Abstract

The thickness change of a film is measured optically using self-interference of a single laser beam incident at the edge of the film. Theory suggests that when a half-plane phase shift is applied to a Gaussian laser beam, interference fringes appear in the near and far field, in which position varies with the amount of phase shift. By measuring fringe pattern displacement, we demonstrate detection of thickness changes in chitosan films induced by temperature rises of a few degrees centigrade. With a laser at 543 nm, the minimum detectable thickness change is 0.8 nm in ideal conditions (quarter wave films), corresponding with a phase shift of 0.02 rad, and the minimum detectable film thickness is 30nm. Potential use for surface temperature measurements is discussed.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]

2008

Z. Montiel-González, G. Luna-Bárcenas, and A. Mendoza-Galván, “Thermal behaviour of chitosan and chitin thin films studied by spectroscopic ellipsometry,” Phys. Status Solidi 5, 1434–1437 (2008).
[CrossRef]

2007

M. Katsav and E. Heyman, “Gaussian beam summation representation of a two-dimensional Gaussian beam diffraction by an half plane,” IEEE Trans. Antennas Propag. AP-55, 2247–2257 (2007).
[CrossRef]

2005

2002

O. Köysal, D. Önal, S. Özder, and F. Necati Ecevit, “Thickness measurement of dielectric films by wavelength scanning method,” Opt. Commun. 205, 1–6 (2002).
[CrossRef]

2001

F. S. Ligler, B. M. Lingerfelt, R. P. Price, and P. E. Schoen, “Development of uniform chitosan thin-film layers on silicon chips,” Langmuir 17, 5082–5084 (2001).
[CrossRef]

2000

Y. Laaziz, A. Bennoun, N. Chahboun, A. Outzourhit, and E. L. Ameziane, “Optical characterization of low optical thickness thin films from transmittance and back reflectance measurements,” Thin Solid Films 372, 149–155 (2000).
[CrossRef]

S. Anokhov, A. Khizhnyak, and R. Lymarenko, “Diffraction of optical beams by a half-plane,” Semicond. Phys. Quantum Electron. Optoelectron. 3, 94–101 (2000).

A. Khizhnyak, S. P. Anokhov, R. A. Lymarenko, M. S. Soskin, and M. V. Vasnetsov, “Structure of an edge-dislocation wave originating in plane-wave diffraction by a half-plane,” J. Opt. Soc. Am. A 17, 2199–2207 (2000).
[CrossRef]

1996

C. D. Zuiker, D. M. Gruen, and A. R. Krauss, “In situ laser reflectance interferometry measurement of diamond film growth” J. Appl. Phys. 79, 3541–3547 (1996).
[CrossRef]

1995

P. Hillion, “Diffraction of a Gaussian beam at a perfectly conducting half-screen,” J. Opt. 26, 57–64 (1995).
[CrossRef]

1982

1979

1971

Almazov, A.

Ameziane, E. L.

Y. Laaziz, A. Bennoun, N. Chahboun, A. Outzourhit, and E. L. Ameziane, “Optical characterization of low optical thickness thin films from transmittance and back reflectance measurements,” Thin Solid Films 372, 149–155 (2000).
[CrossRef]

Anokhov, S.

S. Anokhov, A. Khizhnyak, and R. Lymarenko, “Diffraction of optical beams by a half-plane,” Semicond. Phys. Quantum Electron. Optoelectron. 3, 94–101 (2000).

Anokhov, S. P.

Bennoun, A.

Y. Laaziz, A. Bennoun, N. Chahboun, A. Outzourhit, and E. L. Ameziane, “Optical characterization of low optical thickness thin films from transmittance and back reflectance measurements,” Thin Solid Films 372, 149–155 (2000).
[CrossRef]

Bertoni, H. L.

Chahboun, N.

Y. Laaziz, A. Bennoun, N. Chahboun, A. Outzourhit, and E. L. Ameziane, “Optical characterization of low optical thickness thin films from transmittance and back reflectance measurements,” Thin Solid Films 372, 149–155 (2000).
[CrossRef]

Elfstrom, H.

Felsen, L. B.

Fukumitsu, O.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company Publishers, 2004).

Green, A. C.

Gruen, D. M.

C. D. Zuiker, D. M. Gruen, and A. R. Krauss, “In situ laser reflectance interferometry measurement of diamond film growth” J. Appl. Phys. 79, 3541–3547 (1996).
[CrossRef]

Harrick, N. J.

Heyman, E.

M. Katsav and E. Heyman, “Gaussian beam summation representation of a two-dimensional Gaussian beam diffraction by an half plane,” IEEE Trans. Antennas Propag. AP-55, 2247–2257 (2007).
[CrossRef]

Hillion, P.

P. Hillion, “Diffraction of a Gaussian beam at a perfectly conducting half-screen,” J. Opt. 26, 57–64 (1995).
[CrossRef]

Katsav, M.

M. Katsav and E. Heyman, “Gaussian beam summation representation of a two-dimensional Gaussian beam diffraction by an half plane,” IEEE Trans. Antennas Propag. AP-55, 2247–2257 (2007).
[CrossRef]

Khizhnyak, A.

A. Khizhnyak, S. P. Anokhov, R. A. Lymarenko, M. S. Soskin, and M. V. Vasnetsov, “Structure of an edge-dislocation wave originating in plane-wave diffraction by a half-plane,” J. Opt. Soc. Am. A 17, 2199–2207 (2000).
[CrossRef]

S. Anokhov, A. Khizhnyak, and R. Lymarenko, “Diffraction of optical beams by a half-plane,” Semicond. Phys. Quantum Electron. Optoelectron. 3, 94–101 (2000).

Khonina, Svetlana N.

Kotlyar, V. V.

Köysal, O.

O. Köysal, D. Önal, S. Özder, and F. Necati Ecevit, “Thickness measurement of dielectric films by wavelength scanning method,” Opt. Commun. 205, 1–6 (2002).
[CrossRef]

Krauss, A. R.

C. D. Zuiker, D. M. Gruen, and A. R. Krauss, “In situ laser reflectance interferometry measurement of diamond film growth” J. Appl. Phys. 79, 3541–3547 (1996).
[CrossRef]

Laaziz, Y.

Y. Laaziz, A. Bennoun, N. Chahboun, A. Outzourhit, and E. L. Ameziane, “Optical characterization of low optical thickness thin films from transmittance and back reflectance measurements,” Thin Solid Films 372, 149–155 (2000).
[CrossRef]

Ligler, F. S.

F. S. Ligler, B. M. Lingerfelt, R. P. Price, and P. E. Schoen, “Development of uniform chitosan thin-film layers on silicon chips,” Langmuir 17, 5082–5084 (2001).
[CrossRef]

Lingerfelt, B. M.

F. S. Ligler, B. M. Lingerfelt, R. P. Price, and P. E. Schoen, “Development of uniform chitosan thin-film layers on silicon chips,” Langmuir 17, 5082–5084 (2001).
[CrossRef]

Luna-Bárcenas, G.

Z. Montiel-González, G. Luna-Bárcenas, and A. Mendoza-Galván, “Thermal behaviour of chitosan and chitin thin films studied by spectroscopic ellipsometry,” Phys. Status Solidi 5, 1434–1437 (2008).
[CrossRef]

Lymarenko, R.

S. Anokhov, A. Khizhnyak, and R. Lymarenko, “Diffraction of optical beams by a half-plane,” Semicond. Phys. Quantum Electron. Optoelectron. 3, 94–101 (2000).

Lymarenko, R. A.

Mendoza-Galván, A.

Z. Montiel-González, G. Luna-Bárcenas, and A. Mendoza-Galván, “Thermal behaviour of chitosan and chitin thin films studied by spectroscopic ellipsometry,” Phys. Status Solidi 5, 1434–1437 (2008).
[CrossRef]

Montiel-González, Z.

Z. Montiel-González, G. Luna-Bárcenas, and A. Mendoza-Galván, “Thermal behaviour of chitosan and chitin thin films studied by spectroscopic ellipsometry,” Phys. Status Solidi 5, 1434–1437 (2008).
[CrossRef]

Necati Ecevit, F.

O. Köysal, D. Önal, S. Özder, and F. Necati Ecevit, “Thickness measurement of dielectric films by wavelength scanning method,” Opt. Commun. 205, 1–6 (2002).
[CrossRef]

Önal, D.

O. Köysal, D. Önal, S. Özder, and F. Necati Ecevit, “Thickness measurement of dielectric films by wavelength scanning method,” Opt. Commun. 205, 1–6 (2002).
[CrossRef]

Outzourhit, A.

Y. Laaziz, A. Bennoun, N. Chahboun, A. Outzourhit, and E. L. Ameziane, “Optical characterization of low optical thickness thin films from transmittance and back reflectance measurements,” Thin Solid Films 372, 149–155 (2000).
[CrossRef]

Özder, S.

O. Köysal, D. Önal, S. Özder, and F. Necati Ecevit, “Thickness measurement of dielectric films by wavelength scanning method,” Opt. Commun. 205, 1–6 (2002).
[CrossRef]

Price, R. P.

F. S. Ligler, B. M. Lingerfelt, R. P. Price, and P. E. Schoen, “Development of uniform chitosan thin-film layers on silicon chips,” Langmuir 17, 5082–5084 (2001).
[CrossRef]

Saleh, B. A.

B. A. Saleh and C. Teich, Fundamentals of Photonics (Wiley-Interscience, 1991).

Schoen, P. E.

F. S. Ligler, B. M. Lingerfelt, R. P. Price, and P. E. Schoen, “Development of uniform chitosan thin-film layers on silicon chips,” Langmuir 17, 5082–5084 (2001).
[CrossRef]

Soifer, V. A.

Soskin, M. S.

Takenaka, T.

Teich, C.

B. A. Saleh and C. Teich, Fundamentals of Photonics (Wiley-Interscience, 1991).

Turunen, J.

Vasnetsov, M. V.

Zuiker, C. D.

C. D. Zuiker, D. M. Gruen, and A. R. Krauss, “In situ laser reflectance interferometry measurement of diamond film growth” J. Appl. Phys. 79, 3541–3547 (1996).
[CrossRef]

Appl. Opt.

IEEE Trans. Antennas Propag.

M. Katsav and E. Heyman, “Gaussian beam summation representation of a two-dimensional Gaussian beam diffraction by an half plane,” IEEE Trans. Antennas Propag. AP-55, 2247–2257 (2007).
[CrossRef]

J. Appl. Phys.

C. D. Zuiker, D. M. Gruen, and A. R. Krauss, “In situ laser reflectance interferometry measurement of diamond film growth” J. Appl. Phys. 79, 3541–3547 (1996).
[CrossRef]

J. Opt.

P. Hillion, “Diffraction of a Gaussian beam at a perfectly conducting half-screen,” J. Opt. 26, 57–64 (1995).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Langmuir

F. S. Ligler, B. M. Lingerfelt, R. P. Price, and P. E. Schoen, “Development of uniform chitosan thin-film layers on silicon chips,” Langmuir 17, 5082–5084 (2001).
[CrossRef]

Opt. Commun.

O. Köysal, D. Önal, S. Özder, and F. Necati Ecevit, “Thickness measurement of dielectric films by wavelength scanning method,” Opt. Commun. 205, 1–6 (2002).
[CrossRef]

Phys. Status Solidi

Z. Montiel-González, G. Luna-Bárcenas, and A. Mendoza-Galván, “Thermal behaviour of chitosan and chitin thin films studied by spectroscopic ellipsometry,” Phys. Status Solidi 5, 1434–1437 (2008).
[CrossRef]

Semicond. Phys. Quantum Electron. Optoelectron.

S. Anokhov, A. Khizhnyak, and R. Lymarenko, “Diffraction of optical beams by a half-plane,” Semicond. Phys. Quantum Electron. Optoelectron. 3, 94–101 (2000).

Thin Solid Films

Y. Laaziz, A. Bennoun, N. Chahboun, A. Outzourhit, and E. L. Ameziane, “Optical characterization of low optical thickness thin films from transmittance and back reflectance measurements,” Thin Solid Films 372, 149–155 (2000).
[CrossRef]

Other

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company Publishers, 2004).

B. A. Saleh and C. Teich, Fundamentals of Photonics (Wiley-Interscience, 1991).

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Figures (11)

Fig. 1.
Fig. 1.

Gaussian laser beam centered at the interface between a film and a bare substrate, thereby acquiring a half-plane phase shift. The incidence angle is exaggerated for clarity.

Fig. 2.
Fig. 2.

Intensity profile in the near field of a Gaussian beam with a half-plane phase shift. Here α=50 and β=0.03.

Fig. 3.
Fig. 3.

Near-field 2D intensity patterns corresponding with the results of Fig. 2.

Fig. 4.
Fig. 4.

Fringe displacement (normalized to the spacing between two fringes), and fringe contrast ratio with different amount of phase shift.

Fig. 5.
Fig. 5.

Calculated far-field intensity profile of a Gaussian beam with a half-plane phase shift. Intensities are normalized to the maximum intensity.

Fig. 6.
Fig. 6.

Shape of the intensity profiles at various locations in the far field with Δϕ=π.

Fig. 7.
Fig. 7.

Experimental setup. A reflected probe laser beam is analyzed with a camera, and the reference laser is used to ensure the sample does not move during heating.

Fig. 8.
Fig. 8.

Characteristics of the reflected beam are different whether the beam is positioned on a flat location of the sample (substrate or film) or at the edge of the film. (a) On the substrate, (b) at the edge, and (c) on the film.

Fig. 9.
Fig. 9.

Intensity profile along the x direction of the reflected beam centered at the edge of the chitosan film.

Fig. 10.
Fig. 10.

Position of one interference peak (and parabolic fits) as the film is heated. The spacing between neighboring fringes is 0.13 mm.

Fig. 11.
Fig. 11.

Fringe displacement, in units of fringe spacing, as a function of the temperature of a chitosan film.

Equations (6)

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

F(kx,ky)=E(x,y,0)eikxxikyydxdy,
E(x,y,z)=12πF(kx,ky)ei(kxx+kyy+kzz)dkxdky.
kz=±k2kx2ky2
I(x,y,z>0)|F(xλz,yλz)|2.
E(x,y,0)=Eoex2+y2w2+iϕ(x)
ϕ(x)=0ifx<0,ϕ(x)=Δϕifx0.

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