Abstract

A method of real-time heterodyne imaging interferometry using a three-phase correlation image sensor (3PCIS) is proposed. It simultaneously demodulates the amplitude and phase images of an incident interference pattern at an ordinary frame rate with good accuracy, thus overcoming the trade-off among measurement time, spatial resolution, and demodulation accuracy suffered in conventional interferometry. An experimental system is constructed with a 64×64 3PCIS camera operated at 30  frames∕s and a two-frequency He–Ne laser with a beat frequency of 25   kHz. The results obtained for a scanning mirror and heated silicone oil confirm the proposed method.

© 2007 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. M. C. Pitter, C. W. See, and M. G. Somekh, "Full-field heterodyne interference microscope with spatially incoherent illumination," Opt. Lett. 29, 1200-1202 (2004).
    [CrossRef] [PubMed]
  8. R. Dändliker, Y. Salvadé, and E. Zimmermann, "Distance measurement by multiple-wavelength interferometry," J. Opt. 29, 105-114 (1998).
    [CrossRef]
  9. T. Spirig, P. Seitz, O. Vietze, and F. Heitger, "The lock-in CCD--two-dimensional synchronous detection of light," IEEE J. Quantum Electron. 31, 1705-1708 (1995).
    [CrossRef]
  10. H. Povel, H. Aebersold, and J. O. Stenflo, "Charge-coupled device image sensor as a demodulator in a 2-D polarimeter with a piezoelastic modulator," Appl. Opt. 29, 1186-1190 (1990).
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  11. S. Bourquin, P. Seitz, and R. P. Salathé, "Optical coherence topography based on a two-dimensional smart detector array," Opt. Lett. 26, 512-514 (2001).
    [CrossRef]
  12. S. Bourquin, P. Seitz, and R. P. Salathé, "Two-dimensional smart detector array for interferometric applications," Electron. Lett. 37, 975-976 (2001).
    [CrossRef]
  13. S. Ando, T. Nakamura, and T. Sakaguchi, "Ultrafast correlation image sensor: concept, design and applications," in Proceedings of IEEE Workshop on Charge-Coupled Devices and Advanced Image Sensors (1997).
  14. S. Ando and A. Kimachi, "Correlation image sensor: two-dimensional matched detection of amplitude-modulated light," IEEE Trans. Electron Devices 50, 2059-2066 (2003).
    [CrossRef]
  15. A. Kimachi and M. Ida, "Real-time heterodyne imaging interferometry using three-phase correlation image sensor," in Proceedings of Society of Instrument and Control Engineers (SICE) Annual Conference (2004), pp. 2488-2493.
  16. VLSI Design and Education Center, the University of Tokyo, Japan, http://www.vdec.u-tokyo.ac.jp/.
  17. A. Kimachi and S. Ando, "Measurement and compensation of average-irradiance dependence in frequency response of correlation image sensor," IEE J. Trans. Sensors Micromach . 126, 345-351 (2006).
    [CrossRef]

2006 (1)

A. Kimachi and S. Ando, "Measurement and compensation of average-irradiance dependence in frequency response of correlation image sensor," IEE J. Trans. Sensors Micromach . 126, 345-351 (2006).
[CrossRef]

2004 (2)

A. Kimachi and M. Ida, "Real-time heterodyne imaging interferometry using three-phase correlation image sensor," in Proceedings of Society of Instrument and Control Engineers (SICE) Annual Conference (2004), pp. 2488-2493.

M. C. Pitter, C. W. See, and M. G. Somekh, "Full-field heterodyne interference microscope with spatially incoherent illumination," Opt. Lett. 29, 1200-1202 (2004).
[CrossRef] [PubMed]

2003 (2)

M. Akiba, K. P. Chan, and N. Tanno, "Full-field optical coherence tomography by two-dimensional heterodyne detection with a pair of CCD cameras," Opt. Lett. 28, 816-818 (2003).
[CrossRef] [PubMed]

S. Ando and A. Kimachi, "Correlation image sensor: two-dimensional matched detection of amplitude-modulated light," IEEE Trans. Electron Devices 50, 2059-2066 (2003).
[CrossRef]

2001 (2)

S. Bourquin, P. Seitz, and R. P. Salathé, "Two-dimensional smart detector array for interferometric applications," Electron. Lett. 37, 975-976 (2001).
[CrossRef]

S. Bourquin, P. Seitz, and R. P. Salathé, "Optical coherence topography based on a two-dimensional smart detector array," Opt. Lett. 26, 512-514 (2001).
[CrossRef]

1998 (1)

R. Dändliker, Y. Salvadé, and E. Zimmermann, "Distance measurement by multiple-wavelength interferometry," J. Opt. 29, 105-114 (1998).
[CrossRef]

1997 (1)

S. Ando, T. Nakamura, and T. Sakaguchi, "Ultrafast correlation image sensor: concept, design and applications," in Proceedings of IEEE Workshop on Charge-Coupled Devices and Advanced Image Sensors (1997).

1995 (1)

T. Spirig, P. Seitz, O. Vietze, and F. Heitger, "The lock-in CCD--two-dimensional synchronous detection of light," IEEE J. Quantum Electron. 31, 1705-1708 (1995).
[CrossRef]

1990 (1)

1982 (1)

1979 (1)

1974 (1)

1973 (1)

R. Dändliker, B. Ineichen, and F. M. Mottier, "High-resolution hologram interferometry by electronic phase measurement," Opt. Commun. 9, 412-416 (1973).
[CrossRef]

Aebersold, H.

Akiba, M.

Ando, S.

A. Kimachi and S. Ando, "Measurement and compensation of average-irradiance dependence in frequency response of correlation image sensor," IEE J. Trans. Sensors Micromach . 126, 345-351 (2006).
[CrossRef]

S. Ando and A. Kimachi, "Correlation image sensor: two-dimensional matched detection of amplitude-modulated light," IEEE Trans. Electron Devices 50, 2059-2066 (2003).
[CrossRef]

S. Ando, T. Nakamura, and T. Sakaguchi, "Ultrafast correlation image sensor: concept, design and applications," in Proceedings of IEEE Workshop on Charge-Coupled Devices and Advanced Image Sensors (1997).

Bourquin, S.

S. Bourquin, P. Seitz, and R. P. Salathé, "Two-dimensional smart detector array for interferometric applications," Electron. Lett. 37, 975-976 (2001).
[CrossRef]

S. Bourquin, P. Seitz, and R. P. Salathé, "Optical coherence topography based on a two-dimensional smart detector array," Opt. Lett. 26, 512-514 (2001).
[CrossRef]

Brangaccio, D. J.

Bruning, J. H.

Chan, K. P.

Dändliker, R.

R. Dändliker, Y. Salvadé, and E. Zimmermann, "Distance measurement by multiple-wavelength interferometry," J. Opt. 29, 105-114 (1998).
[CrossRef]

R. Dändliker, B. Ineichen, and F. M. Mottier, "High-resolution hologram interferometry by electronic phase measurement," Opt. Commun. 9, 412-416 (1973).
[CrossRef]

Gallagher, J. E.

Gåsvik, K. J.

K. J. Gåsvik, Optical Metrology, 3rd ed. (Wiley, 2002).
[CrossRef]

Heitger, F.

T. Spirig, P. Seitz, O. Vietze, and F. Heitger, "The lock-in CCD--two-dimensional synchronous detection of light," IEEE J. Quantum Electron. 31, 1705-1708 (1995).
[CrossRef]

Herriott, D. R.

Holly, S.

Ida, M.

A. Kimachi and M. Ida, "Real-time heterodyne imaging interferometry using three-phase correlation image sensor," in Proceedings of Society of Instrument and Control Engineers (SICE) Annual Conference (2004), pp. 2488-2493.

Ineichen, B.

R. Dändliker, B. Ineichen, and F. M. Mottier, "High-resolution hologram interferometry by electronic phase measurement," Opt. Commun. 9, 412-416 (1973).
[CrossRef]

Kimachi, A.

A. Kimachi and S. Ando, "Measurement and compensation of average-irradiance dependence in frequency response of correlation image sensor," IEE J. Trans. Sensors Micromach . 126, 345-351 (2006).
[CrossRef]

A. Kimachi and M. Ida, "Real-time heterodyne imaging interferometry using three-phase correlation image sensor," in Proceedings of Society of Instrument and Control Engineers (SICE) Annual Conference (2004), pp. 2488-2493.

S. Ando and A. Kimachi, "Correlation image sensor: two-dimensional matched detection of amplitude-modulated light," IEEE Trans. Electron Devices 50, 2059-2066 (2003).
[CrossRef]

Massie, N. A.

Morgan, C. J.

Mottier, F. M.

R. Dändliker, B. Ineichen, and F. M. Mottier, "High-resolution hologram interferometry by electronic phase measurement," Opt. Commun. 9, 412-416 (1973).
[CrossRef]

Nakamura, T.

S. Ando, T. Nakamura, and T. Sakaguchi, "Ultrafast correlation image sensor: concept, design and applications," in Proceedings of IEEE Workshop on Charge-Coupled Devices and Advanced Image Sensors (1997).

Nelson, R. D.

Pitter, M. C.

Povel, H.

Rosenfeld, D. P.

Sakaguchi, T.

S. Ando, T. Nakamura, and T. Sakaguchi, "Ultrafast correlation image sensor: concept, design and applications," in Proceedings of IEEE Workshop on Charge-Coupled Devices and Advanced Image Sensors (1997).

Salathé, R. P.

S. Bourquin, P. Seitz, and R. P. Salathé, "Optical coherence topography based on a two-dimensional smart detector array," Opt. Lett. 26, 512-514 (2001).
[CrossRef]

S. Bourquin, P. Seitz, and R. P. Salathé, "Two-dimensional smart detector array for interferometric applications," Electron. Lett. 37, 975-976 (2001).
[CrossRef]

Salvadé, Y.

R. Dändliker, Y. Salvadé, and E. Zimmermann, "Distance measurement by multiple-wavelength interferometry," J. Opt. 29, 105-114 (1998).
[CrossRef]

See, C. W.

Seitz, P.

S. Bourquin, P. Seitz, and R. P. Salathé, "Optical coherence topography based on a two-dimensional smart detector array," Opt. Lett. 26, 512-514 (2001).
[CrossRef]

S. Bourquin, P. Seitz, and R. P. Salathé, "Two-dimensional smart detector array for interferometric applications," Electron. Lett. 37, 975-976 (2001).
[CrossRef]

T. Spirig, P. Seitz, O. Vietze, and F. Heitger, "The lock-in CCD--two-dimensional synchronous detection of light," IEEE J. Quantum Electron. 31, 1705-1708 (1995).
[CrossRef]

Somekh, M. G.

Spirig, T.

T. Spirig, P. Seitz, O. Vietze, and F. Heitger, "The lock-in CCD--two-dimensional synchronous detection of light," IEEE J. Quantum Electron. 31, 1705-1708 (1995).
[CrossRef]

Stenflo, J. O.

Tanno, N.

Vietze, O.

T. Spirig, P. Seitz, O. Vietze, and F. Heitger, "The lock-in CCD--two-dimensional synchronous detection of light," IEEE J. Quantum Electron. 31, 1705-1708 (1995).
[CrossRef]

White, A. D.

Zimmermann, E.

R. Dändliker, Y. Salvadé, and E. Zimmermann, "Distance measurement by multiple-wavelength interferometry," J. Opt. 29, 105-114 (1998).
[CrossRef]

Appl. Opt. (3)

Electron. Lett. (1)

S. Bourquin, P. Seitz, and R. P. Salathé, "Two-dimensional smart detector array for interferometric applications," Electron. Lett. 37, 975-976 (2001).
[CrossRef]

IEE J. Trans. Sensors Micromach (1)

A. Kimachi and S. Ando, "Measurement and compensation of average-irradiance dependence in frequency response of correlation image sensor," IEE J. Trans. Sensors Micromach . 126, 345-351 (2006).
[CrossRef]

IEEE J. Quantum Electron. (1)

T. Spirig, P. Seitz, O. Vietze, and F. Heitger, "The lock-in CCD--two-dimensional synchronous detection of light," IEEE J. Quantum Electron. 31, 1705-1708 (1995).
[CrossRef]

IEEE Trans. Electron Devices (1)

S. Ando and A. Kimachi, "Correlation image sensor: two-dimensional matched detection of amplitude-modulated light," IEEE Trans. Electron Devices 50, 2059-2066 (2003).
[CrossRef]

J. Opt. (1)

R. Dändliker, Y. Salvadé, and E. Zimmermann, "Distance measurement by multiple-wavelength interferometry," J. Opt. 29, 105-114 (1998).
[CrossRef]

Opt. Commun. (1)

R. Dändliker, B. Ineichen, and F. M. Mottier, "High-resolution hologram interferometry by electronic phase measurement," Opt. Commun. 9, 412-416 (1973).
[CrossRef]

Opt. Lett. (4)

Other (4)

A. Kimachi and M. Ida, "Real-time heterodyne imaging interferometry using three-phase correlation image sensor," in Proceedings of Society of Instrument and Control Engineers (SICE) Annual Conference (2004), pp. 2488-2493.

VLSI Design and Education Center, the University of Tokyo, Japan, http://www.vdec.u-tokyo.ac.jp/.

K. J. Gåsvik, Optical Metrology, 3rd ed. (Wiley, 2002).
[CrossRef]

S. Ando, T. Nakamura, and T. Sakaguchi, "Ultrafast correlation image sensor: concept, design and applications," in Proceedings of IEEE Workshop on Charge-Coupled Devices and Advanced Image Sensors (1997).

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Figures (11)

Fig. 1
Fig. 1

Schematic of the 3PCIS pixel circuit.

Fig. 2
Fig. 2

Schematic of the experimental imaging system based on a polarizing Michelson interferometer: BS, beam splitter; PBS, polarizing beam splitter; QWP, quarter-wave plate; POL, polarizer∕analyzer; PD, photodiode.

Fig. 3
Fig. 3

Schematic of the two-frequency He–Ne laser source: HWP, half-wave plate.

Fig. 4
Fig. 4

Photograph of the 64 × 64 3PCIS camera.

Fig. 5
Fig. 5

Example of output images from the 3PCIS: (a) average irradiance, (b) demodulated amplitude, (c) demodulated phase, (d) gray-scale representation of phase.

Fig. 6
Fig. 6

Demodulated phase images for increasing voltages of the piezoactuator.

Fig. 7
Fig. 7

Phase difference images with respect to 30.0   V .

Fig. 8
Fig. 8

Plot of the phase difference with respect to 30 .0   V at a pixel at the image center.

Fig. 9
Fig. 9

Plot of the unwrapped phase difference at a pixel at the image center.

Fig. 10
Fig. 10

Setup for imaging through a time-varying sample: (a) optical arrangement and (b) preparation of silicone oil used as the sample.

Fig. 11
Fig. 11

Real-time sequence of phase difference images with respect to 0 .0   s captured through heated silicone oil.

Tables (1)

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Table 1 Specifications of the Three-Phase Correlation Image Sensor Camera

Equations (13)

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[ Q 1 Q 2 Q 3 ] = I ( t ) 3 [ 1 1 1 ] + ρ [ υ 1 ( t ) I ( t ) υ 2 ( t ) I ( t ) υ 3 ( t ) I ( t ) ] ,
I i j ( t ) = B i j + A i j cos ( 2 π f 0 t + θ i j ) ,
[ υ 1 ( t ) υ 2 ( t ) υ 3 ( t ) ] = υ 0 [ cos 2 π f 0 t cos ( 2 π f 0 t + 2 3 π ) cos ( 2 π f 0 t + 4 3 π ) ] ,
[ Q 1 Q 2 Q 3 ] = T B i j 3 [ 1 1 1 ] + T ρ υ 0 A i j 2 [ cos θ i j cos ( θ i j 2 3 π ) cos ( θ i j 4 3 π ) ] + [ ξ 1 ξ 2 ξ 3 ] ,
A i j = 2 2 3 T ρ υ 0 [ ( Q 1 Q 2 ) 2 + ( Q 2 Q 3 ) 2 + ( Q 3 Q 1 ) 2 ] 1 / 2 ,
θ i j = tan 1 3 ( Q 2 Q 3 ) 2 Q 1 Q 2 Q 3 .
B i j = 1 T ( Q 1 + Q 2 + Q 3 ) .
Δ θ = 4 π λ 0 Δ z .
cos 2 π f 0 t 0 = cos 2 π f 0 t ,
cos ( 2 π f 0 t + 1 3 π ) cos 2 π f 0 t = cos ( 2 π f 0 t + 2 3 π ) ,
0 cos ( 2 π f 0 t + 1 3 π ) = cos ( 2 π f 0 t + 4 3 π ) .
[ υ 1 ( t ) υ 2 ( t ) υ 3 ( t ) ] υ 0 [ cos 2 π f 0 t cos ( 2 π f 0 t + 2 3 π ) cos ( 2 π f 0 t + 4 3 π ) ] + ϵ [ 0 sin ( 2 π f 0 t + 1 3 π ) sin ( 2 π f 0 t + 1 3 π ) ] .
[ Δ Q 1 Δ Q 2 Δ Q 3 ] = T ρ υ 0 A i j 2 ϵ [ 0 sin ( θ i j + 2 3 π ) sin ( θ i j + 2 3 π ) ] ,

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