. Jiang, “Three-dimensional surface profiling and optical characterization of liquid microlens using a Shack–Hartmann wave front sensor,” Appl. Phys. Lett. 98, 171104 (2011).
    [CrossRef]
  24. J. A. Ruff and A. E. Siegman, “Measurement of beam quality degradation due to spherical aberration in a simple lens,” Opt. Quantum Electron. 26, 629–632 (1994).
    [CrossRef]
  25. A. Werber and H. Zappe, “Tunable microfluidic microlenses,” Appl. Opt. 44, 3238–3245 (2005).
    [CrossRef]

2012 (3)

D. Flamm, C. Schulze, R. Brüning, O. A. Schmidt, T. Kaiser, S. Schröter, and M. Duparré, “Fast M2 measurements for fiber beams based on modal analysis,” Appl. Opt. 51, 987–993 (2012).
[CrossRef]

J. Pérez-Vizcaíno, O. Mendoza-Yero, R. Martínez-Cuenca, L. Martínez-León, E. Tajahuerce, and J. Lancis, “Free-motion beam propagation factor measurement by means of a liquid crystal spatial light modulator,” J. Disp. Technol. 8, 539–545(2012).
[CrossRef]

C. Schulze, D. Flamm, M. Duparré, and A. Forbes, “Beam-quality measurements using a spatial light modulator,” Opt. Lett. 37, 4687–4689 (2012).

2011 (4)

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

O. A. Schmidt, C. Schulze, D. Flamm, R. Brüning, T. Kaiser, S. Schröter, and M. Duparré, “Real-time determination of laser beam quality by modal decomposition,” Opt. Express 19, 6741–6748 (2011).
[CrossRef]

P. Marraccini and N. A. Riza, “Multimode laser beam analyzer instrument using electrically programmable optics,” Rev. Sci. Instrum. 82, 123107 (2011).
[CrossRef]

C. Li, G. Hall, X. Zeng, D. Zhu, K. Eliceiri, and H. Jiang, “Three-dimensional surface profiling and optical characterization of liquid microlens using a Shack–Hartmann wave front sensor,” Appl. Phys. Lett. 98, 171104 (2011).
[CrossRef]

2010 (1)

2008 (1)

R. Cortés, R. Villagómez, V. Coello, and R. López, “Laser beam quality factor (M2) measured by distorted fresnel zone plates,” Rev. Mex. Fis. 54, 279–283 (2008).

2006 (1)

A. Letsch and A. Giesen, “Characterization of general astigmatic laser beams,” Proc. SPIE 6101, 610117 (2006).
[CrossRef]

2005 (1)

2001 (1)

2000 (1)

1998 (2)

B. Eppich, C. Gao, and H. Weber, “Determination of the ten second order intensity moments,” Opt. Laser Technol. 30, 337–340 (1998).
[CrossRef]

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

1994 (1)

J. A. Ruff and A. E. Siegman, “Measurement of beam quality degradation due to spherical aberration in a simple lens,” Opt. Quantum Electron. 26, 629–632 (1994).
[CrossRef]

Brüning, R.

Choi, H. K.

Coello, V.

R. Cortés, R. Villagómez, V. Coello, and R. López, “Laser beam quality factor (M2) measured by distorted fresnel zone plates,” Rev. Mex. Fis. 54, 279–283 (2008).

Cook, C. C.

Cortés, R.

R. Cortés, R. Villagómez, V. Coello, and R. López, “Laser beam quality factor (M2) measured by distorted fresnel zone plates,” Rev. Mex. Fis. 54, 279–283 (2008).

Daneu, V.

Duparré, M.

Eliceiri, K.

C. Li, G. Hall, X. Zeng, D. Zhu, K. Eliceiri, and H. Jiang, “Three-dimensional surface profiling and optical characterization of liquid microlens using a Shack–Hartmann wave front sensor,” Appl. Phys. Lett. 98, 171104 (2011).
[CrossRef]

Encinas-Sanz, F.

Eppich, B.

B. Eppich, C. Gao, and H. Weber, “Determination of the ten second order intensity moments,” Opt. Laser Technol. 30, 337–340 (1998).
[CrossRef]

Fan, T. Y.

Flamm, D.

Forbes, A.

Gao, C.

B. Eppich, C. Gao, and H. Weber, “Determination of the ten second order intensity moments,” Opt. Laser Technol. 30, 337–340 (1998).
[CrossRef]

Giesen, A.

A. Letsch and A. Giesen, “Characterization of general astigmatic laser beams,” Proc. SPIE 6101, 610117 (2006).
[CrossRef]

Haas, G.

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

Hall, G.

C. Li, G. Hall, X. Zeng, D. Zhu, K. Eliceiri, and H. Jiang, “Three-dimensional surface profiling and optical characterization of liquid microlens using a Shack–Hartmann wave front sensor,” Appl. Phys. Lett. 98, 171104 (2011).
[CrossRef]

Jiang, H.

C. Li, G. Hall, X. Zeng, D. Zhu, K. Eliceiri, and H. Jiang, “Three-dimensional surface profiling and optical characterization of liquid microlens using a Shack–Hartmann wave front sensor,” Appl. Phys. Lett. 98, 171104 (2011).
[CrossRef]

Johnston, T. F.

Kaiser, T.

Lancis, J.

J. Pérez-Vizcaíno, O. Mendoza-Yero, R. Martínez-Cuenca, L. Martínez-León, E. Tajahuerce, and J. Lancis, “Free-motion beam propagation factor measurement by means of a liquid crystal spatial light modulator,” J. Disp. Technol. 8, 539–545(2012).
[CrossRef]

Letsch, A.

A. Letsch and A. Giesen, “Characterization of general astigmatic laser beams,” Proc. SPIE 6101, 610117 (2006).
[CrossRef]

Li, C.

C. Li, G. Hall, X. Zeng, D. Zhu, K. Eliceiri, and H. Jiang, “Three-dimensional surface profiling and optical characterization of liquid microlens using a Shack–Hartmann wave front sensor,” Appl. Phys. Lett. 98, 171104 (2011).
[CrossRef]

López, R.

R. Cortés, R. Villagómez, V. Coello, and R. López, “Laser beam quality factor (M2) measured by distorted fresnel zone plates,” Rev. Mex. Fis. 54, 279–283 (2008).

Marraccini, P.

P. Marraccini and N. A. Riza, “Multimode laser beam analyzer instrument using electrically programmable optics,” Rev. Sci. Instrum. 82, 123107 (2011).
[CrossRef]

Martínez-Cuenca, R.

J. Pérez-Vizcaíno, O. Mendoza-Yero, R. Martínez-Cuenca, L. Martínez-León, E. Tajahuerce, and J. Lancis, “Free-motion beam propagation factor measurement by means of a liquid crystal spatial light modulator,” J. Disp. Technol. 8, 539–545(2012).
[CrossRef]

Martínez-León, L.

J. Pérez-Vizcaíno, O. Mendoza-Yero, R. Martínez-Cuenca, L. Martínez-León, E. Tajahuerce, and J. Lancis, “Free-motion beam propagation factor measurement by means of a liquid crystal spatial light modulator,” J. Disp. Technol. 8, 539–545(2012).
[CrossRef]

Mendoza-Yero, O.

J. Pérez-Vizcaíno, O. Mendoza-Yero, R. Martínez-Cuenca, L. Martínez-León, E. Tajahuerce, and J. Lancis, “Free-motion beam propagation factor measurement by means of a liquid crystal spatial light modulator,” J. Disp. Technol. 8, 539–545(2012).
[CrossRef]

Nemes, G.

Pérez-Vizcaíno, J.

J. Pérez-Vizcaíno, O. Mendoza-Yero, R. Martínez-Cuenca, L. Martínez-León, E. Tajahuerce, and J. Lancis, “Free-motion beam propagation factor measurement by means of a liquid crystal spatial light modulator,” J. Disp. Technol. 8, 539–545(2012).
[CrossRef]

Riza, N. A.

P. Marraccini and N. A. Riza, “Multimode laser beam analyzer instrument using electrically programmable optics,” Rev. Sci. Instrum. 82, 123107 (2011).
[CrossRef]

M. Sheikh, and N. A. Riza, “Motion-free hybrid design laser beam propagation analyzer using a digital micromirror device and a variable focus liquid lens,” Appl. Opt. 49, D6–D11 (2010).
[CrossRef]

Ruff, J. A.

J. A. Ruff and A. E. Siegman, “Measurement of beam quality degradation due to spherical aberration in a simple lens,” Opt. Quantum Electron. 26, 629–632 (1994).
[CrossRef]

Sanchez, A.

Sasnett, M. W.

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

Scaggs, M.

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

Schmidt, O. A.

Schröter, S.

Schulze, C.

Serna, J.

Sheikh, M.

Siegman, A. E.

J. A. Ruff and A. E. Siegman, “Measurement of beam quality degradation due to spherical aberration in a simple lens,” Opt. Quantum Electron. 26, 629–632 (1994).
[CrossRef]

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

A. E. Siegman, Lasers (University Science, 1986), Section 17.6.

Tajahuerce, E.

J. Pérez-Vizcaíno, O. Mendoza-Yero, R. Martínez-Cuenca, L. Martínez-León, E. Tajahuerce, and J. Lancis, “Free-motion beam propagation factor measurement by means of a liquid crystal spatial light modulator,” J. Disp. Technol. 8, 539–545(2012).
[CrossRef]

Turner, G. W.

Villagómez, R.

R. Cortés, R. Villagómez, V. Coello, and R. López, “Laser beam quality factor (M2) measured by distorted fresnel zone plates,” Rev. Mex. Fis. 54, 279–283 (2008).

Weber, H.

B. Eppich, C. Gao, and H. Weber, “Determination of the ten second order intensity moments,” Opt. Laser Technol. 30, 337–340 (1998).
[CrossRef]

Werber, A.

Zappe, H.

Zeng, X.

C. Li, G. Hall, X. Zeng, D. Zhu, K. Eliceiri, and H. Jiang, “Three-dimensional surface profiling and optical characterization of liquid microlens using a Shack–Hartmann wave front sensor,” Appl. Phys. Lett. 98, 171104 (2011).
[CrossRef]

Zhu, D.

C. Li, G. Hall, X. Zeng, D. Zhu, K. Eliceiri, and H. Jiang, “Three-dimensional surface profiling and optical characterization of liquid microlens using a Shack–Hartmann wave front sensor,” Appl. Phys. Lett. 98, 171104 (2011).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. Lett. (1)

C. Li, G. Hall, X. Zeng, D. Zhu, K. Eliceiri, and H. Jiang, “Three-dimensional surface profiling and optical characterization of liquid microlens using a Shack–Hartmann wave front sensor,” Appl. Phys. Lett. 98, 171104 (2011).
[CrossRef]

J. Disp. Technol. (1)

J. Pérez-Vizcaíno, O. Mendoza-Yero, R. Martínez-Cuenca, L. Martínez-León, E. Tajahuerce, and J. Lancis, “Free-motion beam propagation factor measurement by means of a liquid crystal spatial light modulator,” J. Disp. Technol. 8, 539–545(2012).
[CrossRef]

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

Opt. Express (1)

Opt. Laser Technol. (1)

B. Eppich, C. Gao, and H. Weber, “Determination of the ten second order intensity moments,” Opt. Laser Technol. 30, 337–340 (1998).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

J. A. Ruff and A. E. Siegman, “Measurement of beam quality degradation due to spherical aberration in a simple lens,” Opt. Quantum Electron. 26, 629–632 (1994).
[CrossRef]

Proc. SPIE (2)

A. Letsch and A. Giesen, “Characterization of general astigmatic laser beams,” Proc. SPIE 6101, 610117 (2006).
[CrossRef]

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

Rev. Mex. Fis. (1)

R. Cortés, R. Villagómez, V. Coello, and R. López, “Laser beam quality factor (M2) measured by distorted fresnel zone plates,” Rev. Mex. Fis. 54, 279–283 (2008).

Rev. Sci. Instrum. (1)

P. Marraccini and N. A. Riza, “Multimode laser beam analyzer instrument using electrically programmable optics,” Rev. Sci. Instrum. 82, 123107 (2011).
[CrossRef]

Other (9)

A. E. Siegman, Lasers (University Science, 1986), Section 17.6.

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

Optotune AG, “EL-10-30 Datasheet,” extended form of datasheet available from Optotune AG upon request.

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

Coherent, Inc., “Mode Master PC User Manual” (2011).

DataRay, Inc., “WinCamD+M2DU M2 System User Manual”.

ISO 11146-2:2005, “Lasers and laser related equipment test methods for laser beam widths, divergence angles and beam propagation ratios. Part 2: general astigmatic beams”.

ISO 11146-1:2005, “Lasers and laser related equipment test methods for laser beam widths, divergence angles and beam propagation ratios. Part 1: Stigmatic and simple astigmatic beams.”

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

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Figures (5)

Fig. 1.
Fig. 1.

Schematic describing the variable-focus method of measuring the laser beam propagation factor, M2. The only two components required are a CCD camera and a focus-tunable lens. A beam waist is formed at a position after the lens given by the resting focal length, f(0); applying current I changes the lens focal length, f(I), moving the waist location through the plane of the camera. Fitting Eq. (6) to beam size data, Wf(f), yields the M2 value as well as the initial beam size and RoC, Wi, and Ri. The lens was oriented with its optical axis vertical to avoid wavefront errors.

Fig. 2.
Fig. 2.

Comparison of data obtained using (a) variable-distance and (b) variable-focus methods. Beam widths are measured using a CCD based on the 4σ definition. Uncertainty in the beam width is smaller than the symbol size. Data is fitted using Eq. (6). Reported uncertainties are twice the standard deviation of the fit (95% confidence interval).

Fig. 3.
Fig. 3.

Comparison of (a) variable-distance and (b) variable-focus methods for a multimode beam: a He–Ne laser laser beam passed through 2 m long, 25 μm core fiber. Equation (6) was fit to data. Beam widths were measured along major and minor axes because the beam twists under propagation, as discussed in Section 4. Reported uncertainties are twice the standard deviation of the fit (95% confidence interval). The inset shows the near-field irradiance profile.

Fig. 4.
Fig. 4.

Comparison of (a) variable-distance and (b) variable-focus methods for measuring the 10 second-order moments of a general astigmatic. The test beam was identical to that of Fig. 3, a He–Ne laser laser beam passed through 2 m long, 25 μm core fiber. Equation (9) was fit to data. The nine fit parameters and the separately measured twist parameter completely characterize the beam and allow calculation of an effective M2 value.

Fig. 5.
Fig. 5.

Measured focal length calibration curve for the Optotune EL-10-30 (with LD material), oriented with vertical optical axis.

Tables (3)

Tables Icon

Table 1. Specifications: EL-10-30, LD Material (Values from [17] unless otherwise Indicated)

Tables Icon

Table 2. Comparison of M2 Values using the Variable-Distance and Variable-Focus Methods

Tables Icon

Table 3. Second-Order Moments Measured with the Variable-Focus Method

Equations (11)

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

1qi=1Riiλπωi2.
1qf=Cqi+DAqi+B=dfRiλ+iπ[d(fRi)+fRi]ωi2fRiλ+iπ(fRi)ωi2.
ω2=λπIm[1q],
ωf2=d2λ2π2ωi2+[ωid(fRi)+fRifRi]2.
W=M2ω,
Wf=(M2dλπWi)2+Wi2(1+dRidf)2.
P=(x2xyxθxxθyxyy2yθxyθyxθxyθxθx2θxθyxθyyθyθxθyθy2).
Meff2=4πλ[Det(P)]1/4.
x2=x2i(1df)2+2dxθxi(1df)+d2θx2iy2=y2i(1df)2+2dyθyi(1df)+d2θy2ixy=xyi(1df)2+dsi(1df)+d2θxθyi.
{xyvxyh}(fc,dc)=tdc2fc,
M2M02+12M02(ωiωq)8,

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