Abstract

This paper presents a method to identify the axial location of targets in an optical scanning holography (OSH) system. By combining time reversal (TR) technique with the multiple signal classification (MUSIC) method in OSH, axial location can be detected with high resolution. Both simulation and experimental work have been carried out to verify the feasibility of the proposed work.

© 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. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2, 190–195 (2008).
    [Crossref]
  2. J. Rosen, N. Siegel, and G. Brooker, “Theoretical and experimental demonstration of resolution beyond the rayleigh limit by finch fluorescence microscopic imaging,” Opt. Express 19, 26249 (2011).
    [Crossref]
  3. T.-C. Poon, Optical Scanning Holography with MATLAB (Springer, 2007).
    [Crossref]
  4. B. W. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, Y. Suzuki, and M. H. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett. 22, 1506–1508 (1997).
    [Crossref]
  5. J. Swoger, M. Martínez-Corral, J. Huisken, and E. H. K. Stelzer, “Optical scanning holography as a technique for high-resolution three-dimensional biological microscopy,” J. Opt. Soc. Am. A 19, 1910–1918 (2002).
    [Crossref]
  6. G. Indebetouw and W. Zhong, “Scanning holographic microscopy of three-dimensional fluorescent specimens,” J. Opt. Soc. Am. A 23, 1699–1707 (2006).
    [Crossref]
  7. A. C. S. Chan, K. K. Tsia, and E. Y. Lam, “Subsampled scanning holographic imaging (SuSHI) for fast, non-adaptive recording of three-dimensional objects,” Optica 3, 911–917 (2016).
    [Crossref]
  8. B. W. Schilling and G. C. Templeton, “Three-dimensional remote sensing by optical scanning holography,” Appl. Opt. 40, 5474–5481 (2001).
    [Crossref]
  9. T. Kim, T.-C. Poon, and G. Indebetouw, “Depth detection and image recovery in remote sensing by optical scanning holography,” Opt. Eng. 41, 1331–1338 (2002).
    [Crossref]
  10. T.-C. Poon, T. Kim, and K. Doh, “Optical scanning cryptography for secure wireless transmission,” Appl. Opt. 42, 6496–6503 (2003).
    [Crossref] [PubMed]
  11. H. Di, K. Zheng, X. Zhang, E. Y. Lam, T. Kim, Y. S. Kim, T.-C. Poon, and C. Zhou, “Multiple-image encryption by compressive holography,” Appl. Opt. 51, 1000–1009 (2012).
    [Crossref] [PubMed]
  12. E. Y. Lam, X. Zhang, H. Vo, T.-C. Poon, and G. Indebetouw, “Three-dimensional microscopy and sectional image reconstruction using optical scanning holography,” Appl. Opt. 48, H113–H119 (2009).
    [Crossref] [PubMed]
  13. X. Zhang, E. Y. Lam, and T.-C. Poon, “Reconstruction of sectional images in holography using inverse imaging,” Opt. Express 16, 17215–17226 (2008).
    [Crossref] [PubMed]
  14. T. Kim, “Optical sectioning by optical scanning holography and a Wiener filter,” Appl. Opt. 45, 872–879 (2006).
    [Crossref] [PubMed]
  15. Z. Xin, K. Dobson, Y. Shinoda, and T.-C. Poon, “Sectional image reconstruction in optical scanning holography using a random-phase pupil,” Opt. Lett. 35, 2934–2936 (2010).
    [Crossref] [PubMed]
  16. J. Ke, T.-C. Poon, and E. Y. Lam, “Depth resolution enhancement in optical scanning holography with a dual-wavelength laser source,” Appl. Opt. 50, H285–H296 (2011).
    [Crossref] [PubMed]
  17. H. Ou, T.-C. Poon, K. K. Wong, and E. Y. Lam, “Depth resolution enhancement in double-detection optical scanning holography,” Appl. Opt. 52, 3079–3087 (2013).
    [Crossref] [PubMed]
  18. H. Ou, T.-C. Poon, K. K. Y. Wong, and E. Y. Lam, “Enhanced depth resolution in optical scanning holography using a configurable pupil,” Photon. Res. 2, 64 (2014).
    [Crossref]
  19. Z. Ren, N. Chen, and E. Y. Lam, “Extended focused imaging and depth map reconstruction in optical scanning holography,” Appl. Opt. 55, 1040–1047 (2016).
    [Crossref] [PubMed]
  20. T. Kim and T.-C. Poon, “Autofocusing in optical scanning holography,” Appl. Opt. 48, H153–H159 (2009).
    [Crossref] [PubMed]
  21. X. Zhang, E. Y. Lam, T. Kim, Y. S. Kim, and T.-C. Poon, “Blind sectional image reconstruction for optical scanning holography,” Opt. Lett. 34, 3098–3100 (2009).
    [Crossref] [PubMed]
  22. S. Oh, C.-Y. Hwang, I. K. Jeong, S.-K. Lee, and J.-H. Park, “Fast focus estimation using frequency analysis in digital holography,” Opt. Express 22, 28926 (2014).
    [Crossref] [PubMed]
  23. P. Bouchal and Z. Bouchal, “Non-iterative holographic axial localization using complex amplitude of diffraction-free vortices,” Opt. Express 22, 30200 (2014).
    [Crossref]
  24. Z. Ren, N. Chen, and E. Y. Lam, “Automatic focusing for multisectional objects in digital holography using the structure tensor,” Opt. Lett. 42, 1720 (2017).
    [Crossref] [PubMed]
  25. B. Wu, W. Cai, M. Alrubaiee, M. Xu, and S. K. Gayen, “Time reversal optical tomography: locating targets in a highly scattering turbid medium,” Opt. Express 19, 21956–21976 (2011).
    [Crossref] [PubMed]
  26. B. Wu, W. Cai, and S. K. Gayen, “Three-dimensional localization of fluorescent targets in turbid media using time reversal optical tomography,” Appl. Phys. Lett. 101, 251103 (2012).
    [Crossref]
  27. A. J. Devaney, E. A. Marengo, and F. K. Gruber, “Time-reversal-based imaging and inverse scattering of multiply scattering point targets,” J. Acoust. Soc. Am. 118, 3129–3138 (2005).
    [Crossref]
  28. M. Fink, “Time reversed acoustics,” Reports on Prog. Phys. 50, 34–40 (1997).
  29. K. Dan, “A singularly valuable decomposition: The svd of a matrix,” Coll. Math. J. 27, 2–23 (1996).
    [Crossref]
  30. J. Ke, T. C. Poon, and E. Y. Lam, “Depth resolution enhancement in optical scanning holography with a dual-wavelength laser source,” Appl. Opt. 50, 285–296 (2011).
    [Crossref]
  31. B. Wu, W. Cai, M. Alrubaiee, M. Xu, and S. K. Gayen, “Three dimensional time reversal optical tomography,” in “SPIE BiOS,” (2011), pp. 242–243.
  32. Z. Ren, N. Chen, A. Chan, and E. Y. Lam, “Autofocusing of optical scanning holography based on entropy minimization,” in “Digital Holography and Three-Dimensional Imaging,” (Optical Society of America, 2015), pp. DT4A–4.

2017 (1)

2016 (2)

2014 (3)

2013 (1)

2012 (2)

H. Di, K. Zheng, X. Zhang, E. Y. Lam, T. Kim, Y. S. Kim, T.-C. Poon, and C. Zhou, “Multiple-image encryption by compressive holography,” Appl. Opt. 51, 1000–1009 (2012).
[Crossref] [PubMed]

B. Wu, W. Cai, and S. K. Gayen, “Three-dimensional localization of fluorescent targets in turbid media using time reversal optical tomography,” Appl. Phys. Lett. 101, 251103 (2012).
[Crossref]

2011 (4)

2010 (1)

2009 (3)

2008 (2)

X. Zhang, E. Y. Lam, and T.-C. Poon, “Reconstruction of sectional images in holography using inverse imaging,” Opt. Express 16, 17215–17226 (2008).
[Crossref] [PubMed]

J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2, 190–195 (2008).
[Crossref]

2006 (2)

2005 (1)

A. J. Devaney, E. A. Marengo, and F. K. Gruber, “Time-reversal-based imaging and inverse scattering of multiply scattering point targets,” J. Acoust. Soc. Am. 118, 3129–3138 (2005).
[Crossref]

2003 (1)

2002 (2)

T. Kim, T.-C. Poon, and G. Indebetouw, “Depth detection and image recovery in remote sensing by optical scanning holography,” Opt. Eng. 41, 1331–1338 (2002).
[Crossref]

J. Swoger, M. Martínez-Corral, J. Huisken, and E. H. K. Stelzer, “Optical scanning holography as a technique for high-resolution three-dimensional biological microscopy,” J. Opt. Soc. Am. A 19, 1910–1918 (2002).
[Crossref]

2001 (1)

1997 (2)

1996 (1)

K. Dan, “A singularly valuable decomposition: The svd of a matrix,” Coll. Math. J. 27, 2–23 (1996).
[Crossref]

Alrubaiee, M.

B. Wu, W. Cai, M. Alrubaiee, M. Xu, and S. K. Gayen, “Time reversal optical tomography: locating targets in a highly scattering turbid medium,” Opt. Express 19, 21956–21976 (2011).
[Crossref] [PubMed]

B. Wu, W. Cai, M. Alrubaiee, M. Xu, and S. K. Gayen, “Three dimensional time reversal optical tomography,” in “SPIE BiOS,” (2011), pp. 242–243.

Bouchal, P.

Bouchal, Z.

Brooker, G.

J. Rosen, N. Siegel, and G. Brooker, “Theoretical and experimental demonstration of resolution beyond the rayleigh limit by finch fluorescence microscopic imaging,” Opt. Express 19, 26249 (2011).
[Crossref]

J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2, 190–195 (2008).
[Crossref]

Cai, W.

B. Wu, W. Cai, and S. K. Gayen, “Three-dimensional localization of fluorescent targets in turbid media using time reversal optical tomography,” Appl. Phys. Lett. 101, 251103 (2012).
[Crossref]

B. Wu, W. Cai, M. Alrubaiee, M. Xu, and S. K. Gayen, “Time reversal optical tomography: locating targets in a highly scattering turbid medium,” Opt. Express 19, 21956–21976 (2011).
[Crossref] [PubMed]

B. Wu, W. Cai, M. Alrubaiee, M. Xu, and S. K. Gayen, “Three dimensional time reversal optical tomography,” in “SPIE BiOS,” (2011), pp. 242–243.

Chan, A.

Z. Ren, N. Chen, A. Chan, and E. Y. Lam, “Autofocusing of optical scanning holography based on entropy minimization,” in “Digital Holography and Three-Dimensional Imaging,” (Optical Society of America, 2015), pp. DT4A–4.

Chan, A. C. S.

Chen, N.

Dan, K.

K. Dan, “A singularly valuable decomposition: The svd of a matrix,” Coll. Math. J. 27, 2–23 (1996).
[Crossref]

Devaney, A. J.

A. J. Devaney, E. A. Marengo, and F. K. Gruber, “Time-reversal-based imaging and inverse scattering of multiply scattering point targets,” J. Acoust. Soc. Am. 118, 3129–3138 (2005).
[Crossref]

Di, H.

Dobson, K.

Doh, K.

Fink, M.

M. Fink, “Time reversed acoustics,” Reports on Prog. Phys. 50, 34–40 (1997).

Gayen, S. K.

B. Wu, W. Cai, and S. K. Gayen, “Three-dimensional localization of fluorescent targets in turbid media using time reversal optical tomography,” Appl. Phys. Lett. 101, 251103 (2012).
[Crossref]

B. Wu, W. Cai, M. Alrubaiee, M. Xu, and S. K. Gayen, “Time reversal optical tomography: locating targets in a highly scattering turbid medium,” Opt. Express 19, 21956–21976 (2011).
[Crossref] [PubMed]

B. Wu, W. Cai, M. Alrubaiee, M. Xu, and S. K. Gayen, “Three dimensional time reversal optical tomography,” in “SPIE BiOS,” (2011), pp. 242–243.

Gruber, F. K.

A. J. Devaney, E. A. Marengo, and F. K. Gruber, “Time-reversal-based imaging and inverse scattering of multiply scattering point targets,” J. Acoust. Soc. Am. 118, 3129–3138 (2005).
[Crossref]

Huisken, J.

Hwang, C.-Y.

Indebetouw, G.

Jeong, I. K.

Ke, J.

J. Ke, T. C. Poon, and E. Y. Lam, “Depth resolution enhancement in optical scanning holography with a dual-wavelength laser source,” Appl. Opt. 50, 285–296 (2011).
[Crossref]

J. Ke, T.-C. Poon, and E. Y. Lam, “Depth resolution enhancement in optical scanning holography with a dual-wavelength laser source,” Appl. Opt. 50, H285–H296 (2011).
[Crossref] [PubMed]

Kim, T.

Kim, Y. S.

Lam, E. Y.

Z. Ren, N. Chen, and E. Y. Lam, “Automatic focusing for multisectional objects in digital holography using the structure tensor,” Opt. Lett. 42, 1720 (2017).
[Crossref] [PubMed]

A. C. S. Chan, K. K. Tsia, and E. Y. Lam, “Subsampled scanning holographic imaging (SuSHI) for fast, non-adaptive recording of three-dimensional objects,” Optica 3, 911–917 (2016).
[Crossref]

Z. Ren, N. Chen, and E. Y. Lam, “Extended focused imaging and depth map reconstruction in optical scanning holography,” Appl. Opt. 55, 1040–1047 (2016).
[Crossref] [PubMed]

H. Ou, T.-C. Poon, K. K. Y. Wong, and E. Y. Lam, “Enhanced depth resolution in optical scanning holography using a configurable pupil,” Photon. Res. 2, 64 (2014).
[Crossref]

H. Ou, T.-C. Poon, K. K. Wong, and E. Y. Lam, “Depth resolution enhancement in double-detection optical scanning holography,” Appl. Opt. 52, 3079–3087 (2013).
[Crossref] [PubMed]

H. Di, K. Zheng, X. Zhang, E. Y. Lam, T. Kim, Y. S. Kim, T.-C. Poon, and C. Zhou, “Multiple-image encryption by compressive holography,” Appl. Opt. 51, 1000–1009 (2012).
[Crossref] [PubMed]

J. Ke, T.-C. Poon, and E. Y. Lam, “Depth resolution enhancement in optical scanning holography with a dual-wavelength laser source,” Appl. Opt. 50, H285–H296 (2011).
[Crossref] [PubMed]

J. Ke, T. C. Poon, and E. Y. Lam, “Depth resolution enhancement in optical scanning holography with a dual-wavelength laser source,” Appl. Opt. 50, 285–296 (2011).
[Crossref]

X. Zhang, E. Y. Lam, T. Kim, Y. S. Kim, and T.-C. Poon, “Blind sectional image reconstruction for optical scanning holography,” Opt. Lett. 34, 3098–3100 (2009).
[Crossref] [PubMed]

E. Y. Lam, X. Zhang, H. Vo, T.-C. Poon, and G. Indebetouw, “Three-dimensional microscopy and sectional image reconstruction using optical scanning holography,” Appl. Opt. 48, H113–H119 (2009).
[Crossref] [PubMed]

X. Zhang, E. Y. Lam, and T.-C. Poon, “Reconstruction of sectional images in holography using inverse imaging,” Opt. Express 16, 17215–17226 (2008).
[Crossref] [PubMed]

Z. Ren, N. Chen, A. Chan, and E. Y. Lam, “Autofocusing of optical scanning holography based on entropy minimization,” in “Digital Holography and Three-Dimensional Imaging,” (Optical Society of America, 2015), pp. DT4A–4.

Lee, S.-K.

Marengo, E. A.

A. J. Devaney, E. A. Marengo, and F. K. Gruber, “Time-reversal-based imaging and inverse scattering of multiply scattering point targets,” J. Acoust. Soc. Am. 118, 3129–3138 (2005).
[Crossref]

Martínez-Corral, M.

Oh, S.

Ou, H.

Park, J.-H.

Poon, T. C.

J. Ke, T. C. Poon, and E. Y. Lam, “Depth resolution enhancement in optical scanning holography with a dual-wavelength laser source,” Appl. Opt. 50, 285–296 (2011).
[Crossref]

Poon, T.-C.

H. Ou, T.-C. Poon, K. K. Y. Wong, and E. Y. Lam, “Enhanced depth resolution in optical scanning holography using a configurable pupil,” Photon. Res. 2, 64 (2014).
[Crossref]

H. Ou, T.-C. Poon, K. K. Wong, and E. Y. Lam, “Depth resolution enhancement in double-detection optical scanning holography,” Appl. Opt. 52, 3079–3087 (2013).
[Crossref] [PubMed]

H. Di, K. Zheng, X. Zhang, E. Y. Lam, T. Kim, Y. S. Kim, T.-C. Poon, and C. Zhou, “Multiple-image encryption by compressive holography,” Appl. Opt. 51, 1000–1009 (2012).
[Crossref] [PubMed]

J. Ke, T.-C. Poon, and E. Y. Lam, “Depth resolution enhancement in optical scanning holography with a dual-wavelength laser source,” Appl. Opt. 50, H285–H296 (2011).
[Crossref] [PubMed]

Z. Xin, K. Dobson, Y. Shinoda, and T.-C. Poon, “Sectional image reconstruction in optical scanning holography using a random-phase pupil,” Opt. Lett. 35, 2934–2936 (2010).
[Crossref] [PubMed]

T. Kim and T.-C. Poon, “Autofocusing in optical scanning holography,” Appl. Opt. 48, H153–H159 (2009).
[Crossref] [PubMed]

E. Y. Lam, X. Zhang, H. Vo, T.-C. Poon, and G. Indebetouw, “Three-dimensional microscopy and sectional image reconstruction using optical scanning holography,” Appl. Opt. 48, H113–H119 (2009).
[Crossref] [PubMed]

X. Zhang, E. Y. Lam, T. Kim, Y. S. Kim, and T.-C. Poon, “Blind sectional image reconstruction for optical scanning holography,” Opt. Lett. 34, 3098–3100 (2009).
[Crossref] [PubMed]

X. Zhang, E. Y. Lam, and T.-C. Poon, “Reconstruction of sectional images in holography using inverse imaging,” Opt. Express 16, 17215–17226 (2008).
[Crossref] [PubMed]

T.-C. Poon, T. Kim, and K. Doh, “Optical scanning cryptography for secure wireless transmission,” Appl. Opt. 42, 6496–6503 (2003).
[Crossref] [PubMed]

T. Kim, T.-C. Poon, and G. Indebetouw, “Depth detection and image recovery in remote sensing by optical scanning holography,” Opt. Eng. 41, 1331–1338 (2002).
[Crossref]

B. W. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, Y. Suzuki, and M. H. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett. 22, 1506–1508 (1997).
[Crossref]

T.-C. Poon, Optical Scanning Holography with MATLAB (Springer, 2007).
[Crossref]

Ren, Z.

Rosen, J.

J. Rosen, N. Siegel, and G. Brooker, “Theoretical and experimental demonstration of resolution beyond the rayleigh limit by finch fluorescence microscopic imaging,” Opt. Express 19, 26249 (2011).
[Crossref]

J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2, 190–195 (2008).
[Crossref]

Schilling, B. W.

Shinoda, K.

Shinoda, Y.

Siegel, N.

Stelzer, E. H. K.

Storrie, B.

Suzuki, Y.

Swoger, J.

Templeton, G. C.

Tsia, K. K.

Vo, H.

Wong, K. K.

Wong, K. K. Y.

Wu, B.

B. Wu, W. Cai, and S. K. Gayen, “Three-dimensional localization of fluorescent targets in turbid media using time reversal optical tomography,” Appl. Phys. Lett. 101, 251103 (2012).
[Crossref]

B. Wu, W. Cai, M. Alrubaiee, M. Xu, and S. K. Gayen, “Time reversal optical tomography: locating targets in a highly scattering turbid medium,” Opt. Express 19, 21956–21976 (2011).
[Crossref] [PubMed]

B. Wu, W. Cai, M. Alrubaiee, M. Xu, and S. K. Gayen, “Three dimensional time reversal optical tomography,” in “SPIE BiOS,” (2011), pp. 242–243.

Wu, M. H.

Xin, Z.

Xu, M.

B. Wu, W. Cai, M. Alrubaiee, M. Xu, and S. K. Gayen, “Time reversal optical tomography: locating targets in a highly scattering turbid medium,” Opt. Express 19, 21956–21976 (2011).
[Crossref] [PubMed]

B. Wu, W. Cai, M. Alrubaiee, M. Xu, and S. K. Gayen, “Three dimensional time reversal optical tomography,” in “SPIE BiOS,” (2011), pp. 242–243.

Zhang, X.

Zheng, K.

Zhong, W.

Zhou, C.

Appl. Opt. (10)

J. Ke, T. C. Poon, and E. Y. Lam, “Depth resolution enhancement in optical scanning holography with a dual-wavelength laser source,” Appl. Opt. 50, 285–296 (2011).
[Crossref]

T.-C. Poon, T. Kim, and K. Doh, “Optical scanning cryptography for secure wireless transmission,” Appl. Opt. 42, 6496–6503 (2003).
[Crossref] [PubMed]

T. Kim, “Optical sectioning by optical scanning holography and a Wiener filter,” Appl. Opt. 45, 872–879 (2006).
[Crossref] [PubMed]

B. W. Schilling and G. C. Templeton, “Three-dimensional remote sensing by optical scanning holography,” Appl. Opt. 40, 5474–5481 (2001).
[Crossref]

E. Y. Lam, X. Zhang, H. Vo, T.-C. Poon, and G. Indebetouw, “Three-dimensional microscopy and sectional image reconstruction using optical scanning holography,” Appl. Opt. 48, H113–H119 (2009).
[Crossref] [PubMed]

T. Kim and T.-C. Poon, “Autofocusing in optical scanning holography,” Appl. Opt. 48, H153–H159 (2009).
[Crossref] [PubMed]

J. Ke, T.-C. Poon, and E. Y. Lam, “Depth resolution enhancement in optical scanning holography with a dual-wavelength laser source,” Appl. Opt. 50, H285–H296 (2011).
[Crossref] [PubMed]

H. Di, K. Zheng, X. Zhang, E. Y. Lam, T. Kim, Y. S. Kim, T.-C. Poon, and C. Zhou, “Multiple-image encryption by compressive holography,” Appl. Opt. 51, 1000–1009 (2012).
[Crossref] [PubMed]

H. Ou, T.-C. Poon, K. K. Wong, and E. Y. Lam, “Depth resolution enhancement in double-detection optical scanning holography,” Appl. Opt. 52, 3079–3087 (2013).
[Crossref] [PubMed]

Z. Ren, N. Chen, and E. Y. Lam, “Extended focused imaging and depth map reconstruction in optical scanning holography,” Appl. Opt. 55, 1040–1047 (2016).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

B. Wu, W. Cai, and S. K. Gayen, “Three-dimensional localization of fluorescent targets in turbid media using time reversal optical tomography,” Appl. Phys. Lett. 101, 251103 (2012).
[Crossref]

Coll. Math. J. (1)

K. Dan, “A singularly valuable decomposition: The svd of a matrix,” Coll. Math. J. 27, 2–23 (1996).
[Crossref]

J. Acoust. Soc. Am. (1)

A. J. Devaney, E. A. Marengo, and F. K. Gruber, “Time-reversal-based imaging and inverse scattering of multiply scattering point targets,” J. Acoust. Soc. Am. 118, 3129–3138 (2005).
[Crossref]

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

Nat. Photonics (1)

J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2, 190–195 (2008).
[Crossref]

Opt. Eng. (1)

T. Kim, T.-C. Poon, and G. Indebetouw, “Depth detection and image recovery in remote sensing by optical scanning holography,” Opt. Eng. 41, 1331–1338 (2002).
[Crossref]

Opt. Express (5)

Opt. Lett. (4)

Optica (1)

Photon. Res. (1)

Reports on Prog. Phys. (1)

M. Fink, “Time reversed acoustics,” Reports on Prog. Phys. 50, 34–40 (1997).

Other (3)

T.-C. Poon, Optical Scanning Holography with MATLAB (Springer, 2007).
[Crossref]

B. Wu, W. Cai, M. Alrubaiee, M. Xu, and S. K. Gayen, “Three dimensional time reversal optical tomography,” in “SPIE BiOS,” (2011), pp. 242–243.

Z. Ren, N. Chen, A. Chan, and E. Y. Lam, “Autofocusing of optical scanning holography based on entropy minimization,” in “Digital Holography and Three-Dimensional Imaging,” (Optical Society of America, 2015), pp. DT4A–4.

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Figures (22)

Fig. 1
Fig. 1 OSH system setup [3]. BS, beam splitter; M, mirror; AOFS, acousto-optic frequency shifter; LPF, low-pass filter; BPF, band-pass filter; p1(x, y), p2(x, y) are pupils.
Fig. 2
Fig. 2 (a) Fresnel zone plate, (b) the generated hologram in the frequency domain.
Fig. 3
Fig. 3 (a) The leading 40 eigenvalues of the TR matrix, (b) 2D slice of the pseudo spectrum at z = 34 mm.
Fig. 4
Fig. 4 The accumulated pseudo-spectrum along the z-axis.
Fig. 5
Fig. 5 (a) The first 40 eigenvalues of time reversal matrix, (b) and (c) are the pseudo spectrum at z1 = 34 mm and z2 = 34.4 mm, respectively.
Fig. 6
Fig. 6 The accumulated pseudo spectrum along the z-axis.
Fig. 7
Fig. 7 (a) The leading 40 eigenvalues of the TR matrix, (b) 2D slice of the pseudo spectrum at z = 34 mm, and (c) the accumulated pseudo spectrum along the z-axis.
Fig. 8
Fig. 8 The accumulated pseudo-spectrum along the z-axis.
Fig. 9
Fig. 9 Accumulated pseudo-spectrum along the z-axis, with (a) z1 = 34 mm, z2 = 35 mm, (b) z1 = 34 mm, z2 = 34.4 mm, and (c) z1 = 34 mm, z2 = 34.04 mm.
Fig. 10
Fig. 10 Accumulated pseudo-spectrum along the z-axis, with (a) z1 = 100μm, z2 = 100.1μm, (b) z1 = 100μm, z2 = 100.01μm, and (c) z1 = 100μm, z2 = 100.001μm.
Fig. 11
Fig. 11 The relationship between resolution and the value of z1.
Fig. 12
Fig. 12 Accumulated pseudo-spectrum along the z-axis, with (a) λ = 405 nm, (b) λ = 632 nm, and (c) λ = 780 nm.
Fig. 13
Fig. 13 The relationship between the resolution and SNR.
Fig. 14
Fig. 14 The distribution of eigenvalues with different SNR.
Fig. 15
Fig. 15 The schematic diagram of the points response in x and y directions.
Fig. 16
Fig. 16 (a) section 1 with z1 = 31mm, (b) section 2 with z2 = 32mm, and (c) the generated hologram.
Fig. 17
Fig. 17 (a) The eigenvalues of the TR matrix, (b) the accumulated diagonal elements along the z-axis.
Fig. 18
Fig. 18 The axial localization distribution of TR-MUSIC and entropy minimization, (a) z1 = 31 mm, z2 = 41 mm, (b) z1 = 31 mm, z2 = 35 mm, (c) z1 = 31 mm, z2 = 32 mm.
Fig. 19
Fig. 19 (a) real part, and (b) imaginary part of the hologram.
Fig. 20
Fig. 20 (a) The eigenvalues of the TR matrix, (b) the accumulated diagonal elements along the z-axis.
Fig. 21
Fig. 21 Reconstructed sectional images at (a) z1, and (b) z2.
Fig. 22
Fig. 22 Reconstructed image by using the entropy minimization and inverse image.

Tables (4)

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Table 1 The coordinates of the nine points

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Table 2 Different values of z1 corresponding with different resolution.

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Table 3 Different values of wavelength corresponding with different resolution.

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Table 4 Computational cost with different matrix size.

Equations (21)

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( k x , k y ; z ) = exp [ j z 2 k 0 ( k x 2 + k y 2 ) ]
h ( x , y ; z ) = j k 0 2 π z exp [ j k 0 ( x 2 + y 2 ) 2 z ]
g ( x , y ) = + | Γ ( x , y ; z ) | 2 h ( x , y ; z ) d z ,
G ( k x , k y ) = + { 𝒪 ( x , y ; z ) } ( k x , k y ; z ) d z ,
G ( k x , k y ) = i = 1 N { 𝒪 ( x , y ; z i ) } × ( k x , k y ; z i )
g ( x s , y s ) = i = 1 N 𝒪 ( x s , y s ; z i ) h ( x s , y s , z i ) = i = 1 N + + 𝒪 ( x , y ; z i ) h ( x x s , y y s , z i ) d x d y = m = 1 M 𝒪 ( x m , y m , z m ) h ( x m x s , y m y s , z m ) ,
K = { g ( x s , y s ) } .
h ( x , y ; z ) = j k 0 2 π ( z ) exp [ j k 0 ( x 2 + y 2 ) 2 ( z ) ] = j k 0 2 π z exp [ j k 0 ( x 2 + y 2 ) 2 z ] ,
h ( x , y ; z ) = h * ( x , y ; z )
( k x , k y ; z ) = * ( k x , k y ; z )
T DSSD = 1 { K K H } = g ( x s , y s ) g ( x s , y s ) ,
g ( x s , y s ) = m = 1 M 𝒪 ( x m , y m , z m ) h ( x m x s , y m y s , z m ) + 0 m = M + 1 N 1 h ( x m x s , y m y s , z m ) = m = 1 M v x ( m ) 𝒪 ( x m , y m , z m ) v y T ( m )
T DSSD = [ m = 1 M v x ( m ) 𝒪 ( x m , y m ; z m ) v y T ( m ) ] [ n = 1 M v y * ( n ) 𝒪 ( x n , y n ; z n ) v x H ( n ) ] = m = 1 M v x ( m ) | 𝒪 ( x m , y m , z m ) | 2 v y ( m ) v x H ( m )
T SDDS = { K H K } = g ( x s , y s ) g ( x s . y s ) = [ m = 1 M v y * ( m ) 𝒪 ( x m , y m ; z m ) v x H ( m ) ] [ n = 1 M v x ( n ) 𝒪 ( x n , y n ; z n ) v y T ( n ) ] = m = 1 M v y * ( m ) | 𝒪 ( x m , y m , z m ) | 2 v x ( m ) v y T ( m ) .
T DSSD v x ( m ) = | 𝒪 ( x m , y m , z m ) | 2 v y ( m ) v x ( m ) v x ( m ) T SDDS v y * ( m ) = | 𝒪 ( x m , y m , z m ) | 2 v x ( m ) v y ( m ) v y * ( m ) .
λ m = | 𝒪 ( x m , y m , z m ) | 2 v y ( m ) v x ( m ) , m = 1 , , M
v x ( m = 1 , , M ) , v x ( m = M + 1 , , N 1 ) 0 v y * ( m = 1 , , M ) , v y * ( m = M + 1 , , N 1 ) 0
Q x ( X p , z i ) = m = M + 1 N 1 | ( v x ( m ) ) T v 1 * ( X p , z i ) | 2 Q y ( X p , z i ) = m = M + 1 N 1 | ( v y * ( m ) ) T v 2 ( X p , z i ) | 2
P x ( X p , z i ) = v 1 ( X p , z i ) 2 / Q x ( X p , z i ) P y ( X p , z i ) = v 2 ( X p , z i ) 2 / Q y ( X p , z i )
P ( X p , z i ) = P x ( X p , z i ) P y ( X p , z i ) ,
R ( z i ) = p = 1 N 1 2 P ( X p , z i ) ,

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