Abstract

Quantitative phase measurements by low-coherence interferometry and optical coherence tomography are restricted by the well-known 2π ambiguity to path-length differences smaller than λ/2. We present a method that overcomes this ambiguity. Introducing a slight dispersion imbalance between reference and sample arms of the interferometer causes the short and long wavelengths of the source spectrum to separate within the interferometric signal. This causes the phase slope to vary within the signal. The phase-difference function between two adjacent sample beam components is calculated by subtraction of their phase functions obtained from phase-sensitive interferometric signal recording. Because of the dispersive effect, the phase difference varies across the interferometric signal. The slope of that phase difference is proportional to the optical path difference, without 2π ambiguity.

© 2001 Optical Society of America

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References

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2001

2000

1999

1998

C. K. Hitzenberger, A. Baumgartner, and A. F. Fercher, Opt. Commun. 154, 179 (1998).
[CrossRef]

1997

1993

1992

Badizadegan, K.

Barton, J. K.

Baumgartner, A.

C. K. Hitzenberger, A. Baumgartner, and A. F. Fercher, Opt. Commun. 154, 179 (1998).
[CrossRef]

Chen, Z.

Dasari, R. R.

Davé, D. P.

de Boer, J. F.

de Groot, P.

Deck, L.

Feld, M. S.

Fercher, A. F.

Françon, M.

M. Françon and S. Mallick, Polarization Interferometers (Wiley-Interscience, London, 1971).

Fujimoto, J. G.

Georgakoudi, I.

Hanlon, E. B.

Harris, T. J.

W. J. Tropf, M. Thomas, and T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, 2nd ed., M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), Vol. II.

Hee, M. R.

Hitzenberger, C. K.

Huang, D.

Izatt, J. A.

Kulkarni, M. D.

Leitgeb, R.

Malekafzali, A.

Mallick, S.

M. Françon and S. Mallick, Polarization Interferometers (Wiley-Interscience, London, 1971).

Milner, T. E.

Nelson, J. S.

Saxer, C.

Srinivas, S.

Sticker, M.

Swanson, E. A.

Thomas, M.

W. J. Tropf, M. Thomas, and T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, 2nd ed., M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), Vol. II.

Tropf, W. J.

W. J. Tropf, M. Thomas, and T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, 2nd ed., M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), Vol. II.

van Gemert, M. J. C.

Wang, X.

Wax, A.

Welch, A. J.

Xiang, S.

Yang, C.

Yazdanfar, S.

Zhao, Y.

J. Opt. Soc. Am. B

Opt. Commun.

C. K. Hitzenberger, A. Baumgartner, and A. F. Fercher, Opt. Commun. 154, 179 (1998).
[CrossRef]

Opt. Lett.

Other

W. J. Tropf, M. Thomas, and T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, 2nd ed., M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), Vol. II.

M. Françon and S. Mallick, Polarization Interferometers (Wiley-Interscience, London, 1971).

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Figures (4)

Fig. 1
Fig. 1

Sketch of the instrument: NPBS, nonpolarizing beam splitter; PBS, polarizing beam splitter.

Fig. 2
Fig. 2

Calibration measurement. (a) Phase difference δΦ between the signals recorded for the two sample beam components as a function of position within the coherence envelope (Wollaston decentration corresponds to δz1.9 μm). (b) Mean phase difference gradient δΦ as a function of Wollaston position [the encircled symbol corresponds to the data set of Fig.  2(a)].

Fig. 3
Fig. 3

Measurement of the surface profile of the tip of a fiber-optic frame control–physical contact connector. (a) Sketch of the connector (not drawn to scale). (b) Plot of height differences between sample beam components as a function of transversal position. (c) Surface profile: integral of (b) (aspect ratio of abscissa and ordinate, 90:1).

Fig. 4
Fig. 4

Measurement of the surface profile across a coin. (a) Photograph of the coin (measurement path indicated by the black line). (b) Plot of height differences between sample beam components as a function of transversal position. (c) Surface profile: integral of (b) (aspect ratio of abscissa and ordinate, 30:1).

Equations (2)

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A˜kz=Ikz+iHIkz=AkzexpiΦkz,
δΦ=K0δz+2ηzδz+ηδz2.

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