Abstract

A method is described for measuring various laser beam characteristics with modest experimental complexity by digital processing of the near and far field images. Gaussian spot sizes, peak intensities, and spatial distributions of the images are easily found. Far field beam focusability is determined by computationally applying apertures of circular or elliptical diameters to the digitized image. Visualization of the magnitude of phase and intensity distortions is accomplished by comparing the 2-D fast Fourier transform of both smoothed and unsmoothed near field data to the actual far field data. The digital processing may be performed on current personal computers to give the experimenter unprecedented capabilities for rapid beam characterization at relatively low cost.

© 1989 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Suzaki, A. Tachibana, “Measurement of the μm Sized Radius of Gaussian Laser Beam Using the Scanning Knife-Edge,” Appl. Opt. 14, 1809–2810 (1975).
    [CrossRef]
  2. M. T. Gale, H. Meier, “Rapid Evaluation of Submicron Laser Spots,” RCA Rev. 46, 56 (1985).
  3. S. Kimura, C. Munakata, “Measurement of a Gaussian Laser Beam Spot Size Using a Boundary Diffraction Wave,” Appl. Opt. 27, 84–88 (1988).
    [CrossRef] [PubMed]
  4. P. Langlois, R. A. Lessard, “Simultaneous Laser Beam Profiling and Scaling Using Diffraction Edge Waves (DEW),” Proc. Soc. Photo-Opt. Instrum. Eng. 661, 315 (1986).
  5. S. F. Fulghum et al., “Stokes Phase Preservation during Raman Amplification,” J. Opt. Soc. Am. B 3, 1448–1459 (1986).
    [CrossRef]
  6. This software is published by Big Sky Software Corp., P.O. Box 3220, Bozeman, MT 59772.
  7. H. Kogelnik, T. Li, “Laser Beams and Resonators,” Appl. Opt. 5, 1550–1567 (1966).
    [CrossRef] [PubMed]
  8. A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986), p. 666.
  9. H. J. Nussbaumer, Fast Fourier Transforms and Convolution Algorithms (Springer-Verlag, Berlin, 1981), pp. 94–103.
  10. See, for example,W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U.P., London, 1986), pp. 449–453.
  11. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 461.

1988 (1)

1986 (2)

P. Langlois, R. A. Lessard, “Simultaneous Laser Beam Profiling and Scaling Using Diffraction Edge Waves (DEW),” Proc. Soc. Photo-Opt. Instrum. Eng. 661, 315 (1986).

S. F. Fulghum et al., “Stokes Phase Preservation during Raman Amplification,” J. Opt. Soc. Am. B 3, 1448–1459 (1986).
[CrossRef]

1985 (1)

M. T. Gale, H. Meier, “Rapid Evaluation of Submicron Laser Spots,” RCA Rev. 46, 56 (1985).

1975 (1)

Y. Suzaki, A. Tachibana, “Measurement of the μm Sized Radius of Gaussian Laser Beam Using the Scanning Knife-Edge,” Appl. Opt. 14, 1809–2810 (1975).
[CrossRef]

1966 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 461.

Flannery, B. P.

See, for example,W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U.P., London, 1986), pp. 449–453.

Fulghum, S. F.

Gale, M. T.

M. T. Gale, H. Meier, “Rapid Evaluation of Submicron Laser Spots,” RCA Rev. 46, 56 (1985).

Kimura, S.

Kogelnik, H.

Langlois, P.

P. Langlois, R. A. Lessard, “Simultaneous Laser Beam Profiling and Scaling Using Diffraction Edge Waves (DEW),” Proc. Soc. Photo-Opt. Instrum. Eng. 661, 315 (1986).

Lessard, R. A.

P. Langlois, R. A. Lessard, “Simultaneous Laser Beam Profiling and Scaling Using Diffraction Edge Waves (DEW),” Proc. Soc. Photo-Opt. Instrum. Eng. 661, 315 (1986).

Li, T.

Meier, H.

M. T. Gale, H. Meier, “Rapid Evaluation of Submicron Laser Spots,” RCA Rev. 46, 56 (1985).

Munakata, C.

Nussbaumer, H. J.

H. J. Nussbaumer, Fast Fourier Transforms and Convolution Algorithms (Springer-Verlag, Berlin, 1981), pp. 94–103.

Press, W. H.

See, for example,W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U.P., London, 1986), pp. 449–453.

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986), p. 666.

Suzaki, Y.

Y. Suzaki, A. Tachibana, “Measurement of the μm Sized Radius of Gaussian Laser Beam Using the Scanning Knife-Edge,” Appl. Opt. 14, 1809–2810 (1975).
[CrossRef]

Tachibana, A.

Y. Suzaki, A. Tachibana, “Measurement of the μm Sized Radius of Gaussian Laser Beam Using the Scanning Knife-Edge,” Appl. Opt. 14, 1809–2810 (1975).
[CrossRef]

Teukolsky, S. A.

See, for example,W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U.P., London, 1986), pp. 449–453.

Vetterling, W. T.

See, for example,W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U.P., London, 1986), pp. 449–453.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 461.

Appl. Opt. (3)

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

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

P. Langlois, R. A. Lessard, “Simultaneous Laser Beam Profiling and Scaling Using Diffraction Edge Waves (DEW),” Proc. Soc. Photo-Opt. Instrum. Eng. 661, 315 (1986).

RCA Rev. (1)

M. T. Gale, H. Meier, “Rapid Evaluation of Submicron Laser Spots,” RCA Rev. 46, 56 (1985).

Other (5)

A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986), p. 666.

H. J. Nussbaumer, Fast Fourier Transforms and Convolution Algorithms (Springer-Verlag, Berlin, 1981), pp. 94–103.

See, for example,W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U.P., London, 1986), pp. 449–453.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 461.

This software is published by Big Sky Software Corp., P.O. Box 3220, Bozeman, MT 59772.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Schematic of the experimental configuration used to image both a near field plane and a far field plane onto a single camera. The near field plane P1 is imaged onto planes P2 and P3 using an image transfer telescope and beam splitter BS. Lens L1 transforms the image from plane P3 into the far field at plane P4. Lens L2 images that plane onto the camera plane P5.

Fig. 2
Fig. 2

Example of raw near field (upper left) and far field (lower right) beam data captured digitally from a video camera. The 8.7- × 6.5-mm active area of the camera has been digitized into a 240 × 240 pixel array of which approximately a 240 × 200 subset is shown in the figure. The pixels are distorted due to the evenly spaced digitization of the physically nonsquare pixels. The noise has been enhanced for better visualization. The gray scale below the figure indicates intensity values used for this figure and for all subsequent beam figures.

Fig. 3
Fig. 3

(a) Near and (b) far field images of a good quality laser beam. The low intensity noise has been truncated, and the overall intensity has been linearly stretched and normalized to a peak intensity of 250. The spatial distortion due to the nonsquare pixels of the camera has been removed. All subsequent beam images are processed equivalently.

Fig. 4
Fig. 4

Far field energy throughput vs aperture radius plotted using data from (a) an ideal elliptical Gaussian beam and (b) the far field image shown in Fig 3(b). The ideal Gaussian profile was chosen by using elliptical Gaussian parameters that were fitted to the near field data, Fig. 3(a). The apertures that were applied to the far field data were appropriate elliptical apertures whose ellipticities were chosen by using the same elliptical Gaussian fits. The aperture radius plotted in the figure is from the minor elliptical axis.

Fig. 5
Fig. 5

Images of (a) the FFT of Fig. 3(a) assuming a uniform phase, (b) a calculated Gaussian profile based on parameters obtained by performing Gaussian fits in both dimensions to the data of Fig. 3(a), and (c) the FFT of (b) assuming uniform phase.

Fig. 6
Fig. 6

(a) Near and (b) far field images of an aberrated laser beam.

Fig. 7
Fig. 7

Far field energy throughput vs aperture radius plotted using data from (a) an ideal elliptical Gaussian beam and (b) the far field image shown in Fig. 6(b). The details are the same as for Fig. 4.

Fig. 8
Fig. 8

Images of (a) the FFT of Fig. 6(a) assuming a uniform phase, (b) a calculated Gaussian profile based on parameters obtained by performing Gaussian fits in both dimensions to the data of Fig. 6(a), and (c) the FFT of (b) assuming uniform phase.

Equations (4)

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

w ff x = λ MF π w nf x ,
f ( r ) = 1 exp ( 2 r 2 w 2 ) ,
δ x ff = λ Mf δ x nf N ,
I ff ( x , y ) = { 1 N υ = 0 N 1 u = 0 N 1 A nf ( u , υ ) × [ cos 2 π N ( x u + y υ ) i sin 2 π N ( x u + y υ ) ] 1 N 1 N } ,

Metrics