Abstract

In conventional microscopy, specimens lying within the depth of field are clearly recorded whereas other parts are blurry. Although digital holographic microscopy allows post-processing on holograms to reconstruct multifocus images, it suffers from defocus noise as a traditional microscope in numerical reconstruction. In this paper, we demonstrate a method that can achieve extended focused imaging (EFI) and reconstruct a depth map (DM) of three-dimensional (3D) objects. We first use a depth-from-focus algorithm to create a DM for each pixel based on entropy minimization. Then we show how to achieve EFI of the whole 3D scene computationally. Simulation and experimental results involving objects with multiple axial sections are presented to validate the proposed approach.

© 2016 Optical Society of America

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References

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2014 (3)

M. Matrecano, M. Paturzo, and P. Ferraro, “Extended focus imaging in digital holographic microscopy: a review,” Opt. Eng. 53, 112317 (2014).
[Crossref]

T. Pitkäaho, M. Niemelä, and V. Pitkäkangas, “Partially coherent digital in-line holographic microscopy in characterization of a microscopic target,” Appl. Opt. 53, 3233–3240 (2014).
[Crossref]

H. A. Ilhan, M. Doğar, and M. Özcan, “Digital holographic microscopy and focusing methods based on image sharpness,” J. Microsc. 255, 138–149 (2014).
[Crossref]

2011 (3)

C. Y. Zhou and S. K. Nayar, “Computational cameras: convergence of optics and processing,” IEEE Trans. Image Proc. 20, 3322–3340 (2011).
[Crossref]

T. Pitkäaho and T. J. Naughton, “Calculating depth maps from digital holograms using stereo disparity,” Opt. Lett. 36, 2035–2037 (2011).
[Crossref]

J. J. Zhu, L. Wang, R. G. Yang, J. Davis, and Z. G. Pan, “Reliability fusion of time-of-flight depth and stereo geometry for high quality depth maps,” IEEE Trans. Pattern Anal. Mach. Intell. 33, 1400–1414 (2011).
[Crossref]

2009 (4)

2008 (4)

2007 (1)

2006 (2)

2004 (2)

M. Liebling and M. Unser, “Autofocus for digital Fresnel holograms by use of a Fresnelet-sparsity criterion,” J. Opt. Soc. Am. A 21, 2424–2430 (2004).
[Crossref]

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Proc. 13, 600–612 (2004).
[Crossref]

2002 (1)

A. Torralba and A. Oliva, “Depth estimation from image structure,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 1226–1238 (2002).
[Crossref]

1999 (1)

L. Xi, L. Guosui, and J. Ni, “Autofocusing of ISAR images based on entropy minimization,” IEEE Trans. Aerosp. Electron. Syst. 35, 1240–1252 (1999).
[Crossref]

1997 (1)

1995 (1)

1993 (1)

1987 (1)

D. Vollath, “Automatic focusing by correlative methods,” J. Microsc. 147, 279–288 (1987).
[Crossref]

Antkowiak, M.

Bove, V. M.

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Proc. 13, 600–612 (2004).
[Crossref]

Callens, N.

Cathey, W. T.

Chamberlin-Long, D.

Chan, A.

Z. B. 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 (2015), paper DT4A.4.

Z. B. Ren, N. Chen, A. Chan, and E. Y. Lam, “Extended focused imaging in a holographic microscopy imaging system,” in IEEE International Conference on Imaging Systems and Techniques (2015), pp. 1–6.

Chen, N.

Z. B. 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 (2015), paper DT4A.4.

Z. B. Ren, N. Chen, A. Chan, and E. Y. Lam, “Extended focused imaging in a holographic microscopy imaging system,” in IEEE International Conference on Imaging Systems and Techniques (2015), pp. 1–6.

Chen, W.

W. Chen, C. G. Quan, and C. J. Tay, “Extended depth of focus in a particle field measurement using a single-shot digital hologram,” Appl. Phys. Lett. 95, 201103 (2009).
[Crossref]

Davis, C. S.

Davis, J.

J. J. Zhu, L. Wang, R. G. Yang, J. Davis, and Z. G. Pan, “Reliability fusion of time-of-flight depth and stereo geometry for high quality depth maps,” IEEE Trans. Pattern Anal. Mach. Intell. 33, 1400–1414 (2011).
[Crossref]

Dogar, M.

H. A. Ilhan, M. Doğar, and M. Özcan, “Digital holographic microscopy and focusing methods based on image sharpness,” J. Microsc. 255, 138–149 (2014).
[Crossref]

Dowski, E. R.

Dubois, F.

Ferraro, P.

M. Matrecano, M. Paturzo, and P. Ferraro, “Extended focus imaging in digital holographic microscopy: a review,” Opt. Eng. 53, 112317 (2014).
[Crossref]

Guosui, L.

L. Xi, L. Guosui, and J. Ni, “Autofocusing of ISAR images based on entropy minimization,” IEEE Trans. Aerosp. Electron. Syst. 35, 1240–1252 (1999).
[Crossref]

Hennelly, B. M.

Hu, Q.

Ilhan, H. A.

H. A. Ilhan, M. Doğar, and M. Özcan, “Digital holographic microscopy and focusing methods based on image sharpness,” J. Microsc. 255, 138–149 (2014).
[Crossref]

Indebetouw, G.

Kim, H.

Kim, T.

Kim, Y. S.

Lam, E. Y.

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]

Z. B. Ren, N. Chen, A. Chan, and E. Y. Lam, “Extended focused imaging in a holographic microscopy imaging system,” in IEEE International Conference on Imaging Systems and Techniques (2015), pp. 1–6.

Z. B. 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 (2015), paper DT4A.4.

Lee, B.

Li, W. C.

Liebling, M.

Loomis, N. C.

Matrecano, M.

M. Matrecano, M. Paturzo, and P. Ferraro, “Extended focus imaging in digital holographic microscopy: a review,” Opt. Eng. 53, 112317 (2014).
[Crossref]

McElhinney, C. P.

Min, S.-W.

Naughton, T. J.

Nayar, S. K.

C. Y. Zhou and S. K. Nayar, “Computational cameras: convergence of optics and processing,” IEEE Trans. Image Proc. 20, 3322–3340 (2011).
[Crossref]

Ni, J.

L. Xi, L. Guosui, and J. Ni, “Autofocusing of ISAR images based on entropy minimization,” IEEE Trans. Aerosp. Electron. Syst. 35, 1240–1252 (1999).
[Crossref]

Niemelä, M.

Oliva, A.

A. Torralba and A. Oliva, “Depth estimation from image structure,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 1226–1238 (2002).
[Crossref]

Özcan, M.

H. A. Ilhan, M. Doğar, and M. Özcan, “Digital holographic microscopy and focusing methods based on image sharpness,” J. Microsc. 255, 138–149 (2014).
[Crossref]

Pan, Z. G.

J. J. Zhu, L. Wang, R. G. Yang, J. Davis, and Z. G. Pan, “Reliability fusion of time-of-flight depth and stereo geometry for high quality depth maps,” IEEE Trans. Pattern Anal. Mach. Intell. 33, 1400–1414 (2011).
[Crossref]

Paturzo, M.

M. Matrecano, M. Paturzo, and P. Ferraro, “Extended focus imaging in digital holographic microscopy: a review,” Opt. Eng. 53, 112317 (2014).
[Crossref]

Pitkäaho, T.

Pitkäkangas, V.

Poon, T.-C.

Quan, C. G.

W. Chen, C. G. Quan, and C. J. Tay, “Extended depth of focus in a particle field measurement using a single-shot digital hologram,” Appl. Phys. Lett. 95, 201103 (2009).
[Crossref]

Ren, Z. B.

Z. B. Ren, N. Chen, A. Chan, and E. Y. Lam, “Extended focused imaging in a holographic microscopy imaging system,” in IEEE International Conference on Imaging Systems and Techniques (2015), pp. 1–6.

Z. B. 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 (2015), paper DT4A.4.

Schilling, B. W.

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Proc. 13, 600–612 (2004).
[Crossref]

Shinoda, K.

Simoncelli, E. P.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Proc. 13, 600–612 (2004).
[Crossref]

Storrie, B.

Suzuki, Y.

Tay, C. J.

W. Chen, C. G. Quan, and C. J. Tay, “Extended depth of focus in a particle field measurement using a single-shot digital hologram,” Appl. Phys. Lett. 95, 201103 (2009).
[Crossref]

Torralba, A.

A. Torralba and A. Oliva, “Depth estimation from image structure,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 1226–1238 (2002).
[Crossref]

Unser, M.

Vo, H.

Vollath, D.

D. Vollath, “Automatic focusing by correlative methods,” J. Microsc. 147, 279–288 (1987).
[Crossref]

Wang, L.

J. J. Zhu, L. Wang, R. G. Yang, J. Davis, and Z. G. Pan, “Reliability fusion of time-of-flight depth and stereo geometry for high quality depth maps,” IEEE Trans. Pattern Anal. Mach. Intell. 33, 1400–1414 (2011).
[Crossref]

Wang, Z.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Proc. 13, 600–612 (2004).
[Crossref]

Wu, M. H.

Xi, L.

L. Xi, L. Guosui, and J. Ni, “Autofocusing of ISAR images based on entropy minimization,” IEEE Trans. Aerosp. Electron. Syst. 35, 1240–1252 (1999).
[Crossref]

Yang, R. G.

J. J. Zhu, L. Wang, R. G. Yang, J. Davis, and Z. G. Pan, “Reliability fusion of time-of-flight depth and stereo geometry for high quality depth maps,” IEEE Trans. Pattern Anal. Mach. Intell. 33, 1400–1414 (2011).
[Crossref]

Yourassowsky, C.

Zhang, X.

Zhong, W. W.

Zhou, C. Y.

C. Y. Zhou and S. K. Nayar, “Computational cameras: convergence of optics and processing,” IEEE Trans. Image Proc. 20, 3322–3340 (2011).
[Crossref]

Zhu, J. J.

J. J. Zhu, L. Wang, R. G. Yang, J. Davis, and Z. G. Pan, “Reliability fusion of time-of-flight depth and stereo geometry for high quality depth maps,” IEEE Trans. Pattern Anal. Mach. Intell. 33, 1400–1414 (2011).
[Crossref]

Appl. Opt. (7)

Appl. Phys. Lett. (1)

W. Chen, C. G. Quan, and C. J. Tay, “Extended depth of focus in a particle field measurement using a single-shot digital hologram,” Appl. Phys. Lett. 95, 201103 (2009).
[Crossref]

IEEE Trans. Aerosp. Electron. Syst. (1)

L. Xi, L. Guosui, and J. Ni, “Autofocusing of ISAR images based on entropy minimization,” IEEE Trans. Aerosp. Electron. Syst. 35, 1240–1252 (1999).
[Crossref]

IEEE Trans. Image Proc. (2)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Proc. 13, 600–612 (2004).
[Crossref]

C. Y. Zhou and S. K. Nayar, “Computational cameras: convergence of optics and processing,” IEEE Trans. Image Proc. 20, 3322–3340 (2011).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (2)

A. Torralba and A. Oliva, “Depth estimation from image structure,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 1226–1238 (2002).
[Crossref]

J. J. Zhu, L. Wang, R. G. Yang, J. Davis, and Z. G. Pan, “Reliability fusion of time-of-flight depth and stereo geometry for high quality depth maps,” IEEE Trans. Pattern Anal. Mach. Intell. 33, 1400–1414 (2011).
[Crossref]

J. Microsc. (2)

D. Vollath, “Automatic focusing by correlative methods,” J. Microsc. 147, 279–288 (1987).
[Crossref]

H. A. Ilhan, M. Doğar, and M. Özcan, “Digital holographic microscopy and focusing methods based on image sharpness,” J. Microsc. 255, 138–149 (2014).
[Crossref]

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

Opt. Eng. (1)

M. Matrecano, M. Paturzo, and P. Ferraro, “Extended focus imaging in digital holographic microscopy: a review,” Opt. Eng. 53, 112317 (2014).
[Crossref]

Opt. Express (1)

Opt. Lett. (4)

Other (2)

Z. B. 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 (2015), paper DT4A.4.

Z. B. Ren, N. Chen, A. Chan, and E. Y. Lam, “Extended focused imaging in a holographic microscopy imaging system,” in IEEE International Conference on Imaging Systems and Techniques (2015), pp. 1–6.

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Figures (14)

Fig. 1.
Fig. 1. (a) Schematic diagram of OSH imaging system. ω and ω0 are the initial carrier frequency of the laser source and the shifted frequency, respectively; p1(x,y) and p2(x,y) are pupils; L1, L2, and L3 are lenses; BS is the beam splitter; XY scanner is a 2D scanning mirror; Object is the recorded specimen; PD is a photodetector; and z is the distance between the object and the scanner. (b) An object with two sections of a “circle” and a “rectangle” at z1 and z2, respectively. (c) An object with three sections of a “circle,” a “triangle,” and a “rectangle” at z1, z2, and z3, respectively.
Fig. 2.
Fig. 2. Focus detection based on entropy minimization for the two-sectional object.
Fig. 3.
Fig. 3. Computational procedure of our proposed EFI approach.
Fig. 4.
Fig. 4. (a) Top: the projection of the two-sectional object and local magnification; bottom: the EFI image and local magnification. (b) Top: the projection of the three-sectional object and local magnification; bottom: the EFI image and local magnification.
Fig. 5.
Fig. 5. (a, b) Ground-truth images of the two-sectional and three-sectional objects. (c, d) Reconstructed 2D DMs. (e, f) Reconstructed 3D scenes.
Fig. 6.
Fig. 6. (a) Real and (b) imaginary parts of the complex holograms of two transparent letters. They are the same as in Fig. 2 from [14], but are shown here also for ease of subsequent discussions.
Fig. 7.
Fig. 7. (a) Conventional reconstruction at a middle section, and (b) an EFI image. (c) Reconstructed 2D DM images and (d) a 3D scene of “S” and “H.”
Fig. 8.
Fig. 8. (a) Real and (b) imaginary parts of the complex holograms of fluorescent beads.
Fig. 9.
Fig. 9. (a) Conventional reconstruction at 100 μm. (b) Reconstructed EFI image. (c) Intensity profiles along the red lines in (a) and (b).
Fig. 10.
Fig. 10. (a) DM image of fluorescent beads. (b) Reconstructed 3D scene in space.
Fig. 11.
Fig. 11. Reconstructed sectional images of (a) a “circle,” (b) a “rectangle,” and (c) a “triangle” from simulation data, and (d) “S” and (e) “H” from experimental data.
Fig. 12.
Fig. 12. Depth estimation error when the block sizes are (a) L=25, (b) L=33, (c) L=41, and (d) L=49, for the three-sectional object.
Fig. 13.
Fig. 13. (a, b) PSNR and SSIM curves of the EFI images versus block size. (c, d) PSNR and SSIM curves of the DM images versus block size.
Fig. 14.
Fig. 14. Comparison of the reconstructed EFI and DM images, as well as the EFI and DM error images, produced by each metric. From left to right, the metrics are entropy, Tenenbaum gradient, image power, variance, and wavelet. (a)–(e) EFI images. (f)–(j) EFI error images. (k)–(o) DM images. (p)–(t) DM error images.

Tables (1)

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Table 1. PSNR and SSIM Values of the EFI against the Projection Image, and the DM against the Ground-Truth Image Produced by different Focus Metrics

Equations (5)

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r(x,y;z1)=g(x,y)*h*(x,y;z1)=|O(x,y;z1)|2+|O(x,y;z2)|2*h(x,y;z2z1),
E=x=1My=1N|R(x,y)|2Plog2|R(x,y)|2P,
E(u,v,zi)=x=uL^u+L^y=vL^v+L^|R(x,y,zi)|2Plog2|R(x,y,zi)|2P,
Ψ(x,y)=zi=argminzE(x,y,z).
Ω(x,y)=R(x,y,Ψ(x,y)).

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