Abstract

A two-dimensional surface profile imaging technique that uses a low-coherence heterodyne interferometer is proposed. A double-grating frequency shifter was used in a tandem interferometer to provide the achromatic frequency shift for low-coherence light. A chopper, together with a processing circuit, was implemented to modulate the interference fringes. The surface profile was measured from the interference fringes taken by a CCD camera using a five-step method. The uncertainty in the displacement measurement is 0.34 μm for a displacement range of 43 μm. The surface profile of a glass sample with low effective reflectivity was acquired.

© 2005 Optical Society of America

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    [CrossRef]
  2. Y. L. Lo, C. H. Chuang, “New synthetic-heterodyne demodulator for an optical fiber interferometer,” IEEE J. Quantum Electron. 37, 658–663 (2001).
    [CrossRef]
  3. B. Bowe, V. Toal, “White light interferometric surface profiler,” Opt. Eng. 37, 1796–1799 (1998).
    [CrossRef]
  4. M. Roy, C. J. R. Sheppard, P. Hariharan, “Low-coherence interference microscopy using a ferro-electric liquid crystal phase-modulator,” Opt. Express 12, 2512–2516 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2004

M. Roy, C. J. R. Sheppard, P. Hariharan, “Low-coherence interference microscopy using a ferro-electric liquid crystal phase-modulator,” Opt. Express 12, 2512–2516 (2004).
[CrossRef] [PubMed]

A. R. D. Somervell, M. E. K. Williams, T. H. Barnes, “Direct measurement of fringe amplitude and phase using a heterodyne interferometer operating in broadband light,” Opt. Commun. 229, 59–64 (2004).
[CrossRef]

2002

L. J. Zeng, I. Fujima, A. Hirai, H. Matsumoto, S. Iwasaki, “A two-color heterodyne interferometer for measuring the refractive index of air using an optical diffraction grating,” Opt. Commun. 203, 243–247 (2002).
[CrossRef]

Y. L. Lo, C. H. Chuang, “Fluid velocity measurements in a microchannel performed with two new optical heterodyne microscopes,” Appl. Opt. 41, 6666–6675 (2002).
[CrossRef] [PubMed]

2001

A. Hirai, L. J. Zeng, H. Matsumoto, “Heterodyne Fourier transform spectroscopy using moving diffraction grating,” Jpn. J. Phys. 40, 6138–6142 (2001).
[CrossRef]

H. Z. Zhao, R. Liang, D. C. Li, M. Cao, “Practical common-path heterodyne surface profiling interferometer with automatic focusing,” Opt. Laser Technol. 33, 259–265 (2001).
[CrossRef]

Y. L. Lo, C. H. Chuang, “New synthetic-heterodyne demodulator for an optical fiber interferometer,” IEEE J. Quantum Electron. 37, 658–663 (2001).
[CrossRef]

A. Hirai, H. Matsumoto, “High-sensitivity surface profile measurements by heterodyne white-light interferometer,” Opt. Eng. 40, 387–391 (2001).
[CrossRef]

2000

M. Akiba, K. P. Chan, N. Tanno, “Real-time, micrometer depth-resolved imaging by low-coherence interferometry and a two-dimensional heterodyne detection technique,” Jpn. J. Phys. 39, L1194–L1196 (2000).
[CrossRef]

F. Le Clerc, L. Collot, M. Gross, “Numerical heterodyne holography with two-dimensional photodetector arrays,” Opt. Lett. 25, 716–718 (2000).
[CrossRef]

K. P. Chan, M. Sato, M. Akiba, N. Tanno, “Detection schemes for optical-coherence-domain imaging of biological tissues,” Opt. Rev. 7, 389–395 (2000).
[CrossRef]

1999

H. Matsumoto, A. Hirai, “A white light interferometer using a lamp source and heterodyne detection with acousto-optic modulators,” Opt. Commun. 170, 217–220 (1999).
[CrossRef]

A. Hirai, K. Seta, H. Matsumoto, “White-light interferometry using pseudo random-modulation for high-sensitivity and high-selectivity measurements,” Opt. Commun. 162, 11–15 (1999).
[CrossRef]

1998

B. Bowe, V. Toal, “White light interferometric surface profiler,” Opt. Eng. 37, 1796–1799 (1998).
[CrossRef]

1997

F. Rickermann, S. Riehemann, G. von Bally, S. Breer, K. Buse, “A high resolution real-time temporal heterodyne interferometer for refractive index topography,” Opt. Commun. 144, 173–179 (1997).
[CrossRef]

1994

1993

1992

Akiba, M.

M. Akiba, K. P. Chan, N. Tanno, “Real-time, micrometer depth-resolved imaging by low-coherence interferometry and a two-dimensional heterodyne detection technique,” Jpn. J. Phys. 39, L1194–L1196 (2000).
[CrossRef]

K. P. Chan, M. Sato, M. Akiba, N. Tanno, “Detection schemes for optical-coherence-domain imaging of biological tissues,” Opt. Rev. 7, 389–395 (2000).
[CrossRef]

Barnes, T. H.

A. R. D. Somervell, M. E. K. Williams, T. H. Barnes, “Direct measurement of fringe amplitude and phase using a heterodyne interferometer operating in broadband light,” Opt. Commun. 229, 59–64 (2004).
[CrossRef]

Bowe, B.

B. Bowe, V. Toal, “White light interferometric surface profiler,” Opt. Eng. 37, 1796–1799 (1998).
[CrossRef]

Breer, S.

F. Rickermann, S. Riehemann, G. von Bally, S. Breer, K. Buse, “A high resolution real-time temporal heterodyne interferometer for refractive index topography,” Opt. Commun. 144, 173–179 (1997).
[CrossRef]

Buse, K.

F. Rickermann, S. Riehemann, G. von Bally, S. Breer, K. Buse, “A high resolution real-time temporal heterodyne interferometer for refractive index topography,” Opt. Commun. 144, 173–179 (1997).
[CrossRef]

Cao, M.

H. Z. Zhao, R. Liang, D. C. Li, M. Cao, “Practical common-path heterodyne surface profiling interferometer with automatic focusing,” Opt. Laser Technol. 33, 259–265 (2001).
[CrossRef]

Chan, K. P.

K. P. Chan, M. Sato, M. Akiba, N. Tanno, “Detection schemes for optical-coherence-domain imaging of biological tissues,” Opt. Rev. 7, 389–395 (2000).
[CrossRef]

M. Akiba, K. P. Chan, N. Tanno, “Real-time, micrometer depth-resolved imaging by low-coherence interferometry and a two-dimensional heterodyne detection technique,” Jpn. J. Phys. 39, L1194–L1196 (2000).
[CrossRef]

Chu, K. C.

Chuang, C. H.

Y. L. Lo, C. H. Chuang, “Fluid velocity measurements in a microchannel performed with two new optical heterodyne microscopes,” Appl. Opt. 41, 6666–6675 (2002).
[CrossRef] [PubMed]

Y. L. Lo, C. H. Chuang, “New synthetic-heterodyne demodulator for an optical fiber interferometer,” IEEE J. Quantum Electron. 37, 658–663 (2001).
[CrossRef]

Collot, L.

Deck, L.

Degroot, P.

Dienes, A.

Dresel, T.

Fujima, I.

L. J. Zeng, I. Fujima, A. Hirai, H. Matsumoto, S. Iwasaki, “A two-color heterodyne interferometer for measuring the refractive index of air using an optical diffraction grating,” Opt. Commun. 203, 243–247 (2002).
[CrossRef]

Gross, M.

Hariharan, P.

Hausler, G.

Heritage, J. P.

Hirai, A.

L. J. Zeng, I. Fujima, A. Hirai, H. Matsumoto, S. Iwasaki, “A two-color heterodyne interferometer for measuring the refractive index of air using an optical diffraction grating,” Opt. Commun. 203, 243–247 (2002).
[CrossRef]

A. Hirai, L. J. Zeng, H. Matsumoto, “Heterodyne Fourier transform spectroscopy using moving diffraction grating,” Jpn. J. Phys. 40, 6138–6142 (2001).
[CrossRef]

A. Hirai, H. Matsumoto, “High-sensitivity surface profile measurements by heterodyne white-light interferometer,” Opt. Eng. 40, 387–391 (2001).
[CrossRef]

H. Matsumoto, A. Hirai, “A white light interferometer using a lamp source and heterodyne detection with acousto-optic modulators,” Opt. Commun. 170, 217–220 (1999).
[CrossRef]

A. Hirai, K. Seta, H. Matsumoto, “White-light interferometry using pseudo random-modulation for high-sensitivity and high-selectivity measurements,” Opt. Commun. 162, 11–15 (1999).
[CrossRef]

Iwasaki, S.

L. J. Zeng, I. Fujima, A. Hirai, H. Matsumoto, S. Iwasaki, “A two-color heterodyne interferometer for measuring the refractive index of air using an optical diffraction grating,” Opt. Commun. 203, 243–247 (2002).
[CrossRef]

Kothiyal, M. P.

R. S. Sirohi, M. P. Kothiyal, Optical Components, Systems, and Measurement Techniques (Marcel Dekker, 1990), pp. 236–237.

Kwong, K. F.

Le Clerc, F.

Li, D. C.

H. Z. Zhao, R. Liang, D. C. Li, M. Cao, “Practical common-path heterodyne surface profiling interferometer with automatic focusing,” Opt. Laser Technol. 33, 259–265 (2001).
[CrossRef]

Liang, R.

H. Z. Zhao, R. Liang, D. C. Li, M. Cao, “Practical common-path heterodyne surface profiling interferometer with automatic focusing,” Opt. Laser Technol. 33, 259–265 (2001).
[CrossRef]

Lo, Y. L.

Y. L. Lo, C. H. Chuang, “Fluid velocity measurements in a microchannel performed with two new optical heterodyne microscopes,” Appl. Opt. 41, 6666–6675 (2002).
[CrossRef] [PubMed]

Y. L. Lo, C. H. Chuang, “New synthetic-heterodyne demodulator for an optical fiber interferometer,” IEEE J. Quantum Electron. 37, 658–663 (2001).
[CrossRef]

Matsumoto, H.

L. J. Zeng, I. Fujima, A. Hirai, H. Matsumoto, S. Iwasaki, “A two-color heterodyne interferometer for measuring the refractive index of air using an optical diffraction grating,” Opt. Commun. 203, 243–247 (2002).
[CrossRef]

A. Hirai, L. J. Zeng, H. Matsumoto, “Heterodyne Fourier transform spectroscopy using moving diffraction grating,” Jpn. J. Phys. 40, 6138–6142 (2001).
[CrossRef]

A. Hirai, H. Matsumoto, “High-sensitivity surface profile measurements by heterodyne white-light interferometer,” Opt. Eng. 40, 387–391 (2001).
[CrossRef]

H. Matsumoto, A. Hirai, “A white light interferometer using a lamp source and heterodyne detection with acousto-optic modulators,” Opt. Commun. 170, 217–220 (1999).
[CrossRef]

A. Hirai, K. Seta, H. Matsumoto, “White-light interferometry using pseudo random-modulation for high-sensitivity and high-selectivity measurements,” Opt. Commun. 162, 11–15 (1999).
[CrossRef]

Rickermann, F.

F. Rickermann, S. Riehemann, G. von Bally, S. Breer, K. Buse, “A high resolution real-time temporal heterodyne interferometer for refractive index topography,” Opt. Commun. 144, 173–179 (1997).
[CrossRef]

Riehemann, S.

F. Rickermann, S. Riehemann, G. von Bally, S. Breer, K. Buse, “A high resolution real-time temporal heterodyne interferometer for refractive index topography,” Opt. Commun. 144, 173–179 (1997).
[CrossRef]

Roy, M.

Sato, M.

K. P. Chan, M. Sato, M. Akiba, N. Tanno, “Detection schemes for optical-coherence-domain imaging of biological tissues,” Opt. Rev. 7, 389–395 (2000).
[CrossRef]

Seta, K.

A. Hirai, K. Seta, H. Matsumoto, “White-light interferometry using pseudo random-modulation for high-sensitivity and high-selectivity measurements,” Opt. Commun. 162, 11–15 (1999).
[CrossRef]

Sheppard, C. J. R.

Sirohi, R. S.

R. S. Sirohi, M. P. Kothiyal, Optical Components, Systems, and Measurement Techniques (Marcel Dekker, 1990), pp. 236–237.

Somervell, A. R. D.

A. R. D. Somervell, M. E. K. Williams, T. H. Barnes, “Direct measurement of fringe amplitude and phase using a heterodyne interferometer operating in broadband light,” Opt. Commun. 229, 59–64 (2004).
[CrossRef]

Tanno, N.

M. Akiba, K. P. Chan, N. Tanno, “Real-time, micrometer depth-resolved imaging by low-coherence interferometry and a two-dimensional heterodyne detection technique,” Jpn. J. Phys. 39, L1194–L1196 (2000).
[CrossRef]

K. P. Chan, M. Sato, M. Akiba, N. Tanno, “Detection schemes for optical-coherence-domain imaging of biological tissues,” Opt. Rev. 7, 389–395 (2000).
[CrossRef]

Toal, V.

B. Bowe, V. Toal, “White light interferometric surface profiler,” Opt. Eng. 37, 1796–1799 (1998).
[CrossRef]

Venzke, H.

von Bally, G.

F. Rickermann, S. Riehemann, G. von Bally, S. Breer, K. Buse, “A high resolution real-time temporal heterodyne interferometer for refractive index topography,” Opt. Commun. 144, 173–179 (1997).
[CrossRef]

Williams, M. E. K.

A. R. D. Somervell, M. E. K. Williams, T. H. Barnes, “Direct measurement of fringe amplitude and phase using a heterodyne interferometer operating in broadband light,” Opt. Commun. 229, 59–64 (2004).
[CrossRef]

Yankelevich, D.

Zeng, L. J.

L. J. Zeng, I. Fujima, A. Hirai, H. Matsumoto, S. Iwasaki, “A two-color heterodyne interferometer for measuring the refractive index of air using an optical diffraction grating,” Opt. Commun. 203, 243–247 (2002).
[CrossRef]

A. Hirai, L. J. Zeng, H. Matsumoto, “Heterodyne Fourier transform spectroscopy using moving diffraction grating,” Jpn. J. Phys. 40, 6138–6142 (2001).
[CrossRef]

Zhao, H. Z.

H. Z. Zhao, R. Liang, D. C. Li, M. Cao, “Practical common-path heterodyne surface profiling interferometer with automatic focusing,” Opt. Laser Technol. 33, 259–265 (2001).
[CrossRef]

Appl. Opt.

IEEE J. Quantum Electron.

Y. L. Lo, C. H. Chuang, “New synthetic-heterodyne demodulator for an optical fiber interferometer,” IEEE J. Quantum Electron. 37, 658–663 (2001).
[CrossRef]

Jpn. J. Phys.

M. Akiba, K. P. Chan, N. Tanno, “Real-time, micrometer depth-resolved imaging by low-coherence interferometry and a two-dimensional heterodyne detection technique,” Jpn. J. Phys. 39, L1194–L1196 (2000).
[CrossRef]

A. Hirai, L. J. Zeng, H. Matsumoto, “Heterodyne Fourier transform spectroscopy using moving diffraction grating,” Jpn. J. Phys. 40, 6138–6142 (2001).
[CrossRef]

Opt. Commun.

L. J. Zeng, I. Fujima, A. Hirai, H. Matsumoto, S. Iwasaki, “A two-color heterodyne interferometer for measuring the refractive index of air using an optical diffraction grating,” Opt. Commun. 203, 243–247 (2002).
[CrossRef]

F. Rickermann, S. Riehemann, G. von Bally, S. Breer, K. Buse, “A high resolution real-time temporal heterodyne interferometer for refractive index topography,” Opt. Commun. 144, 173–179 (1997).
[CrossRef]

A. Hirai, K. Seta, H. Matsumoto, “White-light interferometry using pseudo random-modulation for high-sensitivity and high-selectivity measurements,” Opt. Commun. 162, 11–15 (1999).
[CrossRef]

H. Matsumoto, A. Hirai, “A white light interferometer using a lamp source and heterodyne detection with acousto-optic modulators,” Opt. Commun. 170, 217–220 (1999).
[CrossRef]

A. R. D. Somervell, M. E. K. Williams, T. H. Barnes, “Direct measurement of fringe amplitude and phase using a heterodyne interferometer operating in broadband light,” Opt. Commun. 229, 59–64 (2004).
[CrossRef]

Opt. Eng.

A. Hirai, H. Matsumoto, “High-sensitivity surface profile measurements by heterodyne white-light interferometer,” Opt. Eng. 40, 387–391 (2001).
[CrossRef]

B. Bowe, V. Toal, “White light interferometric surface profiler,” Opt. Eng. 37, 1796–1799 (1998).
[CrossRef]

Opt. Express

Opt. Laser Technol.

H. Z. Zhao, R. Liang, D. C. Li, M. Cao, “Practical common-path heterodyne surface profiling interferometer with automatic focusing,” Opt. Laser Technol. 33, 259–265 (2001).
[CrossRef]

Opt. Lett.

Opt. Rev.

K. P. Chan, M. Sato, M. Akiba, N. Tanno, “Detection schemes for optical-coherence-domain imaging of biological tissues,” Opt. Rev. 7, 389–395 (2000).
[CrossRef]

Other

R. S. Sirohi, M. P. Kothiyal, Optical Components, Systems, and Measurement Techniques (Marcel Dekker, 1990), pp. 236–237.

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Figures (5)

Fig. 1
Fig. 1

Experimental setup for a two-dimensional imaging system where a low-coherence heterodyne detection technique is used: BS1, BS2, beam splitters; L, lens; G1, G2, gratings; PZT, piezoelectric transducer; M1–44, mirrors; SPC: signal processing circuit; D/A, digital/analog.

Fig. 2
Fig. 2

Principle of the fringe phase and amplitude measurement.

Fig. 3
Fig. 3

Comparison of displacement measured by the heterodyne method and by linear gauge at pixel position (18, 9).

Fig. 4
Fig. 4

Displacement of M1 measured by all the CCD 80 × 84 pixels: δLH, measured by the heterodyne method; δLR, reference displacement measured by the linear gauge.

Fig. 5
Fig. 5

(a) Image of a glass sample obtained by low-coherence heterodyne detection, (b) image of the sample obtained by the method without heterodyne modulation, (c) camera picture of the sample.

Equations (9)

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

Δ f = m ν / d ,
D 1 - D 2 = ± ( D 3 - D 4 ) ,
n = f c f CCD = 450 25 = 18.
I = I 0 + V cos [ 8 π Δ f t + ϕ 0 + ( j - 1 ) ϕ b ] , t [ m T , T + T / 2 ] , j = 1 , 2 , 3 , 4 , 5 ,
I j = n 0 T 2 I d t = n T 2 I 0 + [ n sin ( 2 π Δ f T ) 4 π Δ f V ] cos [ ( 2 π Δ f T + ϕ 0 ) + ( j - 1 ) ϕ b = I 0 + V cos ( ϕ 0 + ( j - 1 ) ϕ b ] ,
ϕ 0 = tan = 1 [ 2 sin ( ϕ b ) I 2 - I 4 2 I 3 - ( I 1 + I 5 ) ] - 2 ϕ b .
V = I 2 - I 4 2 sin ( ϕ b ) sin ( ϕ 0 + 2 ϕ b )
V = I 1 - I 3 2 sin ( ϕ b ) sin ( ϕ 0 + ϕ b ) .
ϕ b = cos - 1 [ I 1 - I 5 2 ( I 2 - I 4 ) ] .

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