Abstract

We present a statistical study of CCD (or CMOS) camera response to small images. Diffraction patterns simulating particle images of a size around 2–3 pixels were experimentally generated and characterized using three-point Gaussian peak fitting, currently used in particle image velocimetry (PIV) for accurate location estimation. Based on this peak-fitting technique, the bias and RMS error between locations of simulated and real images were accurately calculated by using a homemade program. The influence of the intensity variation of the simulated particle images on the response of the CCD camera was studied. The experimental results show that the accuracy of the position determination is very good and brings attention to superresolution PIV algorithms. Some tracks are proposed in the conclusion to enlarge and improve the study.

© 2013 Optical Society of America

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  1. R. Meynart, “Instantaneous velocity field measurements in unsteady gas flow by speckle velocimetry,” Appl. Opt. 22, 535–540 (1983).
    [CrossRef]
  2. C. Willert and M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).
    [CrossRef]
  3. R. Adrian, “Particle-imaging techniques for experimental fluid mechanics,” Annu. Rev. Fluid Mech. 23, 261–304 (1991).
    [CrossRef]
  4. R. Keane and R. Adrian, “Theory of cross-correlation analysis of PIV images,” Appl. Sci. Res. 49, 191–215 (1992).
    [CrossRef]
  5. J. Westerweel, “Fundamentals of digital particle image velocimetry,” Meas. Sci. Technol. 8, 1379–1392 (1997).
    [CrossRef]
  6. M. Raffel, C. Willert, and J. Kompenhans, Particle Image Velocimetry: A Practical Guide (Springer, 1998).
  7. R. Adrian, “Dynamic ranges of velocity and spatial resolution of particle image velocimetry,” Meas. Sci. Technol. 8, 1393–1398 (1997).
    [CrossRef]
  8. J. Westerweel, D. Daribi, and M. Gharib, “The effect of discrete window offset on the accuracy of cross-correlation analysis of digital PIV recording,” Exp. Fluids 23, 20–28 (1997).
    [CrossRef]
  9. L. Lourenco and A. Krothapalli, “True resolution PIV, a mesh free second order accurate algorithm,” presented at 10th International Symposium on Application Techniques in Fluid Mechanics, Lisbon, Portugal, 10–13 July2000.
  10. B. Lecordier, J. Lecordier, and M. Trinité, “Iterative sub-pixel algorithm for the cross-correlation PIV measurement,” in Third International Workshop on PIV (University of California Santa-Barbara, 1999), pp. 37–43.
  11. F. Scarano and M. L. Riethmuller, “Advances in iterative multigrid PIV image processing,” Exp. Fluids 29, S51–S60 (2000).
    [CrossRef]
  12. J. Nogueira, A. Lecuona, and P. Rodriguez, “Identification of a new source of peak locking, analysis and its removal in conventional and super-resolution PIV techniques,” Exp. Fluids 30, 309–316 (2001).
    [CrossRef]
  13. L. Gui and S. Wereley, “A correlation-based continuous window-shift technique to reduce the peak locking effect in digital PIV image evaluation,” Exp. Fluids 32, 506–517 (2002).
    [CrossRef]
  14. B. Millat, J. Foucaut, N. Pérenne, and M. Stanislas, “Characterization of different PIV algorithms using the EUROPIV synthetic image generator and real images from a turbulent boundary layer,” in Particle Image Velocimetry: Recent Improvements, M. Stanislas, J. Westerweel, and J. Kompenhans, eds. (Springer-Verlag, 2004).
  15. M. Stanislas, K. Okamoto, and C. Kähler, “Main results of the first international PIV Challenge,” Meas. Sci. Technol. 14, R63–R89 (2003).
    [CrossRef]
  16. M. Stanislas, K. Okamoto, C. Kähler, and J. Westerweel, “Main results of the second international PIV challenge,” Exp. Fluids 39, 170–191 (2005).
    [CrossRef]
  17. M. Stanislas, K. Okamoto, C. Kähler, J. Westerweel, and F. Scarano, “Main results of the third international PIV challenge,” Exp. Fluids 45, 27–71 (2008).
    [CrossRef]
  18. B. Lecordier, J. Westerweel, and J. Nogueira, “The EUROPIV synthetic image generator,” in Particle Image Velocimetry: Recent Improvements, M. Stanislas, J. Westerweel, and J. Kompenhans, eds. (Springer-Verlag, 2004).
  19. D. Abdelsalam, M. Stanislas, and S. Coudert, “Highly accurate point spread function estimation for CCD or CMOS camera calibration,” Appl. Opt. (submitted).
  20. R. Keane, R. Adrian, and Y. Zhong, “Super-resolution particle imaging velocimetry,” Meas. Sci. Technol. 6, 754–768 (1995).
    [CrossRef]

2008 (1)

M. Stanislas, K. Okamoto, C. Kähler, J. Westerweel, and F. Scarano, “Main results of the third international PIV challenge,” Exp. Fluids 45, 27–71 (2008).
[CrossRef]

2005 (1)

M. Stanislas, K. Okamoto, C. Kähler, and J. Westerweel, “Main results of the second international PIV challenge,” Exp. Fluids 39, 170–191 (2005).
[CrossRef]

2003 (1)

M. Stanislas, K. Okamoto, and C. Kähler, “Main results of the first international PIV Challenge,” Meas. Sci. Technol. 14, R63–R89 (2003).
[CrossRef]

2002 (1)

L. Gui and S. Wereley, “A correlation-based continuous window-shift technique to reduce the peak locking effect in digital PIV image evaluation,” Exp. Fluids 32, 506–517 (2002).
[CrossRef]

2001 (1)

J. Nogueira, A. Lecuona, and P. Rodriguez, “Identification of a new source of peak locking, analysis and its removal in conventional and super-resolution PIV techniques,” Exp. Fluids 30, 309–316 (2001).
[CrossRef]

2000 (1)

F. Scarano and M. L. Riethmuller, “Advances in iterative multigrid PIV image processing,” Exp. Fluids 29, S51–S60 (2000).
[CrossRef]

1997 (3)

J. Westerweel, “Fundamentals of digital particle image velocimetry,” Meas. Sci. Technol. 8, 1379–1392 (1997).
[CrossRef]

R. Adrian, “Dynamic ranges of velocity and spatial resolution of particle image velocimetry,” Meas. Sci. Technol. 8, 1393–1398 (1997).
[CrossRef]

J. Westerweel, D. Daribi, and M. Gharib, “The effect of discrete window offset on the accuracy of cross-correlation analysis of digital PIV recording,” Exp. Fluids 23, 20–28 (1997).
[CrossRef]

1995 (1)

R. Keane, R. Adrian, and Y. Zhong, “Super-resolution particle imaging velocimetry,” Meas. Sci. Technol. 6, 754–768 (1995).
[CrossRef]

1992 (1)

R. Keane and R. Adrian, “Theory of cross-correlation analysis of PIV images,” Appl. Sci. Res. 49, 191–215 (1992).
[CrossRef]

1991 (2)

C. Willert and M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).
[CrossRef]

R. Adrian, “Particle-imaging techniques for experimental fluid mechanics,” Annu. Rev. Fluid Mech. 23, 261–304 (1991).
[CrossRef]

1983 (1)

Abdelsalam, D.

D. Abdelsalam, M. Stanislas, and S. Coudert, “Highly accurate point spread function estimation for CCD or CMOS camera calibration,” Appl. Opt. (submitted).

Adrian, R.

R. Adrian, “Dynamic ranges of velocity and spatial resolution of particle image velocimetry,” Meas. Sci. Technol. 8, 1393–1398 (1997).
[CrossRef]

R. Keane, R. Adrian, and Y. Zhong, “Super-resolution particle imaging velocimetry,” Meas. Sci. Technol. 6, 754–768 (1995).
[CrossRef]

R. Keane and R. Adrian, “Theory of cross-correlation analysis of PIV images,” Appl. Sci. Res. 49, 191–215 (1992).
[CrossRef]

R. Adrian, “Particle-imaging techniques for experimental fluid mechanics,” Annu. Rev. Fluid Mech. 23, 261–304 (1991).
[CrossRef]

Coudert, S.

D. Abdelsalam, M. Stanislas, and S. Coudert, “Highly accurate point spread function estimation for CCD or CMOS camera calibration,” Appl. Opt. (submitted).

Daribi, D.

J. Westerweel, D. Daribi, and M. Gharib, “The effect of discrete window offset on the accuracy of cross-correlation analysis of digital PIV recording,” Exp. Fluids 23, 20–28 (1997).
[CrossRef]

Foucaut, J.

B. Millat, J. Foucaut, N. Pérenne, and M. Stanislas, “Characterization of different PIV algorithms using the EUROPIV synthetic image generator and real images from a turbulent boundary layer,” in Particle Image Velocimetry: Recent Improvements, M. Stanislas, J. Westerweel, and J. Kompenhans, eds. (Springer-Verlag, 2004).

Gharib, M.

J. Westerweel, D. Daribi, and M. Gharib, “The effect of discrete window offset on the accuracy of cross-correlation analysis of digital PIV recording,” Exp. Fluids 23, 20–28 (1997).
[CrossRef]

C. Willert and M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).
[CrossRef]

Gui, L.

L. Gui and S. Wereley, “A correlation-based continuous window-shift technique to reduce the peak locking effect in digital PIV image evaluation,” Exp. Fluids 32, 506–517 (2002).
[CrossRef]

Kähler, C.

M. Stanislas, K. Okamoto, C. Kähler, J. Westerweel, and F. Scarano, “Main results of the third international PIV challenge,” Exp. Fluids 45, 27–71 (2008).
[CrossRef]

M. Stanislas, K. Okamoto, C. Kähler, and J. Westerweel, “Main results of the second international PIV challenge,” Exp. Fluids 39, 170–191 (2005).
[CrossRef]

M. Stanislas, K. Okamoto, and C. Kähler, “Main results of the first international PIV Challenge,” Meas. Sci. Technol. 14, R63–R89 (2003).
[CrossRef]

Keane, R.

R. Keane, R. Adrian, and Y. Zhong, “Super-resolution particle imaging velocimetry,” Meas. Sci. Technol. 6, 754–768 (1995).
[CrossRef]

R. Keane and R. Adrian, “Theory of cross-correlation analysis of PIV images,” Appl. Sci. Res. 49, 191–215 (1992).
[CrossRef]

Kompenhans, J.

M. Raffel, C. Willert, and J. Kompenhans, Particle Image Velocimetry: A Practical Guide (Springer, 1998).

Krothapalli, A.

L. Lourenco and A. Krothapalli, “True resolution PIV, a mesh free second order accurate algorithm,” presented at 10th International Symposium on Application Techniques in Fluid Mechanics, Lisbon, Portugal, 10–13 July2000.

Lecordier, B.

B. Lecordier, J. Lecordier, and M. Trinité, “Iterative sub-pixel algorithm for the cross-correlation PIV measurement,” in Third International Workshop on PIV (University of California Santa-Barbara, 1999), pp. 37–43.

B. Lecordier, J. Westerweel, and J. Nogueira, “The EUROPIV synthetic image generator,” in Particle Image Velocimetry: Recent Improvements, M. Stanislas, J. Westerweel, and J. Kompenhans, eds. (Springer-Verlag, 2004).

Lecordier, J.

B. Lecordier, J. Lecordier, and M. Trinité, “Iterative sub-pixel algorithm for the cross-correlation PIV measurement,” in Third International Workshop on PIV (University of California Santa-Barbara, 1999), pp. 37–43.

Lecuona, A.

J. Nogueira, A. Lecuona, and P. Rodriguez, “Identification of a new source of peak locking, analysis and its removal in conventional and super-resolution PIV techniques,” Exp. Fluids 30, 309–316 (2001).
[CrossRef]

Lourenco, L.

L. Lourenco and A. Krothapalli, “True resolution PIV, a mesh free second order accurate algorithm,” presented at 10th International Symposium on Application Techniques in Fluid Mechanics, Lisbon, Portugal, 10–13 July2000.

Meynart, R.

Millat, B.

B. Millat, J. Foucaut, N. Pérenne, and M. Stanislas, “Characterization of different PIV algorithms using the EUROPIV synthetic image generator and real images from a turbulent boundary layer,” in Particle Image Velocimetry: Recent Improvements, M. Stanislas, J. Westerweel, and J. Kompenhans, eds. (Springer-Verlag, 2004).

Nogueira, J.

J. Nogueira, A. Lecuona, and P. Rodriguez, “Identification of a new source of peak locking, analysis and its removal in conventional and super-resolution PIV techniques,” Exp. Fluids 30, 309–316 (2001).
[CrossRef]

B. Lecordier, J. Westerweel, and J. Nogueira, “The EUROPIV synthetic image generator,” in Particle Image Velocimetry: Recent Improvements, M. Stanislas, J. Westerweel, and J. Kompenhans, eds. (Springer-Verlag, 2004).

Okamoto, K.

M. Stanislas, K. Okamoto, C. Kähler, J. Westerweel, and F. Scarano, “Main results of the third international PIV challenge,” Exp. Fluids 45, 27–71 (2008).
[CrossRef]

M. Stanislas, K. Okamoto, C. Kähler, and J. Westerweel, “Main results of the second international PIV challenge,” Exp. Fluids 39, 170–191 (2005).
[CrossRef]

M. Stanislas, K. Okamoto, and C. Kähler, “Main results of the first international PIV Challenge,” Meas. Sci. Technol. 14, R63–R89 (2003).
[CrossRef]

Pérenne, N.

B. Millat, J. Foucaut, N. Pérenne, and M. Stanislas, “Characterization of different PIV algorithms using the EUROPIV synthetic image generator and real images from a turbulent boundary layer,” in Particle Image Velocimetry: Recent Improvements, M. Stanislas, J. Westerweel, and J. Kompenhans, eds. (Springer-Verlag, 2004).

Raffel, M.

M. Raffel, C. Willert, and J. Kompenhans, Particle Image Velocimetry: A Practical Guide (Springer, 1998).

Riethmuller, M. L.

F. Scarano and M. L. Riethmuller, “Advances in iterative multigrid PIV image processing,” Exp. Fluids 29, S51–S60 (2000).
[CrossRef]

Rodriguez, P.

J. Nogueira, A. Lecuona, and P. Rodriguez, “Identification of a new source of peak locking, analysis and its removal in conventional and super-resolution PIV techniques,” Exp. Fluids 30, 309–316 (2001).
[CrossRef]

Scarano, F.

M. Stanislas, K. Okamoto, C. Kähler, J. Westerweel, and F. Scarano, “Main results of the third international PIV challenge,” Exp. Fluids 45, 27–71 (2008).
[CrossRef]

F. Scarano and M. L. Riethmuller, “Advances in iterative multigrid PIV image processing,” Exp. Fluids 29, S51–S60 (2000).
[CrossRef]

Stanislas, M.

M. Stanislas, K. Okamoto, C. Kähler, J. Westerweel, and F. Scarano, “Main results of the third international PIV challenge,” Exp. Fluids 45, 27–71 (2008).
[CrossRef]

M. Stanislas, K. Okamoto, C. Kähler, and J. Westerweel, “Main results of the second international PIV challenge,” Exp. Fluids 39, 170–191 (2005).
[CrossRef]

M. Stanislas, K. Okamoto, and C. Kähler, “Main results of the first international PIV Challenge,” Meas. Sci. Technol. 14, R63–R89 (2003).
[CrossRef]

B. Millat, J. Foucaut, N. Pérenne, and M. Stanislas, “Characterization of different PIV algorithms using the EUROPIV synthetic image generator and real images from a turbulent boundary layer,” in Particle Image Velocimetry: Recent Improvements, M. Stanislas, J. Westerweel, and J. Kompenhans, eds. (Springer-Verlag, 2004).

D. Abdelsalam, M. Stanislas, and S. Coudert, “Highly accurate point spread function estimation for CCD or CMOS camera calibration,” Appl. Opt. (submitted).

Trinité, M.

B. Lecordier, J. Lecordier, and M. Trinité, “Iterative sub-pixel algorithm for the cross-correlation PIV measurement,” in Third International Workshop on PIV (University of California Santa-Barbara, 1999), pp. 37–43.

Wereley, S.

L. Gui and S. Wereley, “A correlation-based continuous window-shift technique to reduce the peak locking effect in digital PIV image evaluation,” Exp. Fluids 32, 506–517 (2002).
[CrossRef]

Westerweel, J.

M. Stanislas, K. Okamoto, C. Kähler, J. Westerweel, and F. Scarano, “Main results of the third international PIV challenge,” Exp. Fluids 45, 27–71 (2008).
[CrossRef]

M. Stanislas, K. Okamoto, C. Kähler, and J. Westerweel, “Main results of the second international PIV challenge,” Exp. Fluids 39, 170–191 (2005).
[CrossRef]

J. Westerweel, D. Daribi, and M. Gharib, “The effect of discrete window offset on the accuracy of cross-correlation analysis of digital PIV recording,” Exp. Fluids 23, 20–28 (1997).
[CrossRef]

J. Westerweel, “Fundamentals of digital particle image velocimetry,” Meas. Sci. Technol. 8, 1379–1392 (1997).
[CrossRef]

B. Lecordier, J. Westerweel, and J. Nogueira, “The EUROPIV synthetic image generator,” in Particle Image Velocimetry: Recent Improvements, M. Stanislas, J. Westerweel, and J. Kompenhans, eds. (Springer-Verlag, 2004).

Willert, C.

C. Willert and M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).
[CrossRef]

M. Raffel, C. Willert, and J. Kompenhans, Particle Image Velocimetry: A Practical Guide (Springer, 1998).

Zhong, Y.

R. Keane, R. Adrian, and Y. Zhong, “Super-resolution particle imaging velocimetry,” Meas. Sci. Technol. 6, 754–768 (1995).
[CrossRef]

Annu. Rev. Fluid Mech. (1)

R. Adrian, “Particle-imaging techniques for experimental fluid mechanics,” Annu. Rev. Fluid Mech. 23, 261–304 (1991).
[CrossRef]

Appl. Opt. (1)

Appl. Sci. Res. (1)

R. Keane and R. Adrian, “Theory of cross-correlation analysis of PIV images,” Appl. Sci. Res. 49, 191–215 (1992).
[CrossRef]

Exp. Fluids (7)

C. Willert and M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).
[CrossRef]

J. Westerweel, D. Daribi, and M. Gharib, “The effect of discrete window offset on the accuracy of cross-correlation analysis of digital PIV recording,” Exp. Fluids 23, 20–28 (1997).
[CrossRef]

F. Scarano and M. L. Riethmuller, “Advances in iterative multigrid PIV image processing,” Exp. Fluids 29, S51–S60 (2000).
[CrossRef]

J. Nogueira, A. Lecuona, and P. Rodriguez, “Identification of a new source of peak locking, analysis and its removal in conventional and super-resolution PIV techniques,” Exp. Fluids 30, 309–316 (2001).
[CrossRef]

L. Gui and S. Wereley, “A correlation-based continuous window-shift technique to reduce the peak locking effect in digital PIV image evaluation,” Exp. Fluids 32, 506–517 (2002).
[CrossRef]

M. Stanislas, K. Okamoto, C. Kähler, and J. Westerweel, “Main results of the second international PIV challenge,” Exp. Fluids 39, 170–191 (2005).
[CrossRef]

M. Stanislas, K. Okamoto, C. Kähler, J. Westerweel, and F. Scarano, “Main results of the third international PIV challenge,” Exp. Fluids 45, 27–71 (2008).
[CrossRef]

Meas. Sci. Technol. (4)

J. Westerweel, “Fundamentals of digital particle image velocimetry,” Meas. Sci. Technol. 8, 1379–1392 (1997).
[CrossRef]

R. Adrian, “Dynamic ranges of velocity and spatial resolution of particle image velocimetry,” Meas. Sci. Technol. 8, 1393–1398 (1997).
[CrossRef]

M. Stanislas, K. Okamoto, and C. Kähler, “Main results of the first international PIV Challenge,” Meas. Sci. Technol. 14, R63–R89 (2003).
[CrossRef]

R. Keane, R. Adrian, and Y. Zhong, “Super-resolution particle imaging velocimetry,” Meas. Sci. Technol. 6, 754–768 (1995).
[CrossRef]

Other (6)

M. Raffel, C. Willert, and J. Kompenhans, Particle Image Velocimetry: A Practical Guide (Springer, 1998).

L. Lourenco and A. Krothapalli, “True resolution PIV, a mesh free second order accurate algorithm,” presented at 10th International Symposium on Application Techniques in Fluid Mechanics, Lisbon, Portugal, 10–13 July2000.

B. Lecordier, J. Lecordier, and M. Trinité, “Iterative sub-pixel algorithm for the cross-correlation PIV measurement,” in Third International Workshop on PIV (University of California Santa-Barbara, 1999), pp. 37–43.

B. Lecordier, J. Westerweel, and J. Nogueira, “The EUROPIV synthetic image generator,” in Particle Image Velocimetry: Recent Improvements, M. Stanislas, J. Westerweel, and J. Kompenhans, eds. (Springer-Verlag, 2004).

D. Abdelsalam, M. Stanislas, and S. Coudert, “Highly accurate point spread function estimation for CCD or CMOS camera calibration,” Appl. Opt. (submitted).

B. Millat, J. Foucaut, N. Pérenne, and M. Stanislas, “Characterization of different PIV algorithms using the EUROPIV synthetic image generator and real images from a turbulent boundary layer,” in Particle Image Velocimetry: Recent Improvements, M. Stanislas, J. Westerweel, and J. Kompenhans, eds. (Springer-Verlag, 2004).

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Figures (11)

Fig. 1.
Fig. 1.

False color maximum intensity map in a 50×50μm region of the CCD at the position shown in Fig. 3(a) below on the FlowMaster CCD sensor.

Fig. 2.
Fig. 2.

Schematic diagram of the optical setup.

Fig. 3.
Fig. 3.

(a) Schematic diagram of the position of the 10μm×10μm region scanned with the diffraction patterns simulating a particle image on the FlowMaster3 sensor. (b) Position of the same region in the PSF image of Fig. 1.

Fig. 4.
Fig. 4.

Particle simulation at Φ=7mm: (a) 2D high intensity, (b) 3D fitting of (a), (c) 2D low intensity, and (d) 3D fitting of (c).

Fig. 5.
Fig. 5.

Image position for the high-intensity case of Figs. 4(a) and 4(b). Xfit and Yfit are obtained from the three-point Gaussian fit. Xth and Yth are from the table displacement. (a) Xfit against Xth and (b) Yfit against Yth.

Fig. 6.
Fig. 6.

(a) Bias and (b) random error on the X position of the image from Fig. 5(a).

Fig. 7.
Fig. 7.

(a) Bias and (b) random error on the Y position of the image from Fig. 5(b).

Fig. 8.
Fig. 8.

Offset DY of three-point Gaussian fit from pixel geometric center for two sets separated by 1 μm in X for high-intensity case.

Fig. 9.
Fig. 9.

Image position for the low-intensity case of Figs. 4(a) and 4(b). Xfit and Yfit are obtained from the three-point Gaussian fit. Xth and Yth are from the table displacement. (a) Xfit against Xth and (b) Yfit against Yth.

Fig. 10.
Fig. 10.

Random error on the X (a) and Y (b) position of the image from Fig. 9.

Fig. 11.
Fig. 11.

Offset DY of three-point Gaussian fit from pixel geometric center for two sets separated by 1 μm in X for low-intensity case.

Tables (2)

Tables Icon

Table 1. Position of Center of Pixels 1 (Xop1, Yop1) and 2 (Xop2, Yop2) and Distance between the Two Pixels (deltaX, deltaY) for High-Intensity Case

Tables Icon

Table 2. Position of the Center of Pixel 1 (Xop1, Yop1) and Pixel 2 (Xop2, Yop2) and Distance between the Two Pixels (deltaX, deltaY) for Low-Intensity Case

Metrics