Abstract

We demonstrate that it is possible to measure the local geometrical thickness and the refractive index of a transparent pellicle in air by combining the diffractive properties of a Gaussian beam with the analytical equations of the light that propagates through a thin layer. We show that our measurement technique is immune to inherent piston-like vibrations present in the pellicle. As our measurements are based on characterizing properly the Gaussian beam in a plane of detection, a homodyne technique for this purpose is devised and described. The feasibility of our proposal is confirmed by measuring local geometrical thicknesses and the refractive index of a commercially available stretch film.

© 2014 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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2009

2007

2006

2000

M. Cywiak, J. Murakowski, and G. Wade, “Beam blocking method for optical characterization of surfaces,” Int. J. Imaging Syst. Technol. 11, 164–169 (2000).
[CrossRef]

1996

1989

Azzam, R.

Castro, D.

Ciprian, D.

Cui, Y.

Cywiak, M.

M. Cywiak, A. Morales, J. Flores, and M. Servín, “Fresnel-Gaussian shape invariant for optical ray tracing,” Opt. Express 17, 10564–10572 (2009).
[CrossRef]

M. Cywiak, J. Murakowski, and G. Wade, “Beam blocking method for optical characterization of surfaces,” Int. J. Imaging Syst. Technol. 11, 164–169 (2000).
[CrossRef]

Flores, J.

Hecht, E.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, 1987), pp. 426–431.

Hlubina, P.

Jenkins, F. A.

F. A. Jenkins and H. E. White, “Interference involving multiple reflections,” in Fundamentals of Optics, 3rd ed. (McGraw-Hill, 1957), Chap. 14, pp. 260–264.

Jian, H.

Lee, C.

Lesnák, M.

Lin, J.

Lunácek, J.

Morales, A.

Murakowski, J.

M. Cywiak, J. Murakowski, and G. Wade, “Beam blocking method for optical characterization of surfaces,” Int. J. Imaging Syst. Technol. 11, 164–169 (2000).
[CrossRef]

Ramsteiner, M.

Servín, M.

Vargas, W.

Wade, G.

M. Cywiak, J. Murakowski, and G. Wade, “Beam blocking method for optical characterization of surfaces,” Int. J. Imaging Syst. Technol. 11, 164–169 (2000).
[CrossRef]

Wagner, J.

Wang, C.

White, H. E.

F. A. Jenkins and H. E. White, “Interference involving multiple reflections,” in Fundamentals of Optics, 3rd ed. (McGraw-Hill, 1957), Chap. 14, pp. 260–264.

Wild, C.

Appl. Opt.

Int. J. Imaging Syst. Technol.

M. Cywiak, J. Murakowski, and G. Wade, “Beam blocking method for optical characterization of surfaces,” Int. J. Imaging Syst. Technol. 11, 164–169 (2000).
[CrossRef]

Opt. Express

Other

www.filmetrics.com .

E. Hecht, Optics, 2nd ed. (Addison-Wesley, 1987), pp. 426–431.

F. A. Jenkins and H. E. White, “Interference involving multiple reflections,” in Fundamentals of Optics, 3rd ed. (McGraw-Hill, 1957), Chap. 14, pp. 260–264.

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Figures (5)

Fig. 1.
Fig. 1.

Focusing of a Gaussian laser beam through a transparent pellicle in air by an ideal focusing lens. zT is fixed and chosen to attain the best focusing conditions as described in the text. The dashed rectangle represents the sample.

Fig. 2.
Fig. 2.

Homodyne scanning system for determination of Gaussian semi-widths.

Fig. 3.
Fig. 3.

Gaussian intensity distributions obtained experimentally without the sample (solid line) and with the sample included (dashed line).

Fig. 4.
Fig. 4.

Plot of the theoretical relative power transmitted by the sample as a function of its geometrical thickness obtained with Eq. (8) (oscillating plot). The horizontal line corresponds to the transmitted power measured experimentally. The circles represent the intersection of both plots (the allowable powers).

Fig. 5.
Fig. 5.

Plots of the relative transmitted powers as a function of the geometrical thickness for two neighbor spots obtained with Eq. (8) in a similar way as Fig. 4. The horizontal lines correspond to the relative powers transmitted by the sample, which are measured experimentally as described in the text. Circles correspond to allowable values for the first measurement, squares for the second measurement.

Tables (1)

Tables Icon

Table 1. Values Obtained for the Refractive Index and Geometrical Thickness for Each Combination of the Three Measurements on the Stretch Film

Equations (16)

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zT=z1+t+z2,
Ψ(x1,y1)=Aexp(x12+y12r2)exp[iβ(x12+y12)].
rA=rπ[βλzT+π]2+λ2r4zT2.
rB=rπ[βλ(z1+tn+z2)+π]2+λ2r4(z1+tn+z2)2.
z1+tn+z2=z1+tn+z2=z1+tn+z2=.
tn1n=tn1n=tn1n=.
F=tn1n.
P=(4n0n1M)2,
M=|1110n0n1n100exp(i2πλn0n1t)exp(i2πλn0n1t)10n1exp(i2πλn0n1t)n1exp(i2πλn0n1t)n0|.
P=Aαexp(2x2r02)dx.
α=x0+δ0cos(2πft),
Plinear(x0)=Bexp(2x02r02)cos(2πft),
Prel=PfilmPair.
F=tn1n,
F=tn1n,
FF=tt.

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