Abstract

Lensless imaging based on multi-wavelength phase retrieval becomes a promising technology widely used as it has simple acquisition, miniaturized size and low-cost setup. However, measuring the sample-to-sensor distance with high accuracy, which is the key for high-resolution reconstruction, is still a challenge. In this work, we propose a multi-wavelength criterion to realize autofocusing modulation, i.e., achieving much higher accuracy in determining the sample-to-sensor distance, compared to the conventional methods. Three beams in different spectrums are adopted to illuminate the sample, and the resulting holograms are recorded by a CCD camera. The patterns calculated by performing back propagation of the recorded holograms, with exhaustively searched sample-to-sensor distance value, are adopted to access the criterion. Image sharpness can be accessed and the optimal sample-to-sensor distance can be finely determined by targeting the valley of the curve given by the criterion. Through our novel multi-wavelength based autofocusing strategy and executing further phase retrieval process, high-resolution images can be finally retrieved. The applicability and robustness of our method is validated both in simulations and experiments. Our technique provides a useful tool for multi-wavelength lensless imaging under limited experimental conditions.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (2)

Z. Zhong, X. Xie, L. Liu, C. Wang, and M. Shan, “Autofocusing in dual-wavelength digital holography using correlation coefficient,” Opt. Eng. 58(04), 1 (2019).
[Crossref]

T. Pitkäaho, A. Manninen, and T. J. Naughton, “Focus prediction in digital holographic microscopy using deep convolutional neural networks,” Appl. Opt. 58(5), A202–A208 (2019).
[Crossref] [PubMed]

2018 (7)

S. Jiang, J. Liao, Z. Bian, K. Guo, Y. Zhang, and G. Zheng, “Transform- and multi-domain deep learning for single-frame rapid autofocusing in whole slide imaging,” Biomed. Opt. Express 9(4), 1601–1612 (2018).
[Crossref] [PubMed]

Z. Ren, Z. Xu, and E. Y. Lam, “Learning-based nonparametric autofocusing for digital holography,” Optica 5(4), 337 (2018).
[Crossref]

C. Guo, Y. Zhao, J. Tan, S. Liu, and Z. Liu, “Adaptive lens-free computational coherent imaging using autofocusing quantification with speckle illumination,” Opt. Express 26(11), 14407–14420 (2018).
[Crossref] [PubMed]

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]

T. Seyler, M. Fratz, T. Beckmann, A. Schiller, A. Bertz, and D. Carl, “Extending the Depth of Field beyond Geometrical Imaging Limitations Using Phase Noise as a Focus Measure in Multiwavelength Digital Holography,” Appl. Sci. (Basel) 8(7), 1042 (2018).
[Crossref]

C. Guo, Q. Li, J. Tan, S. Liu, and Z. Liu, “A method of solving tilt illumination for multiple distance phase retrieval,” Opt. Lasers Eng. 106, 17–23 (2018).
[Crossref]

Y. Wu and A. Ozcan, “Lensless digital holographic microscopy and its applications in biomedicine and environmental monitoring,” Methods 136, 4–16 (2018).
[Crossref] [PubMed]

2017 (9)

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).
[Crossref] [PubMed]

A. He, W. Xiao, and F. Pan, “Automatic focus determination through cosine and modified cosine score in digital holography,” Opt. Eng. 56(3), 034103 (2017).
[Crossref]

P. Picart, S. Montresor, O. Sakharuk, and L. Muravsky, “Refocus criterion based on maximization of the coherence factor in digital three-wavelength holographic interferometry,” Opt. Lett. 42(2), 275–278 (2017).
[Crossref] [PubMed]

Y. Zhang, H. Wang, Y. Wu, M. Tamamitsu, and A. Ozcan, “Edge sparsity criterion for robust holographic autofocusing,” Opt. Lett. 42(19), 3824–3827 (2017).
[Crossref] [PubMed]

Z. Ren, N. Chen, and E. Y. Lam, “Automatic focusing for multisectional objects in digital holography using the structure tensor,” Opt. Lett. 42(9), 1720–1723 (2017).
[Crossref] [PubMed]

M. Lyu, C. Yuan, D. Li, and G. Situ, “Fast autofocusing in digital holography using the magnitude differential,” Appl. Opt. 56(13), F152–F157 (2017).
[Crossref] [PubMed]

S. K. Mohammed, L. Bouamama, D. Bahloul, and P. Picart, “Quality assessment of refocus criteria for particle imaging in digital off-axis holography,” Appl. Opt. 56(13), F158–F166 (2017).
[Crossref] [PubMed]

Y. Sun, C. Lou, Z. Jiang, and H. Zhou, “Experimental research of representative wavelengths of tricolor for color CCD camera,” Opt. Lett. 42(2), 275–278 (2017).
[PubMed]

2016 (2)

2015 (4)

2014 (1)

2013 (1)

2012 (5)

2011 (2)

2010 (2)

O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 10(11), 1417–1428 (2010).
[Crossref] [PubMed]

W. Bishara, T.-W. Su, A. F. Coskun, and A. Ozcan, “Lensfree on-chip microscopy over a wide field-of-view using pixel super-resolution,” Opt. Express 18(11), 11181–11191 (2010).
[Crossref] [PubMed]

2008 (3)

2007 (2)

2006 (1)

2005 (3)

2004 (3)

M. Liebling and M. Unser, “Autofocus for digital Fresnel holograms by use of a Fresnelet-sparsity criterion,” J. Opt. Soc. Am. A 21(12), 2424–2430 (2004).
[Crossref] [PubMed]

L. Xiaoxu, Z. Yimo, Z. Liyun, L. Yinlong, and S. Canlin, “Analysis and experiment of phase-shifting coaxial lensless Fourier digital holography,” Acta Opt. Sin. 24(11), 1511–1515 (2004).

L. Ma, H. Wang, Y. Li, and H. Jin, “Numerical reconstruction of digital holograms for three-dimensional shape measurement,” J. Opt. A, Pure Appl. Opt. 6(4), 396–400 (2004).
[Crossref]

2003 (1)

2001 (1)

1991 (1)

J. J. Barton, “Removing multiple scattering and twin images from holographic images,” Phys. Rev. Lett. 67(22), 3106–3109 (1991).
[Crossref] [PubMed]

1989 (1)

J. Gillespie and R. A. King, “The use of self-entropy as a focus measure in digital holography,” Pattern Recognit. Lett. 9(1), 19–25 (1989).
[Crossref]

1985 (1)

F. C. A. Groen, I. T. Young, and G. Ligthart, “A comparison of different focus functions for use in autofocus algorithms,” Cytometry 6(2), 81–91 (1985).
[Crossref] [PubMed]

1977 (1)

A. J. Jerri, “The Shannon sampling theorem—Its various extensions and applications: A tutorial review,” Proc. IEEE 65(11), 1565–1596 (1977).
[Crossref]

Alfieri, D.

Antkowiak, M.

Bahloul, D.

Bao, P.

Bao, X.

Barton, J. J.

J. J. Barton, “Removing multiple scattering and twin images from holographic images,” Phys. Rev. Lett. 67(22), 3106–3109 (1991).
[Crossref] [PubMed]

Beckmann, T.

T. Seyler, M. Fratz, T. Beckmann, A. Schiller, A. Bertz, and D. Carl, “Extending the Depth of Field beyond Geometrical Imaging Limitations Using Phase Noise as a Focus Measure in Multiwavelength Digital Holography,” Appl. Sci. (Basel) 8(7), 1042 (2018).
[Crossref]

Bertz, A.

T. Seyler, M. Fratz, T. Beckmann, A. Schiller, A. Bertz, and D. Carl, “Extending the Depth of Field beyond Geometrical Imaging Limitations Using Phase Noise as a Focus Measure in Multiwavelength Digital Holography,” Appl. Sci. (Basel) 8(7), 1042 (2018).
[Crossref]

Bian, Z.

Bishara, W.

O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 10(11), 1417–1428 (2010).
[Crossref] [PubMed]

W. Bishara, T.-W. Su, A. F. Coskun, and A. Ozcan, “Lensfree on-chip microscopy over a wide field-of-view using pixel super-resolution,” Opt. Express 18(11), 11181–11191 (2010).
[Crossref] [PubMed]

Bouamama, L.

Cai, L.

Callens, N.

Canlin, S.

L. Xiaoxu, Z. Yimo, Z. Liyun, L. Yinlong, and S. Canlin, “Analysis and experiment of phase-shifting coaxial lensless Fourier digital holography,” Acta Opt. Sin. 24(11), 1511–1515 (2004).

Carl, D.

T. Seyler, M. Fratz, T. Beckmann, A. Schiller, A. Bertz, and D. Carl, “Extending the Depth of Field beyond Geometrical Imaging Limitations Using Phase Noise as a Focus Measure in Multiwavelength Digital Holography,” Appl. Sci. (Basel) 8(7), 1042 (2018).
[Crossref]

Chen, N.

Chen, Q.

Coppola, G.

Coskun, A. F.

A. Greenbaum, W. Luo, T.-W. Su, Z. Göröcs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9(9), 889–895 (2012).
[Crossref] [PubMed]

W. Bishara, T.-W. Su, A. F. Coskun, and A. Ozcan, “Lensfree on-chip microscopy over a wide field-of-view using pixel super-resolution,” Opt. Express 18(11), 11181–11191 (2010).
[Crossref] [PubMed]

Cui, X.

X. Cui, L. M. Lee, X. Heng, W. Zhong, P. W. Sternberg, D. Psaltis, and C. Yang, “Lensless high-resolution on-chip optofluidic microscopes for Caenorhabditis elegans and cell imaging,” Proc. Natl. Acad. Sci. U.S.A. 105(31), 10670–10675 (2008).
[Crossref] [PubMed]

Dan, D.

Davis, C. S.

De Nicola, S.

Dirksen, D.

Dohet-Eraly, J.

Dubois, F.

Eikema, K. S. E.

Ferraro, P.

Fiadeiro, P. T.

Finizio, A.

Fonseca, E. S. R.

Fratz, M.

T. Seyler, M. Fratz, T. Beckmann, A. Schiller, A. Bertz, and D. Carl, “Extending the Depth of Field beyond Geometrical Imaging Limitations Using Phase Noise as a Focus Measure in Multiwavelength Digital Holography,” Appl. Sci. (Basel) 8(7), 1042 (2018).
[Crossref]

Gao, P.

García, J.

Garcia-Sucerquia, J.

Gillespie, J.

J. Gillespie and R. A. King, “The use of self-entropy as a focus measure in digital holography,” Pattern Recognit. Lett. 9(1), 19–25 (1989).
[Crossref]

Göröcs, Z.

A. Greenbaum, W. Luo, T.-W. Su, Z. Göröcs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9(9), 889–895 (2012).
[Crossref] [PubMed]

Greenbaum, A.

A. Greenbaum, W. Luo, T.-W. Su, Z. Göröcs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9(9), 889–895 (2012).
[Crossref] [PubMed]

Grilli, S.

Groen, F. C. A.

F. C. A. Groen, I. T. Young, and G. Ligthart, “A comparison of different focus functions for use in autofocus algorithms,” Cytometry 6(2), 81–91 (1985).
[Crossref] [PubMed]

Guo, C.

C. Guo, Q. Li, J. Tan, S. Liu, and Z. Liu, “A method of solving tilt illumination for multiple distance phase retrieval,” Opt. Lasers Eng. 106, 17–23 (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]

C. Guo, Y. Zhao, J. Tan, S. Liu, and Z. Liu, “Adaptive lens-free computational coherent imaging using autofocusing quantification with speckle illumination,” Opt. Express 26(11), 14407–14420 (2018).
[Crossref] [PubMed]

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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Guo, R.

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O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 10(11), 1417–1428 (2010).
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Lei, M.

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C. Guo, Q. Li, J. Tan, S. Liu, and Z. Liu, “A method of solving tilt illumination for multiple distance phase retrieval,” Opt. Lasers Eng. 106, 17–23 (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. Guo, Y. Zhao, J. Tan, S. Liu, and Z. Liu, “Adaptive lens-free computational coherent imaging using autofocusing quantification with speckle illumination,” Opt. Express 26(11), 14407–14420 (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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O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 10(11), 1417–1428 (2010).
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Y. Wu and A. Ozcan, “Lensless digital holographic microscopy and its applications in biomedicine and environmental monitoring,” Methods 136, 4–16 (2018).
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Y. Zhang, H. Wang, Y. Wu, M. Tamamitsu, and A. Ozcan, “Edge sparsity criterion for robust holographic autofocusing,” Opt. Lett. 42(19), 3824–3827 (2017).
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W. Bishara, T.-W. Su, A. F. Coskun, and A. Ozcan, “Lensfree on-chip microscopy over a wide field-of-view using pixel super-resolution,” Opt. Express 18(11), 11181–11191 (2010).
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O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 10(11), 1417–1428 (2010).
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O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 10(11), 1417–1428 (2010).
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Pan, F.

A. He, W. Xiao, and F. Pan, “Automatic focus determination through cosine and modified cosine score in digital holography,” Opt. Eng. 56(3), 034103 (2017).
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Poon, T. C.

Psaltis, D.

X. Cui, L. M. Lee, X. Heng, W. Zhong, P. W. Sternberg, D. Psaltis, and C. Yang, “Lensless high-resolution on-chip optofluidic microscopes for Caenorhabditis elegans and cell imaging,” Proc. Natl. Acad. Sci. U.S.A. 105(31), 10670–10675 (2008).
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T. Seyler, M. Fratz, T. Beckmann, A. Schiller, A. Bertz, and D. Carl, “Extending the Depth of Field beyond Geometrical Imaging Limitations Using Phase Noise as a Focus Measure in Multiwavelength Digital Holography,” Appl. Sci. (Basel) 8(7), 1042 (2018).
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O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 10(11), 1417–1428 (2010).
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Z. Zhong, X. Xie, L. Liu, C. Wang, and M. Shan, “Autofocusing in dual-wavelength digital holography using correlation coefficient,” Opt. Eng. 58(04), 1 (2019).
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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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Sheridan, J. T.

Situ, G.

Sternberg, P. W.

X. Cui, L. M. Lee, X. Heng, W. Zhong, P. W. Sternberg, D. Psaltis, and C. Yang, “Lensless high-resolution on-chip optofluidic microscopes for Caenorhabditis elegans and cell imaging,” Proc. Natl. Acad. Sci. U.S.A. 105(31), 10670–10675 (2008).
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Striano, V.

Su, T.-W.

A. Greenbaum, W. Luo, T.-W. Su, Z. Göröcs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9(9), 889–895 (2012).
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W. Bishara, T.-W. Su, A. F. Coskun, and A. Ozcan, “Lensfree on-chip microscopy over a wide field-of-view using pixel super-resolution,” Opt. Express 18(11), 11181–11191 (2010).
[Crossref] [PubMed]

Sun, J.

Sun, Y.

Tamamitsu, M.

Tan, J.

C. Guo, Y. Zhao, J. Tan, S. Liu, and Z. Liu, “Adaptive lens-free computational coherent imaging using autofocusing quantification with speckle illumination,” Opt. Express 26(11), 14407–14420 (2018).
[Crossref] [PubMed]

C. Guo, Q. Li, J. Tan, S. Liu, and Z. Liu, “A method of solving tilt illumination for multiple distance phase retrieval,” Opt. Lasers Eng. 106, 17–23 (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]

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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Tseng, D.

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Z. Zhong, X. Xie, L. Liu, C. Wang, and M. Shan, “Autofocusing in dual-wavelength digital holography using correlation coefficient,” Opt. Eng. 58(04), 1 (2019).
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Wang, H.

Y. Zhang, H. Wang, Y. Wu, M. Tamamitsu, and A. Ozcan, “Edge sparsity criterion for robust holographic autofocusing,” Opt. Lett. 42(19), 3824–3827 (2017).
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Wei, C.

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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Y. Wu and A. Ozcan, “Lensless digital holographic microscopy and its applications in biomedicine and environmental monitoring,” Methods 136, 4–16 (2018).
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Y. Zhang, H. Wang, Y. Wu, M. Tamamitsu, and A. Ozcan, “Edge sparsity criterion for robust holographic autofocusing,” Opt. Lett. 42(19), 3824–3827 (2017).
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A. He, W. Xiao, and F. Pan, “Automatic focus determination through cosine and modified cosine score in digital holography,” Opt. Eng. 56(3), 034103 (2017).
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L. Xiaoxu, Z. Yimo, Z. Liyun, L. Yinlong, and S. Canlin, “Analysis and experiment of phase-shifting coaxial lensless Fourier digital holography,” Acta Opt. Sin. 24(11), 1511–1515 (2004).

Xie, X.

Z. Zhong, X. Xie, L. Liu, C. Wang, and M. Shan, “Autofocusing in dual-wavelength digital holography using correlation coefficient,” Opt. Eng. 58(04), 1 (2019).
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Xu, Z.

Xue, L.

A. Greenbaum, W. Luo, T.-W. Su, Z. Göröcs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9(9), 889–895 (2012).
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Yaglidere, O.

Yan, S.

Yang, C.

X. Cui, L. M. Lee, X. Heng, W. Zhong, P. W. Sternberg, D. Psaltis, and C. Yang, “Lensless high-resolution on-chip optofluidic microscopes for Caenorhabditis elegans and cell imaging,” Proc. Natl. Acad. Sci. U.S.A. 105(31), 10670–10675 (2008).
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Ye, T.

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L. Xiaoxu, Z. Yimo, Z. Liyun, L. Yinlong, and S. Canlin, “Analysis and experiment of phase-shifting coaxial lensless Fourier digital holography,” Acta Opt. Sin. 24(11), 1511–1515 (2004).

Yinlong, L.

L. Xiaoxu, Z. Yimo, Z. Liyun, L. Yinlong, and S. Canlin, “Analysis and experiment of phase-shifting coaxial lensless Fourier digital holography,” Acta Opt. Sin. 24(11), 1511–1515 (2004).

Young, I. T.

F. C. A. Groen, I. T. Young, and G. Ligthart, “A comparison of different focus functions for use in autofocus algorithms,” Cytometry 6(2), 81–91 (1985).
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Yuan, C.

Zhang, J.

Zhang, Y.

Zhao, Y.

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Zhong, Z.

Z. Zhong, X. Xie, L. Liu, C. Wang, and M. Shan, “Autofocusing in dual-wavelength digital holography using correlation coefficient,” Opt. Eng. 58(04), 1 (2019).
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Zhou, C.

Zhou, H.

Zuo, C.

Acta Opt. Sin. (1)

L. Xiaoxu, Z. Yimo, Z. Liyun, L. Yinlong, and S. Canlin, “Analysis and experiment of phase-shifting coaxial lensless Fourier digital holography,” Acta Opt. Sin. 24(11), 1511–1515 (2004).

Appl. Opt. (8)

P. Langehanenberg, B. Kemper, D. Dirksen, and G. von Bally, “Autofocusing in digital holographic phase contrast microscopy on pure phase objects for live cell imaging,” Appl. Opt. 47(19), D176–D182 (2008).
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P. Bao, G. Situ, G. Pedrini, and W. Osten, “Lensless phase microscopy using phase retrieval with multiple illumination wavelengths,” Appl. Opt. 51(22), 5486–5494 (2012).
[Crossref] [PubMed]

C. Guo, S. Liu, and J. T. Sheridan, “Iterative phase retrieval algorithms. I: optimization,” Appl. Opt. 54(15), 4698–4708 (2015).
[Crossref] [PubMed]

C. Guo, S. Liu, and J. T. Sheridan, “Iterative phase retrieval algorithms. Part II: Attacking optical encryption systems,” Appl. Opt. 54(15), 4709–4719 (2015).
[Crossref] [PubMed]

E. S. R. Fonseca, P. T. Fiadeiro, M. Pereira, and A. Pinheiro, “Comparative analysis of autofocus functions in digital in-line phase-shifting holography,” Appl. Opt. 55(27), 7663–7674 (2016).
[Crossref] [PubMed]

M. Lyu, C. Yuan, D. Li, and G. Situ, “Fast autofocusing in digital holography using the magnitude differential,” Appl. Opt. 56(13), F152–F157 (2017).
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S. K. Mohammed, L. Bouamama, D. Bahloul, and P. Picart, “Quality assessment of refocus criteria for particle imaging in digital off-axis holography,” Appl. Opt. 56(13), F158–F166 (2017).
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T. Pitkäaho, A. Manninen, and T. J. Naughton, “Focus prediction in digital holographic microscopy using deep convolutional neural networks,” Appl. Opt. 58(5), A202–A208 (2019).
[Crossref] [PubMed]

Appl. Sci. (Basel) (1)

T. Seyler, M. Fratz, T. Beckmann, A. Schiller, A. Bertz, and D. Carl, “Extending the Depth of Field beyond Geometrical Imaging Limitations Using Phase Noise as a Focus Measure in Multiwavelength Digital Holography,” Appl. Sci. (Basel) 8(7), 1042 (2018).
[Crossref]

Biomed. Opt. Express (2)

Cytometry (1)

F. C. A. Groen, I. T. Young, and G. Ligthart, “A comparison of different focus functions for use in autofocus algorithms,” Cytometry 6(2), 81–91 (1985).
[Crossref] [PubMed]

J. Opt. A, Pure Appl. Opt. (1)

L. Ma, H. Wang, Y. Li, and H. Jin, “Numerical reconstruction of digital holograms for three-dimensional shape measurement,” J. Opt. A, Pure Appl. Opt. 6(4), 396–400 (2004).
[Crossref]

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

Lab Chip (1)

O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 10(11), 1417–1428 (2010).
[Crossref] [PubMed]

Methods (1)

Y. Wu and A. Ozcan, “Lensless digital holographic microscopy and its applications in biomedicine and environmental monitoring,” Methods 136, 4–16 (2018).
[Crossref] [PubMed]

Nat. Methods (1)

A. Greenbaum, W. Luo, T.-W. Su, Z. Göröcs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9(9), 889–895 (2012).
[Crossref] [PubMed]

Opt. Eng. (2)

A. He, W. Xiao, and F. Pan, “Automatic focus determination through cosine and modified cosine score in digital holography,” Opt. Eng. 56(3), 034103 (2017).
[Crossref]

Z. Zhong, X. Xie, L. Liu, C. Wang, and M. Shan, “Autofocusing in dual-wavelength digital holography using correlation coefficient,” Opt. Eng. 58(04), 1 (2019).
[Crossref]

Opt. Express (11)

P. Ferraro, S. Grilli, D. Alfieri, S. De Nicola, A. Finizio, G. Pierattini, B. Javidi, G. Coppola, and V. Striano, “Extended focused image in microscopy by digital Holography,” Opt. Express 13(18), 6738–6749 (2005).
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F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express 14(13), 5895–5908 (2006).
[Crossref] [PubMed]

N. Warnasooriya and M. K. Kim, “LED-based multi-wavelength phase imaging interference microscopy,” Opt. Express 15(15), 9239–9247 (2007).
[Crossref] [PubMed]

P. Memmolo, M. Iannone, M. Ventre, P. A. Netti, A. Finizio, M. Paturzo, and P. Ferraro, “On the holographic 3D tracking of in vitro cells characterized by a highly-morphological change,” Opt. Express 20(27), 28485–28493 (2012).
[Crossref] [PubMed]

Y. S. Kim, T. Kim, S. S. Woo, H. Kang, T. C. Poon, and C. Zhou, “Speckle-free digital holographic recording of a diffusely reflecting object,” Opt. Express 21(7), 8183–8189 (2013).
[Crossref] [PubMed]

W. Bishara, T.-W. Su, A. F. Coskun, and A. Ozcan, “Lensfree on-chip microscopy over a wide field-of-view using pixel super-resolution,” Opt. Express 18(11), 11181–11191 (2010).
[Crossref] [PubMed]

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Figures (9)

Fig. 1
Fig. 1 Experimental schematic of multi-wavelength lensless imaging system. A white light (broadband laser) passes the filter wheel (three modes used in the experiments), and the filtered light illuminates the sample. The diffraction patterns are recorded by a color CCD camera sensor.
Fig. 2
Fig. 2 Single loop in Serial alternating iteration. The colored arrows represent the propagation at the corresponding color wavelength. k is the kth iteration.
Fig. 3
Fig. 3 The flowchart of MWAF and the multi-wavelength phase retrievals. (a) MWAF algorithm, the combination of colored curved arrows and ㊀ indicates the subtraction of the recovered low-resolution images at the corresponding wavelength. (b) Object plane. The colored arrows represent the Fresnel diffraction propagation (c) Camera plane. (d) Recovered amplitude and phase images.
Fig. 4
Fig. 4 The results of MWAF algorithm. (a-c) The Fresnel diffraction patterns at different wavelengths. (d) MWAF normalized metric value curve. (e-f) The reconstructed amplitude and phase images using 50 iterations phase retrieval. (g) The interplay between the autofocusing method and the phase retrieval algorithm.
Fig. 5
Fig. 5 The normalized metric curves of the eight algorithms under different noise conditions. The first three columns represent different simulated samples, and the fourth column is the recovered amplitude of the complex test corresponding to the third column. (a)-(c) The noise-free case (NF). (e)-(g) The metric curves in the case of adding Gaussian noise (GN, variance = 0.01). (i)-(k) The metric curves in the case of adding speckle noise (SN). (m)-(o) The metric curves in the case of wide bandwidth (WB). (q)-(s) The curves of compound noise (CN).
Fig. 6
Fig. 6 The retrieved results of USAF resolution target. (a) The intensity captured by the CCD camera. (b, d) The reconstructed phase and amplitude images based on MWAF method. (c) The normalized metric curve obtained by the eight methods. (e-f) The reconstruction of the amplitude based on the Grad and Var method using 10 iterations. (g-i) The horizontal-line intensity profile of the marked lines in (d-f), respectively. The scale bar corresponds to 100 μm and is applicable to all images.
Fig. 7
Fig. 7 (a) The normalized metric curve obtained by MWAF at 10 nm bandwidth and 3nm bandwidth. (c-d) The recovered amplitude and phase of the biological specimen. The white bar at the left-down corner corresponds to 300 μm.
Fig. 8
Fig. 8 The retrieved result of USAF resolution target under broadband laser. (a) The diffraction pattern recorded by a color CCD camera. (b) The normalized metric curve. (c-d) The reconstructed amplitude and phase using 10 iterations. The curves show the intensity at the position of the colored line. The white bar corresponds to 100 μm.
Fig. 9
Fig. 9 The reconstructed complex object (Cameraman + Testpat1), and pure phase object (Testpat1) using 50 iterations phase retrieval methods. Phase (0, 1) refers to the input phase without considering the modulation by different wavelength, while phase (lambda) is the input phase considering the modulation of the different wavelength. ‘Old’ refers to phase retrieval process without considering the phase shift caused by different wavelength, while ‘New’ is the phase retrieval taking the phase shift of different wavelength into consideration.

Tables (1)

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Table 1 Performance of focus metrics for eight autofocusing methods

Equations (13)

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E( x,y,z )= e i2πz/λ iλz E( x',y',0 ) e ( iπ/λz )[ ( xx' ) 2 + ( yy' ) 2 ] dx'dy',
H n ( f x , f y )={ exp( i2πz λ n 1 ( λ n f x ) 2 ( λ n f y ) 2 ), if ( λ n f x ) 2 + ( λ n f y ) 2 <1 0, otherwise ,
O= F 1 [ F( I ) H n * ],
MWAF( z )= 1 3 x=1 N x y=1 N y ( | | O 1 || O 2 | | 2 + | | O 1 || O 3 | | 2 + | | O 2 || O 3 | | 2 ) 2 ,
μ OR k = V r k exp[ j φ ^ r k ]=FS T z | A r k exp[ j φ r k ] |( k=1+3i ),
μ RO k =FS T z 1 | I r exp[ j φ ^ r k ] |( k=1+3i ),
μ OR k = V g k exp[ j φ ^ g k ]=FS T z | A g k exp[ j φ g k ] |,
μ RO k =FS T z 1 | I g exp[ j φ ^ g k ] |( k=2+3i ),
μ OR k = V b k exp[ j φ ^ b k ]=FS T z | A b k exp[ j φ b k ] |,
μ RO k =FS T z 1 | I b exp[ j φ ^ b k ] |( k=3+3i ).
Var( z )= 1 N x N y x,y [| O(x,y,z) | | O(x,y,z) | ¯ ] 2 ,
Grad( z )= x=1 N x 1 y=1 N y 1 [| O(x,y,z) || O(x1,y,z) |] 2 + [| O(x,y,z) || O(x,y1,z) |] 2 ,
Lap( z )= x=1 N x 1 y=1 N y 1 [| O(x+1,y,z) |+| O(x1,y,z) |+| O(x,y+1,z) |+| O(x,y1,z) |4| O(x,y,z) |] 2 ,

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