Abstract

In internal-reflection metrology using prisms, the prism is usually mounted on a rotation/translation stage to enable adjusting angle and location of the laser footprint on the surface. If a visual inspection method is used to find the laser footprint, the task becomes impossible if invisible radiation in the near infrared is employed. In addition, it may be desirable to perform angular scan experiments with a stationary footprint on the surface during scans, or even to automatically probe specific points on an extended prism face for predetermined incidence angles. In this paper, a formulation is developed to determine the required translation along the prism face to allow maintaining the laser footprint stationary under a given rotation. A web-based app developed under the scope of this work demonstrates the applicability of the approach for silica, BK7 and SF2 glasses, in the wavelength range from 500 to 1500 nm and for an arbitrary geometry of the glass prism.

© 2013 Optical Society of America

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References

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  1. P. S. Huang, S. Kiyono, and O. Kamada, “Angle measurement based on the internal reflection effect: a new method,” Appl. Opt. 31, 6047–6055 (1992).
    [CrossRef]
  2. M. A. Karabegov, “Metrological and technical characteristics of total internal reflection refractometers,” Meas. Tech. 47, 1106–1112 (2004).
  3. E. Fontana, “Thickness optimization of metal films for the development of surface-plasmon-based sensors for nonabsorbing media,” Appl. Opt. 45, 7632–7642 (2006).
    [CrossRef]
  4. C. E. H. Berger, T. E. M. Beumer, R. P. H. Kooyman, and J. Greve, “Surface plasmon resonance multisensing,” Anal. Chem. 70, 703–706 (1998).
  5. G. O. Cavalcanti, M. A. de Luna, D. F. da Ponte, S. C. Oliveira, and E. Fontana, “Automated surface plasmon spectrometer for infrared operation,” Proceedings of the XII SBMO, Belo Horizonte, Brazil, 2006, paper 335 (in Portuguese).
  6. G. O. Cavalcanti, M. A. de Luna, and E. Fontana, “Automated reflectometer for surface plasmon resonance studies in the infrared and its application for the characterization of Pd films,” Proceedings of the 2007 SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference (IEEE, 2007), pp. 698–701.
  7. G. B. Arfken, H. J. Weber, and F. E. Harris, Mathematical Methods for Physicists: A Comprehensive Guide, 7th ed. (Academic, 2012).
  8. Wolfram Research, Inc., Mathematica, Version 9.0.1.0, Champaign, IL (2013).
  9. Prisma, Version 1.0, http://www.ufpe.br/fontana/prisma .
  10. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205–1209 (1965).
    [CrossRef]
  11. M. Bass, ed., Handbook of Optics, 2nd ed. (McGraw-Hill, 1995), Vol. II, pp. 33.3–33.101, Chap. 33.
  12. E. Fontana, “Prisma—a virtual prism positioner: a demonstration experiment with an equilateral BK7 prism,” http://youtu.be/H62NmCkHxFk .

2006 (1)

2004 (1)

M. A. Karabegov, “Metrological and technical characteristics of total internal reflection refractometers,” Meas. Tech. 47, 1106–1112 (2004).

1998 (1)

C. E. H. Berger, T. E. M. Beumer, R. P. H. Kooyman, and J. Greve, “Surface plasmon resonance multisensing,” Anal. Chem. 70, 703–706 (1998).

1992 (1)

1965 (1)

Arfken, G. B.

G. B. Arfken, H. J. Weber, and F. E. Harris, Mathematical Methods for Physicists: A Comprehensive Guide, 7th ed. (Academic, 2012).

Berger, C. E. H.

C. E. H. Berger, T. E. M. Beumer, R. P. H. Kooyman, and J. Greve, “Surface plasmon resonance multisensing,” Anal. Chem. 70, 703–706 (1998).

Beumer, T. E. M.

C. E. H. Berger, T. E. M. Beumer, R. P. H. Kooyman, and J. Greve, “Surface plasmon resonance multisensing,” Anal. Chem. 70, 703–706 (1998).

Cavalcanti, G. O.

G. O. Cavalcanti, M. A. de Luna, and E. Fontana, “Automated reflectometer for surface plasmon resonance studies in the infrared and its application for the characterization of Pd films,” Proceedings of the 2007 SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference (IEEE, 2007), pp. 698–701.

G. O. Cavalcanti, M. A. de Luna, D. F. da Ponte, S. C. Oliveira, and E. Fontana, “Automated surface plasmon spectrometer for infrared operation,” Proceedings of the XII SBMO, Belo Horizonte, Brazil, 2006, paper 335 (in Portuguese).

da Ponte, D. F.

G. O. Cavalcanti, M. A. de Luna, D. F. da Ponte, S. C. Oliveira, and E. Fontana, “Automated surface plasmon spectrometer for infrared operation,” Proceedings of the XII SBMO, Belo Horizonte, Brazil, 2006, paper 335 (in Portuguese).

de Luna, M. A.

G. O. Cavalcanti, M. A. de Luna, D. F. da Ponte, S. C. Oliveira, and E. Fontana, “Automated surface plasmon spectrometer for infrared operation,” Proceedings of the XII SBMO, Belo Horizonte, Brazil, 2006, paper 335 (in Portuguese).

G. O. Cavalcanti, M. A. de Luna, and E. Fontana, “Automated reflectometer for surface plasmon resonance studies in the infrared and its application for the characterization of Pd films,” Proceedings of the 2007 SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference (IEEE, 2007), pp. 698–701.

Fontana, E.

E. Fontana, “Thickness optimization of metal films for the development of surface-plasmon-based sensors for nonabsorbing media,” Appl. Opt. 45, 7632–7642 (2006).
[CrossRef]

G. O. Cavalcanti, M. A. de Luna, and E. Fontana, “Automated reflectometer for surface plasmon resonance studies in the infrared and its application for the characterization of Pd films,” Proceedings of the 2007 SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference (IEEE, 2007), pp. 698–701.

G. O. Cavalcanti, M. A. de Luna, D. F. da Ponte, S. C. Oliveira, and E. Fontana, “Automated surface plasmon spectrometer for infrared operation,” Proceedings of the XII SBMO, Belo Horizonte, Brazil, 2006, paper 335 (in Portuguese).

Greve, J.

C. E. H. Berger, T. E. M. Beumer, R. P. H. Kooyman, and J. Greve, “Surface plasmon resonance multisensing,” Anal. Chem. 70, 703–706 (1998).

Harris, F. E.

G. B. Arfken, H. J. Weber, and F. E. Harris, Mathematical Methods for Physicists: A Comprehensive Guide, 7th ed. (Academic, 2012).

Huang, P. S.

Kamada, O.

Karabegov, M. A.

M. A. Karabegov, “Metrological and technical characteristics of total internal reflection refractometers,” Meas. Tech. 47, 1106–1112 (2004).

Kiyono, S.

Kooyman, R. P. H.

C. E. H. Berger, T. E. M. Beumer, R. P. H. Kooyman, and J. Greve, “Surface plasmon resonance multisensing,” Anal. Chem. 70, 703–706 (1998).

Malitson, I. H.

Oliveira, S. C.

G. O. Cavalcanti, M. A. de Luna, D. F. da Ponte, S. C. Oliveira, and E. Fontana, “Automated surface plasmon spectrometer for infrared operation,” Proceedings of the XII SBMO, Belo Horizonte, Brazil, 2006, paper 335 (in Portuguese).

Weber, H. J.

G. B. Arfken, H. J. Weber, and F. E. Harris, Mathematical Methods for Physicists: A Comprehensive Guide, 7th ed. (Academic, 2012).

Anal. Chem. (1)

C. E. H. Berger, T. E. M. Beumer, R. P. H. Kooyman, and J. Greve, “Surface plasmon resonance multisensing,” Anal. Chem. 70, 703–706 (1998).

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

Meas. Tech. (1)

M. A. Karabegov, “Metrological and technical characteristics of total internal reflection refractometers,” Meas. Tech. 47, 1106–1112 (2004).

Other (7)

M. Bass, ed., Handbook of Optics, 2nd ed. (McGraw-Hill, 1995), Vol. II, pp. 33.3–33.101, Chap. 33.

E. Fontana, “Prisma—a virtual prism positioner: a demonstration experiment with an equilateral BK7 prism,” http://youtu.be/H62NmCkHxFk .

G. O. Cavalcanti, M. A. de Luna, D. F. da Ponte, S. C. Oliveira, and E. Fontana, “Automated surface plasmon spectrometer for infrared operation,” Proceedings of the XII SBMO, Belo Horizonte, Brazil, 2006, paper 335 (in Portuguese).

G. O. Cavalcanti, M. A. de Luna, and E. Fontana, “Automated reflectometer for surface plasmon resonance studies in the infrared and its application for the characterization of Pd films,” Proceedings of the 2007 SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference (IEEE, 2007), pp. 698–701.

G. B. Arfken, H. J. Weber, and F. E. Harris, Mathematical Methods for Physicists: A Comprehensive Guide, 7th ed. (Academic, 2012).

Wolfram Research, Inc., Mathematica, Version 9.0.1.0, Champaign, IL (2013).

Prisma, Version 1.0, http://www.ufpe.br/fontana/prisma .

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Figures (4)

Fig. 1.
Fig. 1.

Top view of the proposed setup for positioning the laser footprint along the x direction of the horizontal prism surface.

Fig. 2.
Fig. 2.

Top view of the prism and defining parameters.

Fig. 3.
Fig. 3.

(a) Top view of the prism in the initial position and after a counterclockwise rotation. (b) Final configuration after translation along a direction parallel to side a.

Fig. 4.
Fig. 4.

Graphical interface of the Prisma app.

Equations (33)

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r=acot(α/2)+cot(β/2),
l=acot(α/2)cot(α/2)+cot(β/2)=asin(β/2)cos(α/2)sin[(α+β)/2].
b=asinαsin(α+β),
c=asinβsin(α+β).
X=(xy)T
Ux=(10)T,
Uy=(01)T.
V(ϕ,δ)=R(ϕ)[V(0,0)+δUx],
R(ϕ)=(cosϕsinϕsinϕcosϕ),
[R(ϕ)]1=[R(ϕ)]T=R(ϕ),
R(ϕ1)R(ϕ2)=R(ϕ2)R(ϕ1)=R(ϕ1+ϕ2).
A(0,0)A=lUx+rUy,
B(0,0)B=A+aUx,
C(0,0)C=A+cR(α)Ux,
P(0,0)P=A+(a/2)Ux,
F(0,0)F=P+wUx.
X1=P+t1R(α)Uy,
X2=F(θ,d)+t2R(θθi)Uy,
α+(π/2θi)+(π/2+θr)=π,
θi=α+θr,
sinθr=sinθ/n.
cosθr=1nn2(sinθ)2.
P+t1R(α)Uy=F(θ,d)+t2R(θθi)Uy.
UxTUy=UyTUx=0,
UxTUx=UyTUy=1.
t2=UxTR(α)[PF(θ,d)]UxTR(θθr)Uy.
X3=A(θ,d)+t3R(θα)Ux,
t2=UyTA(α,d)F(α,d)UyTR(αθi)Uy.
t2=(a2+w)UyTR(α)UxUyTR(θr)Uy.
d=w+1UxTR(α+θ)Ux{UxT[R(α)R(α+θ)]P+(a2w)[UyTR(α)Ux][UxTR(θθr)Uy][UyTR(θr)Uy]}.
UxTR(ϕ)Ux=UyTR(ϕ)Uy=cosϕ,
UyTR(ϕ)Ux=UxTR(ϕ)Uy=sinϕ,
d=w+1cos(α+θ){2sin(θ2)[(l+a2)sin(α+θ2)+rcos(α+θ2)](w+a/2)sinαsin(θθr)cosθr}.

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