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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 16 — Jun. 1, 2013
  • pp: 3849–3855

Gaussian beam radius measurement with a knife-edge: a polynomial approximation to the inverse error function

Mario González-Cardel, Pedro Arguijo, and Rufino Díaz-Uribe  »View Author Affiliations


Applied Optics, Vol. 52, Issue 16, pp. 3849-3855 (2013)
http://dx.doi.org/10.1364/AO.52.003849


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Abstract

A method for approximating the inverse error function involved in the determination of the radius of a Gaussian beam is proposed. It is based on a polynomial inversion that can be developed to any desired degree, according to an a priori defined error budget. Analytic expressions are obtained and used to determine the radius of a TEMoo He–Ne laser beam from intensity measurements experimentally obtained by using the knife edge method. The error and the interval of validity of the approximation are determined for polynomials of different degrees. The analysis of the theoretical and experimental errors is also presented.

© 2013 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(140.3460) Lasers and laser optics : Lasers
(140.3295) Lasers and laser optics : Laser beam characterization

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: January 25, 2013
Revised Manuscript: April 18, 2013
Manuscript Accepted: April 19, 2013
Published: May 31, 2013

Citation
Mario González-Cardel, Pedro Arguijo, and Rufino Díaz-Uribe, "Gaussian beam radius measurement with a knife-edge: a polynomial approximation to the inverse error function," Appl. Opt. 52, 3849-3855 (2013)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-52-16-3849


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References

  1. P. J. Shayler, “Laser beam distribution in the focal region,” Appl. Opt. 17, 2673–2674 (1978). [CrossRef]
  2. 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). [CrossRef]
  3. M. S. Scholl, “Measured spatial properties of the CW Nd:YAG laser beam,” Appl. Opt. 19, 3655–3659 (1980). [CrossRef]
  4. A. K. Cherri and M. S. Alam, “Accurate measurement of small Gaussian laser beam diameters using various rulings,” Opt. Commun. 223, 255–262 (2003). [CrossRef]
  5. R. L. McCally, “Measurement of Gaussian beam parameters,” Appl. Opt. 23, 2227 (1984). [CrossRef]
  6. A. Rose, Y.-X. Nie, and R. Gupta, “Laser beam profile measurement by photothermal deflection technique,” Appl. Opt. 25, 1738–1741 (1986). [CrossRef]
  7. T. Baba, T. Arai, and A. Ono, “Laser beam profile measurement by a thermographic technique,” Rev. Sci. Instrum. 57, 2739–2742 (1986). [CrossRef]
  8. A. E. Siegman, M. W. Sasnett, and T. F. Johnston, “Choice of clip levels for beam width measurements using knife-edge techniques,” IEEE J. Quantum Electron. 27, 1098–1104 (1991). [CrossRef]
  9. R. Díaz-Uribe, M. Rosete-Aguilar, and R. Ortega-Martínez, “Position sensing of a Gaussian beam with a power meter and knife edge,” Rev. Mex. Fís. 39, 484–492 (1992).
  10. G. Veshapidze, M. L. Trachy, M. H. Shah, and B. D. De Paola, “Reducing the uncertainty in laser beam size measurement with a scanning edge method,” Appl. Opt. 45, 8197–8199 (2006). [CrossRef]
  11. 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]
  12. M. A. C. de Araujo, R. Silva, E. de Lima, D. P. Pereira, and P. C. de Oliveira, “Measurement of Gaussian laser beam radius using the knife-edge technique: improvement on data analysis,” Appl. Opt. 48, 393–396 (2009). [CrossRef]
  13. G. Arfken, Mathematical Methods for Physicists (Academic, 1981).
  14. B. H. Dwight, Tables of Integrals and Other Mathematical Data, 4th ed. (Macmillan, 1961), p. 136.
  15. M. F. González-Cardel, “Determinación de los coeficientes de asfericidad de una superficie óptica rápida (aspheric coefficients determination for a fast optical surface),” M. Sc. dissertation (Facultad de Ciencias, UNAM, México, 2003).
  16. M. F. González-Cardel and R. Díaz-Uribe, “An analysis on the inversion of polynomials,” Rev. Mex. Fís. E 52, 163–171 (2006).
  17. Wolfram Research, “Inverse error function,” ( http://functions.wolfram.com/GammaBetaErf/InverseErf/06/01/01/01/0001/ ).
  18. H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966). [CrossRef]
  19. D. C. Baird, Experimentation: An Introduction to Measurement Theory and Experimental Design (Prentice Hall, 1962).
  20. M. Spivak, Calculus (W. A. Benjamín, 1967), pp. 345–352.

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