Abstract

We propose an optical scanning holography system with enhanced axial resolution using two detections at different depths. By scanning the object twice, we can obtain two different sets of Fresnel zone plates to sample the same object, which in turn provides more information for the sectional image reconstruction process. We develop the computation algorithm that makes use of such information, solving a constrained optimization problem using the conjugate gradient method. Simulation results show that this method can achieve a depth resolution up to 1 μm.

© 2013 Optical Society of America

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References

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  1. T.-C. Poon, Optical Scanning Holography with MATLAB (Springer, 2007).
  2. T.-C. Poon, “On the fundamentals of optical scanning holography,” Am. J. Phys. 76, 738–745 (2008).
    [CrossRef]
  3. T.-C. Poon, “Optical scanning holography: origin, modern capabilities, and beyond,” in OSA Topical Meeting in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2011), pp. DMA1.
  4. 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]
  5. G. Indebetouw and W. Zhong, “Scanning holographic microscopy of three-dimensional fluorescent specimens,” J. Opt. Soc. Am. A 23, 1699–1707 (2006).
    [CrossRef]
  6. 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]
  7. T.-C. Poon, “Recent progress in optical scanning holography,” J. Holography Speckle 1, 6–25 (2004).
    [CrossRef]
  8. T.-C. Poon, “Optical scanning holography—a review of recent progress,” J. Opt. Soc. Korea 13, 406–415 (2009).
    [CrossRef]
  9. 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]
  10. 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]
  11. 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]
  12. T. Kim, “Optical sectioning by optical scanning holography and a Wiener filter,” Appl. Opt. 45, 872–879 (2006).
    [CrossRef]
  13. 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]
  14. 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]
  15. X. Zhang and E. Y. Lam, “Edge detection of three-dimensional object by manipulating pupil functions in optical scanning holography system,” in Proceedings of IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, 2010), pp. 3661–3664.
  16. X. Zhang and E. Y. Lam, “Sectional image reconstruction in optical scanning holography using compressed sensing,” in Proceedings of IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, 2010), pp. 3349–3352.
  17. G. Indebetouw, “Properties of a canning holographic microscope: improved resolution, extended depth-of-focus, and/or optical sectioning,” J. Mod. Opt. 49, 1479–1500(2002).
    [CrossRef]
  18. 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]
  19. C. R. Vogel, Computational Methods for Inverse Problems (SIAM, 2002).
  20. A. N. Tikhonov and V. Arsenin, Solutions of Ill-Posed Problems (V.H. Winston & Sons, 1977).
  21. J. M. Blackledge, Digital Image Processing: Mathematical and Computational Methods (Horwood, 2005).
  22. F. Natterer and F. Wübbeling, Mathematical Methods in Image Reconstruction (SIAM, 2001).
  23. L. Vese, “A study in the BV space of a denoising–deblurring variational problem,” Appl. Math. Optim. 44, 131–161(2001).
    [CrossRef]
  24. G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing: Partial Differential Equations and Calculus of Variations (Springer-Verlag, 2006).
  25. 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]
  26. D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17, 13040–13049 (2009).
    [CrossRef]

2012 (1)

2011 (1)

2010 (1)

2009 (4)

2008 (3)

2006 (2)

2004 (1)

T.-C. Poon, “Recent progress in optical scanning holography,” J. Holography Speckle 1, 6–25 (2004).
[CrossRef]

2002 (3)

G. Indebetouw, “Properties of a canning holographic microscope: improved resolution, extended depth-of-focus, and/or optical sectioning,” J. Mod. Opt. 49, 1479–1500(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]

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)

L. Vese, “A study in the BV space of a denoising–deblurring variational problem,” Appl. Math. Optim. 44, 131–161(2001).
[CrossRef]

Arsenin, V.

A. N. Tikhonov and V. Arsenin, Solutions of Ill-Posed Problems (V.H. Winston & Sons, 1977).

Aubert, G.

G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing: Partial Differential Equations and Calculus of Variations (Springer-Verlag, 2006).

Blackledge, J. M.

J. M. Blackledge, Digital Image Processing: Mathematical and Computational Methods (Horwood, 2005).

Brady, D. J.

Choi, K.

Di, H.

Horisaki, R.

Huisken, J.

Indebetouw, G.

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]

G. Indebetouw and W. Zhong, “Scanning holographic microscopy of three-dimensional fluorescent specimens,” J. Opt. Soc. Am. A 23, 1699–1707 (2006).
[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]

G. Indebetouw, “Properties of a canning holographic microscope: improved resolution, extended depth-of-focus, and/or optical sectioning,” J. Mod. Opt. 49, 1479–1500(2002).
[CrossRef]

Ke, J.

Kim, H.

Kim, T.

Kim, Y. S.

Kornprobst, P.

G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing: Partial Differential Equations and Calculus of Variations (Springer-Verlag, 2006).

Lam, E. Y.

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, “Sectional image reconstruction in optical scanning holography using compressed sensing,” in Proceedings of IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, 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 Proceedings of IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, 2010), pp. 3661–3664.

Lee, B.

Lim, S.

Marks, D. L.

Martínez-Corral, M.

Min, S.-W.

Natterer, F.

F. Natterer and F. Wübbeling, Mathematical Methods in Image Reconstruction (SIAM, 2001).

Poon, T.-C.

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]

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

T.-C. Poon, “Optical scanning holography—a review of recent progress,” J. Opt. Soc. Korea 13, 406–415 (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, “Recent progress in optical scanning holography,” J. Holography Speckle 1, 6–25 (2004).
[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, “Optical scanning holography: origin, modern capabilities, and beyond,” in OSA Topical Meeting in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2011), pp. DMA1.

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

Stelzer, E. H. K.

Swoger, J.

Tikhonov, A. N.

A. N. Tikhonov and V. Arsenin, Solutions of Ill-Posed Problems (V.H. Winston & Sons, 1977).

Vese, L.

L. Vese, “A study in the BV space of a denoising–deblurring variational problem,” Appl. Math. Optim. 44, 131–161(2001).
[CrossRef]

Vo, H.

Vogel, C. R.

C. R. Vogel, Computational Methods for Inverse Problems (SIAM, 2002).

Wübbeling, F.

F. Natterer and F. Wübbeling, Mathematical Methods in Image Reconstruction (SIAM, 2001).

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. Math. Optim. (1)

L. Vese, “A study in the BV space of a denoising–deblurring variational problem,” Appl. Math. Optim. 44, 131–161(2001).
[CrossRef]

Appl. Opt. (5)

J. Holography Speckle (1)

T.-C. Poon, “Recent progress in optical scanning holography,” J. Holography Speckle 1, 6–25 (2004).
[CrossRef]

J. Mod. Opt. (1)

G. Indebetouw, “Properties of a canning holographic microscope: improved resolution, extended depth-of-focus, and/or optical sectioning,” J. Mod. Opt. 49, 1479–1500(2002).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Korea (1)

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. (1)

Other (9)

T.-C. Poon, “Optical scanning holography: origin, modern capabilities, and beyond,” in OSA Topical Meeting in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2011), pp. DMA1.

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

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

C. R. Vogel, Computational Methods for Inverse Problems (SIAM, 2002).

A. N. Tikhonov and V. Arsenin, Solutions of Ill-Posed Problems (V.H. Winston & Sons, 1977).

J. M. Blackledge, Digital Image Processing: Mathematical and Computational Methods (Horwood, 2005).

F. Natterer and F. Wübbeling, Mathematical Methods in Image Reconstruction (SIAM, 2001).

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

G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing: Partial Differential Equations and Calculus of Variations (Springer-Verlag, 2006).

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Figures (13)

Fig. 1.
Fig. 1.

Schematic of a DD-OSH system.

Fig. 2.
Fig. 2.

(a) Real part of the ideal FZP of an OSH system and (b) real part of the FZP with the OSH simulator when D=40mm and f=50mm.

Fig. 3.
Fig. 3.

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

Fig. 4.
Fig. 4.

Holograms containing two sectional images of the object under double-location detection.

Fig. 5.
Fig. 5.

Sectioning results using (a),(b) the conventional method with SD-OSH; (c),(d) conjugate-gradient-based method with SD-OSH; (e),(f) conjugate-gradient-based method with DD-OSH.

Fig. 6.
Fig. 6.

Relationship between Δz and resolution, and the relationship between Δz and correlation of H and H.

Fig. 7.
Fig. 7.

Third section together with the real part of the FZPs of each scan.

Fig. 8.
Fig. 8.

Holograms containing three sectional images of the object under double-location detection.

Fig. 9.
Fig. 9.

Sectioning results using (a)–(c) the conventional method with SD-OSH, (d)–(f) conjugate-gradient-based method with SD-OSH, and (g)–(i) conjugate-gradient-based method with DD-OSH.

Fig. 10.
Fig. 10.

Sectioning results using the DD-OSH method with (a),(b) δz=0mm, z1=34mm, z2=34.001mm; (c),(d) δz=0.625μm, z1=34mm, z2=34.001mm; (e),(f) δz=0.625μm, z1=34mm, z2=34.008mm.

Fig. 11.
Fig. 11.

Relationship between measurement error δz and the depth resolution.

Fig. 12.
Fig. 12.

Real part of the FZPs and sectioning results using simulator with (a)–(c) D=40mm and f=50mm and (d)–(f) D=25mm and f=50mm.

Fig. 13.
Fig. 13.

Real part of the FZPs and sectioning results using simulator with (a)–(c) D=40mm and f=50mm and (d)–(f) D=40mm and f=100mm.

Equations (15)

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

g(x,y;z)=exp{jk0z}jk02πzexp[jk02z(x2+y2)],
C(x,y;z)=P^1(k0xf,k0yf;z)exp{jωt}+P^2(k0xf,k0yf;z)exp{j(ω+Ω)t},
P^i(k0xf,k0yf;z)=F{pi(x,y)}*g(x,y;z),fori=1,2.
H(kx,ky;z)=exp[jz2k0(kx2+ky2)]×p1*(x,y)p2(x+fk0kx,y+fk0ky)exp[jzf(xkx+yky)]dxdy.
h(x,y;z)=j1λzexp{jπλz(x2+y2)},
g(x,y)=i=1n|ψ(x,y;zi)|2*h(x,y;zi),
g1(x,y)=|ψ(x,y;z1)|2*h(x,y;z1)+|ψ(x,y;z2)|2*h(x,y;z2).
g1=HOSH(z1)ψ1+HOSH(z2)ψ2+n1=Hψ+n1.
z1=z1+Δz
z2=z2+Δz.
g2(x,y)=|ψ(x,y;z1)|2*h(x,y;z1)+|ψ(x,y;z2)|2*h(x,y;z2).
g2=HOSH(z1)ψ1+HOSH(z2)ψ2+n2=Hψ+n2,
g=[g1g2]=[HH]ψ+[n1n2]=HDDψ+n,
ψest=argminψHDDψg22+ϑCψ22,
(HDD+HDD+ϑC+C)ψest=HDD+g,

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