Abstract

A wavelength-scanning heterodyne interference confocal microscope quickly accomplishes the simultaneous measurement of the thickness and the refractive index of a sample by detection of the amplitude and the phase of the interference signal during a sample scan. However, the measurement range of the optical path difference (OPD) that is obtained from the phase changes is limited by the time response of the phase-locked loop circuit in the FM demodulator. To overcome this limitation and to improve the accuracy of the separation measurement, we propose an OPD detection using digital signal processing with a Hilbert transform. The measurement range is extended approximately five times, and the resolution of the OPD is improved to 5.5 from 9 µm without the electrical noise of the FM demodulator circuit. By applying this method for simultaneous measurement of thickness and the refractive index, we can measure samples 20–30-µm thick with refractive indices between 1 and 1.5.

© 2002 Optical Society of America

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References

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2002 (1)

2001 (1)

2000 (5)

K. Yoden, M. Ohmi, Y. Ohnishi, N. Kunizawa, M. Haruna, “An approach to optical reflection tomography along the geometrical thickness,” Opt. Rev. 7, 402–405 (2000).
[CrossRef]

M. Ohmi, Y. Ohnishi, K. Yoden, M. Haruna, “In vitro simultaneous measurement of refractive index and thickness by low coherence interferometry,” IEEE Trans. Biomed. Eng. 47, 1266–1270 (2000).
[CrossRef] [PubMed]

A. Knüttel, M. Boehlau-Godau, “Spatially confined and temporally resolved refractive index and scattering evaluation in human skin performed with optical coherence tomography,” J. Biomed. Opt. 5, 83–92 (2000).
[CrossRef] [PubMed]

Y. Zhao, Z. Chen, C. Saxer, S. Xiang, J. F. de Boer, J. S. Nelson, “Phase-resolved optical coherence tomography and optical Doppler tomography for imaging blood flow in human skin with fast scanning and high velocity sensitivity,” Opt. Lett. 25, 114–116 (2000).
[CrossRef]

T. Fukano, I. Yamaguchi, “Geometrical cross-sectional imaging by a heterodyne wavelength-scanning interference confocal microscope,” Opt. Lett. 25, 548–550 (2000).
[CrossRef]

1999 (1)

1998 (1)

1996 (1)

1995 (2)

1991 (2)

1987 (1)

1986 (1)

Boehlau-Godau, M.

A. Knüttel, M. Boehlau-Godau, “Spatially confined and temporally resolved refractive index and scattering evaluation in human skin performed with optical coherence tomography,” J. Biomed. Opt. 5, 83–92 (2000).
[CrossRef] [PubMed]

Bouma, B. E.

Brezinski, M. E.

Chen, Z.

Dalhoff, E.

de Boer, J. F.

den Boef, A. J.

Fercher, A. F.

Fischer, E.

Fujimoto, J. G.

Fukano, T.

Haruna, M.

K. Yoden, M. Ohmi, Y. Ohnishi, N. Kunizawa, M. Haruna, “An approach to optical reflection tomography along the geometrical thickness,” Opt. Rev. 7, 402–405 (2000).
[CrossRef]

M. Ohmi, Y. Ohnishi, K. Yoden, M. Haruna, “In vitro simultaneous measurement of refractive index and thickness by low coherence interferometry,” IEEE Trans. Biomed. Eng. 47, 1266–1270 (2000).
[CrossRef] [PubMed]

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

Hashimoto, M.

Hee, M. R.

Heim, S.

Hitzenberger, C. K.

Hofbauer, U.

Iwata, K.

Kikuta, H.

Knüttel, A.

A. Knüttel, M. Boehlau-Godau, “Spatially confined and temporally resolved refractive index and scattering evaluation in human skin performed with optical coherence tomography,” J. Biomed. Opt. 5, 83–92 (2000).
[CrossRef] [PubMed]

Kunizawa, N.

K. Yoden, M. Ohmi, Y. Ohnishi, N. Kunizawa, M. Haruna, “An approach to optical reflection tomography along the geometrical thickness,” Opt. Rev. 7, 402–405 (2000).
[CrossRef]

Leitgeb, R.

Maruyama, H.

Mitsuyama, T.

Nagata, R.

Nelson, J. S.

Ohmi, M.

K. Yoden, M. Ohmi, Y. Ohnishi, N. Kunizawa, M. Haruna, “An approach to optical reflection tomography along the geometrical thickness,” Opt. Rev. 7, 402–405 (2000).
[CrossRef]

M. Ohmi, Y. Ohnishi, K. Yoden, M. Haruna, “In vitro simultaneous measurement of refractive index and thickness by low coherence interferometry,” IEEE Trans. Biomed. Eng. 47, 1266–1270 (2000).
[CrossRef] [PubMed]

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

Ohnishi, Y.

K. Yoden, M. Ohmi, Y. Ohnishi, N. Kunizawa, M. Haruna, “An approach to optical reflection tomography along the geometrical thickness,” Opt. Rev. 7, 402–405 (2000).
[CrossRef]

M. Ohmi, Y. Ohnishi, K. Yoden, M. Haruna, “In vitro simultaneous measurement of refractive index and thickness by low coherence interferometry,” IEEE Trans. Biomed. Eng. 47, 1266–1270 (2000).
[CrossRef] [PubMed]

Sasaki, O.

Saxer, C.

Southern, J. F.

Sticker, M.

Suematsu, M.

Suzuki, T.

Tajiri, H.

Takeda, M.

Tearney, G. J.

Tiziani, H. J.

Watanabe, Y.

Wilson, T.

T. Wilson, Confocal Microscopy (Academic, New York, 1990).

Xiang, S.

Yamaguchi, I.

Yoden, K.

K. Yoden, M. Ohmi, Y. Ohnishi, N. Kunizawa, M. Haruna, “An approach to optical reflection tomography along the geometrical thickness,” Opt. Rev. 7, 402–405 (2000).
[CrossRef]

M. Ohmi, Y. Ohnishi, K. Yoden, M. Haruna, “In vitro simultaneous measurement of refractive index and thickness by low coherence interferometry,” IEEE Trans. Biomed. Eng. 47, 1266–1270 (2000).
[CrossRef] [PubMed]

Yoshida, T.

Zhao, Y.

Appl. Opt. (7)

IEEE Trans. Biomed. Eng. (1)

M. Ohmi, Y. Ohnishi, K. Yoden, M. Haruna, “In vitro simultaneous measurement of refractive index and thickness by low coherence interferometry,” IEEE Trans. Biomed. Eng. 47, 1266–1270 (2000).
[CrossRef] [PubMed]

J. Biomed. Opt. (1)

A. Knüttel, M. Boehlau-Godau, “Spatially confined and temporally resolved refractive index and scattering evaluation in human skin performed with optical coherence tomography,” J. Biomed. Opt. 5, 83–92 (2000).
[CrossRef] [PubMed]

Opt. Lett. (6)

Opt. Rev. (1)

K. Yoden, M. Ohmi, Y. Ohnishi, N. Kunizawa, M. Haruna, “An approach to optical reflection tomography along the geometrical thickness,” Opt. Rev. 7, 402–405 (2000).
[CrossRef]

Other (1)

T. Wilson, Confocal Microscopy (Academic, New York, 1990).

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Figures (8)

Fig. 1
Fig. 1

Schematic of measurement system. LD, laser diode; BS, beam splitter; AOM, acousto-optic modulator; A/D, analog-digital conversion board.

Fig. 2
Fig. 2

Flow chart of the OPD derivation with the experimental waveforms. (a) Measured signal and its Hilbert transform, (b) phase signal, (c) unwrapped phase signal, and (d) differential unwrapped phase signal.

Fig. 3
Fig. 3

Comparison between the FM demodulator and the digital signal-processing method. The squares show the calculated phase changes of FM signals that are generated by a function generator.

Fig. 4
Fig. 4

Schematic of a wedge sample composed of two glass plates.

Fig. 5
Fig. 5

(a) Confocal signals and (b) OPDs. The inset shows the normalized confocal profile.

Fig. 6
Fig. 6

Positions of (a) confocal peaks and (b) OPDs at the confocal peaks. The squares and the circles represent each glass plate.

Fig. 7
Fig. 7

(a) Refractive indices of three layers. (b) Tomographic image of the refractive indices along the geometrical thickness. (c) Geometrical thickness of the air gap.

Fig. 8
Fig. 8

(a) OPD measurement for different modulation frequencies. (b) Measurable OPD for various carrier frequencies.

Equations (7)

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

νt=ν0+Δνcos2πfmt+ϕ,
ftcos2πft+2πc ΔνΔl cos2πfmt+ϕ+b,
f=fs-fr, b=2πcν0+frlr+2πcν0+fsls,
gt=1π-fτt-τdτ
ht=2πf+2πfm2π/cΔνΔl sin2πfmt+ϕ.
n=12NA2+NA4+41-NA2Δl/Δz21/21/2,
Δn=|nm-nr|/nr,

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