Abstract

Speckle velocimetry is investigated as a means of determining odometry data with potential for application on autonomous robotic vehicles. The technique described here relies on the integration of translation measurements made by normalized cross-correlation of speckle patterns to determine the change in position over time. The use of objective (non-imaged) speckle offers a number of advantages over subjective (imaged) speckle, such as a reduction in the number of optical components, reduced modulation of speckles at the edges of the image, and improved light efficiency. The influence of the source/detector configuration on the speckle translation to vehicle translation scaling factor for objective speckle is investigated using a computer model and verified experimentally. Experimental measurements are presented at velocities up to 80mms1 which show accuracy better than 0.4%.

© 2012 Optical Society of America

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2010 (1)

T. O. H. Charrett, L. Waugh, and R. P. Tatam, “Speckle velocimetry for high accuracy odometry for a Mars exploration rover,” Meas. Sci. Technol. 21, 025301 (2010).
[CrossRef]

2007 (3)

G. Cloud, “Optical methods in experimental mechanics, part 27: Speckle size estimates,” Exp. Tech. 31, 19–22 (2007).
[CrossRef]

M. Maimone, Y. Cheng, and L. Matthies, “Two years of visual odometry on the Mars exploration rovers,” J. Field Robot. 24, 169–186 (2007).
[CrossRef]

P. Šmíd, P. Horváth, and M. Hrabovský, “Speckle correlation method used to measure object’s in-plane velocity,” Appl. Opt. 46, 3709–3715 (2007).
[CrossRef]

2006 (1)

D. Nistér, O. Naroditsky, and J. Bergen, “Visual odometry for ground vehicle applications,” J. Field Robot. 23, 3–20(2006).
[CrossRef]

2005 (4)

P. G. de Santos, E. Garcia, J. Estremera, and M. A. Armada, “DYLEMA: using walking robots for landmine detection and location,” Int. J. Syst. Sci. 36, 545–558 (2005).
[CrossRef]

H. Nobach and M. Honkanen, “Two-dimensional Gaussian regression for sub-pixel displacement estimation in particle image velocimetry or particle position estimation in particle tracking velocimetry,” Exp. Fluids 38, 511–515 (2005).
[CrossRef]

G. E. Elsinga, B. W. van Oudheusden, and F. Scarano, “The effect of particle image blur on the correlation map and velocity measurement in PIV,” Proc. SPIE 5880, 588010 (2005).
[CrossRef]

H. Durrant-White, “Autonomous land vehicles,” Proc. I. Mech. E. Part 1: J Systems Control Eng. 219, 77–98 (2005).
[CrossRef]

2004 (2)

P. Horváth, M. Hrabovský, and P. Šmíd, “Full theory of speckle displacement and decorrelation in the image field by wave and geometrical descriptions and its application in mechanics,” J Mod. Opt. 51, 725–742 (2004).
[CrossRef]

P. Horváth, M. Hrabovský, and P. Šmíd, “Application of speckle decorrelation method for small translation measurements,” Opt. Appl. 34, 203–218 (2004).

2003 (1)

A. Aliverdiev, M. Caponero, and C. Moriconi, “Some issues concerning the development of a speckle velocimeter,” Tech. Phys+. 48, 1460–1463 (2003).
[CrossRef]

2002 (1)

R. S. Sirohi, “Speckle interferometry,” Contemp. Phys. 43 (3), 161–180 (2002).
[CrossRef]

2000 (1)

M. Hrabovský, Z. Bača, and P. Horváth, “Theory of speckle displacement and decorrelation and its application in mechanics,” Opt. Laser Eng. 32, 395–403 (2000).
[CrossRef]

1997 (1)

P. Synnergren, “Measurement of three-dimensional displacement fields and shape using electronic speckle photography,” Opt. Eng. 36, 2302–2310 (1997).
[CrossRef]

1996 (1)

J. Borenstein and L. Feng, “Measurement and correction of systematic odometry errors in mobile robots,” IEEE T. Robotic. Autom. 12, 869–880 (1996).
[CrossRef]

1995 (1)

S. S. Beauchemin and J. L. Barron, “The computation of optical flow,” ACM Comput. Surv. 27, 433–467 (1995).
[CrossRef]

1994 (1)

1981 (1)

I. Yamaguchi, “Speckle displacement and decorrelation in the diffraction and image fields for small object deformation,” Opt. Acta 28, 1359–1376 (1981).
[CrossRef]

Alismail, H.

P. Hansen, H. Alismail, P. Rander, and B. Browning, “Monocular visual odometry for robot localization in LNG pipes,” 2011 IEEE International Conference on Robotics and Automation (ICRA) (IEEE, 2011), 3111–3116.

Aliverdiev, A.

A. Aliverdiev, M. Caponero, and C. Moriconi, “Some issues concerning the development of a speckle velocimeter,” Tech. Phys+. 48, 1460–1463 (2003).
[CrossRef]

Armada, M. A.

P. G. de Santos, E. Garcia, J. Estremera, and M. A. Armada, “DYLEMA: using walking robots for landmine detection and location,” Int. J. Syst. Sci. 36, 545–558 (2005).
[CrossRef]

Baca, Z.

M. Hrabovský, Z. Bača, and P. Horváth, “Theory of speckle displacement and decorrelation and its application in mechanics,” Opt. Laser Eng. 32, 395–403 (2000).
[CrossRef]

Bakari, M. J.

D. W. Seward and M. J. Bakari, “The use of robots and automation in nuclear decommissioning,” in the 22nd International Symposium on Automation and Robotics in Construction (ISARC 2005) , Ferrara, Italy, 11–14 September, 2005.

Barron, J. L.

S. S. Beauchemin and J. L. Barron, “The computation of optical flow,” ACM Comput. Surv. 27, 433–467 (1995).
[CrossRef]

Beauchemin, S. S.

S. S. Beauchemin and J. L. Barron, “The computation of optical flow,” ACM Comput. Surv. 27, 433–467 (1995).
[CrossRef]

Benckert, L. R.

Bergen, J.

D. Nistér, O. Naroditsky, and J. Bergen, “Visual odometry for ground vehicle applications,” J. Field Robot. 23, 3–20(2006).
[CrossRef]

Biesiadecki, J. J.

M. Maimone, P. C. Leger, and J. J. Biesiadecki, “Overview of the Mars Exploration Rovers’ autonomous mobility and vision capabilities,” Presented at the IEEE International Conference on Robotics and Automation (ICRA), Roma, Italy (14 April, 2007).

Borenstein, J.

J. Borenstein and L. Feng, “Measurement and correction of systematic odometry errors in mobile robots,” IEEE T. Robotic. Autom. 12, 869–880 (1996).
[CrossRef]

Browning, B.

P. Hansen, H. Alismail, P. Rander, and B. Browning, “Monocular visual odometry for robot localization in LNG pipes,” 2011 IEEE International Conference on Robotics and Automation (ICRA) (IEEE, 2011), 3111–3116.

Caponero, M.

A. Aliverdiev, M. Caponero, and C. Moriconi, “Some issues concerning the development of a speckle velocimeter,” Tech. Phys+. 48, 1460–1463 (2003).
[CrossRef]

Charrett, T. O. H.

T. O. H. Charrett, L. Waugh, and R. P. Tatam, “Speckle velocimetry for high accuracy odometry for a Mars exploration rover,” Meas. Sci. Technol. 21, 025301 (2010).
[CrossRef]

Cheng, Y.

M. Maimone, Y. Cheng, and L. Matthies, “Two years of visual odometry on the Mars exploration rovers,” J. Field Robot. 24, 169–186 (2007).
[CrossRef]

Cloud, G.

G. Cloud, “Optical methods in experimental mechanics, part 27: Speckle size estimates,” Exp. Tech. 31, 19–22 (2007).
[CrossRef]

Dainty, J. C.

J. C. Dainty, “The statistics of speckle patterns,” Progress Optics XIV, E. Wolf, ed. (North Holland, 1976).

de Almeida, A. T.

S. Larionova, L. Marques, and A. T. de Almeida, “Detection of natural landmarks for mapping by a demining robot,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE, 2006) 4959–4965.

de Santos, P. G.

P. G. de Santos, E. Garcia, J. Estremera, and M. A. Armada, “DYLEMA: using walking robots for landmine detection and location,” Int. J. Syst. Sci. 36, 545–558 (2005).
[CrossRef]

Dillmann, R.

B. Gassmann, F. Zacharias, J. M. Zöllner, and R. Dillmann, “Localization of walking robots,” in IEEE International Conference on Robotics and Automation (ICRA) (IEEE, 2005), 1471–1476.
[CrossRef]

Ding, J.

J. Ding, X. Du, X. Wang, and J. Liu, “Improved real-time correlation-based FPGA stereo vision system,” in the 2010 IEEE International Conference on Mechatronics and Automomation (ICMA) (IEEE, 2010), 104–108.

Du, X.

J. Ding, X. Du, X. Wang, and J. Liu, “Improved real-time correlation-based FPGA stereo vision system,” in the 2010 IEEE International Conference on Mechatronics and Automomation (ICMA) (IEEE, 2010), 104–108.

Durrant-White, H.

H. Durrant-White, “Autonomous land vehicles,” Proc. I. Mech. E. Part 1: J Systems Control Eng. 219, 77–98 (2005).
[CrossRef]

Elsinga, G. E.

G. E. Elsinga, B. W. van Oudheusden, and F. Scarano, “The effect of particle image blur on the correlation map and velocity measurement in PIV,” Proc. SPIE 5880, 588010 (2005).
[CrossRef]

Estremera, J.

P. G. de Santos, E. Garcia, J. Estremera, and M. A. Armada, “DYLEMA: using walking robots for landmine detection and location,” Int. J. Syst. Sci. 36, 545–558 (2005).
[CrossRef]

Feng, L.

J. Borenstein and L. Feng, “Measurement and correction of systematic odometry errors in mobile robots,” IEEE T. Robotic. Autom. 12, 869–880 (1996).
[CrossRef]

Garcia, E.

P. G. de Santos, E. Garcia, J. Estremera, and M. A. Armada, “DYLEMA: using walking robots for landmine detection and location,” Int. J. Syst. Sci. 36, 545–558 (2005).
[CrossRef]

Gassmann, B.

B. Gassmann, F. Zacharias, J. M. Zöllner, and R. Dillmann, “Localization of walking robots,” in IEEE International Conference on Robotics and Automation (ICRA) (IEEE, 2005), 1471–1476.
[CrossRef]

Hansen, P.

P. Hansen, H. Alismail, P. Rander, and B. Browning, “Monocular visual odometry for robot localization in LNG pipes,” 2011 IEEE International Conference on Robotics and Automation (ICRA) (IEEE, 2011), 3111–3116.

Honkanen, M.

H. Nobach and M. Honkanen, “Two-dimensional Gaussian regression for sub-pixel displacement estimation in particle image velocimetry or particle position estimation in particle tracking velocimetry,” Exp. Fluids 38, 511–515 (2005).
[CrossRef]

Horváth, P.

P. Šmíd, P. Horváth, and M. Hrabovský, “Speckle correlation method used to measure object’s in-plane velocity,” Appl. Opt. 46, 3709–3715 (2007).
[CrossRef]

P. Horváth, M. Hrabovský, and P. Šmíd, “Full theory of speckle displacement and decorrelation in the image field by wave and geometrical descriptions and its application in mechanics,” J Mod. Opt. 51, 725–742 (2004).
[CrossRef]

P. Horváth, M. Hrabovský, and P. Šmíd, “Application of speckle decorrelation method for small translation measurements,” Opt. Appl. 34, 203–218 (2004).

M. Hrabovský, Z. Bača, and P. Horváth, “Theory of speckle displacement and decorrelation and its application in mechanics,” Opt. Laser Eng. 32, 395–403 (2000).
[CrossRef]

Hrabovský, M.

P. Šmíd, P. Horváth, and M. Hrabovský, “Speckle correlation method used to measure object’s in-plane velocity,” Appl. Opt. 46, 3709–3715 (2007).
[CrossRef]

P. Horváth, M. Hrabovský, and P. Šmíd, “Application of speckle decorrelation method for small translation measurements,” Opt. Appl. 34, 203–218 (2004).

P. Horváth, M. Hrabovský, and P. Šmíd, “Full theory of speckle displacement and decorrelation in the image field by wave and geometrical descriptions and its application in mechanics,” J Mod. Opt. 51, 725–742 (2004).
[CrossRef]

M. Hrabovský, Z. Bača, and P. Horváth, “Theory of speckle displacement and decorrelation and its application in mechanics,” Opt. Laser Eng. 32, 395–403 (2000).
[CrossRef]

Larionova, S.

S. Larionova, L. Marques, and A. T. de Almeida, “Detection of natural landmarks for mapping by a demining robot,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE, 2006) 4959–4965.

Leger, P. C.

M. Maimone, P. C. Leger, and J. J. Biesiadecki, “Overview of the Mars Exploration Rovers’ autonomous mobility and vision capabilities,” Presented at the IEEE International Conference on Robotics and Automation (ICRA), Roma, Italy (14 April, 2007).

Liu, J.

J. Ding, X. Du, X. Wang, and J. Liu, “Improved real-time correlation-based FPGA stereo vision system,” in the 2010 IEEE International Conference on Mechatronics and Automomation (ICMA) (IEEE, 2010), 104–108.

Maimone, M.

M. Maimone, Y. Cheng, and L. Matthies, “Two years of visual odometry on the Mars exploration rovers,” J. Field Robot. 24, 169–186 (2007).
[CrossRef]

M. Maimone, P. C. Leger, and J. J. Biesiadecki, “Overview of the Mars Exploration Rovers’ autonomous mobility and vision capabilities,” Presented at the IEEE International Conference on Robotics and Automation (ICRA), Roma, Italy (14 April, 2007).

Marques, L.

S. Larionova, L. Marques, and A. T. de Almeida, “Detection of natural landmarks for mapping by a demining robot,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE, 2006) 4959–4965.

Matthies, L.

M. Maimone, Y. Cheng, and L. Matthies, “Two years of visual odometry on the Mars exploration rovers,” J. Field Robot. 24, 169–186 (2007).
[CrossRef]

Moriconi, C.

A. Aliverdiev, M. Caponero, and C. Moriconi, “Some issues concerning the development of a speckle velocimeter,” Tech. Phys+. 48, 1460–1463 (2003).
[CrossRef]

Naroditsky, O.

D. Nistér, O. Naroditsky, and J. Bergen, “Visual odometry for ground vehicle applications,” J. Field Robot. 23, 3–20(2006).
[CrossRef]

Nistér, D.

D. Nistér, O. Naroditsky, and J. Bergen, “Visual odometry for ground vehicle applications,” J. Field Robot. 23, 3–20(2006).
[CrossRef]

Nobach, H.

H. Nobach and M. Honkanen, “Two-dimensional Gaussian regression for sub-pixel displacement estimation in particle image velocimetry or particle position estimation in particle tracking velocimetry,” Exp. Fluids 38, 511–515 (2005).
[CrossRef]

Rander, P.

P. Hansen, H. Alismail, P. Rander, and B. Browning, “Monocular visual odometry for robot localization in LNG pipes,” 2011 IEEE International Conference on Robotics and Automation (ICRA) (IEEE, 2011), 3111–3116.

Scarano, F.

G. E. Elsinga, B. W. van Oudheusden, and F. Scarano, “The effect of particle image blur on the correlation map and velocity measurement in PIV,” Proc. SPIE 5880, 588010 (2005).
[CrossRef]

Seward, D. W.

D. W. Seward and M. J. Bakari, “The use of robots and automation in nuclear decommissioning,” in the 22nd International Symposium on Automation and Robotics in Construction (ISARC 2005) , Ferrara, Italy, 11–14 September, 2005.

Sirohi, R. S.

R. S. Sirohi, “Speckle interferometry,” Contemp. Phys. 43 (3), 161–180 (2002).
[CrossRef]

Sjödahl, M.

M. Sjödahl and L. R. Benckert, “Systematic and random errors in electronic speckle photography,” Appl. Opt. 33, 7461–7471 (1994).
[CrossRef]

M. Sjödahl, “Digital speckle photography,” in Digital Speckle Interferometry and Related Techniques, P. Rastogi, ed. (Wiley, 2001).

Šmíd, P.

P. Šmíd, P. Horváth, and M. Hrabovský, “Speckle correlation method used to measure object’s in-plane velocity,” Appl. Opt. 46, 3709–3715 (2007).
[CrossRef]

P. Horváth, M. Hrabovský, and P. Šmíd, “Full theory of speckle displacement and decorrelation in the image field by wave and geometrical descriptions and its application in mechanics,” J Mod. Opt. 51, 725–742 (2004).
[CrossRef]

P. Horváth, M. Hrabovský, and P. Šmíd, “Application of speckle decorrelation method for small translation measurements,” Opt. Appl. 34, 203–218 (2004).

Synnergren, P.

P. Synnergren, “Measurement of three-dimensional displacement fields and shape using electronic speckle photography,” Opt. Eng. 36, 2302–2310 (1997).
[CrossRef]

Tatam, R. P.

T. O. H. Charrett, L. Waugh, and R. P. Tatam, “Speckle velocimetry for high accuracy odometry for a Mars exploration rover,” Meas. Sci. Technol. 21, 025301 (2010).
[CrossRef]

van Oudheusden, B. W.

G. E. Elsinga, B. W. van Oudheusden, and F. Scarano, “The effect of particle image blur on the correlation map and velocity measurement in PIV,” Proc. SPIE 5880, 588010 (2005).
[CrossRef]

Wang, X.

J. Ding, X. Du, X. Wang, and J. Liu, “Improved real-time correlation-based FPGA stereo vision system,” in the 2010 IEEE International Conference on Mechatronics and Automomation (ICMA) (IEEE, 2010), 104–108.

Waugh, L.

T. O. H. Charrett, L. Waugh, and R. P. Tatam, “Speckle velocimetry for high accuracy odometry for a Mars exploration rover,” Meas. Sci. Technol. 21, 025301 (2010).
[CrossRef]

Yamaguchi, I.

I. Yamaguchi, “Speckle displacement and decorrelation in the diffraction and image fields for small object deformation,” Opt. Acta 28, 1359–1376 (1981).
[CrossRef]

Zacharias, F.

B. Gassmann, F. Zacharias, J. M. Zöllner, and R. Dillmann, “Localization of walking robots,” in IEEE International Conference on Robotics and Automation (ICRA) (IEEE, 2005), 1471–1476.
[CrossRef]

Zöllner, J. M.

B. Gassmann, F. Zacharias, J. M. Zöllner, and R. Dillmann, “Localization of walking robots,” in IEEE International Conference on Robotics and Automation (ICRA) (IEEE, 2005), 1471–1476.
[CrossRef]

ACM Comput. Surv. (1)

S. S. Beauchemin and J. L. Barron, “The computation of optical flow,” ACM Comput. Surv. 27, 433–467 (1995).
[CrossRef]

Appl. Opt. (2)

Contemp. Phys. (1)

R. S. Sirohi, “Speckle interferometry,” Contemp. Phys. 43 (3), 161–180 (2002).
[CrossRef]

Exp. Fluids (1)

H. Nobach and M. Honkanen, “Two-dimensional Gaussian regression for sub-pixel displacement estimation in particle image velocimetry or particle position estimation in particle tracking velocimetry,” Exp. Fluids 38, 511–515 (2005).
[CrossRef]

Exp. Tech. (1)

G. Cloud, “Optical methods in experimental mechanics, part 27: Speckle size estimates,” Exp. Tech. 31, 19–22 (2007).
[CrossRef]

IEEE T. Robotic. Autom. (1)

J. Borenstein and L. Feng, “Measurement and correction of systematic odometry errors in mobile robots,” IEEE T. Robotic. Autom. 12, 869–880 (1996).
[CrossRef]

Int. J. Syst. Sci. (1)

P. G. de Santos, E. Garcia, J. Estremera, and M. A. Armada, “DYLEMA: using walking robots for landmine detection and location,” Int. J. Syst. Sci. 36, 545–558 (2005).
[CrossRef]

J Mod. Opt. (1)

P. Horváth, M. Hrabovský, and P. Šmíd, “Full theory of speckle displacement and decorrelation in the image field by wave and geometrical descriptions and its application in mechanics,” J Mod. Opt. 51, 725–742 (2004).
[CrossRef]

J. Field Robot. (2)

D. Nistér, O. Naroditsky, and J. Bergen, “Visual odometry for ground vehicle applications,” J. Field Robot. 23, 3–20(2006).
[CrossRef]

M. Maimone, Y. Cheng, and L. Matthies, “Two years of visual odometry on the Mars exploration rovers,” J. Field Robot. 24, 169–186 (2007).
[CrossRef]

Meas. Sci. Technol. (1)

T. O. H. Charrett, L. Waugh, and R. P. Tatam, “Speckle velocimetry for high accuracy odometry for a Mars exploration rover,” Meas. Sci. Technol. 21, 025301 (2010).
[CrossRef]

Opt. Acta (1)

I. Yamaguchi, “Speckle displacement and decorrelation in the diffraction and image fields for small object deformation,” Opt. Acta 28, 1359–1376 (1981).
[CrossRef]

Opt. Appl. (1)

P. Horváth, M. Hrabovský, and P. Šmíd, “Application of speckle decorrelation method for small translation measurements,” Opt. Appl. 34, 203–218 (2004).

Opt. Eng. (1)

P. Synnergren, “Measurement of three-dimensional displacement fields and shape using electronic speckle photography,” Opt. Eng. 36, 2302–2310 (1997).
[CrossRef]

Opt. Laser Eng. (1)

M. Hrabovský, Z. Bača, and P. Horváth, “Theory of speckle displacement and decorrelation and its application in mechanics,” Opt. Laser Eng. 32, 395–403 (2000).
[CrossRef]

Proc. I. Mech. E. Part 1: J Systems Control Eng. (1)

H. Durrant-White, “Autonomous land vehicles,” Proc. I. Mech. E. Part 1: J Systems Control Eng. 219, 77–98 (2005).
[CrossRef]

Proc. SPIE (1)

G. E. Elsinga, B. W. van Oudheusden, and F. Scarano, “The effect of particle image blur on the correlation map and velocity measurement in PIV,” Proc. SPIE 5880, 588010 (2005).
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Figures (13)

Fig. 1.
Fig. 1.

The principle of speckle velocimetry.

Fig. 2.
Fig. 2.

Formation of objective speckle (a) and subjective speckle (b).

Fig. 3.
Fig. 3.

Principle of normalized cross-correlation (NXC). The peak in the resulting image corresponds to the point where the features of the template, t most closely match those of the image, f.

Fig. 4.
Fig. 4.

Coordinate system used for the speckle model, showing the location of the laser point source S, the origin at the centre of the illuminated region on the object O, and the centre of the detector array D.

Fig. 5.
Fig. 5.

Plots showing the variation in scaling factor with increasing detector-source separation (a) and increasing object distance (b). The square (red) and circle (blue) points were calculated using the speckle model and normalized cross-correlation and the solid lines by Eq. (10).

Fig. 6.
Fig. 6.

Plots showing the variation in scaling factor with the detector kept fixed at 400 mm and varying the vertical source position. The points were calculated using the speckle model and normalized cross-correlation and the black lines by Eq. (10).

Fig. 7.
Fig. 7.

Schematic illustrating the design of the test system. The volume of the frame is approximately 1m3 and the distance between the camera/laser and the sand approximately 0.5 m [red sand texture from (27)].

Fig. 8.
Fig. 8.

Variation in scaling factor against angular separation of the observation and illumination directions. The laser-camera separation was kept fixed at 140 mm and the angle altered by varying the height of the laser and camera. The points correspond to calibrations made with the test system and the continuous lines correspond to measurements of observation and illumination positions and are calculated using Eq. (10).

Fig. 9.
Fig. 9.

Variation in scaling factor against angular separation of the observation and illumination directions. The laser-camera separation was kept fixed at 65 mm and the angle altered by varying the height of the laser and camera.

Fig. 10.
Fig. 10.

Path traversed by stages (travelling at 3mms1) calculated from the feedback from the stage encoders (arrows indicate direction of travel) (a). The change in position (b) and velocity (c) of the x-axis stage (dashed-blue) and y axis stage (continuous-red).

Fig. 11.
Fig. 11.

Path traversed (at 3mms1) calculated by integration of translation measurements from normalized crosscorrelation (a). The change in position (b) and velocity (c) of the x-axis stage (dashed-blue) and y axis stage (continuous-red).

Fig. 12.
Fig. 12.

The path calculated by cross-correlation with the stages running at a maximum velocity of 80mms1 (a). A pair of speckle patterns in successive frames at a point where the stages are moving at maximum velocity (b) and (c), and the normalized cross-correlation between them (d).

Fig. 13.
Fig. 13.

The path calculated by cross-correlation of subjective speckle patterns with the stages running at a maximum velocity of 50mms1 (a). A pair of speckle patterns in successive frames at a point where the stages are moving at maximum velocity (b) and (c), and the normalized cross-correlation between them (d). The field of view in the speckle images is 3.0mm2.

Tables (2)

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Table 1. Summary of Parameters Pertinent to Choice of Speckle Type for Velocimetry Applications

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Table 2. Summary of the Advantages and Disadvantages of Objective and Subjective Speckle

Equations (10)

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σO=λLA,
σS=λF(1+M)a,
γ(u,v)=x,yf(x,y)t(xu,yv),
γ(u,v)=F1{F(f)F*(t)},
γ(u,v)=x,y[f(x,y)f¯u,v][t(xu,yv)t¯]{x,y[f(x,y)f¯u,v]2x,y[t(xu,yv)t¯]2}0.5.
px=x+ln[γ(x1,y)]ln[γ(x+1,y)]2ln[γ(x1,y)]4ln[γ(x,y)]+2ln[γ(x+1,y)],py=y+ln[γ(x,y1)]ln[γ(x,y+1)]2ln[γ(x,y1)]4ln[γ(x,y)]+2ln[γ(x,y+1)],
Ax=ax[LDLS(lSx21)+lx21]ay[LDLSlSxlSy+lxly]az[LDLSlSxlSz+lxlz]LD[εxx(lSx+lx)+εxy(lSy+ly)+Ωz(lSy+ly)+Ωy(lSz+lz)],Ay=ax[LDLSlSxlSy+lxly]ay[LDLS(lSy21)+ly21]az[LDLSlSylSz+lylz]LD[εyy(lSy+ly)+εxy(lSx+lx)+Ωz(lSx+lx)+Ωx(lSz+lz)],
E(x,y)=Najexp(iϕj)exp(i2πλ·PL),
I(x,y)=E(x,y)·E*(x,y).
Ax=ax(LDcos2θSLScosθD+cosθD),Ay=ay(LDLS+1),

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