Abstract

A real-time method for heterodyne speckle pattern interferometry using the correlation image sensor (CIS) is proposed. The CIS demodulates the interference phase of heterodyned speckle wavefronts pixelwise at an ordinary video frame rate. The proposed method neither suffers loss of spatial resolution nor requires a high frame rate. Interferometers for out-of-plane and in-plane deformation are developed with a 200×200 pixel CIS camera. Experimental results confirm that the proposed method realizes real-time imaging of a rough-surfaced object under deformation. The average standard deviations of demodulated phase-difference images for the out-of-plane and in-plane interferometers are 0.33 and 0.13rad, respectively.

© 2010 Optical Society of America

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References

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  1. R. Jones and C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge University, 1989).
  2. R.S.Sirohi, ed., Speckle Metrology (Marcel Dekker, 1993).
  3. P.K.Rastogi, ed., Digital Speckle Pattern Interferometry and Related Techniques (Wiley, 2001).
  4. J. Kato, I. Yamaguchi and Q. Ping, “Automatic deformation analysis by a TV speckle interferometer using a laser diode,” Appl. Opt. 32, 77–83 (1993).
    [CrossRef] [PubMed]
  5. K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. 24, 3053–3058 (1985).
    [CrossRef] [PubMed]
  6. M. Takeda and H. Yamamoto, “Fourier-transform speckle profilometry: three-dimensional shape measurements of diffuse objects with large height steps and/or spatially isolated surfaces,” Appl. Opt. 33, 7829–7837 (1994).
    [CrossRef] [PubMed]
  7. T. Wu, J. D. C. Jones, and A. J. Moore, “High-speed phase-stepped digital speckle pattern interferometry using a complementary metal-oxide semiconductor camera,” Appl. Opt. 45, 5845–5855 (2006).
    [CrossRef] [PubMed]
  8. P. Haible, M. P. Kothiyal, and H. J. Tiziani, “Heterodyne temporal speckle-pattern interferometry,” Appl. Opt. 39, 114–117 (2000).
    [CrossRef]
  9. M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, “Heterodyne speckle interferometer for full-field velocity profile measurements of a vibrating membrane by electronic scanning,” Opt. Lasers Eng. 45, 677–683 (2007).
    [CrossRef]
  10. L. Bruno and A. Poggialini, “Phase shifting speckle interferometry for dynamic phenomena,” Opt. Express 16, 4665–4670(2008).
    [CrossRef] [PubMed]
  11. M. North-Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE 5869, 58691B (2005).
    [CrossRef]
  12. T. Kiire, S. Nakadate, and M. Shibuya, “Simultaneous formation of four fringes by using a polarization quadrature phase-shifting interferometer with wave plates and a diffraction grating,” Appl. Opt. 47, 4787–4792 (2008).
    [CrossRef] [PubMed]
  13. 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]
  14. A. Kimachi, “Real-time heterodyne imaging interferometry: focal-plane amplitude and phase demodulation using a three-phase correlation image sensor,” Appl. Opt. 46, 87–94(2007).
    [CrossRef]
  15. S. Ando, S. Ozaki, and A. Kimachi, “Active acousto-holographic imaging system with heterodyne interferometry and correlation image sensor,” in Proceedings of the 15th International Congress on Sound and Vibration (International Institute of Acoustics and Vibration, 2008), pp. 682–689.
  16. S. Ando, S. Sato, and T. Kurihara, “Real-time tracking experiment of higher-order Laguerre-Gaussian beam for remote six-axis deformation sensing,” in Proceedings of the Sixth International Conference on Networked Sensing Systems (IEEE, 2009), pp. 106–109.
  17. A. Kimachi, “Real-time phase demodulation of heterodyne speckle interference patterns using correlation image sensor,” Proc. SPIE 7790, 779007 (2010).
    [CrossRef]
  18. A. Kimachi and S. Ando, “Real-time phase-stamp range finder using correlation image sensor,” IEEE Sens. J. 9, 1784–1792(2009).
    [CrossRef]
  19. K. J. Gåsvik, Optical Metrology, 3rd ed. (Wiley, 2002).
    [CrossRef]

2010 (1)

A. Kimachi, “Real-time phase demodulation of heterodyne speckle interference patterns using correlation image sensor,” Proc. SPIE 7790, 779007 (2010).
[CrossRef]

2009 (1)

A. Kimachi and S. Ando, “Real-time phase-stamp range finder using correlation image sensor,” IEEE Sens. J. 9, 1784–1792(2009).
[CrossRef]

2008 (2)

2007 (2)

A. Kimachi, “Real-time heterodyne imaging interferometry: focal-plane amplitude and phase demodulation using a three-phase correlation image sensor,” Appl. Opt. 46, 87–94(2007).
[CrossRef]

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, “Heterodyne speckle interferometer for full-field velocity profile measurements of a vibrating membrane by electronic scanning,” Opt. Lasers Eng. 45, 677–683 (2007).
[CrossRef]

2006 (1)

2005 (1)

M. North-Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE 5869, 58691B (2005).
[CrossRef]

2003 (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]

2000 (1)

1994 (1)

1993 (1)

1985 (1)

Aguanno, M. V.

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, “Heterodyne speckle interferometer for full-field velocity profile measurements of a vibrating membrane by electronic scanning,” Opt. Lasers Eng. 45, 677–683 (2007).
[CrossRef]

Ando, S.

A. Kimachi and S. Ando, “Real-time phase-stamp range finder using correlation image sensor,” IEEE Sens. J. 9, 1784–1792(2009).
[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, S. Sato, and T. Kurihara, “Real-time tracking experiment of higher-order Laguerre-Gaussian beam for remote six-axis deformation sensing,” in Proceedings of the Sixth International Conference on Networked Sensing Systems (IEEE, 2009), pp. 106–109.

S. Ando, S. Ozaki, and A. Kimachi, “Active acousto-holographic imaging system with heterodyne interferometry and correlation image sensor,” in Proceedings of the 15th International Congress on Sound and Vibration (International Institute of Acoustics and Vibration, 2008), pp. 682–689.

Brock, N.

M. North-Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE 5869, 58691B (2005).
[CrossRef]

Bruno, L.

Connelly, M. J.

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, “Heterodyne speckle interferometer for full-field velocity profile measurements of a vibrating membrane by electronic scanning,” Opt. Lasers Eng. 45, 677–683 (2007).
[CrossRef]

Creath, K.

Gåsvik, K. J.

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

Haible, P.

Hayes, J.

M. North-Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE 5869, 58691B (2005).
[CrossRef]

Jones, J. D. C.

Jones, R.

R. Jones and C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge University, 1989).

Kato, J.

Kiire, T.

Kimachi, A.

A. Kimachi, “Real-time phase demodulation of heterodyne speckle interference patterns using correlation image sensor,” Proc. SPIE 7790, 779007 (2010).
[CrossRef]

A. Kimachi and S. Ando, “Real-time phase-stamp range finder using correlation image sensor,” IEEE Sens. J. 9, 1784–1792(2009).
[CrossRef]

A. Kimachi, “Real-time heterodyne imaging interferometry: focal-plane amplitude and phase demodulation using a three-phase correlation image sensor,” Appl. Opt. 46, 87–94(2007).
[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, S. Ozaki, and A. Kimachi, “Active acousto-holographic imaging system with heterodyne interferometry and correlation image sensor,” in Proceedings of the 15th International Congress on Sound and Vibration (International Institute of Acoustics and Vibration, 2008), pp. 682–689.

Kothiyal, M. P.

Kurihara, T.

S. Ando, S. Sato, and T. Kurihara, “Real-time tracking experiment of higher-order Laguerre-Gaussian beam for remote six-axis deformation sensing,” in Proceedings of the Sixth International Conference on Networked Sensing Systems (IEEE, 2009), pp. 106–109.

Lakestani, F.

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, “Heterodyne speckle interferometer for full-field velocity profile measurements of a vibrating membrane by electronic scanning,” Opt. Lasers Eng. 45, 677–683 (2007).
[CrossRef]

Millerd, J.

M. North-Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE 5869, 58691B (2005).
[CrossRef]

Moore, A. J.

Nakadate, S.

North-Morris, M.

M. North-Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE 5869, 58691B (2005).
[CrossRef]

Ozaki, S.

S. Ando, S. Ozaki, and A. Kimachi, “Active acousto-holographic imaging system with heterodyne interferometry and correlation image sensor,” in Proceedings of the 15th International Congress on Sound and Vibration (International Institute of Acoustics and Vibration, 2008), pp. 682–689.

Ping, Q.

Poggialini, A.

Saif, B.

M. North-Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE 5869, 58691B (2005).
[CrossRef]

Sato, S.

S. Ando, S. Sato, and T. Kurihara, “Real-time tracking experiment of higher-order Laguerre-Gaussian beam for remote six-axis deformation sensing,” in Proceedings of the Sixth International Conference on Networked Sensing Systems (IEEE, 2009), pp. 106–109.

Shibuya, M.

Takeda, M.

Tiziani, H. J.

Whelan, M. P.

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, “Heterodyne speckle interferometer for full-field velocity profile measurements of a vibrating membrane by electronic scanning,” Opt. Lasers Eng. 45, 677–683 (2007).
[CrossRef]

Wu, T.

Wykes, C.

R. Jones and C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge University, 1989).

Yamaguchi, I.

Yamamoto, H.

Appl. Opt. (7)

IEEE Sens. J. (1)

A. Kimachi and S. Ando, “Real-time phase-stamp range finder using correlation image sensor,” IEEE Sens. J. 9, 1784–1792(2009).
[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]

Opt. Express (1)

Opt. Lasers Eng. (1)

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, “Heterodyne speckle interferometer for full-field velocity profile measurements of a vibrating membrane by electronic scanning,” Opt. Lasers Eng. 45, 677–683 (2007).
[CrossRef]

Proc. SPIE (2)

M. North-Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE 5869, 58691B (2005).
[CrossRef]

A. Kimachi, “Real-time phase demodulation of heterodyne speckle interference patterns using correlation image sensor,” Proc. SPIE 7790, 779007 (2010).
[CrossRef]

Other (6)

R. Jones and C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge University, 1989).

R.S.Sirohi, ed., Speckle Metrology (Marcel Dekker, 1993).

P.K.Rastogi, ed., Digital Speckle Pattern Interferometry and Related Techniques (Wiley, 2001).

S. Ando, S. Ozaki, and A. Kimachi, “Active acousto-holographic imaging system with heterodyne interferometry and correlation image sensor,” in Proceedings of the 15th International Congress on Sound and Vibration (International Institute of Acoustics and Vibration, 2008), pp. 682–689.

S. Ando, S. Sato, and T. Kurihara, “Real-time tracking experiment of higher-order Laguerre-Gaussian beam for remote six-axis deformation sensing,” in Proceedings of the Sixth International Conference on Networked Sensing Systems (IEEE, 2009), pp. 106–109.

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

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Figures (10)

Fig. 1
Fig. 1

Schematic of a real-time heterodyne SPI imaging system using a CIS camera to measure (a) out-of-plane deformation and (b) in-plane deformation.

Fig. 2
Fig. 2

Correlation image sensor: (a) photograph of the 200 × 200 pixel CIS camera and (b) schematic of the sensor architecture.

Fig. 3
Fig. 3

Example of CIS output images for the out-of-plane deformation interferomter: (a) average intensity image f i j ( t ) , (b) interference amplitude image A i j , (c) interference phase image θ i j , (d) interference phase image after the object was moved by 80 nm , (e) difference between the interference phase images in (c) and (d), (f) result of smoothing the image in (e) with a 5 × 5 Gaussian filter, (g) gray-scale chart of phase.

Fig. 4
Fig. 4

Sequence of smoothed difference images of speckle interference phase obtained in the out-of-plane deformation interferometer for displacement of the object from 40 to 480 nm in 40 nm steps.

Fig. 5
Fig. 5

Accuracy evaluation of the out-of-plane deformation interferometer. (a) The mean of the smoothed difference image of speckle interference phase within the central 50 × 50 pixel region, plotted against the displacement of the object. (b) Unwrapped result for the mean of the smoothed phase difference image, including a theoretical response and the standard deviation within the region.

Fig. 6
Fig. 6

Sequence of smoothed difference images of speckle interference phase obtained in the in-plane deformation interferometer for displacement of the object from 40 to 480 nm in 40 nm steps.

Fig. 7
Fig. 7

Accuracy evaluation of the in-plane deformation interferometer. (a) The mean of the smoothed difference image of speckle interference phase within the central 50 × 50 pixel region, plotted against the displacement of the object. (b) Unwrapped result for the mean of the smoothed phase difference image, including a theoretical response and the standard deviation within the region.

Fig. 8
Fig. 8

Illustration of the object for real-time SPI imaging.

Fig. 9
Fig. 9

Real-time sequence of smoothed difference images of speckle interference phase for the object in Fig. 8 under horizontal extension, obtained in the in-plane deformation interferometer over 1.92 s .

Fig. 10
Fig. 10

Unwrapped profiles along the horizontal white lines in the smoothed phase difference images in Fig. 9.

Equations (25)

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[ Q 1 ( i , j ) Q 2 ( i , j ) Q 3 ( i , j ) ] = [ Δ Q 1 ( i , j ) Δ Q 2 ( i , j ) Δ Q 3 ( i , j ) ] + [ 1 3 f i j ( t ) 1 3 f i j ( t ) 1 3 f i j ( t ) ] ,
Δ Q k ( i , j ) = f i j ( t ) g k ( t ) ( k = 1 , 2 , 3 ) ,
[ g 1 ( t ) g 2 ( t ) g 3 ( t ) ] = [ cos 2 π ν t cos ( 2 π ν t + 2 3 π ) cos ( 2 π ν t + 4 3 π ) ] .
u i j = U i j exp ( i ϕ i j ) ,
v i j = V i j exp [ i ( ψ i j 2 π ν t ) ] ,
f i j ( t ) = | u i j + v i j | 2 + n i j ( t ) = A i j cos ( 2 π ν t + θ i j ) + B i j + n i j ( t ) ,
A i j = 2 U i j V i j ,
B i j = U i j 2 + V i j 2 ,
θ i j = ϕ i j ψ i j ,
[ Δ Q 1 ( i , j ) Δ Q 2 ( i , j ) Δ Q 3 ( i , j ) ] = T A i j 2 [ cos θ i j cos ( θ i j 2 3 π ) cos ( θ i j 4 3 π ) ] ,
A i j = 2 2 3 T [ ( Δ Q 1 Δ Q 2 ) 2 + ( Δ Q 2 Δ Q 3 ) 2 + ( Δ Q 3 Δ Q 1 ) 2 ] 1 / 2 ,
θ i j = tan 1 3 ( Δ Q 2 Δ Q 3 ) 2 Δ Q 1 Δ Q 2 Δ Q 3 ,
δ θ i j = 4 π λ δ z i j ,
δ θ i j = 4 π λ δ x i j sin α .
[ Δ Q 1 Δ Q 2 Δ Q 3 ] = T A 2 [ cos θ cos ( θ 2 3 π ) cos ( θ 4 3 π ) ] + [ ϵ 1 ϵ 2 ϵ 3 ] ,
2 Δ Q 1 Δ Q 2 Δ Q 3 = X + Δ X ,
3 ( Δ Q 2 Δ Q 3 ) = Y + Δ Y ,
X = 3 2 T A cos θ ,
Δ X = 2 ϵ 1 ϵ 2 ϵ 3 ,
Y = 3 2 T A sin θ ,
Δ Y = 3 ( ϵ 2 ϵ 3 ) .
tan ( θ + Δ θ ) = Y + Δ Y X + Δ X .
Δ θ X Δ Y Y Δ X X 2 + Y 2 = 2 3 T A [ 3 ( ϵ 2 ϵ 3 ) cos θ ( 2 ϵ 1 ϵ 2 ϵ 3 ) sin θ ] = 4 3 T A ρ cos ( θ + β ) ,
ρ = [ ( ϵ 1 ϵ 2 ) 2 + ( ϵ 2 ϵ 3 ) 2 + ( ϵ 3 ϵ 1 ) 2 ] 1 / 2 ,
β = tan 1 2 ϵ 1 ϵ 2 ϵ 3 3 ( ϵ 2 ϵ 3 ) .

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