Abstract

Laser speckle dynamics manifest themselves in photon Doppler velocimetry (PDV) data as low-frequency amplitude fluctuations, and analysis of these fluctuations provides insight into the transverse speed of the surface under observation. We previously demonstrated that a single measurement probe is capable of simultaneously measuring (1) axial motion, through frequency analysis of Doppler shifts, and (2) transverse speed, through analysis of the speckle’s coherence time. However, the performance of this technique hinges on a correct understanding of the speckle pattern’s response to surface motion. In this paper, we model the origination of the speckle pattern, and we describe a methodology for calculating the speckle’s coherence time from the autocorrelation of a noisy signal. We then test a suite of optical probes over a range of standoff distances, demonstrating a significant reduction in the speckle’s coherence time, which correlates to the increase in speckle boiling when the target surface is located near a probe’s focal length. We show that spatial regions of decreased coherence time may be predicted a priori by a probe’s parameters, since they stem from boiling dominance. We analyze this result as a function of probe parameters for a surface-scattering target and a volume-scattering target. Although the coherence time’s behavior in the focal plane makes velocity extraction difficult, far from the probe’s focal lengths, we are able to measure rigid body transverse speeds exceeding 20m/s with an absolute accuracy of ±15% using the speckle dynamics measured by a PDV setup.

© 2013 Optical Society of America

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  1. O. T. Strand, D. R. Goosman, C. Martinez, T. L. Whitworth, and W. W. Kuhlow, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108 (2006).
    [CrossRef]
  2. B. J. Jenson, D. B. Holtkamp, P. A. Rigg, and D. H. Dolan, “Accuracy limits and window corrections for photon Doppler velocimetry,” J. Appl. Phys. 101, 013523 (2007).
    [CrossRef]
  3. M. E. Briggs, L. G. Hill, L. M. Hull, M. A. Shinas, and D. H. Dolan, “Applications and principles of photon-Doppler velocimetry for explosive testing,” in Proceedings of 14th International Detonation Symposium, Coeur d’Alene, Idaho (2010).
  4. D. H. Dolan, “What does ‘velocity’ interferometry really measure?” AIP Conf. Proc. 1195, 589–594 (2009).
    [CrossRef]
  5. E. A. Moro and M. E. Briggs, “Note: simultaneous measurement of transverse speed and axial velocity from a single optical beam,” Rev. Sci. Instrum. 84, 016110 (2013).
    [CrossRef]
  6. J. W. Goodman, “Origins and manifestations of speckle,” in Speckle Phenomena in Optics, 1st ed. (Roberts and Company, 2007), Chap. 1, pp. 1–6.
  7. T. Iwai, N. Takai, and T. Asakura, “Dynamic statistical properties of laser speckle produced by a moving diffuse object under illumination of a Gaussian laser beam,” J. Opt. Soc. Am. 72, 460–467 (1982).
    [CrossRef]
  8. N. Takai, I. Iwai, and T. Asakura, “Correlation distance of dynamic speckles,” Appl. Opt. 22, 170–177 (1983).
    [CrossRef]
  9. A. F. Fercher, “Velocity measurement by first order statistics of time-differentiated laser speckles,” Opt. Commun. 33, 129–135 (1980).
    [CrossRef]
  10. J. D. Briers, “Laser Doppler and time-varying speckle: a reconciliation,” J. Opt. Soc. Am. A 13, 345–350 (1996).
    [CrossRef]
  11. P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, 1963).
  12. J. W. Goodman, “Higher-order statistical properties of speckle,” in Speckle Phenomena in Optics, 1st ed. (Roberts and Company, 2007), Chap. 4, pp. 59–140.
  13. M. Kowalczyk, “Laser speckle velocimetry,” Proc. SPIE 2729, 139–145 (1996).
    [CrossRef]
  14. L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, and J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 367–440 (1992).
  15. H. J. Tiziani, “Physical properties of speckles” in Speckle Metrology (Academic, 1978), Chap. 2, pp. 5–9.
  16. J. W. Goodman, “Speckle in certain imaging applications,” in Speckle Phenomena in Optics, 1st ed. (Roberts and Company, 2007), Chap. 6, pp. 187–234.
  17. E. A. Moro, M. E. Briggs, and L. M. Hull, “A comparison of techniques for extracting transverse speed from photon Doppler velocimetry signal content,” in Proceedings of IEEE Sensors, Baltimore, Maryland (2013).
  18. A. V. Oppenheim, R. W. Schafer, and J. R. Buck, “Discrete Hilbert transforms,” in Discrete-Time Signal Processing (Prentice-Hall, 1999), Chap. 11, pp. 775–810.
  19. H. Fuji, T. Okamoto, and T. Asakura, “Power spectra of speckle signals detected by optical-fiber probe,” J. Opt. Soc. Am. A 4, 1366–1375 (1987).
    [CrossRef]

2013 (1)

E. A. Moro and M. E. Briggs, “Note: simultaneous measurement of transverse speed and axial velocity from a single optical beam,” Rev. Sci. Instrum. 84, 016110 (2013).
[CrossRef]

2009 (1)

D. H. Dolan, “What does ‘velocity’ interferometry really measure?” AIP Conf. Proc. 1195, 589–594 (2009).
[CrossRef]

2007 (1)

B. J. Jenson, D. B. Holtkamp, P. A. Rigg, and D. H. Dolan, “Accuracy limits and window corrections for photon Doppler velocimetry,” J. Appl. Phys. 101, 013523 (2007).
[CrossRef]

2006 (1)

O. T. Strand, D. R. Goosman, C. Martinez, T. L. Whitworth, and W. W. Kuhlow, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108 (2006).
[CrossRef]

1996 (2)

1992 (1)

L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, and J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 367–440 (1992).

1987 (1)

1983 (1)

1982 (1)

1980 (1)

A. F. Fercher, “Velocity measurement by first order statistics of time-differentiated laser speckles,” Opt. Commun. 33, 129–135 (1980).
[CrossRef]

Ariel, E. D.

L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, and J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 367–440 (1992).

Asakura, T.

Beckmann, P.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, 1963).

Briers, J. D.

Briggs, M. E.

E. A. Moro and M. E. Briggs, “Note: simultaneous measurement of transverse speed and axial velocity from a single optical beam,” Rev. Sci. Instrum. 84, 016110 (2013).
[CrossRef]

M. E. Briggs, L. G. Hill, L. M. Hull, M. A. Shinas, and D. H. Dolan, “Applications and principles of photon-Doppler velocimetry for explosive testing,” in Proceedings of 14th International Detonation Symposium, Coeur d’Alene, Idaho (2010).

E. A. Moro, M. E. Briggs, and L. M. Hull, “A comparison of techniques for extracting transverse speed from photon Doppler velocimetry signal content,” in Proceedings of IEEE Sensors, Baltimore, Maryland (2013).

Buck, J. R.

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, “Discrete Hilbert transforms,” in Discrete-Time Signal Processing (Prentice-Hall, 1999), Chap. 11, pp. 775–810.

Dolan, D. H.

D. H. Dolan, “What does ‘velocity’ interferometry really measure?” AIP Conf. Proc. 1195, 589–594 (2009).
[CrossRef]

B. J. Jenson, D. B. Holtkamp, P. A. Rigg, and D. H. Dolan, “Accuracy limits and window corrections for photon Doppler velocimetry,” J. Appl. Phys. 101, 013523 (2007).
[CrossRef]

M. E. Briggs, L. G. Hill, L. M. Hull, M. A. Shinas, and D. H. Dolan, “Applications and principles of photon-Doppler velocimetry for explosive testing,” in Proceedings of 14th International Detonation Symposium, Coeur d’Alene, Idaho (2010).

Fercher, A. F.

A. F. Fercher, “Velocity measurement by first order statistics of time-differentiated laser speckles,” Opt. Commun. 33, 129–135 (1980).
[CrossRef]

Fuji, H.

Goodman, J. W.

J. W. Goodman, “Origins and manifestations of speckle,” in Speckle Phenomena in Optics, 1st ed. (Roberts and Company, 2007), Chap. 1, pp. 1–6.

J. W. Goodman, “Higher-order statistical properties of speckle,” in Speckle Phenomena in Optics, 1st ed. (Roberts and Company, 2007), Chap. 4, pp. 59–140.

J. W. Goodman, “Speckle in certain imaging applications,” in Speckle Phenomena in Optics, 1st ed. (Roberts and Company, 2007), Chap. 6, pp. 187–234.

Goosman, D. R.

O. T. Strand, D. R. Goosman, C. Martinez, T. L. Whitworth, and W. W. Kuhlow, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108 (2006).
[CrossRef]

Hallerman, G. R.

L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, and J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 367–440 (1992).

Hill, L. G.

M. E. Briggs, L. G. Hill, L. M. Hull, M. A. Shinas, and D. H. Dolan, “Applications and principles of photon-Doppler velocimetry for explosive testing,” in Proceedings of 14th International Detonation Symposium, Coeur d’Alene, Idaho (2010).

Holtkamp, D. B.

B. J. Jenson, D. B. Holtkamp, P. A. Rigg, and D. H. Dolan, “Accuracy limits and window corrections for photon Doppler velocimetry,” J. Appl. Phys. 101, 013523 (2007).
[CrossRef]

Hull, L. M.

M. E. Briggs, L. G. Hill, L. M. Hull, M. A. Shinas, and D. H. Dolan, “Applications and principles of photon-Doppler velocimetry for explosive testing,” in Proceedings of 14th International Detonation Symposium, Coeur d’Alene, Idaho (2010).

E. A. Moro, M. E. Briggs, and L. M. Hull, “A comparison of techniques for extracting transverse speed from photon Doppler velocimetry signal content,” in Proceedings of IEEE Sensors, Baltimore, Maryland (2013).

Iwai, I.

Iwai, T.

Jenson, B. J.

B. J. Jenson, D. B. Holtkamp, P. A. Rigg, and D. H. Dolan, “Accuracy limits and window corrections for photon Doppler velocimetry,” J. Appl. Phys. 101, 013523 (2007).
[CrossRef]

Kowalczyk, M.

M. Kowalczyk, “Laser speckle velocimetry,” Proc. SPIE 2729, 139–145 (1996).
[CrossRef]

Kuhlow, W. W.

O. T. Strand, D. R. Goosman, C. Martinez, T. L. Whitworth, and W. W. Kuhlow, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108 (2006).
[CrossRef]

Martinez, C.

O. T. Strand, D. R. Goosman, C. Martinez, T. L. Whitworth, and W. W. Kuhlow, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108 (2006).
[CrossRef]

Moro, E. A.

E. A. Moro and M. E. Briggs, “Note: simultaneous measurement of transverse speed and axial velocity from a single optical beam,” Rev. Sci. Instrum. 84, 016110 (2013).
[CrossRef]

E. A. Moro, M. E. Briggs, and L. M. Hull, “A comparison of techniques for extracting transverse speed from photon Doppler velocimetry signal content,” in Proceedings of IEEE Sensors, Baltimore, Maryland (2013).

Okamoto, T.

Oppenheim, A. V.

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, “Discrete Hilbert transforms,” in Discrete-Time Signal Processing (Prentice-Hall, 1999), Chap. 11, pp. 775–810.

Payson, H. C.

L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, and J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 367–440 (1992).

Rigg, P. A.

B. J. Jenson, D. B. Holtkamp, P. A. Rigg, and D. H. Dolan, “Accuracy limits and window corrections for photon Doppler velocimetry,” J. Appl. Phys. 101, 013523 (2007).
[CrossRef]

Schafer, R. W.

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, “Discrete Hilbert transforms,” in Discrete-Time Signal Processing (Prentice-Hall, 1999), Chap. 11, pp. 775–810.

Shinas, M. A.

M. E. Briggs, L. G. Hill, L. M. Hull, M. A. Shinas, and D. H. Dolan, “Applications and principles of photon-Doppler velocimetry for explosive testing,” in Proceedings of 14th International Detonation Symposium, Coeur d’Alene, Idaho (2010).

Shirley, L. G.

L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, and J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 367–440 (1992).

Spizzichino, A.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, 1963).

Strand, O. T.

O. T. Strand, D. R. Goosman, C. Martinez, T. L. Whitworth, and W. W. Kuhlow, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108 (2006).
[CrossRef]

Takai, N.

Tiziani, H. J.

H. J. Tiziani, “Physical properties of speckles” in Speckle Metrology (Academic, 1978), Chap. 2, pp. 5–9.

Vivilecchia, J. R.

L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, and J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 367–440 (1992).

Whitworth, T. L.

O. T. Strand, D. R. Goosman, C. Martinez, T. L. Whitworth, and W. W. Kuhlow, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108 (2006).
[CrossRef]

AIP Conf. Proc. (1)

D. H. Dolan, “What does ‘velocity’ interferometry really measure?” AIP Conf. Proc. 1195, 589–594 (2009).
[CrossRef]

Appl. Opt. (1)

J. Appl. Phys. (1)

B. J. Jenson, D. B. Holtkamp, P. A. Rigg, and D. H. Dolan, “Accuracy limits and window corrections for photon Doppler velocimetry,” J. Appl. Phys. 101, 013523 (2007).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Lincoln Lab. J. (1)

L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, and J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 367–440 (1992).

Opt. Commun. (1)

A. F. Fercher, “Velocity measurement by first order statistics of time-differentiated laser speckles,” Opt. Commun. 33, 129–135 (1980).
[CrossRef]

Proc. SPIE (1)

M. Kowalczyk, “Laser speckle velocimetry,” Proc. SPIE 2729, 139–145 (1996).
[CrossRef]

Rev. Sci. Instrum. (2)

O. T. Strand, D. R. Goosman, C. Martinez, T. L. Whitworth, and W. W. Kuhlow, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108 (2006).
[CrossRef]

E. A. Moro and M. E. Briggs, “Note: simultaneous measurement of transverse speed and axial velocity from a single optical beam,” Rev. Sci. Instrum. 84, 016110 (2013).
[CrossRef]

Other (8)

J. W. Goodman, “Origins and manifestations of speckle,” in Speckle Phenomena in Optics, 1st ed. (Roberts and Company, 2007), Chap. 1, pp. 1–6.

M. E. Briggs, L. G. Hill, L. M. Hull, M. A. Shinas, and D. H. Dolan, “Applications and principles of photon-Doppler velocimetry for explosive testing,” in Proceedings of 14th International Detonation Symposium, Coeur d’Alene, Idaho (2010).

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, 1963).

J. W. Goodman, “Higher-order statistical properties of speckle,” in Speckle Phenomena in Optics, 1st ed. (Roberts and Company, 2007), Chap. 4, pp. 59–140.

H. J. Tiziani, “Physical properties of speckles” in Speckle Metrology (Academic, 1978), Chap. 2, pp. 5–9.

J. W. Goodman, “Speckle in certain imaging applications,” in Speckle Phenomena in Optics, 1st ed. (Roberts and Company, 2007), Chap. 6, pp. 187–234.

E. A. Moro, M. E. Briggs, and L. M. Hull, “A comparison of techniques for extracting transverse speed from photon Doppler velocimetry signal content,” in Proceedings of IEEE Sensors, Baltimore, Maryland (2013).

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, “Discrete Hilbert transforms,” in Discrete-Time Signal Processing (Prentice-Hall, 1999), Chap. 11, pp. 775–810.

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Figures (11)

Fig. 1.
Fig. 1.

(a) We assume a surface that is rough compared to λ. The surface features whose backscatter is “seen” by the probe are indicated (a) with solid lines. This backscatter experiences a random phase modulation by virtue of the distance traveled to/from a particular feature. The five randomly phased fields in (a) are shown in the complex plane along with their sum in (b).

Fig. 2.
Fig. 2.

PDV architecture is shown here, illustrating (a) the shape of the lensed probe’s transmission and (b) a typical speckle pattern from the diffuse reflector. The spatial region within (b) that corresponds to the probe’s aperture is integrated and recoupled to the optical fiber, yielding a measurement of the speckle pattern at the photodetector.

Fig. 3.
Fig. 3.

η is plotted as a function of distance to the target surface (l0) for w0=25μm (a) and w0=50μm (b). The region in which boiling dominates (|η|<1) is between the dashed lines.

Fig. 4.
Fig. 4.

Filtering removes a bias in the autocorrelation (a). The exponential fit exp(τ2τc2)bears close resemblance to the envelope of the autocorrelation function, which is calculated from the absolute value of the autocorrelation function’s Hilbert transform (b). Either the exponential fit or the Hilbert transform may be used to characterize the coherence time (i.e., the autocorrelation’s decay behavior).

Fig. 5.
Fig. 5.

Speckle imaging test setup (a) is related to the typical PDV architecture (b). The setup in (a) was used to measure the speckle reflected by the diffuse target surface immediately before imaging by the probe’s lens, providing insight into the speckle patterns that are typically observed in PDV.

Fig. 6.
Fig. 6.

PDV system was used with this setup (a) to compare the normal probe’s measured speckle dynamics to the magnitude of the velocity |v|, measured by the bore probe. The detailed view of the probe arrangement is shown in (b).

Fig. 7.
Fig. 7.

Images of speckle at λ=1550nm demonstrate (1) the average size of the speckle to be on the order of 2.0 mm and (2) the dominance of boiling behavior is seen in response to 100 μm of surface translation. The dashed ring (2.0 mm in diameter) indicates the approximate aperture of a the optical probe used for these tests, and the measurement by this probe and PDV channel is closely related to the intensity integrated over this detecting aperture.

Fig. 8.
Fig. 8.

A 20 mm focusing probe illuminates a diffusely reflecting copper surface and measures the reflected speckle dynamics. The resulting coherence time multiplied by the magnitude of the velocity (τc|v|) is shown as a function of standoff l0. The region near the focal length where boiling is significant (|η|<1) is indicated with the dashed lines (see Fig. 3).

Fig. 9.
Fig. 9.

Experimental results are shown here. The dynamic length (or the product of the coherence time and the transverse velocity) measured by a particular probe drops when the standoff is equal to the probe’s focal length.

Fig. 10.
Fig. 10.

Changing the reflective surface results in a change in the speckle’s dynamics.

Fig. 11.
Fig. 11.

Magnitude of the transverse velocity is measured from coherence time and is compared to the known magnitude as measured by the bore probe.

Tables (1)

Tables Icon

Table 1. Optical Probes Used for Tests

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

E=Er+Em.
Em=1Nk=1Nake(jϕk).
I=EE*=ErEr*+EmEm*+ErEm*+Er*Em=Ir+Im+2IrImcos(ϕrm),
Im=|Em2|=1N{[k=1Nakcos(ϕk)]2+[k=1Naksin(ϕk)]2}1/2.
ϕEm=arctan{[k=1Naksin(ϕk)]/[k=1Nakcos(ϕk)]}.
I=Ir+Im+2IrImcos[4πnl0λ+ϕEm],
A¯s=λ2l02A,
r¯s=λl0πw.
η=z(l0+z)/a+al0z,
a=πw02λ,
|v|=w0τc,

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