Abstract

We present a simple technique for simultaneous determination of refractive index and thickness of moderately thick plane-parallel transparent glass plates (GPs) using a cyclic path optical configuration (CPOC) setup and a wedge shear plate as lateral shearing interferometer. The CPOC setup is used to simultaneously focus the counterpropagating converging beams at a common point at its hypotenuse arm. The apparent thickness and real thickness of the test GP are determined by observing three retrocollimation positions of the GP surfaces with respect to the common focus point. The RI is obtained by dividing the real thickness with apparent thickness of the GP. Presented in this paper are the results obtained for a test GP with a thickness of 14.983 mm and a RI of 1.515.

© 2012 Optical Society of America

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References

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  1. Y. P. Kumar and S. Chatterjee, “Noncontact thickness measurement of plane-parallel transparent plates with a lateral shearing interferometer,” Opt. Eng. 46, 035602 (2007).
    [CrossRef]
  2. Y. P. Kumar and S. Chatterjee, “Thickness measurement of transparent glass plates using a lateral shearing cyclic path optical configuration setup and polarization phase shifting interferometry,” Appl. Opt. 49, 6552–6557 (2010).
    [CrossRef]
  3. S. Ri and T. Muramatsu, “A simple technique for measuring thickness distribution of transparent plates from a single image by using the sampling moiré method,” Meas. Sci. Technol. 21, 025305 (2010).
    [CrossRef]
  4. C. H. Liu, S. C. Yeh, and H. L. Huang, “Thickness measurement system for transparent plates using dual digital versatile disc (DVD) pickups,” Appl. Opt. 49, 637–643 (2010).
    [CrossRef]
  5. S. Y. El-Zaiat, “Measuring the thickness and refractive index of a thick transparent plate by an unexpanded laser beam,” Opt. Laser Technol. 29, 63–65 (1997).
    [CrossRef]
  6. G. Coppola, P. Ferraro, M. Iodice, and S. De Nicola, “Method for measuring the refractive index and the thickness of transparent plates with a lateral-shearing, wavelength-scanning interferometer,” Appl. Opt. 42, 3882–3887 (2003).
    [CrossRef]
  7. T. Fukano and I. Yamaguchi, “Separation of measurement of the refractive index and the geometrical thickness by use of a wavelength-scanning interferometer with a confocal microscope,” Appl. Opt. 38, 4065–4073 (1999).
    [CrossRef]
  8. S. A. Alexandrov and I. V. Chernyh, “Interference method for determination of the refractive index and thickness,” Opt. Eng. 39, 2480–2486 (2000).
    [CrossRef]
  9. R. Ince and E. Huseyinoglu, “Decoupling refractive index and geometrical thickness from interferometric measurements of a quartz sample using a fourth-order polynomial,” Appl. Opt. 46, 3498–3503 (2007).
    [CrossRef]
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    [CrossRef]
  11. M. Grindel, “Testing collimation using shearing interferometry,” Proc. SPIE 680, 44–47 (1986).
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    [CrossRef]
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    [CrossRef]

2012 (1)

2010 (4)

2007 (2)

Y. P. Kumar and S. Chatterjee, “Noncontact thickness measurement of plane-parallel transparent plates with a lateral shearing interferometer,” Opt. Eng. 46, 035602 (2007).
[CrossRef]

R. Ince and E. Huseyinoglu, “Decoupling refractive index and geometrical thickness from interferometric measurements of a quartz sample using a fourth-order polynomial,” Appl. Opt. 46, 3498–3503 (2007).
[CrossRef]

2003 (1)

2000 (1)

S. A. Alexandrov and I. V. Chernyh, “Interference method for determination of the refractive index and thickness,” Opt. Eng. 39, 2480–2486 (2000).
[CrossRef]

1999 (2)

T. Fukano and I. Yamaguchi, “Separation of measurement of the refractive index and the geometrical thickness by use of a wavelength-scanning interferometer with a confocal microscope,” Appl. Opt. 38, 4065–4073 (1999).
[CrossRef]

P. J. Thomas, R. Mani, and N. Khalil, “Noncontact measurement of etalon spacing using a retroreflection technique,” Rev. Sci. Instrum. 70, 2225–2229 (1999).
[CrossRef]

1997 (1)

S. Y. El-Zaiat, “Measuring the thickness and refractive index of a thick transparent plate by an unexpanded laser beam,” Opt. Laser Technol. 29, 63–65 (1997).
[CrossRef]

1986 (1)

M. Grindel, “Testing collimation using shearing interferometry,” Proc. SPIE 680, 44–47 (1986).

Alexandrov, S. A.

S. A. Alexandrov and I. V. Chernyh, “Interference method for determination of the refractive index and thickness,” Opt. Eng. 39, 2480–2486 (2000).
[CrossRef]

Cha, M.

Chatterjee, S.

Chernyh, I. V.

S. A. Alexandrov and I. V. Chernyh, “Interference method for determination of the refractive index and thickness,” Opt. Eng. 39, 2480–2486 (2000).
[CrossRef]

Choi, H. J.

Coppola, G.

De Nicola, S.

El-Zaiat, S. Y.

S. Y. El-Zaiat, “Measuring the thickness and refractive index of a thick transparent plate by an unexpanded laser beam,” Opt. Laser Technol. 29, 63–65 (1997).
[CrossRef]

Eom, T. B.

Ferraro, P.

Fukano, T.

Grindel, M.

M. Grindel, “Testing collimation using shearing interferometry,” Proc. SPIE 680, 44–47 (1986).

Huang, H. L.

Huseyinoglu, E.

Ince, R.

Iodice, M.

Ju, J. J.

Khalil, N.

P. J. Thomas, R. Mani, and N. Khalil, “Noncontact measurement of etalon spacing using a retroreflection technique,” Rev. Sci. Instrum. 70, 2225–2229 (1999).
[CrossRef]

Kumar, Y. P.

Lim, H. H.

Liu, C. H.

Mani, R.

P. J. Thomas, R. Mani, and N. Khalil, “Noncontact measurement of etalon spacing using a retroreflection technique,” Rev. Sci. Instrum. 70, 2225–2229 (1999).
[CrossRef]

Moon, H. S.

Muramatsu, T.

S. Ri and T. Muramatsu, “A simple technique for measuring thickness distribution of transparent plates from a single image by using the sampling moiré method,” Meas. Sci. Technol. 21, 025305 (2010).
[CrossRef]

Ri, S.

S. Ri and T. Muramatsu, “A simple technique for measuring thickness distribution of transparent plates from a single image by using the sampling moiré method,” Meas. Sci. Technol. 21, 025305 (2010).
[CrossRef]

Thomas, P. J.

P. J. Thomas, R. Mani, and N. Khalil, “Noncontact measurement of etalon spacing using a retroreflection technique,” Rev. Sci. Instrum. 70, 2225–2229 (1999).
[CrossRef]

Yamaguchi, I.

Yeh, S. C.

Appl. Opt. (6)

Meas. Sci. Technol. (1)

S. Ri and T. Muramatsu, “A simple technique for measuring thickness distribution of transparent plates from a single image by using the sampling moiré method,” Meas. Sci. Technol. 21, 025305 (2010).
[CrossRef]

Opt. Eng. (2)

Y. P. Kumar and S. Chatterjee, “Noncontact thickness measurement of plane-parallel transparent plates with a lateral shearing interferometer,” Opt. Eng. 46, 035602 (2007).
[CrossRef]

S. A. Alexandrov and I. V. Chernyh, “Interference method for determination of the refractive index and thickness,” Opt. Eng. 39, 2480–2486 (2000).
[CrossRef]

Opt. Express (1)

Opt. Laser Technol. (1)

S. Y. El-Zaiat, “Measuring the thickness and refractive index of a thick transparent plate by an unexpanded laser beam,” Opt. Laser Technol. 29, 63–65 (1997).
[CrossRef]

Proc. SPIE (1)

M. Grindel, “Testing collimation using shearing interferometry,” Proc. SPIE 680, 44–47 (1986).

Rev. Sci. Instrum. (1)

P. J. Thomas, R. Mani, and N. Khalil, “Noncontact measurement of etalon spacing using a retroreflection technique,” Rev. Sci. Instrum. 70, 2225–2229 (1999).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Schematic of the experimental setup.

Fig. 2.
Fig. 2.

Alignment of the GP surfaces for the three retrocollimation positions for measuring the real and apparent thickness of the GP.

Fig. 3.
Fig. 3.

Illustration to derive the formulation n=tt.

Equations (7)

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

n=tt,
n=sinisinr.
tani=OXt,andtanr=OXt.
tanitanr=tt.
n=tt.
dn=(dndt)2dt2+(dndt)2dt2,
dn=(1t)2dt2+(tt2)2dt2.

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