Abstract

We report a highly accurate phase-based technique for measuring arbitrarily long optical distance with subnanometer precision. The method employs a Michelson interferometer with a pair of harmonically related light sources, one cw and the other low coherence. By slightly detuning 2 nm the center wavelength of the low-coherence source between scans of the target sample, we can use the phase relationship between the heterodyne signals of the cw and the low-coherence light to measure the separation between reflecting interfaces with subnanometer precision. As this technique is completely free of 2π ambiguity, an issue that plagues most phase-based techniques, it can be used to measure arbitrarily long optical distances without loss of precision. We demonstrate one application of this technique, the high-precision determination of the differential refractive index.

© 2002 Optical Society of America

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References

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  1. A. Lannes, J. Opt. Soc. Am. A 18, 1046 (2001).
    [CrossRef]
  2. G. Fornaro, G. Franceschetti, R. Lanari, and E. Sansosti, J. Opt. Soc. Am. A 13, 2355 (1996).
    [CrossRef]
  3. D. P. Dave, T. Akkin, T. E. Milner, and H. G. Rylander, Opt. Commun. 193, 39 (2001).
    [CrossRef]
  4. C. Yang, A. Wax, M. S. Hahn, K. Badizadegan, R. R. Dasari, and M. S. Feld, Opt. Lett. 26, 1271 (2001).
    [CrossRef]
  5. C. K. Hitzenberger, M. Sticker, R. Leitgeb, H. Sattmann, and A. F. Fercher, Proc. SPIE 4251, 81 (2001).
    [CrossRef]
  6. A. F. Fercher, J. Biomed. Opt. 1, 157 (1996).
    [CrossRef] [PubMed]
  7. C. Yang, A. Wax, K. Badizadegan, R. R. Dasari, and M. S. Feld, Opt. Lett. 25, 1526 (2000).
    [CrossRef]
  8. C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, Opt. Commun. 110, 381 (1994).
    [CrossRef]

2001 (4)

D. P. Dave, T. Akkin, T. E. Milner, and H. G. Rylander, Opt. Commun. 193, 39 (2001).
[CrossRef]

C. Yang, A. Wax, M. S. Hahn, K. Badizadegan, R. R. Dasari, and M. S. Feld, Opt. Lett. 26, 1271 (2001).
[CrossRef]

C. K. Hitzenberger, M. Sticker, R. Leitgeb, H. Sattmann, and A. F. Fercher, Proc. SPIE 4251, 81 (2001).
[CrossRef]

A. Lannes, J. Opt. Soc. Am. A 18, 1046 (2001).
[CrossRef]

2000 (1)

1996 (2)

1994 (1)

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, Opt. Commun. 110, 381 (1994).
[CrossRef]

Akkin, T.

D. P. Dave, T. Akkin, T. E. Milner, and H. G. Rylander, Opt. Commun. 193, 39 (2001).
[CrossRef]

Badizadegan, K.

Calatroni, J.

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, Opt. Commun. 110, 381 (1994).
[CrossRef]

Dasari, R. R.

Dave, D. P.

D. P. Dave, T. Akkin, T. E. Milner, and H. G. Rylander, Opt. Commun. 193, 39 (2001).
[CrossRef]

Escalona, R.

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, Opt. Commun. 110, 381 (1994).
[CrossRef]

Feld, M. S.

Fercher, A. F.

C. K. Hitzenberger, M. Sticker, R. Leitgeb, H. Sattmann, and A. F. Fercher, Proc. SPIE 4251, 81 (2001).
[CrossRef]

A. F. Fercher, J. Biomed. Opt. 1, 157 (1996).
[CrossRef] [PubMed]

Fornaro, G.

Franceschetti, G.

Hahn, M. S.

Hitzenberger, C. K.

C. K. Hitzenberger, M. Sticker, R. Leitgeb, H. Sattmann, and A. F. Fercher, Proc. SPIE 4251, 81 (2001).
[CrossRef]

Jourdain, P.

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, Opt. Commun. 110, 381 (1994).
[CrossRef]

Lanari, R.

Lannes, A.

Leitgeb, R.

C. K. Hitzenberger, M. Sticker, R. Leitgeb, H. Sattmann, and A. F. Fercher, Proc. SPIE 4251, 81 (2001).
[CrossRef]

Milner, T. E.

D. P. Dave, T. Akkin, T. E. Milner, and H. G. Rylander, Opt. Commun. 193, 39 (2001).
[CrossRef]

Rylander, H. G.

D. P. Dave, T. Akkin, T. E. Milner, and H. G. Rylander, Opt. Commun. 193, 39 (2001).
[CrossRef]

Sainz, C.

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, Opt. Commun. 110, 381 (1994).
[CrossRef]

Sansosti, E.

Sattmann, H.

C. K. Hitzenberger, M. Sticker, R. Leitgeb, H. Sattmann, and A. F. Fercher, Proc. SPIE 4251, 81 (2001).
[CrossRef]

Sticker, M.

C. K. Hitzenberger, M. Sticker, R. Leitgeb, H. Sattmann, and A. F. Fercher, Proc. SPIE 4251, 81 (2001).
[CrossRef]

Wax, A.

Yang, C.

J. Biomed. Opt. (1)

A. F. Fercher, J. Biomed. Opt. 1, 157 (1996).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (2)

Opt. Commun. (2)

D. P. Dave, T. Akkin, T. E. Milner, and H. G. Rylander, Opt. Commun. 193, 39 (2001).
[CrossRef]

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, Opt. Commun. 110, 381 (1994).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (1)

C. K. Hitzenberger, M. Sticker, R. Leitgeb, H. Sattmann, and A. F. Fercher, Proc. SPIE 4251, 81 (2001).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Experimental setup: M, reference mirror; BS, beam splitter; D1, D2, photodetectors; DM, 775nm/1550nm dichroic mirror. ADC, analog–digital converter.

Fig. 2
Fig. 2

Typical scan of a sample with two interfaces: (a) low-coherence heterodyne signal, (b) ψcwx trace. The magnified view in (b) shows the phase fringes. Each fringe corresponds to an optical distance of λcw. (c) Traces of ψDx at two different values of Δ. The arrows indicate the phase-crossing points. In (b) and (c), the vertical axis is in radians.

Tables (2)

Tables Icon

Table 1 Measurments of (n775 nmL) of a Piece of Quartz Coverslip

Tables Icon

Table 2 Measurements of n775 nm/n1550 nm for Different Materials

Equations (6)

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ψLCx=mod2πargRLC,1 expi2kLCx-x1×exp-2ax-x12+RLC,2×expi2kLCx-x2exp-2ax-x22hcx-x1mod2π2kLCx-x1+hcx-x2mod2π2kLCx-x2,
ψcwx=mod2πargRcw,1 expi2kcwx-x1+Rcw,2 expi2kcwx-x1+n1550 nmL=mod2πargR¯expi2kcwx-x¯=mod2π2kcwx-x¯,
kLC=2kcw+Δ,
ψDx=ψLCx-2ψcwx=hcx-x1mod2π4kcwx¯-x1+2Δx-x1+hcx-x2mod2π4kcwx¯-x2+2Δx-x2.
Sphase=mod2πψDx=x1-ψDx=x22π=mod2π4kcwx2-x12π.
x2-x1measured=n775 nmLmeasured=λcw4intSfringe+UΔS-12-U-ΔS-12+Sphase,

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