Abstract

We propose a novel technique for simultaneous measurement of layer thicknesses and refractive indices of multiple layers. It is based on a combination of a confocal microscope and low-coherence interferometry. We derived an expression for the geometrical thickness and the refractive index of each layer from both tracing of a marginal ray accepted by a microscope objective and optical path matching conditions. Experimental verification of this method is illustrated by several samples that have a maximum of 13 layers. The geometrical thicknesses and refractive indices thus derived agreed well with those measured by a micrometer or cited from the literature.

© 1996 Optical Society of America

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References

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1995 (2)

1994 (1)

1992 (2)

1991 (2)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

B. L. Danielson, C. Y. Boisrobert, Appl. Opt. 30, 2975 (1991).
[CrossRef] [PubMed]

1987 (1)

1972 (1)

Boisrobert, C. Y.

Bonner, R. F.

Bouma, B. E.

Brezinski, M. E.

Carr, S.

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Cogswell, C. J.

Connolly, T. J.

Danielson, B. L.

Davies, D. E. N.

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Flournoy, P. A.

Fujimoto, J. G.

Fukano, T.

T. Fukano, I. Yamaguchi, presented at the 15th Meeting on Lightwave Sensing Technology, Tokyo, June 1995.

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Haruna, M.

M. Ohmi, T. Shiraishi, H. Taijiri, M. Haruna, presented at the 11th International Conference on Optical Fiber Sensors, Sapporo, Japan, May 1996.

Hee, M. R.

Hitzenberger, C. K.

Huang, D.

E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, C. A. Puliafito, Opt. Lett. 17, 151 (1992).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Ichihara, Y.

T. Tsuruta, Y. Ichihara, presented at the International Commission for Optics Conference, Tokyo, August 1974.

Lee, J.

Lin, C. P.

E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, C. A. Puliafito, Opt. Lett. 17, 151 (1992).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

McClure, R. W.

Ohmi, M.

M. Ohmi, T. Shiraishi, H. Taijiri, M. Haruna, presented at the 11th International Conference on Optical Fiber Sensors, Sapporo, Japan, May 1996.

Puliafito, C. A.

E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, C. A. Puliafito, Opt. Lett. 17, 151 (1992).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Schmitt, J. M.

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Sheppard, C. J. R.

Shiraishi, T.

M. Ohmi, T. Shiraishi, H. Taijiri, M. Haruna, presented at the 11th International Conference on Optical Fiber Sensors, Sapporo, Japan, May 1996.

Southern, J. F.

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, C. A. Puliafito, Opt. Lett. 17, 151 (1992).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Taijiri, H.

M. Ohmi, T. Shiraishi, H. Taijiri, M. Haruna, presented at the 11th International Conference on Optical Fiber Sensors, Sapporo, Japan, May 1996.

Tearney, G. J.

Tsuruta, T.

T. Tsuruta, Y. Ichihara, presented at the International Commission for Optics Conference, Tokyo, August 1974.

Wyntjes, G.

Yadlowsky, M. J.

Yamaguchi, I.

T. Fukano, I. Yamaguchi, presented at the 15th Meeting on Lightwave Sensing Technology, Tokyo, June 1995.

Youngquist, R. C.

Appl. Opt. (5)

Opt. Lett. (3)

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Other (3)

T. Fukano, I. Yamaguchi, presented at the 15th Meeting on Lightwave Sensing Technology, Tokyo, June 1995.

M. Ohmi, T. Shiraishi, H. Taijiri, M. Haruna, presented at the 11th International Conference on Optical Fiber Sensors, Sapporo, Japan, May 1996.

T. Tsuruta, Y. Ichihara, presented at the International Commission for Optics Conference, Tokyo, August 1974.

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Figures (4)

Fig. 1
Fig. 1

Left, setup for measurement of the layer thicknesses and refractive indices of multiple layers; right, focusing on (a) the front and (b) the rear surfaces of the mth layer. BS, beam splitter; PMT, photomultiplier tube.

Fig. 2
Fig. 2

Shift of the marginal ray caused by a focal change.

Fig. 3
Fig. 3

(a) Cross-sectional image of the prepared sample. Each layer has a thickness of 150 μm. ( b) Confocal signals obtained from the sample scanning. (c) Interferograms obtained from the reference mirror scanning at each peak of (b).

Fig. 4
Fig. 4

Measured results for thicknesses (●) and refractive indices (bars) versus the number of layers. The catalog values for thicknesses (long-and-short-dashed curves) and refractive indices (short-dashed curves) are also shown. The odd and even layers correspond to glass and air layers, respectively.

Equations (5)

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

d m tan  θ m = Δ z m tan  θ 0 ,
n m sin  θ m = sin  θ 0 = NA            ( m = 0 , 1 , 2 m , ) ,
Δ l m = n m d m - Δ z m .
n m 2 = ½ { NA 2 + [ NA 4 + 4 ( 1 - NA 2 ) ( 1 + Δ l m Δ z m ) 2 ] 1 / 2 } .
d m = Δ l m + Δ z m n m .

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