Abstract

A new signal-processing technique is proposed that involves a phase-resolved correlation method that one can use to determine the phase distribution of low-coherence interferograms. This method improves the sensitivity and resolution of low-coherence interferometers. The depth structure of an aluminum oxide–coated aluminum mirror was determined by use of a low-coherence interferometer with this method. Three signal peaks were successfully extracted from a noisy interferogram.

© 2001 Optical Society of America

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References

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1999

A. Hirai and H. Matsumoto, Opt. Commun. 161, 11 (1999).
[CrossRef]

H. Matsumoto and A. Hirai, Opt. Commun. 170, 217 (1999).
[CrossRef]

1998

A. C. Oliveira, F. M. M. Yasuoka, J. B. Santos, L. A. V. Carvalho, and J. C. Castro, Rev. Sci. Instrum. 69, 1877 (1998).
[CrossRef]

B. Bowe and V. Toal, Opt. Eng. 37, 1796 (1998).
[CrossRef]

1996

1992

1983

Bowe, B.

B. Bowe and V. Toal, Opt. Eng. 37, 1796 (1998).
[CrossRef]

Carvalho, L. A. V.

A. C. Oliveira, F. M. M. Yasuoka, J. B. Santos, L. A. V. Carvalho, and J. C. Castro, Rev. Sci. Instrum. 69, 1877 (1998).
[CrossRef]

Castro, J. C.

A. C. Oliveira, F. M. M. Yasuoka, J. B. Santos, L. A. V. Carvalho, and J. C. Castro, Rev. Sci. Instrum. 69, 1877 (1998).
[CrossRef]

Fujimoto, J. G.

Hee, M. R.

Hirai, A.

A. Hirai and H. Matsumoto, Opt. Commun. 161, 11 (1999).
[CrossRef]

H. Matsumoto and A. Hirai, Opt. Commun. 170, 217 (1999).
[CrossRef]

Huang, D.

Larkin, K. G.

Lin, C. P.

Matsumoto, H.

A. Hirai and H. Matsumoto, Opt. Commun. 161, 11 (1999).
[CrossRef]

H. Matsumoto and A. Hirai, Opt. Commun. 170, 217 (1999).
[CrossRef]

Mutoh, K.

Oliveira, A. C.

A. C. Oliveira, F. M. M. Yasuoka, J. B. Santos, L. A. V. Carvalho, and J. C. Castro, Rev. Sci. Instrum. 69, 1877 (1998).
[CrossRef]

Puliafito, C. A.

Santos, J. B.

A. C. Oliveira, F. M. M. Yasuoka, J. B. Santos, L. A. V. Carvalho, and J. C. Castro, Rev. Sci. Instrum. 69, 1877 (1998).
[CrossRef]

Swanson, E. A.

Takeda, M.

Toal, V.

B. Bowe and V. Toal, Opt. Eng. 37, 1796 (1998).
[CrossRef]

Yasuoka, F. M. M.

A. C. Oliveira, F. M. M. Yasuoka, J. B. Santos, L. A. V. Carvalho, and J. C. Castro, Rev. Sci. Instrum. 69, 1877 (1998).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Commun.

A. Hirai and H. Matsumoto, Opt. Commun. 161, 11 (1999).
[CrossRef]

H. Matsumoto and A. Hirai, Opt. Commun. 170, 217 (1999).
[CrossRef]

Opt. Eng.

B. Bowe and V. Toal, Opt. Eng. 37, 1796 (1998).
[CrossRef]

Opt. Lett.

Rev. Sci. Instrum.

A. C. Oliveira, F. M. M. Yasuoka, J. B. Santos, L. A. V. Carvalho, and J. C. Castro, Rev. Sci. Instrum. 69, 1877 (1998).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Analyzed fringe signal. Three peaks, which have separate carrier phases, are present in the signal.

Fig. 2
Fig. 2

Reference wavelet for correlation. The envelope is a Gaussian function, and its width is determined as the coherence length of the light source of the interferometer.

Fig. 3
Fig. 3

Phase-resolved correlation of the signal in Fig.  1. We can confirm that the three peaks have different carrier phases.

Fig. 4
Fig. 4

Interferometer for measurement: SLD, superluminescent diode; L’s, lenses; M, mirror: BS, beam splitter; SM, stepping motor; PIN, pinhole. The focal length of lenses L2 and L3 is 10  mm. The sample is aluminum covered by an aluminum oxide layer. The stepping motor is driven with a period of 100  nm.

Fig. 5
Fig. 5

Unprocessed low-coherence interferogram of the aluminum mirror. Although three signal peaks, (a)–(c), are in fact present, they are masked by noise.

Fig. 6
Fig. 6

Phase-resolved correlation of the signal of Fig.  5. The raw signal is spread into a three two-dimensional distribution, ϕ phase, z position. Two peaks, (b) and (c), of three peaks are barely identifiable because of the rough period of the contours, so the peaks are marked here by crosses.

Equations (4)

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

hz,ϕ,ν=hez×hcz,ϕ,ν,
hcz,ϕ,ν=sin2πνz+ϕ,
hez=exp-πz/β2,
Wnz/ν,ϕ,ν=-+hz-nz/ν,ϕ,νfzdz,nz=,-2,-1,0,1,2,,ϕ=-π,+π,ν=0,+,

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