Abstract

We present a simple high-precision method to quickly and accurately measure the diameters of Gaussian beams, Airy spots, and central peaks of Bessel beams ranging from sub-millimeter to many centimeters without specialized equipment. By simply moving a wire through the beam and recording the relative losses using an optical power meter, one can easily measure the beam diameters with a precision of 1%. The accuracy of this method has been experimentally verified for Gaussian beams down to the limit of a commercial slit-based beam profiler (3%).

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
  2. S. K. Tiwari, S. P. Ram, J. Jayabalan, and S. R. Mishra, “Measuring a narrow Bessel beam spot by scanning a charge-coupled device (CCD) pixel,” Meas. Sci. Technol. 21, 025308 (2010).
    [Crossref]
  3. Y. Suzaki and A. Tachibana, “Measurement of the μm sized radius of Gaussian laser beam using the scanning knife-edge,” Appl. Opt. 14, 2809–2810 (1975).
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  5. J. M. Khosrofian and B. A. Garetz, “Measurement of a Gaussian laser beam diameter through the direct inversion of knife-edge data,” Appl. Opt. 22, 3406–3410 (1983).
    [Crossref]
  6. Z. A. Talib and W. M. M. Yunus, “Measuring Gaussian laser beam diameter using piezoelectric detection,” Meas. Sci. Technol. 4, 22–25 (1993).
    [Crossref]
  7. W. J. Marshall, “Two methods for measuring laser beam diameter,” J. Laser Appl. 22, 132–136 (2010).
    [Crossref]
  8. C. Courtney and W. M. Steen, “Measurement of the diameter of a laser beam,” Appl. Phys. 17, 303–307 (1978).
    [Crossref]
  9. S. Kimura and C. Munakata, “Method for measuring the spot size of a laser beam using a boundary-diffraction wave,” Opt. Lett. 12, 552–554 (1987).
    [Crossref]
  10. T. W. Ng, H. Y. Tan, and S. L. Foo, “Small Gaussian laser beam diameter measurement using a quadrant photodiode,” Opt. Laser Technol. 39, 1098–1100 (2007).
    [Crossref]
  11. A. Yoshida and T. Asakura, “A simple technique for quickly measuring the spot size of Gaussian laser beams,” Opt. Laser Technol. 8, 273–274 (1976).
    [Crossref]
  12. A. Siegman, M. Sasnett, and T. Johnston, “Choice of clip levels for beam width measurements using knife-edge techniques,” IEEE J. Quantum Electron. 27, 1098–1104 (1991).
    [Crossref]
  13. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).

2010 (2)

S. K. Tiwari, S. P. Ram, J. Jayabalan, and S. R. Mishra, “Measuring a narrow Bessel beam spot by scanning a charge-coupled device (CCD) pixel,” Meas. Sci. Technol. 21, 025308 (2010).
[Crossref]

W. J. Marshall, “Two methods for measuring laser beam diameter,” J. Laser Appl. 22, 132–136 (2010).
[Crossref]

2007 (1)

T. W. Ng, H. Y. Tan, and S. L. Foo, “Small Gaussian laser beam diameter measurement using a quadrant photodiode,” Opt. Laser Technol. 39, 1098–1100 (2007).
[Crossref]

1993 (1)

Z. A. Talib and W. M. M. Yunus, “Measuring Gaussian laser beam diameter using piezoelectric detection,” Meas. Sci. Technol. 4, 22–25 (1993).
[Crossref]

1992 (1)

1991 (1)

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

1987 (1)

1983 (1)

1981 (1)

1978 (1)

C. Courtney and W. M. Steen, “Measurement of the diameter of a laser beam,” Appl. Phys. 17, 303–307 (1978).
[Crossref]

1976 (1)

A. Yoshida and T. Asakura, “A simple technique for quickly measuring the spot size of Gaussian laser beams,” Opt. Laser Technol. 8, 273–274 (1976).
[Crossref]

1975 (1)

Asakura, T.

A. Yoshida and T. Asakura, “A simple technique for quickly measuring the spot size of Gaussian laser beams,” Opt. Laser Technol. 8, 273–274 (1976).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).

Courtney, C.

C. Courtney and W. M. Steen, “Measurement of the diameter of a laser beam,” Appl. Phys. 17, 303–307 (1978).
[Crossref]

Foo, S. L.

T. W. Ng, H. Y. Tan, and S. L. Foo, “Small Gaussian laser beam diameter measurement using a quadrant photodiode,” Opt. Laser Technol. 39, 1098–1100 (2007).
[Crossref]

Garetz, B. A.

Jayabalan, J.

S. K. Tiwari, S. P. Ram, J. Jayabalan, and S. R. Mishra, “Measuring a narrow Bessel beam spot by scanning a charge-coupled device (CCD) pixel,” Meas. Sci. Technol. 21, 025308 (2010).
[Crossref]

Johnston, T.

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

Khosrofian, J. M.

Kimura, S.

Marshall, W. J.

W. J. Marshall, “Two methods for measuring laser beam diameter,” J. Laser Appl. 22, 132–136 (2010).
[Crossref]

Mishra, S. R.

S. K. Tiwari, S. P. Ram, J. Jayabalan, and S. R. Mishra, “Measuring a narrow Bessel beam spot by scanning a charge-coupled device (CCD) pixel,” Meas. Sci. Technol. 21, 025308 (2010).
[Crossref]

Munakata, C.

Ng, T. W.

T. W. Ng, H. Y. Tan, and S. L. Foo, “Small Gaussian laser beam diameter measurement using a quadrant photodiode,” Opt. Laser Technol. 39, 1098–1100 (2007).
[Crossref]

Ram, S. P.

S. K. Tiwari, S. P. Ram, J. Jayabalan, and S. R. Mishra, “Measuring a narrow Bessel beam spot by scanning a charge-coupled device (CCD) pixel,” Meas. Sci. Technol. 21, 025308 (2010).
[Crossref]

Ruff, J. A.

Sasnett, M.

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

Schneider, M. B.

Siegman, A.

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

Siegman, A. E.

Steen, W. M.

C. Courtney and W. M. Steen, “Measurement of the diameter of a laser beam,” Appl. Phys. 17, 303–307 (1978).
[Crossref]

Suzaki, Y.

Tachibana, A.

Talib, Z. A.

Z. A. Talib and W. M. M. Yunus, “Measuring Gaussian laser beam diameter using piezoelectric detection,” Meas. Sci. Technol. 4, 22–25 (1993).
[Crossref]

Tan, H. Y.

T. W. Ng, H. Y. Tan, and S. L. Foo, “Small Gaussian laser beam diameter measurement using a quadrant photodiode,” Opt. Laser Technol. 39, 1098–1100 (2007).
[Crossref]

Tiwari, S. K.

S. K. Tiwari, S. P. Ram, J. Jayabalan, and S. R. Mishra, “Measuring a narrow Bessel beam spot by scanning a charge-coupled device (CCD) pixel,” Meas. Sci. Technol. 21, 025308 (2010).
[Crossref]

Webb, W. W.

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).

Yoshida, A.

A. Yoshida and T. Asakura, “A simple technique for quickly measuring the spot size of Gaussian laser beams,” Opt. Laser Technol. 8, 273–274 (1976).
[Crossref]

Yunus, W. M. M.

Z. A. Talib and W. M. M. Yunus, “Measuring Gaussian laser beam diameter using piezoelectric detection,” Meas. Sci. Technol. 4, 22–25 (1993).
[Crossref]

Appl. Opt. (4)

Appl. Phys. (1)

C. Courtney and W. M. Steen, “Measurement of the diameter of a laser beam,” Appl. Phys. 17, 303–307 (1978).
[Crossref]

IEEE J. Quantum Electron. (1)

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

J. Laser Appl. (1)

W. J. Marshall, “Two methods for measuring laser beam diameter,” J. Laser Appl. 22, 132–136 (2010).
[Crossref]

Meas. Sci. Technol. (2)

S. K. Tiwari, S. P. Ram, J. Jayabalan, and S. R. Mishra, “Measuring a narrow Bessel beam spot by scanning a charge-coupled device (CCD) pixel,” Meas. Sci. Technol. 21, 025308 (2010).
[Crossref]

Z. A. Talib and W. M. M. Yunus, “Measuring Gaussian laser beam diameter using piezoelectric detection,” Meas. Sci. Technol. 4, 22–25 (1993).
[Crossref]

Opt. Laser Technol. (2)

T. W. Ng, H. Y. Tan, and S. L. Foo, “Small Gaussian laser beam diameter measurement using a quadrant photodiode,” Opt. Laser Technol. 39, 1098–1100 (2007).
[Crossref]

A. Yoshida and T. Asakura, “A simple technique for quickly measuring the spot size of Gaussian laser beams,” Opt. Laser Technol. 8, 273–274 (1976).
[Crossref]

Opt. Lett. (1)

Other (1)

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).

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Figures (4)

Fig. 1.
Fig. 1. Basic principle of the method: a wire moves across a Gaussian laser beam partially blocking it, where D is the diameter of the wire and θ is the angle between the wire’s normal to the x axis when the wire crosses the center of the beam. Note that the coordinate system is chosen here so that it coincides with the minor and major axes of the beam.
Fig. 2.
Fig. 2. Beam diameter of Gaussian beams (solid red line), Airy spots (blue dashed line), and central peaks of Bessel beams (green dash-dotted line) as a function of the minimum transmissivity ( T min ) . The parameter w 50 of the left vertical axis can be used together with Eqs. (4), (6), and (8) to accurately determine the beam parameters from T min . The right vertical axis directly shows the normalized Gaussian diameter ( 2 w G / D ) calculated according to Eq. (4). The black circles depict the beam diameters as measured using the slit-based beam profiler divided by the wire thickness, as depicted in Table 1. The error bars are from the beam profiler only. The red dot denotes the value for the smallest beam diameter 630 μm, for which the beam profiler gives the largest relative error. The diameter solid black dot was measured using the knife-edge method.
Fig. 3.
Fig. 3. Schematic of the experimental setup. It consists of a laser source, a neutral density filter, mirrors, a beam expander, a wire, a photodiode, and an oscilloscope. Please note that the mirrors and lenses were only used to achieve variable diameter collimated beams in the same setup.
Fig. 4.
Fig. 4. Oscilloscope trace of the transmitted power of a Gaussian beam of 2 w = 2.8    mm diameter with a 1 mm diameter wire being scanned across it. The solid blue lines correspond to the minimum and maximum voltages with T min = U min / U max . The dashed red line stands for the trigger voltage ( U trig = 56.7    mV ) used.

Tables (1)

Tables Icon

Table 1. Comparison of Beam Diameter Measurements Using the Wire Method (column 2) with a Commercial Slit-Based Beam Profiler (column 1, 0.6    mm < 2 w < 4.3    mm ) and—for the 30 mm Beam Only (marked by †)—Using the Knife-Edge Method [3] a

Equations (8)

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T min = 1 [ D / 2 D / 2 I ( x , y ) d x d y ] × [ I ( x , y ) d x d y ] 1 ,
I G ( x , y ) = I 0 e 2 ( x 2 w x 2 + y 2 w y 2 ) ,
T min = 1 1 w G 2 π D / 2 D / 2 e 2 s 2 w G 2 d s ,
w G = D 2 erf 1 ( 1 T min ) = 1.483 D w 50 ,
I A ( r ) = 4 I 0 [ J 1 ( w t / f k r ) w t / f k r ] 2 ,
w t / f = 2.025 k D w 50 .
I B ( r ) = I 0 { J 0 [ sin ( γ ) k r ] } 2 .
sin γ = 1.143 k D w 50 .

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