Abstract

To overcome longitudinal sampling rate fluctuation in axial multi-image computational imaging, an effortless and high-efficient optical scanning imaging system via the rotation of single cylindrical lens (RSCL) is proposed for reconstructing the amplitude and phase information of sample. Here the cylinder is a non-axial-symmetry phase modulator for generating diffracted intensity patterns. To determine the explicit rotation angle as a core parameter in the perfect reconstruction of the light field, two-step Radon transform (TsRT) is designed to obtain accurate rotation status of the cylindrical lens with diffraction patterns at the focal plane. All rotation operations are at a lateral plane for keeping the same scale in this multiple parameter computational imaging system. As a kind of scanning imaging approach, the experiment of RSCL is greatly simplified.

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

Full Article  |  PDF Article
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References

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2018 (4)

C. Guo, C. Shen, J. Tan, X. Bao, S. Liu, and Z. Liu, “A robust multi-image phase retrieval,” Opt. Lasers Eng. 101, 16–22 (2018).
[Crossref]

J. Zhang, E. Moradi, M. G. Somekh, and M. L. Mather, “Label-free, high resolution, multi-modal light microscopy for discrimination of live stem cell differentiation status,” Sci. Rep. 8(1), 697 (2018).
[Crossref] [PubMed]

O. E. Olarte, J. Andilla, E. J. Gualda, and P. Loza-Alvarez, “Light-sheet microscopy: a tutorial,” Adv. Opt. Photonics 10(1), 111–179 (2018).
[Crossref]

C. Shen, C. Guo, J. Tan, S. Liu, and Z. Liu, “Complex amplitude reconstruction by iterative amplitude-phase retrieval algorithm with reference,” Opt. Lasers Eng. 105, 54–59 (2018).
[Crossref]

2017 (6)

2016 (5)

D. Di Battista, D. Ancora, H. S. Zhang, K. Lemonaki, E. Marakis, E. Liapis, S. Tzortzakis, and G. Zacharakis, “Tailored light sheets through opaque cylindrical lenses,” Optica 3(11), 1237–1240 (2016).
[Crossref]

C. Shen, J. Tan, C. Wei, and Z. Liu, “Coherent diffraction imaging by moving a lens,” Opt. Express 24(15), 16520–16529 (2016).
[Crossref] [PubMed]

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[Crossref] [PubMed]

M. N. Lakshmanan, R. E. Morris, J. A. Greenberg, E. Samei, and A. J. Kapadia, ““Coded aperture coherent scatter imaging for breast cancer detection: a Monte Carlo evaluation,” Medical Imaging 2016,” Phys. Med. Imag. 9783, 978321 (2016).

L. Sun and X. Pu, “A novel visualization technique for measuring liquid diffusion coefficient based on asymmetric liquid-core cylindrical lens,” Sci. Rep. 6(1), 28264 (2016).
[Crossref] [PubMed]

2015 (6)

J. Sun, Y. Zhang, C. Zuo, Q. Chen, S. Feng, Y. Hu, and J. Zhang, “Coded multi-angular illumination for Fourier ptychography based on Hadamard codes,” Proc. SPIE 9524, 95242C (2015).

Z. Liu, C. Guo, J. Tan, Q. Wu, L. Pan, and S. Liu, “Iterative phase-amplitude retrieval with multiple intensity images at output plane of gyrator transforms,” J. Opt. 17(2), 025701 (2015).
[Crossref]

H. Liu, L. Yang, Y. Guo, R. Guan, and J. Zhu, “Precise calibration of linear camera equipped with cylindrical lenses using a radial basis function-based mapping technique,” Opt. Express 23(3), 3412–3426 (2015).
[Crossref] [PubMed]

X. Shao, X. Dai, and X. He, “Noise robustness and parallel computation of the inverse compositional Gauss-Newton algorithm in digital image correlation,” Opt. Lasers Eng. 71, 9–19 (2015).
[Crossref]

J. Qian, M. Lei, D. Dan, B. Yao, X. Zhou, Y. Yang, S. Yan, J. Min, and X. Yu, “Full-color structured illumination optical sectioning microscopy,” Sci. Rep. 5(1), 14513 (2015).
[Crossref] [PubMed]

S. Dong, P. Nanda, K. Guo, J. Liao, and G. Zheng, “Incoherent Fourier ptychographic photography using structured light,” Photon. Res. 3(1), 19–23 (2015).
[Crossref]

2013 (4)

D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination super-resolution and optical sectioning microscopy,” Sci. Rep. 3(1), 1116 (2013).
[Crossref] [PubMed]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref] [PubMed]

X. Pan, C. Liu, Q. Lin, and J. Zhu, “Ptycholographic iterative engine with self-positioned scanning illumination,” Opt. Express 21(5), 6162–6168 (2013).
[Crossref] [PubMed]

C. J. R. Sheppard, “Cylindrical lenses--focusing and imaging: a review [Invited],” Appl. Opt. 52(4), 538–545 (2013).
[Crossref] [PubMed]

2012 (2)

A. Danielyan, V. Katkovnik, and K. Egiazarian, “BM3D frames and variational image deblurring,” IEEE Trans. Image Process. 21(4), 1715–1728 (2012).
[Crossref] [PubMed]

L. Li, C. Kuang, D. Luo, and X. Liu, “Axial nanodisplacement measurement based on astigmatism effect of crossed cylindrical lenses,” Appl. Opt. 51(13), 2379–2387 (2012).
[Crossref] [PubMed]

2010 (1)

2006 (2)

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

2005 (4)

2004 (2)

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[Crossref]

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

2000 (2)

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
[Crossref] [PubMed]

T. A. Klar, S. Jakobs, M. Dyba, A. Egner, and S. W. Hell, “Fluorescence microscopy with diffraction resolution barrier broken by stimulated emission,” Proc. Natl. Acad. Sci. U.S.A. 97(15), 8206–8210 (2000).
[Crossref] [PubMed]

1999 (2)

J. Courtial and M. J. Padgett, “Performance of a cylindrical lens mode converter for producing Laguerre-Gaussian laser modes,” Opt. Commun. 159(1–3), 13–18 (1999).
[Crossref]

R. Heintzmann and C. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE 3569, 185–196 (1999).
[Crossref]

1994 (2)

1986 (1)

J. Radon, “On the determination of functions from their integral values along certain manifolds,” IEEE Trans. Med. Imaging 5(4), 170–176 (1986).
[Crossref] [PubMed]

1984 (1)

Alieva, T.

Ancora, D.

Andilla, J.

O. E. Olarte, J. Andilla, E. J. Gualda, and P. Loza-Alvarez, “Light-sheet microscopy: a tutorial,” Adv. Opt. Photonics 10(1), 111–179 (2018).
[Crossref]

Attard, A. E.

Bao, X.

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Campbell, K.

Chen, K.

C. Guo, C. Wei, J. Tan, K. Chen, S. Liu, Q. Wu, and Z. Liu, “A review of iterative phase retrieval for measurement and encryption,” Opt. Lasers Eng. 89, 2–12 (2017).
[Crossref]

Chen, P.

Chen, Q.

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Efficient positional misalignment correction method for Fourier ptychographic microscopy,” Biomed. Opt. Express 7(4), 1336–1350 (2016).
[Crossref] [PubMed]

J. Sun, Y. Zhang, C. Zuo, Q. Chen, S. Feng, Y. Hu, and J. Zhang, “Coded multi-angular illumination for Fourier ptychography based on Hadamard codes,” Proc. SPIE 9524, 95242C (2015).

Courtial, J.

J. Courtial and M. J. Padgett, “Performance of a cylindrical lens mode converter for producing Laguerre-Gaussian laser modes,” Opt. Commun. 159(1–3), 13–18 (1999).
[Crossref]

Cremer, C.

R. Heintzmann and C. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE 3569, 185–196 (1999).
[Crossref]

Dai, X.

X. Shao, X. Dai, and X. He, “Noise robustness and parallel computation of the inverse compositional Gauss-Newton algorithm in digital image correlation,” Opt. Lasers Eng. 71, 9–19 (2015).
[Crossref]

Dan, D.

J. Qian, M. Lei, D. Dan, B. Yao, X. Zhou, Y. Yang, S. Yan, J. Min, and X. Yu, “Full-color structured illumination optical sectioning microscopy,” Sci. Rep. 5(1), 14513 (2015).
[Crossref] [PubMed]

D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination super-resolution and optical sectioning microscopy,” Sci. Rep. 3(1), 1116 (2013).
[Crossref] [PubMed]

Danielyan, A.

A. Danielyan, V. Katkovnik, and K. Egiazarian, “BM3D frames and variational image deblurring,” IEEE Trans. Image Process. 21(4), 1715–1728 (2012).
[Crossref] [PubMed]

Davidson, M. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Di Battista, D.

Dong, B. Z.

Dong, S.

Duadi, H.

Duan, F.

Dyba, M.

T. A. Klar, S. Jakobs, M. Dyba, A. Egner, and S. W. Hell, “Fluorescence microscopy with diffraction resolution barrier broken by stimulated emission,” Proc. Natl. Acad. Sci. U.S.A. 97(15), 8206–8210 (2000).
[Crossref] [PubMed]

Egiazarian, K.

Egner, A.

T. A. Klar, S. Jakobs, M. Dyba, A. Egner, and S. W. Hell, “Fluorescence microscopy with diffraction resolution barrier broken by stimulated emission,” Proc. Natl. Acad. Sci. U.S.A. 97(15), 8206–8210 (2000).
[Crossref] [PubMed]

Ersoy, O. K.

Fainman, Y.

Fang, X.

Faulkner, H. M. L.

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[Crossref]

Feng, S.

J. Sun, Y. Zhang, C. Zuo, Q. Chen, S. Feng, Y. Hu, and J. Zhang, “Coded multi-angular illumination for Fourier ptychography based on Hadamard codes,” Proc. SPIE 9524, 95242C (2015).

Fu, X.

Gao, P.

D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination super-resolution and optical sectioning microscopy,” Sci. Rep. 3(1), 1116 (2013).
[Crossref] [PubMed]

Greenberg, J. A.

M. N. Lakshmanan, R. E. Morris, J. A. Greenberg, E. Samei, and A. J. Kapadia, ““Coded aperture coherent scatter imaging for breast cancer detection: a Monte Carlo evaluation,” Medical Imaging 2016,” Phys. Med. Imag. 9783, 978321 (2016).

Groisman, A.

Gu, B. Y.

Gualda, E. J.

O. E. Olarte, J. Andilla, E. J. Gualda, and P. Loza-Alvarez, “Light-sheet microscopy: a tutorial,” Adv. Opt. Photonics 10(1), 111–179 (2018).
[Crossref]

Guan, R.

Guo, C.

C. Shen, C. Guo, J. Tan, S. Liu, and Z. Liu, “Complex amplitude reconstruction by iterative amplitude-phase retrieval algorithm with reference,” Opt. Lasers Eng. 105, 54–59 (2018).
[Crossref]

C. Guo, C. Shen, J. Tan, X. Bao, S. Liu, and Z. Liu, “A robust multi-image phase retrieval,” Opt. Lasers Eng. 101, 16–22 (2018).
[Crossref]

C. Guo, C. Wei, J. Tan, K. Chen, S. Liu, Q. Wu, and Z. Liu, “A review of iterative phase retrieval for measurement and encryption,” Opt. Lasers Eng. 89, 2–12 (2017).
[Crossref]

C. Guo, Q. Li, C. Wei, J. Tan, S. Liu, and Z. Liu, “Axial multi-image phase retrieval under tilt illumination,” Sci. Rep. 7(1), 7562 (2017).
[Crossref] [PubMed]

Z. Liu, C. Guo, J. Tan, Q. Wu, L. Pan, and S. Liu, “Iterative phase-amplitude retrieval with multiple intensity images at output plane of gyrator transforms,” J. Opt. 17(2), 025701 (2015).
[Crossref]

Guo, K.

Guo, Y.

Gustafsson, M. G. L.

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U.S.A. 102(37), 13081–13086 (2005).
[Crossref] [PubMed]

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
[Crossref] [PubMed]

Han, S.

He, X.

X. Shao, X. Dai, and X. He, “Noise robustness and parallel computation of the inverse compositional Gauss-Newton algorithm in digital image correlation,” Opt. Lasers Eng. 71, 9–19 (2015).
[Crossref]

Heintzmann, R.

R. Heintzmann and C. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE 3569, 185–196 (1999).
[Crossref]

Hell, S. W.

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G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
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Jakobs, S.

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Kim, D.

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J. Qian, M. Lei, D. Dan, B. Yao, X. Zhou, Y. Yang, S. Yan, J. Min, and X. Yu, “Full-color structured illumination optical sectioning microscopy,” Sci. Rep. 5(1), 14513 (2015).
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Levy, U.

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E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
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Liu, H.

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C. Shen, C. Guo, J. Tan, S. Liu, and Z. Liu, “Complex amplitude reconstruction by iterative amplitude-phase retrieval algorithm with reference,” Opt. Lasers Eng. 105, 54–59 (2018).
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C. Guo, C. Shen, J. Tan, X. Bao, S. Liu, and Z. Liu, “A robust multi-image phase retrieval,” Opt. Lasers Eng. 101, 16–22 (2018).
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C. Guo, Q. Li, C. Wei, J. Tan, S. Liu, and Z. Liu, “Axial multi-image phase retrieval under tilt illumination,” Sci. Rep. 7(1), 7562 (2017).
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C. Shen, X. Bao, J. Tan, S. Liu, and Z. Liu, “Two noise-robust axial scanning multi-image phase retrieval algorithms based on Pauta criterion and smoothness constraint,” Opt. Express 25(14), 16235–16249 (2017).
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Z. Liu, C. Guo, J. Tan, Q. Wu, L. Pan, and S. Liu, “Iterative phase-amplitude retrieval with multiple intensity images at output plane of gyrator transforms,” J. Opt. 17(2), 025701 (2015).
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Liu, Z.

C. Shen, C. Guo, J. Tan, S. Liu, and Z. Liu, “Complex amplitude reconstruction by iterative amplitude-phase retrieval algorithm with reference,” Opt. Lasers Eng. 105, 54–59 (2018).
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C. Guo, C. Shen, J. Tan, X. Bao, S. Liu, and Z. Liu, “A robust multi-image phase retrieval,” Opt. Lasers Eng. 101, 16–22 (2018).
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C. Guo, C. Wei, J. Tan, K. Chen, S. Liu, Q. Wu, and Z. Liu, “A review of iterative phase retrieval for measurement and encryption,” Opt. Lasers Eng. 89, 2–12 (2017).
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C. Guo, Q. Li, C. Wei, J. Tan, S. Liu, and Z. Liu, “Axial multi-image phase retrieval under tilt illumination,” Sci. Rep. 7(1), 7562 (2017).
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C. Shen, X. Bao, J. Tan, S. Liu, and Z. Liu, “Two noise-robust axial scanning multi-image phase retrieval algorithms based on Pauta criterion and smoothness constraint,” Opt. Express 25(14), 16235–16249 (2017).
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C. Shen, J. Tan, C. Wei, and Z. Liu, “Coherent diffraction imaging by moving a lens,” Opt. Express 24(15), 16520–16529 (2016).
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Z. Liu, C. Guo, J. Tan, Q. Wu, L. Pan, and S. Liu, “Iterative phase-amplitude retrieval with multiple intensity images at output plane of gyrator transforms,” J. Opt. 17(2), 025701 (2015).
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O. E. Olarte, J. Andilla, E. J. Gualda, and P. Loza-Alvarez, “Light-sheet microscopy: a tutorial,” Adv. Opt. Photonics 10(1), 111–179 (2018).
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Luo, D.

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J. Zhang, E. Moradi, M. G. Somekh, and M. L. Mather, “Label-free, high resolution, multi-modal light microscopy for discrimination of live stem cell differentiation status,” Sci. Rep. 8(1), 697 (2018).
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J. Qian, M. Lei, D. Dan, B. Yao, X. Zhou, Y. Yang, S. Yan, J. Min, and X. Yu, “Full-color structured illumination optical sectioning microscopy,” Sci. Rep. 5(1), 14513 (2015).
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J. Zhang, E. Moradi, M. G. Somekh, and M. L. Mather, “Label-free, high resolution, multi-modal light microscopy for discrimination of live stem cell differentiation status,” Sci. Rep. 8(1), 697 (2018).
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M. N. Lakshmanan, R. E. Morris, J. A. Greenberg, E. Samei, and A. J. Kapadia, ““Coded aperture coherent scatter imaging for breast cancer detection: a Monte Carlo evaluation,” Medical Imaging 2016,” Phys. Med. Imag. 9783, 978321 (2016).

Nanda, P.

Olarte, O. E.

O. E. Olarte, J. Andilla, E. J. Gualda, and P. Loza-Alvarez, “Light-sheet microscopy: a tutorial,” Adv. Opt. Photonics 10(1), 111–179 (2018).
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E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
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Z. Liu, C. Guo, J. Tan, Q. Wu, L. Pan, and S. Liu, “Iterative phase-amplitude retrieval with multiple intensity images at output plane of gyrator transforms,” J. Opt. 17(2), 025701 (2015).
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Pan, X.

Pang, L.

Park, H.

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E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
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D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination super-resolution and optical sectioning microscopy,” Sci. Rep. 3(1), 1116 (2013).
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Qian, J.

J. Qian, M. Lei, D. Dan, B. Yao, X. Zhou, Y. Yang, S. Yan, J. Min, and X. Yu, “Full-color structured illumination optical sectioning microscopy,” Sci. Rep. 5(1), 14513 (2015).
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J. Radon, “On the determination of functions from their integral values along certain manifolds,” IEEE Trans. Med. Imaging 5(4), 170–176 (1986).
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Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
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Samei, E.

M. N. Lakshmanan, R. E. Morris, J. A. Greenberg, E. Samei, and A. J. Kapadia, ““Coded aperture coherent scatter imaging for breast cancer detection: a Monte Carlo evaluation,” Medical Imaging 2016,” Phys. Med. Imag. 9783, 978321 (2016).

Shao, X.

X. Shao, X. Dai, and X. He, “Noise robustness and parallel computation of the inverse compositional Gauss-Newton algorithm in digital image correlation,” Opt. Lasers Eng. 71, 9–19 (2015).
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Shen, C.

C. Guo, C. Shen, J. Tan, X. Bao, S. Liu, and Z. Liu, “A robust multi-image phase retrieval,” Opt. Lasers Eng. 101, 16–22 (2018).
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C. Shen, C. Guo, J. Tan, S. Liu, and Z. Liu, “Complex amplitude reconstruction by iterative amplitude-phase retrieval algorithm with reference,” Opt. Lasers Eng. 105, 54–59 (2018).
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C. Shen, X. Bao, J. Tan, S. Liu, and Z. Liu, “Two noise-robust axial scanning multi-image phase retrieval algorithms based on Pauta criterion and smoothness constraint,” Opt. Express 25(14), 16235–16249 (2017).
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C. Shen, J. Tan, C. Wei, and Z. Liu, “Coherent diffraction imaging by moving a lens,” Opt. Express 24(15), 16520–16529 (2016).
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Shevkunov, I.

Somekh, M. G.

J. Zhang, E. Moradi, M. G. Somekh, and M. L. Mather, “Label-free, high resolution, multi-modal light microscopy for discrimination of live stem cell differentiation status,” Sci. Rep. 8(1), 697 (2018).
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E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
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J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Efficient positional misalignment correction method for Fourier ptychographic microscopy,” Biomed. Opt. Express 7(4), 1336–1350 (2016).
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J. Sun, Y. Zhang, C. Zuo, Q. Chen, S. Feng, Y. Hu, and J. Zhang, “Coded multi-angular illumination for Fourier ptychography based on Hadamard codes,” Proc. SPIE 9524, 95242C (2015).

Sun, L.

L. Sun and X. Pu, “A novel visualization technique for measuring liquid diffusion coefficient based on asymmetric liquid-core cylindrical lens,” Sci. Rep. 6(1), 28264 (2016).
[Crossref] [PubMed]

Tan, J.

C. Shen, C. Guo, J. Tan, S. Liu, and Z. Liu, “Complex amplitude reconstruction by iterative amplitude-phase retrieval algorithm with reference,” Opt. Lasers Eng. 105, 54–59 (2018).
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C. Guo, C. Shen, J. Tan, X. Bao, S. Liu, and Z. Liu, “A robust multi-image phase retrieval,” Opt. Lasers Eng. 101, 16–22 (2018).
[Crossref]

C. Guo, C. Wei, J. Tan, K. Chen, S. Liu, Q. Wu, and Z. Liu, “A review of iterative phase retrieval for measurement and encryption,” Opt. Lasers Eng. 89, 2–12 (2017).
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C. Guo, Q. Li, C. Wei, J. Tan, S. Liu, and Z. Liu, “Axial multi-image phase retrieval under tilt illumination,” Sci. Rep. 7(1), 7562 (2017).
[Crossref] [PubMed]

C. Shen, X. Bao, J. Tan, S. Liu, and Z. Liu, “Two noise-robust axial scanning multi-image phase retrieval algorithms based on Pauta criterion and smoothness constraint,” Opt. Express 25(14), 16235–16249 (2017).
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C. Shen, J. Tan, C. Wei, and Z. Liu, “Coherent diffraction imaging by moving a lens,” Opt. Express 24(15), 16520–16529 (2016).
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Z. Liu, C. Guo, J. Tan, Q. Wu, L. Pan, and S. Liu, “Iterative phase-amplitude retrieval with multiple intensity images at output plane of gyrator transforms,” J. Opt. 17(2), 025701 (2015).
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Wang, W.

D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination super-resolution and optical sectioning microscopy,” Sci. Rep. 3(1), 1116 (2013).
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Wei, C.

C. Guo, C. Wei, J. Tan, K. Chen, S. Liu, Q. Wu, and Z. Liu, “A review of iterative phase retrieval for measurement and encryption,” Opt. Lasers Eng. 89, 2–12 (2017).
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C. Guo, Q. Li, C. Wei, J. Tan, S. Liu, and Z. Liu, “Axial multi-image phase retrieval under tilt illumination,” Sci. Rep. 7(1), 7562 (2017).
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C. Shen, J. Tan, C. Wei, and Z. Liu, “Coherent diffraction imaging by moving a lens,” Opt. Express 24(15), 16520–16529 (2016).
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Wichmann, J.

Winterhalder, M.

D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination super-resolution and optical sectioning microscopy,” Sci. Rep. 3(1), 1116 (2013).
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Wu, Q.

C. Guo, C. Wei, J. Tan, K. Chen, S. Liu, Q. Wu, and Z. Liu, “A review of iterative phase retrieval for measurement and encryption,” Opt. Lasers Eng. 89, 2–12 (2017).
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Z. Liu, C. Guo, J. Tan, Q. Wu, L. Pan, and S. Liu, “Iterative phase-amplitude retrieval with multiple intensity images at output plane of gyrator transforms,” J. Opt. 17(2), 025701 (2015).
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D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination super-resolution and optical sectioning microscopy,” Sci. Rep. 3(1), 1116 (2013).
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Xiao, M.

Yan, S.

J. Qian, M. Lei, D. Dan, B. Yao, X. Zhou, Y. Yang, S. Yan, J. Min, and X. Yu, “Full-color structured illumination optical sectioning microscopy,” Sci. Rep. 5(1), 14513 (2015).
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D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination super-resolution and optical sectioning microscopy,” Sci. Rep. 3(1), 1116 (2013).
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Yang, C.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
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Yang, G. Z.

Yang, H.

Yang, L.

Yang, Y.

J. Qian, M. Lei, D. Dan, B. Yao, X. Zhou, Y. Yang, S. Yan, J. Min, and X. Yu, “Full-color structured illumination optical sectioning microscopy,” Sci. Rep. 5(1), 14513 (2015).
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D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination super-resolution and optical sectioning microscopy,” Sci. Rep. 3(1), 1116 (2013).
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Yao, B.

J. Qian, M. Lei, D. Dan, B. Yao, X. Zhou, Y. Yang, S. Yan, J. Min, and X. Yu, “Full-color structured illumination optical sectioning microscopy,” Sci. Rep. 5(1), 14513 (2015).
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D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination super-resolution and optical sectioning microscopy,” Sci. Rep. 3(1), 1116 (2013).
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Ye, T.

D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination super-resolution and optical sectioning microscopy,” Sci. Rep. 3(1), 1116 (2013).
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Yu, X.

J. Qian, M. Lei, D. Dan, B. Yao, X. Zhou, Y. Yang, S. Yan, J. Min, and X. Yu, “Full-color structured illumination optical sectioning microscopy,” Sci. Rep. 5(1), 14513 (2015).
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Zalevsky, Z.

Zhang, H. S.

Zhang, J.

J. Zhang, E. Moradi, M. G. Somekh, and M. L. Mather, “Label-free, high resolution, multi-modal light microscopy for discrimination of live stem cell differentiation status,” Sci. Rep. 8(1), 697 (2018).
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J. Sun, Y. Zhang, C. Zuo, Q. Chen, S. Feng, Y. Hu, and J. Zhang, “Coded multi-angular illumination for Fourier ptychography based on Hadamard codes,” Proc. SPIE 9524, 95242C (2015).

Zhang, Y.

Zhao, W.

D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination super-resolution and optical sectioning microscopy,” Sci. Rep. 3(1), 1116 (2013).
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Zhou, X.

J. Qian, M. Lei, D. Dan, B. Yao, X. Zhou, Y. Yang, S. Yan, J. Min, and X. Yu, “Full-color structured illumination optical sectioning microscopy,” Sci. Rep. 5(1), 14513 (2015).
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Zhu, J.

Zhuang, J. Y.

Zhuang, X.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
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Zumbusch, A.

D. Dan, M. Lei, B. Yao, W. Wang, M. Winterhalder, A. Zumbusch, Y. Qi, L. Xia, S. Yan, Y. Yang, P. Gao, T. Ye, and W. Zhao, “DMD-based LED-illumination super-resolution and optical sectioning microscopy,” Sci. Rep. 3(1), 1116 (2013).
[Crossref] [PubMed]

Zuo, C.

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Efficient positional misalignment correction method for Fourier ptychographic microscopy,” Biomed. Opt. Express 7(4), 1336–1350 (2016).
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J. Sun, Y. Zhang, C. Zuo, Q. Chen, S. Feng, Y. Hu, and J. Zhang, “Coded multi-angular illumination for Fourier ptychography based on Hadamard codes,” Proc. SPIE 9524, 95242C (2015).

Adv. Opt. Photonics (1)

O. E. Olarte, J. Andilla, E. J. Gualda, and P. Loza-Alvarez, “Light-sheet microscopy: a tutorial,” Adv. Opt. Photonics 10(1), 111–179 (2018).
[Crossref]

Appl. Opt. (5)

Appl. Phys. Lett. (1)

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[Crossref]

Biomed. Opt. Express (1)

IEEE Trans. Image Process. (1)

A. Danielyan, V. Katkovnik, and K. Egiazarian, “BM3D frames and variational image deblurring,” IEEE Trans. Image Process. 21(4), 1715–1728 (2012).
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IEEE Trans. Med. Imaging (1)

J. Radon, “On the determination of functions from their integral values along certain manifolds,” IEEE Trans. Med. Imaging 5(4), 170–176 (1986).
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J. Opt. (1)

Z. Liu, C. Guo, J. Tan, Q. Wu, L. Pan, and S. Liu, “Iterative phase-amplitude retrieval with multiple intensity images at output plane of gyrator transforms,” J. Opt. 17(2), 025701 (2015).
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Nat. Methods (1)

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

Nat. Photonics (1)

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref] [PubMed]

Opt. Commun. (1)

J. Courtial and M. J. Padgett, “Performance of a cylindrical lens mode converter for producing Laguerre-Gaussian laser modes,” Opt. Commun. 159(1–3), 13–18 (1999).
[Crossref]

Opt. Express (7)

Opt. Lasers Eng. (4)

C. Shen, C. Guo, J. Tan, S. Liu, and Z. Liu, “Complex amplitude reconstruction by iterative amplitude-phase retrieval algorithm with reference,” Opt. Lasers Eng. 105, 54–59 (2018).
[Crossref]

X. Shao, X. Dai, and X. He, “Noise robustness and parallel computation of the inverse compositional Gauss-Newton algorithm in digital image correlation,” Opt. Lasers Eng. 71, 9–19 (2015).
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C. Guo, C. Shen, J. Tan, X. Bao, S. Liu, and Z. Liu, “A robust multi-image phase retrieval,” Opt. Lasers Eng. 101, 16–22 (2018).
[Crossref]

C. Guo, C. Wei, J. Tan, K. Chen, S. Liu, Q. Wu, and Z. Liu, “A review of iterative phase retrieval for measurement and encryption,” Opt. Lasers Eng. 89, 2–12 (2017).
[Crossref]

Opt. Lett. (3)

Optica (2)

Photon. Res. (1)

Phys. Med. Imag. (1)

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Figures (10)

Fig. 1
Fig. 1 RSCL and its flowchart of data processing. (a) Layout of diffraction imaging system with RSCL. (b) Data processing flowchart of the computational imaging based on the rotation of single cylinder lens.
Fig. 2
Fig. 2 Schematic diagram of TsRT and the result of Radon transform. (a) Schematic diagram of rough scanning (green sector) and fine scanning (red sector). Background sample is one diffractive pattern recorded by sCMOS camera. (b) The scanning calculating result of rough scanning by Radon transform.
Fig. 3
Fig. 3 Simulation sample images and LMSE curves: (a) binary resolution chart and (b) a campus landscape picture, which are served as the amplitude and phase of the input complex amplitude, respectively. (c) LMSE curve.
Fig. 4
Fig. 4 Reconstructed binary resolution chart images with four sets of simulations including different numbers rotation degrees and iterations.
Fig. 5
Fig. 5 Reconstructed amplitude and phase with different rotation degree offsets.
Fig. 6
Fig. 6 Diffraction patterns and calculated degree error by TsRT method. (a) Amplitude distribution (background patterns) of nine random rotation degrees in RSCL and calculated absolute degree error (white font number) by TsRT method. (b) the distribution retrieved errors of rotation degree by TsRT.
Fig. 7
Fig. 7 LMSE curves of four sets of random rotation degree and corresponding reconstructed results.
Fig. 8
Fig. 8 Reconstructed experiment results. (a) Square-shape sample. (b) Recorded diffraction patterns by sCMOS camera. (c, d) Reconstructed amplitude and phase of square-shaped sample. (e, h) two cross-shaped arrow samples of different sizes. (f, g) and (i, j) Reconstructed amplitude and phase of two arrow samples, in which the white bars correspond to 650 μm.
Fig. 9
Fig. 9 Filtered amplitude patterns of bigger size cross-shaped arrow processed by four different filters: (a) 3D figure of red square frame in Fig. 7(i). (b) Gaussian filter, (d) Mean filter, (f) Median filter and (h) BM3D. (c, e, g, i) the corresponding local 3D figures of red square areas in (b, d, f, h). The white bars correspond to 650 μm.
Fig. 10
Fig. 10 LMSE curves of RSCL and multi-distance methods.

Tables (2)

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Table 1 Assigned values of rotation degree in RSCL

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Table 2 Variance of ten different magenta rectangle areas

Equations (6)

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U d ( x , y )=D{ U obj ( x,y ) } = F 1 { F[ U obj ( x,y ) ]exp[ j 2πd λ 1 ( λu ) 2 ( λv ) 2 ] },
I α ( x 1 , y 1 )= | D{ U d ( x , y ) R α ( x , y ) } | 2 ,
R α ( x , y )=exp[ j π λf ( x cosα+ y sinα ) 2 ],
NCC= C A,B C A,A C B,B
C A,B = 1 MN x=1 M y=1 N [A(x,y) A ¯ (x,y)][B(x,y) B ¯ (x,y)] .
LMSE=log 10 { 1 MN m=1 M n=1 N [A(m,n)B(m,n)] 2 }.