Abstract

We propose and demonstrate the novel method of refractive index (RI) measurement for each layer of multilayered samples, which is based on numerical refocusing in full field optical coherence tomography (FF-OCT). The en-face FF-OCT image on an inner layer boundary of a multilayered sample is unintentionally blurred or defocused due to the RI of the sample itself, but can be numerically refocused. The refocusing is performed by numerically shifting the image sensor plane of the system, in general. However, by calculating the corresponding sample shift and then compared it with the actual sample shifting distance, we could extract the average RI of the layer between any two layer boundaries within the multilayered sample. In addition, the thickness of that particular layer could be derived at the same time. For the idea proof, several samples were prepared by stacking, for each sample, two transparent plates with a gap in between. While changing the material of the plate and filling the gap with oil, the RIs of the plate and the oil were measured. For oils of various RIs, from 1.2977 to 1.3857, the measured RIs were well matched with the reported ones within 0.205%. Moreover, even with a stack of various and multiple plates in front of the same oil layer, the oil RI and the physical thickness of the oil layer were extracted with average errors of only 0.065% and 0.990%, respectively.

© 2013 Optical Society of America

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References

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    [CrossRef]
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2013

2012

2011

2009

J. Na, H. Y. Choi, E. S. Choi, C. S. Lee, and B. H. Lee, “Self-referenced spectral interferometry for simultaneous measurements of thickness and refractive index,” Appl. Opt.48(13), 2461–2467 (2009).
[CrossRef] [PubMed]

S. Labiau, G. David, S. Gigan, and A. C. Boccara, “Defocus test and defocus correction in full-field optical coherence tomography,” Opt. Lett.34(10), 1576–1578 (2009).
[CrossRef] [PubMed]

K. Lee, S. Y. Ryu, Y. K. Kwak, S. Kim, and Y. W. Lee, “Separation algorithm for a 2D refractive index distribution and thickness profile of a phase object by laser diode-based multiwavelength interferometry,” Rev. Sci. Instrum.80(5), 053114 (2009).
[CrossRef] [PubMed]

J. Na, W. J. Choi, H. Y. Choi, S. Y. Ryu, E. S. Choi, and B. H. Lee, “Thickness and refractive index measurements by full-field optical coherence tomography,” IEEE Sens. J.9(12), 1996–1997 (2009).
[CrossRef]

2008

2007

W. J. Choi, J. Na, S. Y. Ryu, B. H. Lee, and D.-S. Ko, “Realization of 3-D topographic and tomographic images with ultrahigh-resolution full-field optical coherence tomography,” J. Opt. Soc. Kor.11(1), 18–25 (2007).
[CrossRef]

2006

2003

2001

2000

D. F. Murphy and D. A. Flavin, “Dispersion-insensitive measurement of thickness and group refractive index by low-coherence interferometry,” Appl. Opt.39(25), 4607–4615 (2000).
[CrossRef] [PubMed]

M. Ohmi, K. Yoden, Y. Ohnishi, and M. Haruna, “Optical tomography along the geometrical thickness by combination of coherence-gate and confocal imagings,” OFS14, 288–291 (2000).

H. Maruyama, T. Mitsuyama, M. Ohmi, and M. Haruna, “Simultaneous Measurement of Refractive Index and Thickness by Low Coherence Interferometry Considering Chromatic Dispersion of Index,” Opt. Rev.7(5), 468–472 (2000).
[CrossRef]

1999

1998

1996

1995

1992

W. V. Sorin and D. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photon. Technol. Lett.4(1), 105–107 (1992).
[CrossRef]

Ahmed, M.

Alexandrov, S. A.

Armstrong, J. J.

Aslam Zia, M.

Barry, S.

Ben Arous, J.

Binding, J.

Boccara, A. C.

Boccara, C.

Bouma, B. E.

Bourdieu, L.

Brezinski, M. E.

Cable, A. E.

Callens, N.

Chan, K. K. H.

Chen, L.

Chen, W.

Choi, E. S.

J. Na, H. Y. Choi, E. S. Choi, C. S. Lee, and B. H. Lee, “Self-referenced spectral interferometry for simultaneous measurements of thickness and refractive index,” Appl. Opt.48(13), 2461–2467 (2009).
[CrossRef] [PubMed]

J. Na, W. J. Choi, H. Y. Choi, S. Y. Ryu, E. S. Choi, and B. H. Lee, “Thickness and refractive index measurements by full-field optical coherence tomography,” IEEE Sens. J.9(12), 1996–1997 (2009).
[CrossRef]

Choi, H. Y.

J. Na, W. J. Choi, H. Y. Choi, S. Y. Ryu, E. S. Choi, and B. H. Lee, “Thickness and refractive index measurements by full-field optical coherence tomography,” IEEE Sens. J.9(12), 1996–1997 (2009).
[CrossRef]

J. Na, H. Y. Choi, E. S. Choi, C. S. Lee, and B. H. Lee, “Self-referenced spectral interferometry for simultaneous measurements of thickness and refractive index,” Appl. Opt.48(13), 2461–2467 (2009).
[CrossRef] [PubMed]

Choi, W. J.

G. Min, J. W. Kim, W. J. Choi, and B. H. Lee, “Numerical correction of distorted images in full-field optical coherence tomography,” Meas. Sci. Technol.23(3), 035403 (2012).
[CrossRef]

J. Na, W. J. Choi, H. Y. Choi, S. Y. Ryu, E. S. Choi, and B. H. Lee, “Thickness and refractive index measurements by full-field optical coherence tomography,” IEEE Sens. J.9(12), 1996–1997 (2009).
[CrossRef]

W. J. Choi, J. Na, S. Y. Ryu, B. H. Lee, and D.-S. Ko, “Realization of 3-D topographic and tomographic images with ultrahigh-resolution full-field optical coherence tomography,” J. Opt. Soc. Kor.11(1), 18–25 (2007).
[CrossRef]

David, G.

Dubois, F.

Flavin, D. A.

Fujimoto, J. G.

Fukano, T.

Gigan, S.

Gray, D. F.

W. V. Sorin and D. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photon. Technol. Lett.4(1), 105–107 (1992).
[CrossRef]

Guo, X.

Hao, J.

Haruna, M.

M. Ohmi, K. Yoden, Y. Ohnishi, and M. Haruna, “Optical tomography along the geometrical thickness by combination of coherence-gate and confocal imagings,” OFS14, 288–291 (2000).

H. Maruyama, T. Mitsuyama, M. Ohmi, and M. Haruna, “Simultaneous Measurement of Refractive Index and Thickness by Low Coherence Interferometry Considering Chromatic Dispersion of Index,” Opt. Rev.7(5), 468–472 (2000).
[CrossRef]

M. Haruna, M. Ohmi, T. Mitsuyama, H. Tajiri, H. Maruyama, and M. Hashimoto, “Simultaneous measurement of the phase and group indices and the thickness of transparent plates by low-coherence interferometry,” Opt. Lett.23(12), 966–968 (1998).
[CrossRef] [PubMed]

Hashimoto, M.

Hee, M. R.

Hillman, T. R.

Hussain, B.

Iqbal, M.

Jiang, J. Y.

Kato, J.

Kim, J. W.

G. Min, J. W. Kim, W. J. Choi, and B. H. Lee, “Numerical correction of distorted images in full-field optical coherence tomography,” Meas. Sci. Technol.23(3), 035403 (2012).
[CrossRef]

Kim, M. J.

Kim, S.

K. Lee, S. Y. Ryu, Y. K. Kwak, S. Kim, and Y. W. Lee, “Separation algorithm for a 2D refractive index distribution and thickness profile of a phase object by laser diode-based multiwavelength interferometry,” Rev. Sci. Instrum.80(5), 053114 (2009).
[CrossRef] [PubMed]

S. Kim, J. Na, M. J. Kim, and B. H. Lee, “Simultaneous measurement of refractive index and thickness by combining low-coherence interferometry and confocal optics,” Opt. Express16(8), 5516–5526 (2008).
[CrossRef] [PubMed]

Ko, D.-S.

W. J. Choi, J. Na, S. Y. Ryu, B. H. Lee, and D.-S. Ko, “Realization of 3-D topographic and tomographic images with ultrahigh-resolution full-field optical coherence tomography,” J. Opt. Soc. Kor.11(1), 18–25 (2007).
[CrossRef]

Kwak, Y. K.

K. Lee, S. Y. Ryu, Y. K. Kwak, S. Kim, and Y. W. Lee, “Separation algorithm for a 2D refractive index distribution and thickness profile of a phase object by laser diode-based multiwavelength interferometry,” Rev. Sci. Instrum.80(5), 053114 (2009).
[CrossRef] [PubMed]

Labiau, S.

Lai, T.

Lee, B. H.

G. Min, J. W. Kim, W. J. Choi, and B. H. Lee, “Numerical correction of distorted images in full-field optical coherence tomography,” Meas. Sci. Technol.23(3), 035403 (2012).
[CrossRef]

J. Na, H. Y. Choi, E. S. Choi, C. S. Lee, and B. H. Lee, “Self-referenced spectral interferometry for simultaneous measurements of thickness and refractive index,” Appl. Opt.48(13), 2461–2467 (2009).
[CrossRef] [PubMed]

J. Na, W. J. Choi, H. Y. Choi, S. Y. Ryu, E. S. Choi, and B. H. Lee, “Thickness and refractive index measurements by full-field optical coherence tomography,” IEEE Sens. J.9(12), 1996–1997 (2009).
[CrossRef]

S. Kim, J. Na, M. J. Kim, and B. H. Lee, “Simultaneous measurement of refractive index and thickness by combining low-coherence interferometry and confocal optics,” Opt. Express16(8), 5516–5526 (2008).
[CrossRef] [PubMed]

W. J. Choi, J. Na, S. Y. Ryu, B. H. Lee, and D.-S. Ko, “Realization of 3-D topographic and tomographic images with ultrahigh-resolution full-field optical coherence tomography,” J. Opt. Soc. Kor.11(1), 18–25 (2007).
[CrossRef]

Lee, C. S.

Lee, K.

K. Lee, S. Y. Ryu, Y. K. Kwak, S. Kim, and Y. W. Lee, “Separation algorithm for a 2D refractive index distribution and thickness profile of a phase object by laser diode-based multiwavelength interferometry,” Rev. Sci. Instrum.80(5), 053114 (2009).
[CrossRef] [PubMed]

Lee, Y. W.

K. Lee, S. Y. Ryu, Y. K. Kwak, S. Kim, and Y. W. Lee, “Separation algorithm for a 2D refractive index distribution and thickness profile of a phase object by laser diode-based multiwavelength interferometry,” Rev. Sci. Instrum.80(5), 053114 (2009).
[CrossRef] [PubMed]

Léger, J.-F.

Long, X.

Maruyama, H.

H. Maruyama, T. Mitsuyama, M. Ohmi, and M. Haruna, “Simultaneous Measurement of Refractive Index and Thickness by Low Coherence Interferometry Considering Chromatic Dispersion of Index,” Opt. Rev.7(5), 468–472 (2000).
[CrossRef]

M. Haruna, M. Ohmi, T. Mitsuyama, H. Tajiri, H. Maruyama, and M. Hashimoto, “Simultaneous measurement of the phase and group indices and the thickness of transparent plates by low-coherence interferometry,” Opt. Lett.23(12), 966–968 (1998).
[CrossRef] [PubMed]

Min, G.

G. Min, J. W. Kim, W. J. Choi, and B. H. Lee, “Numerical correction of distorted images in full-field optical coherence tomography,” Meas. Sci. Technol.23(3), 035403 (2012).
[CrossRef]

Mitsuyama, T.

H. Maruyama, T. Mitsuyama, M. Ohmi, and M. Haruna, “Simultaneous Measurement of Refractive Index and Thickness by Low Coherence Interferometry Considering Chromatic Dispersion of Index,” Opt. Rev.7(5), 468–472 (2000).
[CrossRef]

M. Haruna, M. Ohmi, T. Mitsuyama, H. Tajiri, H. Maruyama, and M. Hashimoto, “Simultaneous measurement of the phase and group indices and the thickness of transparent plates by low-coherence interferometry,” Opt. Lett.23(12), 966–968 (1998).
[CrossRef] [PubMed]

Mizuno, J.

Murphy, D. F.

Na, J.

J. Na, W. J. Choi, H. Y. Choi, S. Y. Ryu, E. S. Choi, and B. H. Lee, “Thickness and refractive index measurements by full-field optical coherence tomography,” IEEE Sens. J.9(12), 1996–1997 (2009).
[CrossRef]

J. Na, H. Y. Choi, E. S. Choi, C. S. Lee, and B. H. Lee, “Self-referenced spectral interferometry for simultaneous measurements of thickness and refractive index,” Appl. Opt.48(13), 2461–2467 (2009).
[CrossRef] [PubMed]

S. Kim, J. Na, M. J. Kim, and B. H. Lee, “Simultaneous measurement of refractive index and thickness by combining low-coherence interferometry and confocal optics,” Opt. Express16(8), 5516–5526 (2008).
[CrossRef] [PubMed]

W. J. Choi, J. Na, S. Y. Ryu, B. H. Lee, and D.-S. Ko, “Realization of 3-D topographic and tomographic images with ultrahigh-resolution full-field optical coherence tomography,” J. Opt. Soc. Kor.11(1), 18–25 (2007).
[CrossRef]

Nawaz, M.

Ohmi, M.

M. Ohmi, K. Yoden, Y. Ohnishi, and M. Haruna, “Optical tomography along the geometrical thickness by combination of coherence-gate and confocal imagings,” OFS14, 288–291 (2000).

H. Maruyama, T. Mitsuyama, M. Ohmi, and M. Haruna, “Simultaneous Measurement of Refractive Index and Thickness by Low Coherence Interferometry Considering Chromatic Dispersion of Index,” Opt. Rev.7(5), 468–472 (2000).
[CrossRef]

M. Haruna, M. Ohmi, T. Mitsuyama, H. Tajiri, H. Maruyama, and M. Hashimoto, “Simultaneous measurement of the phase and group indices and the thickness of transparent plates by low-coherence interferometry,” Opt. Lett.23(12), 966–968 (1998).
[CrossRef] [PubMed]

Ohnishi, Y.

M. Ohmi, K. Yoden, Y. Ohnishi, and M. Haruna, “Optical tomography along the geometrical thickness by combination of coherence-gate and confocal imagings,” OFS14, 288–291 (2000).

Ohta, S.

Radhakrishnan, H.

Razzaq, M.

Ryu, S. Y.

K. Lee, S. Y. Ryu, Y. K. Kwak, S. Kim, and Y. W. Lee, “Separation algorithm for a 2D refractive index distribution and thickness profile of a phase object by laser diode-based multiwavelength interferometry,” Rev. Sci. Instrum.80(5), 053114 (2009).
[CrossRef] [PubMed]

J. Na, W. J. Choi, H. Y. Choi, S. Y. Ryu, E. S. Choi, and B. H. Lee, “Thickness and refractive index measurements by full-field optical coherence tomography,” IEEE Sens. J.9(12), 1996–1997 (2009).
[CrossRef]

W. J. Choi, J. Na, S. Y. Ryu, B. H. Lee, and D.-S. Ko, “Realization of 3-D topographic and tomographic images with ultrahigh-resolution full-field optical coherence tomography,” J. Opt. Soc. Kor.11(1), 18–25 (2007).
[CrossRef]

Saleem, M.

Sampson, D. D.

Schockaert, C.

Silva, K. K.

Sorin, W. V.

W. V. Sorin and D. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photon. Technol. Lett.4(1), 105–107 (1992).
[CrossRef]

Southern, J. F.

Srinivasan, V. J.

Tajiri, H.

Tang, S.

Tearney, G. J.

Tong, Q.-B.

Q.-B. Tong, “Accurate measurement method of the thickness of a quartz pendulous reed by combining polarized reflectance and vision image,” J. Russ. Laser Res.32(6), 537–546 (2011).
[CrossRef]

Tsuzuki, T.

Yamaguchi, I.

Yoden, K.

M. Ohmi, K. Yoden, Y. Ohnishi, and M. Haruna, “Optical tomography along the geometrical thickness by combination of coherence-gate and confocal imagings,” OFS14, 288–291 (2000).

Yourassowsky, C.

Zhang, S.

Zhou, Y.

Zvyagin, A. V.

Appl. Opt.

Biomed. Opt. Express

IEEE Photon. Technol. Lett.

W. V. Sorin and D. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photon. Technol. Lett.4(1), 105–107 (1992).
[CrossRef]

IEEE Sens. J.

J. Na, W. J. Choi, H. Y. Choi, S. Y. Ryu, E. S. Choi, and B. H. Lee, “Thickness and refractive index measurements by full-field optical coherence tomography,” IEEE Sens. J.9(12), 1996–1997 (2009).
[CrossRef]

J. Opt. Soc. Kor.

W. J. Choi, J. Na, S. Y. Ryu, B. H. Lee, and D.-S. Ko, “Realization of 3-D topographic and tomographic images with ultrahigh-resolution full-field optical coherence tomography,” J. Opt. Soc. Kor.11(1), 18–25 (2007).
[CrossRef]

J. Russ. Laser Res.

Q.-B. Tong, “Accurate measurement method of the thickness of a quartz pendulous reed by combining polarized reflectance and vision image,” J. Russ. Laser Res.32(6), 537–546 (2011).
[CrossRef]

Meas. Sci. Technol.

G. Min, J. W. Kim, W. J. Choi, and B. H. Lee, “Numerical correction of distorted images in full-field optical coherence tomography,” Meas. Sci. Technol.23(3), 035403 (2012).
[CrossRef]

OFS

M. Ohmi, K. Yoden, Y. Ohnishi, and M. Haruna, “Optical tomography along the geometrical thickness by combination of coherence-gate and confocal imagings,” OFS14, 288–291 (2000).

Opt. Express

Opt. Lett.

Opt. Rev.

H. Maruyama, T. Mitsuyama, M. Ohmi, and M. Haruna, “Simultaneous Measurement of Refractive Index and Thickness by Low Coherence Interferometry Considering Chromatic Dispersion of Index,” Opt. Rev.7(5), 468–472 (2000).
[CrossRef]

Rev. Sci. Instrum.

K. Lee, S. Y. Ryu, Y. K. Kwak, S. Kim, and Y. W. Lee, “Separation algorithm for a 2D refractive index distribution and thickness profile of a phase object by laser diode-based multiwavelength interferometry,” Rev. Sci. Instrum.80(5), 053114 (2009).
[CrossRef] [PubMed]

Other

E. Hecht, Optics (Addison Wesley Longman, 2002), Chap. 5.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, 2000), Chap. 2.

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Figures (5)

Fig. 1
Fig. 1

Image coordinates in the FF-OCT system and the ray tracing for the cases of n0 = n1 = n2 (dashed line), n0n1n2 (black and red solid line), and n0n1 = n2 (green solid line). The image coordinates of (a) the initial sample position, (b) when the sample is moved by ds, and (c) when the sample moved further to ds1 + ds2. L1 and L2: lenses, FP1, FP1′ and FP2: focal planes, IP1 and IP2: image planes, CP1 and CP2: CCD positions for imaging of IP1 and IP2, respectively, CJP1 and CJP2: conjugate planes of CP1 and CP2 in the n0 medium, respectively. MIB: middle interface boundary.

Fig. 2
Fig. 2

Flowchart for obtaining the RI profile of a multilayered sample by using the numerical correction method.

Fig. 3
Fig. 3

Empirical equation for Eq. (4). The sample position was moved by i ' for having a focused target pattern image at the CCD located at a given distance Zi. The solid line is a fitted exponential curve.

Fig. 4
Fig. 4

Schematic of the sample A having double layers, the top substrate and the middle air layer.

Fig. 5
Fig. 5

The FF-OCT images and numerically corrected images in the double-layered sample A. (a) FF-OCT image of the top resolution target through its glass substrate. (b) the enlarged image of the red box region in (a). (c) and (d) FF-OCT image of the bottom resolution target and its enlarged image. (e) the numerically corrected image of (a) obtained at Z1 = 58.55 mm. (f) the enlarged image of the red box region in (e). (g) and (h) the numerically corrected image of (d) obtained at Z2 = 45 mm and its enlarged image. (i) and (j) AMP values used for obtaining (e) and (h), respectively.

Tables (2)

Tables Icon

Table 1 Tomographic RIs and thicknesses measured for several double layered samples

Tables Icon

Table 2 RI and thickness of the same oil layer hidden in several kinds of multi-layered samples

Equations (18)

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

1 = d ip + d fp = ( n 1 n 0 n 0 n 1 ) d s 1
Φ(X,Y, Z i )= F 1 [ exp( jπλ Z i ( ξ 2 + η 2 ) )F[ Ψ( x,y ) ] ],
s i2 ( d f 2 ( s o2 / n 0 )( f 1 / n 0 ) ( s o2 / n 0 )( f 1 / n 0 ) )= f 2 d ( f 1 / n 0 ) f 2 ( s o2 / n 0 ) ( s o2 / n 0 )( f 1 / n 0 ) .
Z 1 = s i1 + f 2 d f 1 f 2 ( s o1 1 ' ) ( s o1 1 ' f 1 ) n 0 d f 2 f 1 ( s o1 1 ' ) ( s o1 1 ' f 1 ) n 0 .
1 = n 1 n 0 1 '.
1 '=( 1 n 0 2 n 1 2 ) d s1 .
n 1 = ( d s1 d s1 1 ' ) 1/2 n 0 .
z fp1 = n 1 n 0 ( d s1 + d s2 ).
z fp2 = n 2 n 1 ( z fp1 t 1 ),
t 1 = n 0 n 1 d s1 .
t 2 = n 0 n 2 d s2 .
2 = z fp2 t 2 .
2 =( n 2 n 0 n 2 n 0 n 1 2 ) d s1 +( n 2 n 0 n 0 n 2 ) d s2 .
2 '= n 0 n 2 2 .
2 ' 1 '= n 0 n 2 2 n 0 n 1 1 =( 1 n 0 2 n 2 2 ) d s2 .
n 2 = ( d s2 d s2 ( 2 ' 1 ' ) ) 1/2 n 0 .
n i = ( d s i d s i ( i ' i 1 ' ) ) 1 / 2 n 0 ,
t i = n 0 n i d s i .

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