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Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 4, Iss. 10 — Oct. 1, 2013
  • pp: 1883–1889
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Effects of speckle/pixel size ratio on temporal and spatial speckle-contrast analysis of dynamic scattering systems: Implications for measurements of blood-flow dynamics

J. C. Ramirez-San-Juan, E. Mendez-Aguilar, N. Salazar-Hermenegildo, A. Fuentes-Garcia, R. Ramos-Garcia, and B. Choi  »View Author Affiliations


Biomedical Optics Express, Vol. 4, Issue 10, pp. 1883-1889 (2013)
http://dx.doi.org/10.1364/BOE.4.001883


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Abstract

Laser Speckle Contrast Imaging (LSCI) is an optical technique used to generate blood flow maps with high spatial and temporal resolution. It is well known that in LSCI, the speckle size must exceed the Nyquist criterion to maximize the speckle's pattern contrast. In this work, we study experimentally the effect of speckle-pixel size ratio not only in dynamic speckle contrast, but also on the calculation of the relative flow speed for temporal and spatial analysis. Our data suggest that the temporal LSCI algorithm is more accurate at assessing the relative changes in flow speed than the spatial algorithm.

© 2013 OSA

1. Introduction

When coherent light is used to illuminate a rough or optically inhomogeneous object, the scattered light forms a random interference pattern called speckle [1

1. J. W. Goodman, Statistical Optics (New York: Wiley, 1985).

]. In 1981, Fercher and Briers [2

2. F. Fercher and J. D. Briers, “Flow visualization by means of single-exposure speckle photography,” Opt. Commun. 37(5), 326–330 (1981). [CrossRef]

] demonstrated that analysis of the speckle contrast in a time-integrated speckle pattern enables visualization of blood flow in the retina. With subsequent advances in charge-coupled device (CCD) technology and an associated reduction in cost, LSCI method has been implemented in real time [3

3. O. Yang, D. Cuccia, and B. Choi, “Real-time blood flow visualization using the graphics processing unit,” J. Biomed. Opt. 16(1), 016009 (2011). [CrossRef] [PubMed]

] and employed in numerous preclinical [4

4. A. K. Dunn, “Laser speckle contrast imaging of cerebral blood flow,” Ann. Biomed. Eng. 40(2), 367–377 (2012). [CrossRef] [PubMed]

,5

5. W. J. Moy, S. J. Patel, B. S. Lertsakdadet, R. P. Arora, K. M. Nielsen, K. M. Kelly, and B. Choi, “Preclinical in vivo evaluation of NPe6-mediated photodynamic therapy on normal vasculature,” Lasers Surg. Med. 44(2), 158–162 (2012). [CrossRef] [PubMed]

] and clinical [6

6. A. B. Parthasarathy, E. L. Weber, L. M. Richards, D. J. Fox, and A. K. Dunn, “Laser speckle contrast imaging of cerebral blood flow in humans during neurosurgery: a pilot clinical study,” J. Biomed. Opt. 15(6), 066030 (2010). [CrossRef] [PubMed]

] research studies as a simple method to quantify blood-flow dynamics [7

7. A. Humeau-Heurtier, B. Buard, G. Mahe, and P. Abraham, “Laser speckle contrast imaging of the skin: interest in processing the perfusion data,” Med. Biol. Eng. Comput. 50(2), 103–105 (2012). [CrossRef] [PubMed]

].

The data from Kirkpatrick et al. [8

8. S. J. Kirkpatrick, D. D. Duncan, and E. M. Wells-Gray, “Detrimental effects of speckle-pixel size matching in laser speckle contrast imaging,” Opt. Lett. 33(24), 2886–2888 (2008). [CrossRef] [PubMed]

] represent one extreme condition, in which the speckle pattern consists solely of static speckle. However, in biological samples, a mixture of static and dynamic contributions to the imaged speckle pattern is expected. As a consequence, blurring of the image and subsequent decrease of the maximum achievable speckle contrast due to spatial and temporal integration of the light is produced. In this work, we present in-vitro experimental data that support this concept and discuss the implications for LSI-based characterization of dynamic scattering systems.

2. Materials and methods

2.1 Flow phantom

The flow phantom (Fig. 2
Fig. 2 (a) Skin phantom employed in this study. Intralipid was injected into the inlet. K (contrast) and SFI (Speckle Flow Index) measurements were determined at regions within channels C1, C3 and C5. (b) Representative speckle contrast image of the skin phantom during flow at 6 mm/sec. See text for details.
) consists of a micro-channel slide (thinXXS Microtechnology AG) with channels of 300-µm diameter. The slide was placed on a rigid resin substrate polymerized with a suspension of TiO2 particles to simulate the scattering properties of human skin. A syringe-based infusion pump was used to induce flow of 1% Intralipid through the channels, at flow speeds from 4 to 20 mm/s in step of 2 mm/sec.

2.2 Laser speckle contrast imaging (LSCI)

An expanded and collimated 532-nm laser (Verdi, Coherent Inc.) illuminates an engineered diffuser, which in turn, homogenously illuminates the flow phantom. Raw speckle images were acquired with a Retiga CCD camera (7.4µm x 7.4µm pixel area) equipped with a macro lens with variable aperture. A linear polarizer was placed in front of the camera lens and its orientation is set to be perpendicular to that of the incident light's polarization to minimize specular reflection from the skin phantom. In order to modulate the speckle's size, and therefore the speckle/pixel size ratio, we changed the f/# setting of the lens (Eq. (1)), and the laser power was adjusted to achieve a consistent mean gray level measured from the CCD sensor. The exposure time was fixed at 10 ms because this value is common for in-vivo LSI applications.

2.3 Experimental design and data analysis

For each flow-speed setting, we collected a sequence of 30 raw speckle images. The sequences were processed using either temporal [11

11. H. Y. Cheng, Q. M. Luo, S. Q. Zeng, S. B. Chen, J. Cen, and H. Gong, “Modified laser speckle imaging method with improved spatial resolution,” J. Biomed. Opt. 8(3), 559–564 (2003). [CrossRef] [PubMed]

] or spatial [2

2. F. Fercher and J. D. Briers, “Flow visualization by means of single-exposure speckle photography,” Opt. Commun. 37(5), 326–330 (1981). [CrossRef]

] algorithms to calculate resultant speckle-contrast images. The temporal algorithm, analysis was done on a pixel-by-pixel basis, using the previously-published temporal LSI algorithm [11

11. H. Y. Cheng, Q. M. Luo, S. Q. Zeng, S. B. Chen, J. Cen, and H. Gong, “Modified laser speckle imaging method with improved spatial resolution,” J. Biomed. Opt. 8(3), 559–564 (2003). [CrossRef] [PubMed]

]. While for the spatial algorithm, each of the 30 images were converted to corresponding speckle-contrast images, using a 5 × 5 sliding-window operator, and an average speckle contrast image was calculated. With the resultant speckle-contrast images, we focused our analysis on 30 × 100 regions of interest within channels C1, C3 and C5.

Parthasarathy et al. [12

12. A. B. Parthasarathy, W. J. Tom, A. Gopal, X. Zhang, and A. K. Dunn, “Robust flow measurement with multi-exposure speckle imaging,” Opt. Express 16(3), 1975–1989 (2008). [CrossRef] [PubMed]

] and Boas et al. [13

13. D. A. Boas and A. K. Dunn, “Laser speckle contrast imaging in biomedical optics,” J. Biomed. Opt. 15(1), 011109 (2010). [CrossRef] [PubMed]

] derived an equation that relates speckle contrast (K) and the correlation time (τc) of the backscattered light from the sample:
K(T,τc)=[βρ2e2x1+2x2x2+4βρ(1ρ)ex1+xx2+(1ρ)2]1/2+Cnoise
(2)
where x = T/τC, T is the camera exposure time, ρ = If ⁄(If + Is) is the fraction of total light that is scattered by moving optical scatterers, Cnoise is a constant term that accounts for noise [12

12. A. B. Parthasarathy, W. J. Tom, A. Gopal, X. Zhang, and A. K. Dunn, “Robust flow measurement with multi-exposure speckle imaging,” Opt. Express 16(3), 1975–1989 (2008). [CrossRef] [PubMed]

], and β accounts for the effect of spatial integration of the speckle pattern due to the finite size of the pixel [14

14. P. A. Lemieux and D. J. Durian, “Investigating non-Gaussian scattering process by using nth-order intensity correlation function,” J. Opt. Soc. Am. A 16(7), 1651–1664 (1999). [CrossRef]

,15

15. Y. Atchia, H. Levy, S. Dufour, and O. Levi, “Rapid multiexposure in vivo brain imaging system using vertical cavity surface emitting lasers as a light source,” Appl. Opt. 52(7), C64–C71 (2013). [CrossRef] [PubMed]

]. In the absence of static optical scatterers (ρ →1) and noise (Cnoise→0), Eq. (2) simplifies to [12

12. A. B. Parthasarathy, W. J. Tom, A. Gopal, X. Zhang, and A. K. Dunn, “Robust flow measurement with multi-exposure speckle imaging,” Opt. Express 16(3), 1975–1989 (2008). [CrossRef] [PubMed]

]:

K(T,τc)=[βe2x1+2x2x2]12
(3)

In the long exposure regime (i.e., T >> τc) [16

16. J. C. Ramirez-San-Juan, R. Ramos-García, I. Guizar-Iturbide, G. Martínez-Niconoff, and B. Choi, “Impact of velocity distribution assumption on simplified laser speckle imaging equation,” Opt. Express 16(5), 3197 (2008). [CrossRef]

] and considering that the flow speed V 1/τc≡SFI, where SFI is Speckle Flow Index [17

17. K. Basak, M. Manjunatha, and P. K. Dutta, “Review of laser speckle-based analysis in medical imaging,” Med. Biol. Eng. Comput. 50(6), 547–558 (2012). [CrossRef] [PubMed]

], Eq. (3) can be approximated as:
K=aV12
(4)
where a is a proportionality constant. In [12

12. A. B. Parthasarathy, W. J. Tom, A. Gopal, X. Zhang, and A. K. Dunn, “Robust flow measurement with multi-exposure speckle imaging,” Opt. Express 16(3), 1975–1989 (2008). [CrossRef] [PubMed]

] the authors reported τc values in the order of microseconds, in our experiments the exposure time is 10 ms, it means that the experiments developed in this work are in the long exposure regime and therefore we can use Eq. (4).

3. Results and discussion

Figure 3
Fig. 3 Average speckle contrast of a region within channel C1, vs. flow speed, for different ratios of spatial sampling of the speckle pattern (i.e., “pixels-per-speckle” values) for (a) temporal and (b) spatial speckle contrast analysis. The symbols represent experimental data and the solid lines are the corresponding fits to Eq. (4).
shows the average speckle contrast of a region within channel C1 obtained with the temporal (Fig. 3(a)) and the spatial (Fig. 3(b)) contrast analysis as a function of the actual flow speed, for different values of N, which is the number of pixels per speckle (Fig. 1).

From our experimental data, for predominantly dynamic speckle, the speckle contrast depends on the spatial sampling of the speckle pattern, for both temporal and spatial speckle-contrast analysis. Equation (4) fits the temporal- and spatial-contrast data well for all experimental values of N (Fig. 3), although the fit is less accurate for the latter.

For dynamic scattering, K increases with N (Fig. 4
Fig. 4 Speckle contrast as a function of the pixels-per-speckle ratio for (a) temporal and (b) spatial analysis. Note that the value of K increase even when the Nyquist criterion of two pixels per speckle is satisfied.
). A notable difference between the data in Fig. 4 and those from [8

8. S. J. Kirkpatrick, D. D. Duncan, and E. M. Wells-Gray, “Detrimental effects of speckle-pixel size matching in laser speckle contrast imaging,” Opt. Lett. 33(24), 2886–2888 (2008). [CrossRef] [PubMed]

] is that K increases even for N values greater than two. In other words, even when the Nyquist criterion is met a reduction in speckle contrast remains due to the spatial averaging of the speckle pattern due to the finite pixel-size. With a static scattering substrate, the data from [8

8. S. J. Kirkpatrick, D. D. Duncan, and E. M. Wells-Gray, “Detrimental effects of speckle-pixel size matching in laser speckle contrast imaging,” Opt. Lett. 33(24), 2886–2888 (2008). [CrossRef] [PubMed]

] reached a plateau value for all N > 2. As with experimental data collected from a substrate with static optical scatterers [8

8. S. J. Kirkpatrick, D. D. Duncan, and E. M. Wells-Gray, “Detrimental effects of speckle-pixel size matching in laser speckle contrast imaging,” Opt. Lett. 33(24), 2886–2888 (2008). [CrossRef] [PubMed]

], our data demonstrate that speckle contrast from dynamic scatterers depends on N. Since most experimental studies involve use of LSI to assess relative changes in blood flow, an important practical question is to assess the effect of N on the relative flow-speed measurements (i.e., relative changes in SFI).

Our experimental data demonstrate that, over a large range of N values (0.39 to 12.5) and flow speeds (up to 20 mm/s), the relative change in SFI is the same (Fig. 5
Fig. 5 Relative flow speed [i.e., (SFI in C1)/(SFI in C3)] is only weakly dependent on N and actual flow speed. The dependence is noticeably weaker with the (a) temporal speckle contrast approach than with the (b) spatial speckle contrast approach.
). For example, the ratio in SFI values between channels C1 and C3 is equal to ~2 for each of the N values used in this study; this ratio is in agreement with the expected ratio in flow speed based on the relative dimensions of the two channels.

Note that the C1/C3 ratio is more accurate using temporal contrast analysis (Fig. 5(a)) than with spatial contrast analysis (Fig. 5(b)). While the relative flow speed remains at a value of ~2 with temporal analysis, the relative speed decreases linearly with actual flow speed when spatial analysis is used. A similar trend was found for C1/C5 ratio, for this time the relative flow speed remains at a value slightly below 4 (probably due to friction) for the temporal algorithm and it decays linearly for the spatial analysis. The same result was observed using various sliding-window sizes (5x5, 7x7 and 9x9) [18

18. D. D. Duncan, S. J. Kirkpatrick, and R. K. Wang, “Statistics of local speckle contrast,” J. Opt. Soc. Am. A 25(1), 9–15 (2008). [CrossRef] [PubMed]

].

This difference in behavior of the spatial and temporal speckle-contrast algorithms is an unexpected finding. Recently Parthasarathy et al. [12

12. A. B. Parthasarathy, W. J. Tom, A. Gopal, X. Zhang, and A. K. Dunn, “Robust flow measurement with multi-exposure speckle imaging,” Opt. Express 16(3), 1975–1989 (2008). [CrossRef] [PubMed]

, 19

19. P. Li, S. Ni, L. Zhang, S. Zeng, and Q. Luo, “Imaging cerebral blood flow through the intact rat skull with temporal laser speckle imaging,” Opt. Lett. 31(12), 1824–1826 (2006). [CrossRef] [PubMed]

] suggested that the spatial algorithm is more sensitive to the static component of the scattered light than is the temporal algorithm. Based in this hypothesis, we explain the linear decay shown in Fig. 5(b) as follows. Based on Eq. (2) and assuming no noise, we define the spatial speckle contrast in channel C1 (KS,C1) as:
Ks,C12=βρ2e2x1+2x2x2+4βρ(1ρ)ex1+xx2+(1ρ)2
(5)
Similarly, the spatial speckle contrast in channel C3 is:

Ks,C32=βρ2e2(x/2)1+2(x/2)2(x/2)2+4βρ(1ρ)e(x/2)1+(x/2)(x/2)2+(1ρ)2
(6)

The last two terms in Eq. (5) account for the static component of the scattered light. Assuming that the temporal speckle-contrast algorithm is insensitive to the static component of the scattered light, we define the temporal contrast for C1 and C3 as:

Kt,C12=ρβe2x1+2x2x2
(7)
Kt,C32=ρβe2(x/2)1+2(x/2)2(x/2)2
(8)

In the long-exposure regime (e.g., T >> τc) the relative flow speed (RFS) is:
RFS=SFI_C1SFI_C3=KC12KC32
(9)
where SFI in C1 is defined as SFI_C1 = 1/(TK2C1) and the SFI in C3 as SFI_C3 = 1/(TK2C3). Note that Eq. (9) does depends on ρ for the spatial algorithm (Eqs. (5) and (6)), but it does not depend on ρ for the temporal algorithm (Eqs. (7) and (8)), moreover both algorithm predict the same RFS when ρ = 1. Figure 6
Fig. 6 RFS as a function of x (which is proportional to SFI) for three values of ρ. It is assumed that the actual RFS is two. The RFS associated with the temporal speckle-contrast algorithm is two for different values of x (continuous line), for ρ = 0.98 to 1.00. However, with spatial speckle-contrast analysis, the RFS decreases with x for all values of ρ below unity.
shows Eq. (9) plotted versus x (which is proportional to flow speed) for the temporal algorithm (solid lines which are overlaped) and the spatial algorithm (dashed lines) for three values of ρ.

4. Conclusions

Our in-vitro experimental data collected from a dynamic-scattering phantom demonstrate that speckle contrast increases with the ratio of pixel size to speckle size, even at values beyond the Nyquist sampling criterion of N = 2. For monitoring of relative changes in blood flow, however, the relative change in SFI is minimally affected by N and flow speed, over a large range of values for the two parameters. Use of the temporal speckle-contrast algorithm, is more accurate at assessing relative changes in blood flow, especially at faster flow speeds, than the commonly-used spatial algorithm. Based on these findings, we recommend that, for measurement of relative changes in blood flow in samples with minimal motion artifact, such as a rodent brain fixed in a stereotactic frame, that the temporal LSCI algorithm be used.

Acknowledgments

This research was supported in part by CONACYT (Mexico) under the grant CB-2010-156876-F, the Arnold and Mabel Beckman Foundation, and the National Institutes of Health (P41 EB015890, R01 DE022831, R01 HD065536).

References and links

1.

J. W. Goodman, Statistical Optics (New York: Wiley, 1985).

2.

F. Fercher and J. D. Briers, “Flow visualization by means of single-exposure speckle photography,” Opt. Commun. 37(5), 326–330 (1981). [CrossRef]

3.

O. Yang, D. Cuccia, and B. Choi, “Real-time blood flow visualization using the graphics processing unit,” J. Biomed. Opt. 16(1), 016009 (2011). [CrossRef] [PubMed]

4.

A. K. Dunn, “Laser speckle contrast imaging of cerebral blood flow,” Ann. Biomed. Eng. 40(2), 367–377 (2012). [CrossRef] [PubMed]

5.

W. J. Moy, S. J. Patel, B. S. Lertsakdadet, R. P. Arora, K. M. Nielsen, K. M. Kelly, and B. Choi, “Preclinical in vivo evaluation of NPe6-mediated photodynamic therapy on normal vasculature,” Lasers Surg. Med. 44(2), 158–162 (2012). [CrossRef] [PubMed]

6.

A. B. Parthasarathy, E. L. Weber, L. M. Richards, D. J. Fox, and A. K. Dunn, “Laser speckle contrast imaging of cerebral blood flow in humans during neurosurgery: a pilot clinical study,” J. Biomed. Opt. 15(6), 066030 (2010). [CrossRef] [PubMed]

7.

A. Humeau-Heurtier, B. Buard, G. Mahe, and P. Abraham, “Laser speckle contrast imaging of the skin: interest in processing the perfusion data,” Med. Biol. Eng. Comput. 50(2), 103–105 (2012). [CrossRef] [PubMed]

8.

S. J. Kirkpatrick, D. D. Duncan, and E. M. Wells-Gray, “Detrimental effects of speckle-pixel size matching in laser speckle contrast imaging,” Opt. Lett. 33(24), 2886–2888 (2008). [CrossRef] [PubMed]

9.

O. Thompson, M. Andrews, and E. Hirst, “Correction for spatial averaging in laser speckle contrast analysis,” Biomed. Opt. Express 2(4), 1021–1029 (2011). [CrossRef] [PubMed]

10.

A. Ennos, “Speckle interferometry,” in Laser Speckle and Related Phenomena J.C. Dainty (Springer-Verlag) [CrossRef]

11.

H. Y. Cheng, Q. M. Luo, S. Q. Zeng, S. B. Chen, J. Cen, and H. Gong, “Modified laser speckle imaging method with improved spatial resolution,” J. Biomed. Opt. 8(3), 559–564 (2003). [CrossRef] [PubMed]

12.

A. B. Parthasarathy, W. J. Tom, A. Gopal, X. Zhang, and A. K. Dunn, “Robust flow measurement with multi-exposure speckle imaging,” Opt. Express 16(3), 1975–1989 (2008). [CrossRef] [PubMed]

13.

D. A. Boas and A. K. Dunn, “Laser speckle contrast imaging in biomedical optics,” J. Biomed. Opt. 15(1), 011109 (2010). [CrossRef] [PubMed]

14.

P. A. Lemieux and D. J. Durian, “Investigating non-Gaussian scattering process by using nth-order intensity correlation function,” J. Opt. Soc. Am. A 16(7), 1651–1664 (1999). [CrossRef]

15.

Y. Atchia, H. Levy, S. Dufour, and O. Levi, “Rapid multiexposure in vivo brain imaging system using vertical cavity surface emitting lasers as a light source,” Appl. Opt. 52(7), C64–C71 (2013). [CrossRef] [PubMed]

16.

J. C. Ramirez-San-Juan, R. Ramos-García, I. Guizar-Iturbide, G. Martínez-Niconoff, and B. Choi, “Impact of velocity distribution assumption on simplified laser speckle imaging equation,” Opt. Express 16(5), 3197 (2008). [CrossRef]

17.

K. Basak, M. Manjunatha, and P. K. Dutta, “Review of laser speckle-based analysis in medical imaging,” Med. Biol. Eng. Comput. 50(6), 547–558 (2012). [CrossRef] [PubMed]

18.

D. D. Duncan, S. J. Kirkpatrick, and R. K. Wang, “Statistics of local speckle contrast,” J. Opt. Soc. Am. A 25(1), 9–15 (2008). [CrossRef] [PubMed]

19.

P. Li, S. Ni, L. Zhang, S. Zeng, and Q. Luo, “Imaging cerebral blood flow through the intact rat skull with temporal laser speckle imaging,” Opt. Lett. 31(12), 1824–1826 (2006). [CrossRef] [PubMed]

OCIS Codes
(030.6140) Coherence and statistical optics : Speckle
(120.6150) Instrumentation, measurement, and metrology : Speckle imaging
(120.7250) Instrumentation, measurement, and metrology : Velocimetry

ToC Category:
Speckle Imaging and Diagnostics

History
Original Manuscript: May 24, 2013
Revised Manuscript: July 25, 2013
Manuscript Accepted: July 26, 2013
Published: August 30, 2013

Citation
J. C. Ramirez-San-Juan, E. Mendez-Aguilar, N. Salazar-Hermenegildo, A. Fuentes-Garcia, R. Ramos-Garcia, and B. Choi, "Effects of speckle/pixel size ratio on temporal and spatial speckle-contrast analysis of dynamic scattering systems: Implications for measurements of blood-flow dynamics," Biomed. Opt. Express 4, 1883-1889 (2013)
http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-4-10-1883


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References

  1. J. W. Goodman, Statistical Optics (New York: Wiley, 1985).
  2. F. Fercher and J. D. Briers, “Flow visualization by means of single-exposure speckle photography,” Opt. Commun.37(5), 326–330 (1981). [CrossRef]
  3. O. Yang, D. Cuccia, and B. Choi, “Real-time blood flow visualization using the graphics processing unit,” J. Biomed. Opt.16(1), 016009 (2011). [CrossRef] [PubMed]
  4. A. K. Dunn, “Laser speckle contrast imaging of cerebral blood flow,” Ann. Biomed. Eng.40(2), 367–377 (2012). [CrossRef] [PubMed]
  5. W. J. Moy, S. J. Patel, B. S. Lertsakdadet, R. P. Arora, K. M. Nielsen, K. M. Kelly, and B. Choi, “Preclinical in vivo evaluation of NPe6-mediated photodynamic therapy on normal vasculature,” Lasers Surg. Med.44(2), 158–162 (2012). [CrossRef] [PubMed]
  6. A. B. Parthasarathy, E. L. Weber, L. M. Richards, D. J. Fox, and A. K. Dunn, “Laser speckle contrast imaging of cerebral blood flow in humans during neurosurgery: a pilot clinical study,” J. Biomed. Opt.15(6), 066030 (2010). [CrossRef] [PubMed]
  7. A. Humeau-Heurtier, B. Buard, G. Mahe, and P. Abraham, “Laser speckle contrast imaging of the skin: interest in processing the perfusion data,” Med. Biol. Eng. Comput.50(2), 103–105 (2012). [CrossRef] [PubMed]
  8. S. J. Kirkpatrick, D. D. Duncan, and E. M. Wells-Gray, “Detrimental effects of speckle-pixel size matching in laser speckle contrast imaging,” Opt. Lett.33(24), 2886–2888 (2008). [CrossRef] [PubMed]
  9. O. Thompson, M. Andrews, and E. Hirst, “Correction for spatial averaging in laser speckle contrast analysis,” Biomed. Opt. Express2(4), 1021–1029 (2011). [CrossRef] [PubMed]
  10. A. Ennos, “Speckle interferometry,” in Laser Speckle and Related Phenomena J.C. Dainty (Springer-Verlag) [CrossRef]
  11. H. Y. Cheng, Q. M. Luo, S. Q. Zeng, S. B. Chen, J. Cen, and H. Gong, “Modified laser speckle imaging method with improved spatial resolution,” J. Biomed. Opt.8(3), 559–564 (2003). [CrossRef] [PubMed]
  12. A. B. Parthasarathy, W. J. Tom, A. Gopal, X. Zhang, and A. K. Dunn, “Robust flow measurement with multi-exposure speckle imaging,” Opt. Express16(3), 1975–1989 (2008). [CrossRef] [PubMed]
  13. D. A. Boas and A. K. Dunn, “Laser speckle contrast imaging in biomedical optics,” J. Biomed. Opt.15(1), 011109 (2010). [CrossRef] [PubMed]
  14. P. A. Lemieux and D. J. Durian, “Investigating non-Gaussian scattering process by using nth-order intensity correlation function,” J. Opt. Soc. Am. A16(7), 1651–1664 (1999). [CrossRef]
  15. Y. Atchia, H. Levy, S. Dufour, and O. Levi, “Rapid multiexposure in vivo brain imaging system using vertical cavity surface emitting lasers as a light source,” Appl. Opt.52(7), C64–C71 (2013). [CrossRef] [PubMed]
  16. J. C. Ramirez-San-Juan, R. Ramos-García, I. Guizar-Iturbide, G. Martínez-Niconoff, and B. Choi, “Impact of velocity distribution assumption on simplified laser speckle imaging equation,” Opt. Express16(5), 3197 (2008). [CrossRef]
  17. K. Basak, M. Manjunatha, and P. K. Dutta, “Review of laser speckle-based analysis in medical imaging,” Med. Biol. Eng. Comput.50(6), 547–558 (2012). [CrossRef] [PubMed]
  18. D. D. Duncan, S. J. Kirkpatrick, and R. K. Wang, “Statistics of local speckle contrast,” J. Opt. Soc. Am. A25(1), 9–15 (2008). [CrossRef] [PubMed]
  19. P. Li, S. Ni, L. Zhang, S. Zeng, and Q. Luo, “Imaging cerebral blood flow through the intact rat skull with temporal laser speckle imaging,” Opt. Lett.31(12), 1824–1826 (2006). [CrossRef] [PubMed]

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