Abstract

The absolute optical thickness of a transparent plate 6-mm thick and 10 mm in diameter was measured by the excess fraction method and a wavelength-tuning Fizeau interferometer. The optical thickness, defined by the group refractive index at the central wavelength, was measured by wavelength scanning. The optical thickness deviation, defined by the ordinary refractive index, was measured using the phase-shifting technique. Two kinds of optical thicknesses, measured by discrete Fourier analysis and the phase-shifting technique, were synthesized to obtain the optical thickness with respect to the ordinary refractive index using Sellmeier equation and least-square fitting.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]

2014 (1)

2013 (1)

Y. Kim, K. Hibino, N. Sugita, and M. Mitsuishi, “Optical thickness measurement of mask blank glass plate by the excess fraction method using wavelength-tuning interferometer,” Opt. Lasers Eng. 51(10), 1173–1178 (2013).
[Crossref]

2011 (3)

2010 (2)

2008 (1)

2004 (2)

2003 (2)

2000 (1)

1999 (1)

1998 (1)

1996 (1)

1981 (1)

1978 (1)

F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66(1), 51–83 (1978).
[Crossref]

Bitou, Y.

Burke, J.

Cha, M.

Chang, W. Y.

Chen, Y. L.

Cheng, H. C.

Choi, H. J.

Coppola, G.

de Groot, P.

De Nicola, S.

Deck, L. L.

Eom, T. B.

Fairman, P. S.

Falaggis, K.

Ferraro, P.

Fukano, T.

Hanayama, R.

Harris, F. J.

F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66(1), 51–83 (1978).
[Crossref]

Haruna, M.

Hashimoto, M.

Hibino, K.

Hsieh, H. C.

Iodice, M.

Ju, J. J.

Kim, M. J.

Kim, S.

Kim, Y.

Y. Kim, K. Hibino, R. Hanayama, N. Sugita, and M. Mitsuishi, “Multiple-surface interferometry of highly reflective wafer by wavelength tuning,” Opt. Express 22(18), 21145–21156 (2014).
[Crossref] [PubMed]

Y. Kim, K. Hibino, N. Sugita, and M. Mitsuishi, “Optical thickness measurement of mask blank glass plate by the excess fraction method using wavelength-tuning interferometer,” Opt. Lasers Eng. 51(10), 1173–1178 (2013).
[Crossref]

Lee, B. H.

Lim, H. H.

Littman, M. G.

Liu, K.

Liu, Y. C.

Maruyama, H.

Mitsuishi, M.

Mitsuyama, T.

Moon, H. S.

Na, J.

Ohmi, M.

Oreb, B. F.

Su, D. C.

Sugita, N.

Y. Kim, K. Hibino, R. Hanayama, N. Sugita, and M. Mitsuishi, “Multiple-surface interferometry of highly reflective wafer by wavelength tuning,” Opt. Express 22(18), 21145–21156 (2014).
[Crossref] [PubMed]

Y. Kim, K. Hibino, N. Sugita, and M. Mitsuishi, “Optical thickness measurement of mask blank glass plate by the excess fraction method using wavelength-tuning interferometer,” Opt. Lasers Eng. 51(10), 1173–1178 (2013).
[Crossref]

Tajiri, H.

Takatsuji, T.

Tani, Y.

Towers, C. E.

Towers, D. P.

Warisawa, S.

Wu, W. T.

Yamaguchi, I.

Appl. Opt. (9)

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(19), 4065–4073 (1999).
[Crossref] [PubMed]

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-shear, wavelength-scanning interferometer,” Appl. Opt. 42(19), 3882–3887 (2003).
[Crossref] [PubMed]

K. Hibino, B. F. Oreb, P. S. Fairman, and J. Burke, “Simultaneous measurement of surface shape and variation in optical thickness of a transparent parallel plate in wavelength-scanning Fizeau interferometer,” Appl. Opt. 43(6), 1241–1249 (2004).
[Crossref] [PubMed]

H. C. Cheng and Y. C. Liu, “Simultaneous measurement of group refractive index and thickness of optical samples using optical coherence tomography,” Appl. Opt. 49(5), 790–797 (2010).
[Crossref] [PubMed]

W. T. Wu, H. C. Hsieh, W. Y. Chang, Y. L. Chen, and D. C. Su, “High-accuracy thickness measurement of a transparent plate with the heterodyne central fringe identification technique,” Appl. Opt. 50(21), 4011–4016 (2011).
[Crossref] [PubMed]

P. de Groot, “Measurement of transparent plates with wavelength-tuned phase-shifting interferometry,” Appl. Opt. 39(16), 2658–2663 (2000).
[Crossref] [PubMed]

L. L. Deck, “Fourier-transform phase-shifting interferometry,” Appl. Opt. 42(13), 2354–2365 (2003).
[Crossref] [PubMed]

K. Falaggis, D. P. Towers, and C. E. Towers, “Method of excess fractions with application to absolute distance metrology: theoretical analysis,” Appl. Opt. 50(28), 5484–5498 (2011).
[Crossref] [PubMed]

K. Hibino, Y. Tani, Y. Bitou, T. Takatsuji, S. Warisawa, and M. Mitsuishi, “Discontinuous surface measurement by wavelength-tuning interferometry with the excess fraction method correcting scanning nonlinearity,” Appl. Opt. 50(6), 962–969 (2011).
[Crossref] [PubMed]

Opt. Express (4)

Opt. Lasers Eng. (1)

Y. Kim, K. Hibino, N. Sugita, and M. Mitsuishi, “Optical thickness measurement of mask blank glass plate by the excess fraction method using wavelength-tuning interferometer,” Opt. Lasers Eng. 51(10), 1173–1178 (2013).
[Crossref]

Opt. Lett. (3)

Proc. IEEE (1)

F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66(1), 51–83 (1978).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Wavelength-tuning Fizeau interferometer for measuring the absolute optical thickness of a transparent plate. PBS denotes the polarization beam splitter; QWP is the quarter-wave plate; HWP is the half-wave plate. The thickness of the sample and the air gap distance are T and L, respectively.
Fig. 2
Fig. 2 Temporal variations in the source wavelength scanned by a piezoelectric transducer (fine tuning) and a picomotor (coarse tuning) attached to the end mirror of the external cavity of the laser diode (not-to-scale principle sketch).
Fig. 3
Fig. 3 Summary of the measurement procedure.
Fig. 4
Fig. 4 (a) Laboratory photo of transparent plate in wavelength-tuning Fizeau interferometer, (b) raw interferogram at wavelength of 632.8 nm.
Fig. 5
Fig. 5 (a) Fraction p1, (b) absolute optical thickness distribution at initial wavelength.
Fig. 6
Fig. 6 (a) Final absolute optical thickness distribution at initial wavelength, (b) interference order at initial wavelength.

Equations (17)

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n 1,2 T= λ 1,2 2 ( N 1,2 + p 1,2 ),
n 1 + n 2 2 ( 1 λ 1 + λ 2 n 1 + n 2 n 2 n 1 λ 2 λ 1 )T= λ 1 λ 2 2( λ 2 λ 1 ) ( N 1 N 2 + p 1 p 2 ).
n g ( λ c )= n 1 + n 2 2 ( 1 λ 1 + λ 2 n 1 + n 2 n 2 n 1 λ 2 λ 1 )n( 1 λ n dn dλ ).
[ n g ( λ c )T ] meas = λ s 2 ( N 1 N 2 + p 1 p 2 ).
n 2 1= 0.6961663 λ 2 λ 2 0.0684043 2 + 0.4079426 λ 2 λ 2 0.1162414 2 + 0.8974794 λ 2 λ 2 9.896161 2 .
( n 1 T ) meas = n 1 n g ( n g T ) meas .
p 1 = 1 2π arctan r=1 77 w r I r sin πr 10 r=1 77 w r I r cos πr 10 ,
w r =[ 1 6 r( r+1 )( r+2 ) ]( 1r20 ), w r =[ 5340+ 1 2 | r39 |( | r39 | 2 40| r39 |1 ) ]( 21r57 ), w r =[ 1 6 ( 80r )( 79r )( 78r ) ]( 58r77 ).
F( f )= { [ j=1 593 I j h( j )cos2πf( j1 ) ]/593 } 2 + { [ j=1 593 I j h( j )sin2πf( j1 ) ]/593 } 2 ,
h( j )= 2 297 cos 2 j297 593 .
M=round( N 1 N 2 + p 1 p 2 )
( n 1 T ) dev = λ 1 4π unwrap[ p 1 ( x,y ) ],
n 1 T 0 = λ 1 2 A 1 .
1 P i=1 P { [ ( n 1 T ) meas ] i [ ( n 1 T ) dev ] i n 1 T 0 } 2 =min,
n 1 T= n 1 T 0 + ( n 1 T ) dev .
N 1 =round( 2 n 1 T λ 1 p 1 ),
( n 1 T ) n 1 T = λ 1 λ 1 + ( N 1 + p 1 ) N 1 + p 1 λ 1 λ 1 + p 1 N 1 .

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