Abstract

The optical scanning holography (OSH) technique can capture all the three-dimensional volume information of an object in a hologram via a single raster scan. The digital hologram can then be processed to reconstruct individual sectional images of the object. In this paper, we present a scheme to reconstruct sectional images in OSH with enhanced depth resolution, where a spatial light modulator (SLM) is adopted as a configurable point pupil. By switching the SLM between two states, different Fresnel zone plates (FZPs) are generated based on the same optical system. With extra information provided by different FZPs, a depth resolution at 0.7 μm can be achieved.

© 2014 Chinese Laser Press

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References

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  1. J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
    [CrossRef]
  2. J. W. Goodman, “Digital image formation from holograms: early motivations and modern capabilities,” in OSA Topical Meeting in Digital Holography and Three-Dimensional Imaging (2007), paper JMA1.
  3. T.-C. Poon, Optical Scanning Holography with MATLAB (Springer, 2007).
  4. T.-C. Poon and A. Korpel, “Optical transfer function of an acousto-optic heterodyning image processor,” Opt. Lett. 4, 317–319 (1979).
    [CrossRef]
  5. T.-C. Poon, “Scanning holography and two-dimensional image processing by acousto-optic two-pupil synthesis,” J. Opt. Soc. Am. A 2, 521–527 (1985).
    [CrossRef]
  6. T.-C. Poon, B. D. Duncan, M. H. Wu, K. Shinoda, and Y. Suzuki, “Real-time optical holography using a spatial light modulator,” Jpn. J. Appl. Phys. 29, L1840–L1842 (1990).
    [CrossRef]
  7. 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]
  8. G. Indebetouw and W. Zhong, “Scanning holographic microscopy of three-dimensional fluorescent specimens,” J. Opt. Soc. Am. A 23, 1699–1707 (2006).
    [CrossRef]
  9. B. W. Schilling and G. C. Templeton, “Three-dimensional remote sensing by optical scanning holography,” Appl. Opt. 40, 5474–5481 (2001).
    [CrossRef]
  10. 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]
  11. T.-C. Poon, T. Kim, and K. Doh, “Optical scanning cryptography for secure wireless transmission,” Appl. Opt. 42, 6496–6503 (2003).
    [CrossRef]
  12. W. Denk, J. Strickler, and W. Webb, “Two-photon laser scanning fluorescence microscopy,” Nature 248, 73–76 (1990).
  13. J. S. Ploem, “Laser scanning fluorescence microscopy,” Appl. Opt. 26, 3226–3231 (1987).
    [CrossRef]
  14. S. Nie, D. Chiu, and R. Zare, “Probing individual molecules with confocal fluorescence microscopy,” Science 266, 1018–1021 (1994).
    [CrossRef]
  15. J. Korlach, P. Schwille, W. Webb, and G. Feigenson, “Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 96, 8461–8466 (1999).
    [CrossRef]
  16. T. Kim, “Optical sectioning by optical scanning holography and a Wiener filter,” Appl. Opt. 45, 872–879 (2006).
    [CrossRef]
  17. H. Kim, S.-W. Min, B. Lee, and T.-C. Poon, “Optical sectioning for optical scanning holography using phase-space filtering with Wigner distribution functions,” Appl. Opt. 47, D164–D175 (2008).
    [CrossRef]
  18. 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]
  19. 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]
  20. 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]
  21. X. Zhang and E. Y. Lam, “Sectional image reconstruction in optical scanning holography using compressed sensing,” in IEEE International Conference on Image Processing (2010), pp. 3349–3352.
  22. X. Zhang and E. Y. Lam, “Edge detection of three-dimensional object by manipulating pupil functions in optical scanning holography system,” in IEEE International Conference on Image Processing (2010), pp. 3661–3664.
  23. X. Zhang and E. Y. Lam, “Edge-preserving sectional image reconstruction in optical scanning holography,” J. Opt. Soc. Am. A 27, 1630–1637 (2010).
    [CrossRef]
  24. 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]
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  26. 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]
  27. 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]
  28. T.-C. Poon, “On the fundamentals of optical scanning holography,” Am. J. Phys. 76, 738–745 (2008).
    [CrossRef]
  29. 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]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2013 (1)

2012 (1)

2011 (1)

2010 (2)

2009 (3)

2008 (4)

H. Kim, S.-W. Min, B. Lee, and T.-C. Poon, “Optical sectioning for optical scanning holography using phase-space filtering with Wigner distribution functions,” Appl. Opt. 47, D164–D175 (2008).
[CrossRef]

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]

T.-C. Poon, “On the fundamentals of optical scanning holography,” Am. J. Phys. 76, 738–745 (2008).
[CrossRef]

S. Wei and S. Lai, “Fast template matching based on normalized cross correlation with adaptive multilevel winner update,” IEEE Trans. Image Process. 17, 2227–2235 (2008).
[CrossRef]

2006 (3)

2003 (1)

2002 (2)

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]

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]

2001 (1)

1999 (1)

J. Korlach, P. Schwille, W. Webb, and G. Feigenson, “Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 96, 8461–8466 (1999).
[CrossRef]

1994 (1)

S. Nie, D. Chiu, and R. Zare, “Probing individual molecules with confocal fluorescence microscopy,” Science 266, 1018–1021 (1994).
[CrossRef]

1990 (2)

T.-C. Poon, B. D. Duncan, M. H. Wu, K. Shinoda, and Y. Suzuki, “Real-time optical holography using a spatial light modulator,” Jpn. J. Appl. Phys. 29, L1840–L1842 (1990).
[CrossRef]

W. Denk, J. Strickler, and W. Webb, “Two-photon laser scanning fluorescence microscopy,” Nature 248, 73–76 (1990).

1987 (1)

1985 (1)

1979 (1)

1967 (1)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

Bai, Z.-Z.

Z.-Z. Bai and Z.-Q. Wang, “Restrictive preconditioners for conjugate gradient methods for symmetric positive definite linear systems,” J. Comput. Appl. Math. 187, 202–226 (2006).
[CrossRef]

Brady, D. J.

Chiu, D.

S. Nie, D. Chiu, and R. Zare, “Probing individual molecules with confocal fluorescence microscopy,” Science 266, 1018–1021 (1994).
[CrossRef]

Choi, K.

Denk, W.

W. Denk, J. Strickler, and W. Webb, “Two-photon laser scanning fluorescence microscopy,” Nature 248, 73–76 (1990).

Di, H.

Dobson, K.

Doh, K.

Duncan, B. D.

T.-C. Poon, B. D. Duncan, M. H. Wu, K. Shinoda, and Y. Suzuki, “Real-time optical holography using a spatial light modulator,” Jpn. J. Appl. Phys. 29, L1840–L1842 (1990).
[CrossRef]

Feigenson, G.

J. Korlach, P. Schwille, W. Webb, and G. Feigenson, “Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 96, 8461–8466 (1999).
[CrossRef]

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

J. W. Goodman, “Digital image formation from holograms: early motivations and modern capabilities,” in OSA Topical Meeting in Digital Holography and Three-Dimensional Imaging (2007), paper JMA1.

Horisaki, R.

Huisken, J.

Indebetouw, G.

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, H285–H296 (2011).
[CrossRef]

J. Ke and E. Y. Lam, “Using a dual-wavelength source for depth resolution enhancement in optical scanning holography,” in OSA Topical Meeting in Digital Holography and Three-Dimensional Imaging (2011), paper DTuC30.

Kim, H.

Kim, T.

Kim, Y. S.

Korlach, J.

J. Korlach, P. Schwille, W. Webb, and G. Feigenson, “Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 96, 8461–8466 (1999).
[CrossRef]

Korpel, A.

Lai, S.

S. Wei and S. Lai, “Fast template matching based on normalized cross correlation with adaptive multilevel winner update,” IEEE Trans. Image Process. 17, 2227–2235 (2008).
[CrossRef]

Lam, E. Y.

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]

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]

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]

X. Zhang and E. Y. Lam, “Edge-preserving sectional image reconstruction in optical scanning holography,” J. Opt. Soc. Am. A 27, 1630–1637 (2010).
[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]

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]

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]

X. Zhang and E. Y. Lam, “Edge detection of three-dimensional object by manipulating pupil functions in optical scanning holography system,” in IEEE International Conference on Image Processing (2010), pp. 3661–3664.

X. Zhang and E. Y. Lam, “Sectional image reconstruction in optical scanning holography using compressed sensing,” in IEEE International Conference on Image Processing (2010), pp. 3349–3352.

J. Ke and E. Y. Lam, “Using a dual-wavelength source for depth resolution enhancement in optical scanning holography,” in OSA Topical Meeting in Digital Holography and Three-Dimensional Imaging (2011), paper DTuC30.

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

Lee, B.

Lim, S.

Marks, D. L.

Martínez-Corral, M.

Min, S.-W.

Nie, S.

S. Nie, D. Chiu, and R. Zare, “Probing individual molecules with confocal fluorescence microscopy,” Science 266, 1018–1021 (1994).
[CrossRef]

Ou, H.

Ploem, J. S.

Poon, T.-C.

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]

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]

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]

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]

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]

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]

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]

T.-C. Poon, “On the fundamentals of optical scanning holography,” Am. J. Phys. 76, 738–745 (2008).
[CrossRef]

H. Kim, S.-W. Min, B. Lee, and T.-C. Poon, “Optical sectioning for optical scanning holography using phase-space filtering with Wigner distribution functions,” Appl. Opt. 47, D164–D175 (2008).
[CrossRef]

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

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]

T.-C. Poon, B. D. Duncan, M. H. Wu, K. Shinoda, and Y. Suzuki, “Real-time optical holography using a spatial light modulator,” Jpn. J. Appl. Phys. 29, L1840–L1842 (1990).
[CrossRef]

T.-C. Poon, “Scanning holography and two-dimensional image processing by acousto-optic two-pupil synthesis,” J. Opt. Soc. Am. A 2, 521–527 (1985).
[CrossRef]

T.-C. Poon and A. Korpel, “Optical transfer function of an acousto-optic heterodyning image processor,” Opt. Lett. 4, 317–319 (1979).
[CrossRef]

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

Schilling, B. W.

Schwille, P.

J. Korlach, P. Schwille, W. Webb, and G. Feigenson, “Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 96, 8461–8466 (1999).
[CrossRef]

Shinoda, K.

T.-C. Poon, B. D. Duncan, M. H. Wu, K. Shinoda, and Y. Suzuki, “Real-time optical holography using a spatial light modulator,” Jpn. J. Appl. Phys. 29, L1840–L1842 (1990).
[CrossRef]

Shinoda, Y.

Stelzer, E. H. K.

Strickler, J.

W. Denk, J. Strickler, and W. Webb, “Two-photon laser scanning fluorescence microscopy,” Nature 248, 73–76 (1990).

Suzuki, Y.

T.-C. Poon, B. D. Duncan, M. H. Wu, K. Shinoda, and Y. Suzuki, “Real-time optical holography using a spatial light modulator,” Jpn. J. Appl. Phys. 29, L1840–L1842 (1990).
[CrossRef]

Swoger, J.

Templeton, G. C.

Vo, H.

Wang, Z.-Q.

Z.-Z. Bai and Z.-Q. Wang, “Restrictive preconditioners for conjugate gradient methods for symmetric positive definite linear systems,” J. Comput. Appl. Math. 187, 202–226 (2006).
[CrossRef]

Webb, W.

J. Korlach, P. Schwille, W. Webb, and G. Feigenson, “Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 96, 8461–8466 (1999).
[CrossRef]

W. Denk, J. Strickler, and W. Webb, “Two-photon laser scanning fluorescence microscopy,” Nature 248, 73–76 (1990).

Wei, S.

S. Wei and S. Lai, “Fast template matching based on normalized cross correlation with adaptive multilevel winner update,” IEEE Trans. Image Process. 17, 2227–2235 (2008).
[CrossRef]

Wong, K. K.

Wu, M. H.

T.-C. Poon, B. D. Duncan, M. H. Wu, K. Shinoda, and Y. Suzuki, “Real-time optical holography using a spatial light modulator,” Jpn. J. Appl. Phys. 29, L1840–L1842 (1990).
[CrossRef]

Xin, Z.

Zare, R.

S. Nie, D. Chiu, and R. Zare, “Probing individual molecules with confocal fluorescence microscopy,” Science 266, 1018–1021 (1994).
[CrossRef]

Zhang, X.

Zheng, K.

Zhong, W.

Zhou, C.

Am. J. Phys. (1)

T.-C. Poon, “On the fundamentals of optical scanning holography,” Am. J. Phys. 76, 738–745 (2008).
[CrossRef]

Appl. Opt. (9)

J. S. Ploem, “Laser scanning fluorescence microscopy,” Appl. Opt. 26, 3226–3231 (1987).
[CrossRef]

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

H. Kim, S.-W. Min, B. Lee, and T.-C. Poon, “Optical sectioning for optical scanning holography using phase-space filtering with Wigner distribution functions,” Appl. Opt. 47, D164–D175 (2008).
[CrossRef]

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

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

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]

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]

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]

Appl. Phys. Lett. (1)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

IEEE Trans. Image Process. (1)

S. Wei and S. Lai, “Fast template matching based on normalized cross correlation with adaptive multilevel winner update,” IEEE Trans. Image Process. 17, 2227–2235 (2008).
[CrossRef]

J. Comput. Appl. Math. (1)

Z.-Z. Bai and Z.-Q. Wang, “Restrictive preconditioners for conjugate gradient methods for symmetric positive definite linear systems,” J. Comput. Appl. Math. 187, 202–226 (2006).
[CrossRef]

J. Opt. Soc. Am. A (4)

Jpn. J. Appl. Phys. (1)

T.-C. Poon, B. D. Duncan, M. H. Wu, K. Shinoda, and Y. Suzuki, “Real-time optical holography using a spatial light modulator,” Jpn. J. Appl. Phys. 29, L1840–L1842 (1990).
[CrossRef]

Nature (1)

W. Denk, J. Strickler, and W. Webb, “Two-photon laser scanning fluorescence microscopy,” Nature 248, 73–76 (1990).

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 (2)

Opt. Lett. (3)

Proc. Natl. Acad. Sci. USA (1)

J. Korlach, P. Schwille, W. Webb, and G. Feigenson, “Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy,” Proc. Natl. Acad. Sci. USA 96, 8461–8466 (1999).
[CrossRef]

Science (1)

S. Nie, D. Chiu, and R. Zare, “Probing individual molecules with confocal fluorescence microscopy,” Science 266, 1018–1021 (1994).
[CrossRef]

Other (5)

X. Zhang and E. Y. Lam, “Sectional image reconstruction in optical scanning holography using compressed sensing,” in IEEE International Conference on Image Processing (2010), pp. 3349–3352.

X. Zhang and E. Y. Lam, “Edge detection of three-dimensional object by manipulating pupil functions in optical scanning holography system,” in IEEE International Conference on Image Processing (2010), pp. 3661–3664.

J. Ke and E. Y. Lam, “Using a dual-wavelength source for depth resolution enhancement in optical scanning holography,” in OSA Topical Meeting in Digital Holography and Three-Dimensional Imaging (2011), paper DTuC30.

J. W. Goodman, “Digital image formation from holograms: early motivations and modern capabilities,” in OSA Topical Meeting in Digital Holography and Three-Dimensional Imaging (2007), paper JMA1.

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

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Figures (12)

Fig. 1.
Fig. 1.

Schematic of OSH.

Fig. 2.
Fig. 2.

Two sections together with the real part of the FZPs for each scan.

Fig. 3.
Fig. 3.

Holograms containing two-sectional images of the object with different pupil functions (a), (b) for x0=y0=0 and (c), (d) for x0=0.48mm, y0=0.

Fig. 4.
Fig. 4.

Sectioning results using (a), (b) the conventional method; (c), (d) the conjugate-gradient-based method with a single measurement; (e), (f) the conjugate-gradient-based method with the proposed method.

Fig. 5.
Fig. 5.

Relationship between x0 and the resolution and the relationship between x0 and the correlation of H1 and H2.

Fig. 6.
Fig. 6.

Relationship between spatial shift and the correlation of H1 and H2.

Fig. 7.
Fig. 7.

Relationship between spatial shift and resolution.

Fig. 8.
Fig. 8.

Object with three sections.

Fig. 9.
Fig. 9.

Holograms containing three-section images of the object with different pupil functions (a), (b) for x0=y0=0 and (c), (d) for x0=0.48mm, y0=0.

Fig. 10.
Fig. 10.

Sectioning results using (a)–(c) the conventional method; (d)–(f) the conjugate-gradient-based method with a single measurement; (g)–(i) the conjugate-gradient-based method with the proposed method.

Fig. 11.
Fig. 11.

Sectioning results using the proposed method with (a)–(b) Δx=0nm, z1=34mm, z2=34.0007mm; (c)–(d) Δx=100nm, z1=34mm, z2=34.0007mm; (e)–(f) Δx=100nm, z1=34mm, z2=34.01mm.

Fig. 12.
Fig. 12.

Relationship between measurement error and the depth resolution.

Equations (10)

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

H(kx,ky;z)=exp[jz2k0(kx2+ky2)]×p1*(x,y)p2(x+fk0kx,y+fk0ky)×exp[jzf(xkx+yky)]dxdy,
h1(x,y;z)=j1λzexp{jπλz(x2+y2)},
g1(x,y)=i=1nφ(x,y;zi)*h1(x,y;zi),
H2(kx,ky;z)=exp[jz2k0(kx2+ky2)]×δ[(xx0)+fk0kx,(yy0)+fk0ky]×exp[jzf(xkx+yky)]dxdy,
h2(x,y;z)=j1λzexp{jπλz[(xx0)2+(yy0)2]},
g2(x,y)=i=1nφ(x,y;zi)*h2(x,y;zi).
g=[g1g2]=[H1(z1)H1(z2)H1(zn)H2(z1)H2(z2)H2(zn)][φ1φ2φn]+[ϵ1ϵ2ϵn]=[H1H2]φ+ϵ=Hφ+ϵ,
φest=argminφHφg22+λCφ22,
(H+H+λC+C)φest=H+g,
N=x=1Ny=1Mi=1Nj=1MH1(x+i,y+j)·H2(i,j)i=1Nj=1MH1(x+i,y+j)2·i=1Nj=1MH2(i,j)2.

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