Abstract

The problem of resolution enhancement for speckle patterns analysis-based movement estimation is considered. In our previous publications we showed that this movement represents the corresponding tilt vibrations of the illuminated object and can be measured as a relative spatial shift between time adjacent images of the speckle pattern. In this paper we show how to overcome the resolution limitation obtained when using an optical sensor available in an optical mouse and which measures the Cartesian coordinates of the shift as an integer number of pixels. To overcome such a resolution limitation, it is proposed here to use simultaneous measurements from the same illuminated spot by a few cameras (sensors) each having imaging lenses with different amounts of defocusing. The amount of defocusing defines the proportion ratio between actual changes in the tilt plane and measured shift between speckle images. To utilize the diversity of such ratios we apply a beam-forming signal processing approach that makes it possible to achieve different design criteria and improve the measurement accuracy, respectively. The validity and properties of the proposed solution are demonstrated by a few examples of in-vivo touchless measurements of human heart beat sounds.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. J. C. Dainty, Laser Speckle and Related Phenomena, (2nd ed., Springer-Verlag, Berlin, 1989).
  2. H. M. Pedersen, “Intensity correlation metrology: a comparative study,” Opt. Acta (Lond.) 29(1), 105–118 (1982).
    [Crossref]
  3. P. K. Rastogi and P. Jacquot, “Measurement of difference deformation using speckle interferometry,” Opt. Lett. 12(8), 596–598 (1987).
    [Crossref] [PubMed]
  4. J. A. Leedertz, “Interferometric displacement measurements on scattering surfaces utilizing speckle effects,” J. Phys. E Sci. Instrum. 3(3), 214–218 (1970).
    [Crossref]
  5. P. K. Rastogi and P. Jacquot, “Measurement of difference deformation using speckle interferometry,” Opt. Lett. 12(8), 596–598 (1987).
    [Crossref] [PubMed]
  6. J. García, Z. Zalevsky, and D. Fixler, “Synthetic aperture superresolution by speckle pattern projection,” Opt. Express 13(16), 6073–6078 (2005).
    [Crossref] [PubMed]
  7. V. V. Tuchin, A. V. Ampilogov, A. G. Bogoroditsky, E. M. Rabinovich, V. P. Ryabukhov, S. S. Ul’yanov, and M. E. V’yushkin, “Laser speckle and optical fiber sensors for micromovements monitoring in biotissue,” Proc. SPIE 1420, 81–92 (1991).
    [Crossref]
  8. S. P. Slight, C. Franz, M. Olugbile, H. V. Brown, D. W. Bates, and E. Zimlichman, “The return on investment of implementing a continuous monitoring system in general medical-surgical units,” Crit. Care Med. 42(8), 1862–1868 (2014).
    [Crossref] [PubMed]
  9. S. S. Ul’yanov, V. P. Ryabukho, and V. V. Tuchin, “Speckle interferometry for biotissue vibration measurement,” Opt. Eng. 33(3), 908–914 (1994).
    [Crossref]
  10. Z. Zalevsky and J. Garcia, “Motion detection system and method,” Israeli Patent Application No. 184868 (July 2007).
  11. Z. Zalevsky, Y. Beiderman, I. Margalit, S. Gingold, M. Teicher, V. Mico, and J. Garcia, “Simultaneous remote extraction of multiple speech sources and heart beats from secondary speckles pattern,” Opt. Express 17(24), 21566–21580 (2009).
    [Crossref] [PubMed]
  12. Y. Beiderman, I. Horovitz, N. Burshtein, M. Teicher, J. Garcia, V. Mico, and Z. Zalevsky, “Remote estimation of blood pulse pressure via temporal tracking of reflected secondary speckles pattern,” J. Biomed. Opt. 15(6), 061707 (2010).
    [Crossref] [PubMed]
  13. STMicroelectronics VD5377 datasheet,” Ultra-low power motion sensor for optical finger navigation (OFN),” http://www.st.com/en/imaging-and-photonics-solutions/vd5377.html
  14. J. Hu, Y. Chang, and Y. Hsu, “Calibration and on-line data selection of multiple optical flow sensors for odometry application,” Sens. Actuators A Phys. 149(1), 74–80 (2009).
    [Crossref]
  15. P. Stoica and R. Moses, Spectral Analysis of Signals, (Prientice Hall,2005).
  16. H. L. Van Trees, Detection, Estimation and Modulation Theory, Part IV: Optimum Array Processing, (John Willey & Sons, Inc. 2002).
  17. S. K. Mitra, “On the probability distribution of the sum of uniformly distributed random variables,” SIAM J. Appl. Math. 20(2), 195–198 (1971).
    [Crossref]
  18. S. Sadooghi-Alvandi, A. Nematollahi, and R. Habibi, “On the distribution of the sum of independent uniform random variables,” Stat. Papers 50(1), 171–175 (2009).
    [Crossref]

2014 (1)

S. P. Slight, C. Franz, M. Olugbile, H. V. Brown, D. W. Bates, and E. Zimlichman, “The return on investment of implementing a continuous monitoring system in general medical-surgical units,” Crit. Care Med. 42(8), 1862–1868 (2014).
[Crossref] [PubMed]

2010 (1)

Y. Beiderman, I. Horovitz, N. Burshtein, M. Teicher, J. Garcia, V. Mico, and Z. Zalevsky, “Remote estimation of blood pulse pressure via temporal tracking of reflected secondary speckles pattern,” J. Biomed. Opt. 15(6), 061707 (2010).
[Crossref] [PubMed]

2009 (3)

J. Hu, Y. Chang, and Y. Hsu, “Calibration and on-line data selection of multiple optical flow sensors for odometry application,” Sens. Actuators A Phys. 149(1), 74–80 (2009).
[Crossref]

Z. Zalevsky, Y. Beiderman, I. Margalit, S. Gingold, M. Teicher, V. Mico, and J. Garcia, “Simultaneous remote extraction of multiple speech sources and heart beats from secondary speckles pattern,” Opt. Express 17(24), 21566–21580 (2009).
[Crossref] [PubMed]

S. Sadooghi-Alvandi, A. Nematollahi, and R. Habibi, “On the distribution of the sum of independent uniform random variables,” Stat. Papers 50(1), 171–175 (2009).
[Crossref]

2005 (1)

1994 (1)

S. S. Ul’yanov, V. P. Ryabukho, and V. V. Tuchin, “Speckle interferometry for biotissue vibration measurement,” Opt. Eng. 33(3), 908–914 (1994).
[Crossref]

1991 (1)

V. V. Tuchin, A. V. Ampilogov, A. G. Bogoroditsky, E. M. Rabinovich, V. P. Ryabukhov, S. S. Ul’yanov, and M. E. V’yushkin, “Laser speckle and optical fiber sensors for micromovements monitoring in biotissue,” Proc. SPIE 1420, 81–92 (1991).
[Crossref]

1987 (2)

1982 (1)

H. M. Pedersen, “Intensity correlation metrology: a comparative study,” Opt. Acta (Lond.) 29(1), 105–118 (1982).
[Crossref]

1971 (1)

S. K. Mitra, “On the probability distribution of the sum of uniformly distributed random variables,” SIAM J. Appl. Math. 20(2), 195–198 (1971).
[Crossref]

1970 (1)

J. A. Leedertz, “Interferometric displacement measurements on scattering surfaces utilizing speckle effects,” J. Phys. E Sci. Instrum. 3(3), 214–218 (1970).
[Crossref]

Ampilogov, A. V.

V. V. Tuchin, A. V. Ampilogov, A. G. Bogoroditsky, E. M. Rabinovich, V. P. Ryabukhov, S. S. Ul’yanov, and M. E. V’yushkin, “Laser speckle and optical fiber sensors for micromovements monitoring in biotissue,” Proc. SPIE 1420, 81–92 (1991).
[Crossref]

Bates, D. W.

S. P. Slight, C. Franz, M. Olugbile, H. V. Brown, D. W. Bates, and E. Zimlichman, “The return on investment of implementing a continuous monitoring system in general medical-surgical units,” Crit. Care Med. 42(8), 1862–1868 (2014).
[Crossref] [PubMed]

Beiderman, Y.

Y. Beiderman, I. Horovitz, N. Burshtein, M. Teicher, J. Garcia, V. Mico, and Z. Zalevsky, “Remote estimation of blood pulse pressure via temporal tracking of reflected secondary speckles pattern,” J. Biomed. Opt. 15(6), 061707 (2010).
[Crossref] [PubMed]

Z. Zalevsky, Y. Beiderman, I. Margalit, S. Gingold, M. Teicher, V. Mico, and J. Garcia, “Simultaneous remote extraction of multiple speech sources and heart beats from secondary speckles pattern,” Opt. Express 17(24), 21566–21580 (2009).
[Crossref] [PubMed]

Bogoroditsky, A. G.

V. V. Tuchin, A. V. Ampilogov, A. G. Bogoroditsky, E. M. Rabinovich, V. P. Ryabukhov, S. S. Ul’yanov, and M. E. V’yushkin, “Laser speckle and optical fiber sensors for micromovements monitoring in biotissue,” Proc. SPIE 1420, 81–92 (1991).
[Crossref]

Brown, H. V.

S. P. Slight, C. Franz, M. Olugbile, H. V. Brown, D. W. Bates, and E. Zimlichman, “The return on investment of implementing a continuous monitoring system in general medical-surgical units,” Crit. Care Med. 42(8), 1862–1868 (2014).
[Crossref] [PubMed]

Burshtein, N.

Y. Beiderman, I. Horovitz, N. Burshtein, M. Teicher, J. Garcia, V. Mico, and Z. Zalevsky, “Remote estimation of blood pulse pressure via temporal tracking of reflected secondary speckles pattern,” J. Biomed. Opt. 15(6), 061707 (2010).
[Crossref] [PubMed]

Chang, Y.

J. Hu, Y. Chang, and Y. Hsu, “Calibration and on-line data selection of multiple optical flow sensors for odometry application,” Sens. Actuators A Phys. 149(1), 74–80 (2009).
[Crossref]

Fixler, D.

Franz, C.

S. P. Slight, C. Franz, M. Olugbile, H. V. Brown, D. W. Bates, and E. Zimlichman, “The return on investment of implementing a continuous monitoring system in general medical-surgical units,” Crit. Care Med. 42(8), 1862–1868 (2014).
[Crossref] [PubMed]

Garcia, J.

Y. Beiderman, I. Horovitz, N. Burshtein, M. Teicher, J. Garcia, V. Mico, and Z. Zalevsky, “Remote estimation of blood pulse pressure via temporal tracking of reflected secondary speckles pattern,” J. Biomed. Opt. 15(6), 061707 (2010).
[Crossref] [PubMed]

Z. Zalevsky, Y. Beiderman, I. Margalit, S. Gingold, M. Teicher, V. Mico, and J. Garcia, “Simultaneous remote extraction of multiple speech sources and heart beats from secondary speckles pattern,” Opt. Express 17(24), 21566–21580 (2009).
[Crossref] [PubMed]

García, J.

Gingold, S.

Habibi, R.

S. Sadooghi-Alvandi, A. Nematollahi, and R. Habibi, “On the distribution of the sum of independent uniform random variables,” Stat. Papers 50(1), 171–175 (2009).
[Crossref]

Horovitz, I.

Y. Beiderman, I. Horovitz, N. Burshtein, M. Teicher, J. Garcia, V. Mico, and Z. Zalevsky, “Remote estimation of blood pulse pressure via temporal tracking of reflected secondary speckles pattern,” J. Biomed. Opt. 15(6), 061707 (2010).
[Crossref] [PubMed]

Hsu, Y.

J. Hu, Y. Chang, and Y. Hsu, “Calibration and on-line data selection of multiple optical flow sensors for odometry application,” Sens. Actuators A Phys. 149(1), 74–80 (2009).
[Crossref]

Hu, J.

J. Hu, Y. Chang, and Y. Hsu, “Calibration and on-line data selection of multiple optical flow sensors for odometry application,” Sens. Actuators A Phys. 149(1), 74–80 (2009).
[Crossref]

Jacquot, P.

Leedertz, J. A.

J. A. Leedertz, “Interferometric displacement measurements on scattering surfaces utilizing speckle effects,” J. Phys. E Sci. Instrum. 3(3), 214–218 (1970).
[Crossref]

Margalit, I.

Mico, V.

Y. Beiderman, I. Horovitz, N. Burshtein, M. Teicher, J. Garcia, V. Mico, and Z. Zalevsky, “Remote estimation of blood pulse pressure via temporal tracking of reflected secondary speckles pattern,” J. Biomed. Opt. 15(6), 061707 (2010).
[Crossref] [PubMed]

Z. Zalevsky, Y. Beiderman, I. Margalit, S. Gingold, M. Teicher, V. Mico, and J. Garcia, “Simultaneous remote extraction of multiple speech sources and heart beats from secondary speckles pattern,” Opt. Express 17(24), 21566–21580 (2009).
[Crossref] [PubMed]

Mitra, S. K.

S. K. Mitra, “On the probability distribution of the sum of uniformly distributed random variables,” SIAM J. Appl. Math. 20(2), 195–198 (1971).
[Crossref]

Nematollahi, A.

S. Sadooghi-Alvandi, A. Nematollahi, and R. Habibi, “On the distribution of the sum of independent uniform random variables,” Stat. Papers 50(1), 171–175 (2009).
[Crossref]

Olugbile, M.

S. P. Slight, C. Franz, M. Olugbile, H. V. Brown, D. W. Bates, and E. Zimlichman, “The return on investment of implementing a continuous monitoring system in general medical-surgical units,” Crit. Care Med. 42(8), 1862–1868 (2014).
[Crossref] [PubMed]

Pedersen, H. M.

H. M. Pedersen, “Intensity correlation metrology: a comparative study,” Opt. Acta (Lond.) 29(1), 105–118 (1982).
[Crossref]

Rabinovich, E. M.

V. V. Tuchin, A. V. Ampilogov, A. G. Bogoroditsky, E. M. Rabinovich, V. P. Ryabukhov, S. S. Ul’yanov, and M. E. V’yushkin, “Laser speckle and optical fiber sensors for micromovements monitoring in biotissue,” Proc. SPIE 1420, 81–92 (1991).
[Crossref]

Rastogi, P. K.

Ryabukho, V. P.

S. S. Ul’yanov, V. P. Ryabukho, and V. V. Tuchin, “Speckle interferometry for biotissue vibration measurement,” Opt. Eng. 33(3), 908–914 (1994).
[Crossref]

Ryabukhov, V. P.

V. V. Tuchin, A. V. Ampilogov, A. G. Bogoroditsky, E. M. Rabinovich, V. P. Ryabukhov, S. S. Ul’yanov, and M. E. V’yushkin, “Laser speckle and optical fiber sensors for micromovements monitoring in biotissue,” Proc. SPIE 1420, 81–92 (1991).
[Crossref]

Sadooghi-Alvandi, S.

S. Sadooghi-Alvandi, A. Nematollahi, and R. Habibi, “On the distribution of the sum of independent uniform random variables,” Stat. Papers 50(1), 171–175 (2009).
[Crossref]

Slight, S. P.

S. P. Slight, C. Franz, M. Olugbile, H. V. Brown, D. W. Bates, and E. Zimlichman, “The return on investment of implementing a continuous monitoring system in general medical-surgical units,” Crit. Care Med. 42(8), 1862–1868 (2014).
[Crossref] [PubMed]

Teicher, M.

Y. Beiderman, I. Horovitz, N. Burshtein, M. Teicher, J. Garcia, V. Mico, and Z. Zalevsky, “Remote estimation of blood pulse pressure via temporal tracking of reflected secondary speckles pattern,” J. Biomed. Opt. 15(6), 061707 (2010).
[Crossref] [PubMed]

Z. Zalevsky, Y. Beiderman, I. Margalit, S. Gingold, M. Teicher, V. Mico, and J. Garcia, “Simultaneous remote extraction of multiple speech sources and heart beats from secondary speckles pattern,” Opt. Express 17(24), 21566–21580 (2009).
[Crossref] [PubMed]

Tuchin, V. V.

S. S. Ul’yanov, V. P. Ryabukho, and V. V. Tuchin, “Speckle interferometry for biotissue vibration measurement,” Opt. Eng. 33(3), 908–914 (1994).
[Crossref]

V. V. Tuchin, A. V. Ampilogov, A. G. Bogoroditsky, E. M. Rabinovich, V. P. Ryabukhov, S. S. Ul’yanov, and M. E. V’yushkin, “Laser speckle and optical fiber sensors for micromovements monitoring in biotissue,” Proc. SPIE 1420, 81–92 (1991).
[Crossref]

Ul’yanov, S. S.

S. S. Ul’yanov, V. P. Ryabukho, and V. V. Tuchin, “Speckle interferometry for biotissue vibration measurement,” Opt. Eng. 33(3), 908–914 (1994).
[Crossref]

V. V. Tuchin, A. V. Ampilogov, A. G. Bogoroditsky, E. M. Rabinovich, V. P. Ryabukhov, S. S. Ul’yanov, and M. E. V’yushkin, “Laser speckle and optical fiber sensors for micromovements monitoring in biotissue,” Proc. SPIE 1420, 81–92 (1991).
[Crossref]

V’yushkin, M. E.

V. V. Tuchin, A. V. Ampilogov, A. G. Bogoroditsky, E. M. Rabinovich, V. P. Ryabukhov, S. S. Ul’yanov, and M. E. V’yushkin, “Laser speckle and optical fiber sensors for micromovements monitoring in biotissue,” Proc. SPIE 1420, 81–92 (1991).
[Crossref]

Zalevsky, Z.

Zimlichman, E.

S. P. Slight, C. Franz, M. Olugbile, H. V. Brown, D. W. Bates, and E. Zimlichman, “The return on investment of implementing a continuous monitoring system in general medical-surgical units,” Crit. Care Med. 42(8), 1862–1868 (2014).
[Crossref] [PubMed]

Crit. Care Med. (1)

S. P. Slight, C. Franz, M. Olugbile, H. V. Brown, D. W. Bates, and E. Zimlichman, “The return on investment of implementing a continuous monitoring system in general medical-surgical units,” Crit. Care Med. 42(8), 1862–1868 (2014).
[Crossref] [PubMed]

J. Biomed. Opt. (1)

Y. Beiderman, I. Horovitz, N. Burshtein, M. Teicher, J. Garcia, V. Mico, and Z. Zalevsky, “Remote estimation of blood pulse pressure via temporal tracking of reflected secondary speckles pattern,” J. Biomed. Opt. 15(6), 061707 (2010).
[Crossref] [PubMed]

J. Phys. E Sci. Instrum. (1)

J. A. Leedertz, “Interferometric displacement measurements on scattering surfaces utilizing speckle effects,” J. Phys. E Sci. Instrum. 3(3), 214–218 (1970).
[Crossref]

Opt. Acta (Lond.) (1)

H. M. Pedersen, “Intensity correlation metrology: a comparative study,” Opt. Acta (Lond.) 29(1), 105–118 (1982).
[Crossref]

Opt. Eng. (1)

S. S. Ul’yanov, V. P. Ryabukho, and V. V. Tuchin, “Speckle interferometry for biotissue vibration measurement,” Opt. Eng. 33(3), 908–914 (1994).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Proc. SPIE (1)

V. V. Tuchin, A. V. Ampilogov, A. G. Bogoroditsky, E. M. Rabinovich, V. P. Ryabukhov, S. S. Ul’yanov, and M. E. V’yushkin, “Laser speckle and optical fiber sensors for micromovements monitoring in biotissue,” Proc. SPIE 1420, 81–92 (1991).
[Crossref]

Sens. Actuators A Phys. (1)

J. Hu, Y. Chang, and Y. Hsu, “Calibration and on-line data selection of multiple optical flow sensors for odometry application,” Sens. Actuators A Phys. 149(1), 74–80 (2009).
[Crossref]

SIAM J. Appl. Math. (1)

S. K. Mitra, “On the probability distribution of the sum of uniformly distributed random variables,” SIAM J. Appl. Math. 20(2), 195–198 (1971).
[Crossref]

Stat. Papers (1)

S. Sadooghi-Alvandi, A. Nematollahi, and R. Habibi, “On the distribution of the sum of independent uniform random variables,” Stat. Papers 50(1), 171–175 (2009).
[Crossref]

Other (5)

P. Stoica and R. Moses, Spectral Analysis of Signals, (Prientice Hall,2005).

H. L. Van Trees, Detection, Estimation and Modulation Theory, Part IV: Optimum Array Processing, (John Willey & Sons, Inc. 2002).

J. C. Dainty, Laser Speckle and Related Phenomena, (2nd ed., Springer-Verlag, Berlin, 1989).

Z. Zalevsky and J. Garcia, “Motion detection system and method,” Israeli Patent Application No. 184868 (July 2007).

STMicroelectronics VD5377 datasheet,” Ultra-low power motion sensor for optical finger navigation (OFN),” http://www.st.com/en/imaging-and-photonics-solutions/vd5377.html

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Figures (12)

Fig. 1
Fig. 1 Comparison of the recorded signals for different defocusing that are estimated with integer and sub-pixel accuracy.
Fig. 2
Fig. 2 Errors (rounding noise) between signals with sub-pixel and integer accuracy estimated by sensors with different defocusing.
Fig. 3
Fig. 3 Errors (rounding noise) between signals with sub-pixel and integer accuracy estimated by sensors with different defocusing.
Fig. 4
Fig. 4 Examples of the independent uniformly distributed components (distributed in [-0.5 0.5] with zero-mean for all of them).
Fig. 5
Fig. 5 Dependence of the parameters for the distribution of linear combination (normal PDF approximation) on number of components.
Fig. 6
Fig. 6 Dependence of the parameters for the distribution of linear combination (normal PDF approximation) on linear coefficients (weights).
Fig. 7
Fig. 7 Experimental data. (a)-(c). Illuminated spots from different cameras. Blue points mark estimated spots’ center of mass.
Fig. 8
Fig. 8 Estimated relative defocusing ratio for different sensors.
Fig. 9
Fig. 9 (a)-(c). Resolution performance based on fixed beam-forming solutions.
Fig. 10
Fig. 10 (a)-(c). Resolution improvement based on adaptive beam-forming.
Fig. 11
Fig. 11 Error PDF for major eigenvector beamformer.
Fig. 12
Fig. 12 (a)-(c). Performance (time domain errors) comparison for different schemes.

Equations (18)

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y i =a s i ,      i=1M
y i =a s i + v i ,      i=1M
y i =a s i + n i + v i       i=1M
s i ^ = w T y i
E{ | w T v | 2 }=E{ | j=1 N w j v j | 2 }= σ q 2 j=1 N w j 2
w T y=s w T a+ w T v,
SNR= P s | w T a | 2 E{ | w T v | 2 }
SNR= P s a 2 σ q 2
w= a j a j
max w E{ w T y y T w }
w= a a
min w E{ w T y y T w },   w T a=1
w= R 1 a a T R 1 a ,R=E{ y y T }
Y N×M :    Y=[ y 1 y M ]
R 1 M Y Y T
w T a=c,
w= R v 1 a a T R v 1 a , R v =E{ v v T }
R= P s a a T + σ 2 I

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