Abstract

A scanning spatial low-coherence interferometer (S-LCI), using an off-axis converging single wavelength laser beam as the probe, resembles a conventional or temporal low-coherence interferometer (T-LCI) in signal formation and data processing. However, the S-LCI is advantageous over a T-LCI with the combination of angle resolving and depth discrimination capabilities. The S-LCI is demonstrated by measuring the angle dependent phase shifts among the multiple reflections of a glass plate, with incident angles accurately scaled in the Fourier domain. The refractive index and geometric thickness of the glass plate are simultaneously produced in this one-step measurement.

© 2011 Optical Society of America

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2010 (1)

2009 (1)

2008 (1)

2007 (1)

2005 (1)

2004 (1)

2003 (3)

2000 (3)

1998 (1)

1991 (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, and J. G. Futimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

1987 (1)

Alexandrov, S. A.

S. A. Alexandrov and I. V. Chernyh, Opt. Eng. 39, 2480(2000).
[CrossRef]

Beaumont, A.

Carr, S.

Chan, N.

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, and J. G. Futimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Chernyh, I. V.

S. A. Alexandrov and I. V. Chernyh, Opt. Eng. 39, 2480(2000).
[CrossRef]

Contag, D.

Coppola, G.

Davies, D. E. N.

de Groot, P.

de Lega, X.

De Nicola, S.

Drexler, W.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, Rep. Prog. Phys. 66, 239 (2003).
[CrossRef]

Fercher, A. F.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, Rep. Prog. Phys. 66, 239 (2003).
[CrossRef]

Ferraro, P.

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, and J. G. Futimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Futimoto, J. 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, and J. G. Futimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Ge, J.

Gokhler, M.

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, and J. G. Futimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Hart, C.

Haruna, M.

Hashimoto, M.

Hee, M. R.

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, and J. G. Futimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Hitzenberger, C. K.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, Rep. Prog. Phys. 66, 239 (2003).
[CrossRef]

Huang, D.

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, and J. G. Futimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Indebetouw, G.

Iodice, M.

Kino, G.

Klysubun, P.

Lasser, T.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, Rep. Prog. Phys. 66, 239 (2003).
[CrossRef]

Lin, C. P.

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, and J. G. Futimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Mandella, M.

Maruyama, H.

Mitsuyama, T.

Ohmi, M.

Puliafito, C. A.

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, and J. G. Futimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Rosen, J.

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, and J. G. Futimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

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, and J. G. Futimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

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, and J. G. Futimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Tajiri, H.

Takeda, M.

Tedaldi, M.

Tomlins, P. H.

Wan, X.

Wang, J.

Wang, T.

Woolliams, P.

Youngquist, R. C.

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Figures (3)

Fig. 1
Fig. 1

Scanning S-LCI measuring the refractive index and the thickness of an uncoated sample plate. Most essential transmitted and reflected beams are shown. Tilt angles of the beam splitter and reflector are exaggerated. The inlet shows the surface reflections from the sample forming the first three LCI signals.

Fig. 2
Fig. 2

(a)–(c) Three cleaved windows of the low-coherence signal and reference signal over a continuous scan of~25,000 (on-axis) fringes. The vertical scale in (c) is ten times different from (a) and (b). (d) Detailed signal waveform shows that the low-coherence signal oscillates at a lower rate compared to the on-axis signal.

Fig. 3
Fig. 3

(a) Fourier amplitude and (b) unfolded Fourier phase of the low-coherence signals. The amplitude of the S III signal is displayed with a 5 × magnification in panel (a).

Tables (1)

Tables Icon

Table 1 Measured Relative Refractive Index and Thickness Values Compared to the Commercial Values of the BK7 Sample

Equations (6)

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ϕ S I ( x , cos j ) = 4 π λ ( n air x cos j + n 1 t 1 cos q ) ,
ϕ S II ( x , cos j ) = ϕ S I ( x , cos j ) 4 π λ n 2 t 2 cos k ± π ,
ϕ S III ( x , cos j ) = ϕ S I ( x , cos j ) 8 π λ n 2 t 2 cos k ± π ,
G l ( cos j ) exp ( i ϕ S l ( d l , cos j ) ) = d l W l d l W l S l ( x ) exp ( i 4 π λ ( d l x ) cos j ) d x ,
4 π λ n 2 t 2 * cos k = ϕ S I ( d I , cos j ) ϕ S II ( d II , cos j ) + ( ϕ ref ( d II ) ϕ ref ( d I ) ) * cos j ± π ,
n 2 sin k = n air sin j ,

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