Abstract

A digital speckle pattern interferometer based on a complementary metal-oxide semiconductor (CMOS) camera is described. The temporal evolution of dynamic deformation is measured using interframe phase stepping. The flexibility of the CMOS detector is used to identify regions of interest with full-field time-averaged measurements and then to interrogate those regions with time-resolved measurements sampled at up to 70  kHz. A numerical and analytical investigation shows that the maximum surface velocity that can be reliably measured with interframe phase stepping corresponds to ±0.3 times the surface velocity at which the interferogram is sampled at the Nyquist limit.

© 2006 Optical Society of America

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References

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  1. P.K.Rastogi, ed., Digital Speckle Pattern Interferometry and Related Techniques (Wiley, 2001).
  2. J. M. Kilpatrick, A. J. Moore, J. S. Barton, J. D. C. Jones, M. Reeves, and C. Buckberry, "Measurement of complex surface deformation by high-speed dynamic phase-stepped digital speckle pattern interferometry," Opt. Lett. 25, 1068-1070 (2000).
    [CrossRef]
  3. C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, "Speckle interferometry with temporal phase evaluation for measuring large-object deformation," Appl. Opt. 37, 2608-2614 (1998).
    [CrossRef]
  4. J. M. Huntley, G. H. Kaufmann, and D. Kerr, "Phase-shifted dynamic speckle pattern interferometry at 1 kHz," Appl. Opt. 38, 6556-6563 (1999).
    [CrossRef]
  5. A. Davila, J. M. Huntley, G. H. Kaufmann, and D. Kerr, "High-speed dynamic speckle interferometry: phase errors due to intensity, velocity and speckle decorrelation," Appl. Opt. 44, 3954-3962 (2005).
    [CrossRef] [PubMed]
  6. H. Helmers and M. Schellenberg, "CMOS vs. CCD sensors in speckle interferometry," Opt. Laser Technol. 35, 587-595 (2003).
    [CrossRef]
  7. A. J. Moore, D. P. Hand, J. S. Barton, and J. D. C. Jones, "Transient deformation measurement with electronic speckle pattern interferometry and a high-speed camera," Appl. Opt. 38, 1159-1162 (1999).
    [CrossRef]
  8. H. Helmers, D. D. Carl, and T. Sievers, "CMOS-ESPI-system with in-line digital phase stabilization using unresolved speckles," in Interferometry XI: Techniques and Analysis, K. Creath and J. Schmit, eds., Proc. SPIE 4777, 232-241 (2002).
    [CrossRef]
  9. M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, "Speckle interferometry using a CMOS-DSP camera for static and dynamic deformation measurements," in ICEM12--12th International Conference on Experimental Mechanics (2004).
  10. J. D. Briers, "Laser Doppler, speckle and related techniques for blood perfusion mapping and imaging," Physiol. Meas. 22, R35-R66 (2001).
    [CrossRef]
  11. A. Serov, W. Steenbergen, and F. de Mul, "Laser Doppler perfusion imaging with a complementary metal oxide semiconductor image sensor," Opt. Lett. 27, 300-302 (2002).
    [CrossRef]
  12. A. Serov, B. Steinacher, and T. Lasser, "Full-field laser Doppler perfusion imaging and monitoring with an intelligent CMOS camera," Opt. Express 13, 3681-3689 (2005).
    [CrossRef] [PubMed]
  13. H. Fujji, K. Nohira, Y. Yamamoto, H. Ikawa, and T. Ohura, "Evaluation of blood flow by laser speckle image sensing. Part 1," Appl. Opt. 26, 5321-5325 (1987).
    [CrossRef]
  14. P. Carré, "Installation et utilisation du comparateur photoélectrique et interférential du Bureau International des Poids et Mesures," Metrologia 2, 13-23 (1966).
    [CrossRef]
  15. J. Schwider, R. Burrow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, and K. Merkel, "Digital wave-front measuring interferometry: some systematic error sources," Appl. Opt. 22, 3421-3432 (1983).
    [CrossRef] [PubMed]
  16. K. Creath, "Temporal phase measurement methods," in Interferogram Analysis, D.W.Robinson and G.T.Reid, eds. (IOP, 1993).
  17. A. J. P. Van Haasteren and J. Frankena, "Real time displacement measurement using a multicamera phase-stepping speckle interferometer," Appl. Opt. 33, 4137-4142 (1994).
    [CrossRef]

2005 (2)

2003 (1)

H. Helmers and M. Schellenberg, "CMOS vs. CCD sensors in speckle interferometry," Opt. Laser Technol. 35, 587-595 (2003).
[CrossRef]

2002 (2)

H. Helmers, D. D. Carl, and T. Sievers, "CMOS-ESPI-system with in-line digital phase stabilization using unresolved speckles," in Interferometry XI: Techniques and Analysis, K. Creath and J. Schmit, eds., Proc. SPIE 4777, 232-241 (2002).
[CrossRef]

A. Serov, W. Steenbergen, and F. de Mul, "Laser Doppler perfusion imaging with a complementary metal oxide semiconductor image sensor," Opt. Lett. 27, 300-302 (2002).
[CrossRef]

2001 (1)

J. D. Briers, "Laser Doppler, speckle and related techniques for blood perfusion mapping and imaging," Physiol. Meas. 22, R35-R66 (2001).
[CrossRef]

2000 (1)

1999 (2)

1998 (1)

1994 (1)

1987 (1)

1983 (1)

1966 (1)

P. Carré, "Installation et utilisation du comparateur photoélectrique et interférential du Bureau International des Poids et Mesures," Metrologia 2, 13-23 (1966).
[CrossRef]

Aguanno, M. V.

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, "Speckle interferometry using a CMOS-DSP camera for static and dynamic deformation measurements," in ICEM12--12th International Conference on Experimental Mechanics (2004).

Barton, J. S.

Briers, J. D.

J. D. Briers, "Laser Doppler, speckle and related techniques for blood perfusion mapping and imaging," Physiol. Meas. 22, R35-R66 (2001).
[CrossRef]

Buckberry, C.

Burrow, R.

Carl, D. D.

H. Helmers, D. D. Carl, and T. Sievers, "CMOS-ESPI-system with in-line digital phase stabilization using unresolved speckles," in Interferometry XI: Techniques and Analysis, K. Creath and J. Schmit, eds., Proc. SPIE 4777, 232-241 (2002).
[CrossRef]

Carré, P.

P. Carré, "Installation et utilisation du comparateur photoélectrique et interférential du Bureau International des Poids et Mesures," Metrologia 2, 13-23 (1966).
[CrossRef]

Connelly, M. J.

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, "Speckle interferometry using a CMOS-DSP camera for static and dynamic deformation measurements," in ICEM12--12th International Conference on Experimental Mechanics (2004).

Creath, K.

K. Creath, "Temporal phase measurement methods," in Interferogram Analysis, D.W.Robinson and G.T.Reid, eds. (IOP, 1993).

Davila, A.

de Mul, F.

Elssner, K.-E.

Frankena, J.

Franze, B.

Fujji, H.

Grzanna, J.

Haible, P.

Hand, D. P.

Helmers, H.

H. Helmers and M. Schellenberg, "CMOS vs. CCD sensors in speckle interferometry," Opt. Laser Technol. 35, 587-595 (2003).
[CrossRef]

H. Helmers, D. D. Carl, and T. Sievers, "CMOS-ESPI-system with in-line digital phase stabilization using unresolved speckles," in Interferometry XI: Techniques and Analysis, K. Creath and J. Schmit, eds., Proc. SPIE 4777, 232-241 (2002).
[CrossRef]

Huntley, J. M.

Ikawa, H.

Joenathan, C.

Jones, J. D. C.

Kaufmann, G. H.

Kerr, D.

Kilpatrick, J. M.

Lakestani, F.

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, "Speckle interferometry using a CMOS-DSP camera for static and dynamic deformation measurements," in ICEM12--12th International Conference on Experimental Mechanics (2004).

Lasser, T.

Merkel, K.

Moore, A. J.

Nohira, K.

Ohura, T.

Reeves, M.

Schellenberg, M.

H. Helmers and M. Schellenberg, "CMOS vs. CCD sensors in speckle interferometry," Opt. Laser Technol. 35, 587-595 (2003).
[CrossRef]

Schwider, J.

Serov, A.

Sievers, T.

H. Helmers, D. D. Carl, and T. Sievers, "CMOS-ESPI-system with in-line digital phase stabilization using unresolved speckles," in Interferometry XI: Techniques and Analysis, K. Creath and J. Schmit, eds., Proc. SPIE 4777, 232-241 (2002).
[CrossRef]

Spolaczyk, R.

Steenbergen, W.

Steinacher, B.

Tiziani, H. J.

Van Haasteren, A. J. P.

Whelan, M. P.

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, "Speckle interferometry using a CMOS-DSP camera for static and dynamic deformation measurements," in ICEM12--12th International Conference on Experimental Mechanics (2004).

Yamamoto, Y.

Appl. Opt. (7)

Metrologia (1)

P. Carré, "Installation et utilisation du comparateur photoélectrique et interférential du Bureau International des Poids et Mesures," Metrologia 2, 13-23 (1966).
[CrossRef]

Opt. Express (1)

Opt. Laser Technol. (1)

H. Helmers and M. Schellenberg, "CMOS vs. CCD sensors in speckle interferometry," Opt. Laser Technol. 35, 587-595 (2003).
[CrossRef]

Opt. Lett. (2)

Physiol. Meas. (1)

J. D. Briers, "Laser Doppler, speckle and related techniques for blood perfusion mapping and imaging," Physiol. Meas. 22, R35-R66 (2001).
[CrossRef]

Proc. SPIE (1)

H. Helmers, D. D. Carl, and T. Sievers, "CMOS-ESPI-system with in-line digital phase stabilization using unresolved speckles," in Interferometry XI: Techniques and Analysis, K. Creath and J. Schmit, eds., Proc. SPIE 4777, 232-241 (2002).
[CrossRef]

Other (3)

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, "Speckle interferometry using a CMOS-DSP camera for static and dynamic deformation measurements," in ICEM12--12th International Conference on Experimental Mechanics (2004).

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

K. Creath, "Temporal phase measurement methods," in Interferogram Analysis, D.W.Robinson and G.T.Reid, eds. (IOP, 1993).

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Figures (11)

Fig. 1
Fig. 1

Schematic of experimental setup. PBS, polarizing beam splitter; P, polarizer; PM, phase modulator, L1, optional cylindrical lens; BS, beam splitter, and ZL, zoom lens.

Fig. 2
Fig. 2

Variation in mean modulation amplitude plotted against the delay between the frame signal and the applied π / 2 phase steps for images recorded at 70   Hz . The curve is a numerical simulation where the delay has been offset to approximately match the experimental points.

Fig. 3
Fig. 3

(a) Interframe phase-step size plotted against the frame number and (b) phase-step size distribution for all frames recorded for a stationary object with a frame rate of 33   kHz . (c) Interframe phase difference plotted against the frame number and (d) phase difference distribution, for the same image sequences as (a) and (b). In (a) and (c), a different symbol is used for every fourth point to emphasize the periodic phase fluctuation (discussed in Section 4) and the error bars show plus and minus one standard deviation about the mean.

Fig. 4
Fig. 4

Time-averaged subtraction fringe pattern recorded at 70 frames∕s showing the target vibrating at 250   Hz . The horizontal ROI was interrogated at 33   kHz , corresponding to a maximum normalized velocity of 0.25 (maximum surface velocity of 1.1 mm / s , λ = 532   nm , and η = 2 ). The vertical ROI was interrogated at 10   kHz , corresponding to a maximum normalized velocity of 0.19 (maximum surface velocity of 0.25 mm / s , λ = 532   nm , and η = 2 ).

Fig. 5
Fig. 5

Spatiotemporal speckle pattern showing intensity variation for the horizontal ROI (128 × 1 pixels) recorded at 33   kHz for an object vibrating harmonically at 250   Hz .

Fig. 6
Fig. 6

(a) Normalized velocity, Δ Φ / π , and (b) normalized acceleration Δ 2 Φ / ( 2 π 2 f t s ) for the horizontal ROI (camera operating at 33   kHz ). (c) Normalized velocity and (d) normalized acceleration for the vertical ROI (camera operating at 10   kHz ), rotated to show the y-axis horizontally.

Fig. 7
Fig. 7

Maximum normalized velocity error plotted against the normalized surface velocity for (a) Carré's algorithm [Eq. (2)], (b) the four-frame algorithm [Eq. (19)], and (c) the five-frame algorithm [Eq. (23)].

Fig. 8
Fig. 8

Maximum normalized velocity error plotted against the number of frames per vibration period for (a) Carré's algorithm [Eq. (2)] and (b) the five-frame algorithm [Eq. (23)]. Influence of maximum normalized surface velocity.

Fig. 9
Fig. 9

Maximum normalized velocity error plotted against the number of frames per vibration period for (a) Carré's algorithm [Eq. (2)] and (b) the five-frame algorithm [Eq. (23)]. Influence of intensity noise for v max / | v Nyq | = 0.3 .

Fig. 10
Fig. 10

Maximum normalized velocity error plotted against the number of frames per vibration period for Carré's algorithm [Eq. (2)]. Influence of staircase phase-step error for v max / | v Nyq | = 0.3 .

Fig. 11
Fig. 11

Maximum normalized velocity error plotted against the number of frames per vibration period for Carré's algorithm [Eq. (2)]. Influence of exposure for v max / | v Nyq | = 0.3 .

Equations (25)

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I n ( x , y , t n ) = I O ( x , y ) { 1 + γ O sin c ( Δ 2 ) cos [ Φ O ( x , y , t n ) Φ R ( x , y , t n ) ] } ,
Φ O ( x , y , t n ) Φ R ( x , y , t n ) = tan 1 { [ 3 ( I n I n + 1 ) ( I n 1 I n + 2 ) ] [ ( I n I n + 1 ) + ( I n 1 I n + 2 ) ] } 1 / 2 ( I n + I n + 1 ) ( I n 1 + I n + 2 )
I O ( x , y ) γ O = { [ ( I n I n + 1 ) + ( I n 1 I n + 2 ) ] 2 + [ ( I n + I n + 1 ) ( I n 1 + I n + 2 ) ] 2 } 1 / 2 2 2
Φ R ( x , y , t n ) = 2 tan 1 3 ( I n I n + 1 ) ( I n 1 I n + 2 ) ( I n I n + 1 ) + ( I n 1 I n + 2 )
Φ O ( x , y , t n ) Φ R ( x , y , t n ) [ Φ O ( x , y , t n 1 )
Φ R ( x , y , t n 1 ) ] = Δ Φ O ( x , y , t n ) + π 2 ,
v Nyq = ± λ 2 η t s
w ( x , y , t n ) = λ 2 π η t s Δ Φ O ( x , y , t n )
w ( x , y , t n ) | v Nyq | = Δ Φ O ( x , y , t n ) π ,
w ( x , y , t n ) = λ 2 πη t s 2 Δ 2 Φ O ( x , y , t n ) ,
w ( x , y , t n ) 2 π f | v Nyq | = 1 2 π 2 f t s Δ 2 Φ O ( x , y , t n ) ,
v Nyq,PS = ± λ 2 η t s [ 1 ( 2 N ) ] ,
v min = - v PS ,
v max = v Nyq,PS = v Nyq v PS .
Φ O ( x , t n ) = 2 π η λ w 0 sin ( 2 π f t n ) sin ( 2 π x ) + 2 π x ,
w 0 = ( v max | v Nyq | ) | v Nyq | 2 π f ,
Φ O ( x , t n ) = π ( v max | v Nyq | ) t n t s + 2 π x .
α = α ( 1 + ε α ) ,
α = π 2 + 2 π 2 f t s ( v max | v Nyq | ) = π 2 [ 1 + 8 f t s ( v max | v Nyq | ) π 2 ]
Δϕ π = 1 π tan 1 1 N n = 1 N ε α 2 = 1 π tan 1 [ 3 π 2 f t s ( v max | v Nyq | ) ]
Φ O ( x , y , t n ) Φ R ( x , y , t n ) = tan 1 ( I n I n + 2 ) ( I n 1 + I n + 1 )
α = α ( 1 + ε ) ,
α = π 2 + π ( v max | v Nyq | ) = π 2 [ 1 + 2 ( v max | v Nyq | ) ]
Δϕ π = 1 π tan 1 1 N n = 1 N ε α = 1 π tan 1 [ 3 2 π ( v max v Nyq ) ] ,
Φ O ( x , y , t n ) Φ R ( x , y , t n ) = tan 1 2 ( I n - 1 + I n +1 ) ( 2 I n I n 2 I n + 2 )

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