Abstract

Lensless imaging is a technique that records diffraction patterns without using lenses and recovers the complex field of object via phase retrieval. Robust lensless phase retrieval process usually requires multiple measurements with defocus variation, transverse translation or angle-varied illumination. However, making such diverse measurements is time-consuming and limits the application of lensless setup for dynamic samples. In this paper, we propose a single-shot lensless imaging scheme via simultaneous multi-angle LED illumination. Diffraction patterns under multi-angle lights are recorded by different areas of the sensor within a single shot. An optimization algorithm is applied to utilize the single-shot measurement and retrieve the aliasing information for reconstruction. We first use numerical simulations to evaluate the proposed scheme quantitatively by comparisons with the multi-acquisition case. Then a proof-of-concept lensless setup is built to validate the method by imaging a resolution chart and biological samples, achieving ∼ 4.92 μm half-pitch resolution and ∼ 1.202 mm2 field of view (FOV). We also discuss different design tradeoffs and present a 4-frame acquisition scheme (with ∼ 3.48 μm half-pitch resolution and ∼ 2.35 × 2.55 mm2 FOV) to show the flexibility of performance enhancement by capturing more measurements.

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

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References

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2018 (5)

N. Antipa, G. Kuo, R. Heckel, B. Mildenhall, E. Bostan, R. Ng, and L. Waller, “Diffusercam: lensless single-exposure 3d imaging,” Optica 5, 1–9 (2018).
[Crossref]

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light-Sci. Appl. 7, 17141 (2018).
[Crossref]

X. He, C. Liu, and J. Zhu, “Single-shot fourier ptychography based on diffractive beam splitting,” Opt. Lett. 43, 214–217 (2018).
[Crossref] [PubMed]

Z. Zhang, Y. Zhou, S. Jiang, K. Guo, K. Hoshino, J. Zhong, J. Suo, Q. Dai, and G. Zheng, “Invited article: Mask-modulated lensless imaging with multi-angle illuminations,” APL Photonics 3, 060803 (2018).
[Crossref]

P. Li and A. Maiden, “Lensless led matrix ptychographic microscope: problems and solutions,” Appl. Optics 57, 1800–1806 (2018).
[Crossref]

2017 (5)

A. Sinha, J. Lee, S. Li, and G. Barbastathis, “Lensless computational imaging through deep learning,” Optica 4, 1117–1125 (2017).
[Crossref]

Y. Zhou, J. Wu, Z. Bian, J. Suo, G. Zheng, and Q. Dai, “Fourier ptychographic microscopy using wavelength multiplexing,” J. Biomed. Opt. 22, 066006 (2017).
[Crossref]

A. Sun, X. He, Y. Kong, H. Cui, X. Song, L. Xue, S. Wang, and C. Liu, “Ultra-high speed digital micro-mirror device based ptychographic iterative engine method,” Biomed. Opt. Express 8, 3155–3162 (2017).
[Crossref] [PubMed]

C. Allier, S. Morel, R. Vincent, L. Ghenim, F. Navarro, M. Menneteau, T. Bordy, L. Hervé, O. Cioni, X. Gidrol, Y. Usson, and J.-M. Dinten, “Imaging of dense cell cultures by multiwavelength lens-free video microscopy,” Cytom. Part A 91, 433–442 (2017).
[Crossref]

A. Maiden, D. Johnson, and P. Li, “Further improvements to the ptychographical iterative engine,” Optica 4, 736–745 (2017).
[Crossref]

2016 (6)

2015 (8)

Z. F. Phillips, M. V. D’Ambrosio, L. Tian, J. J. Rulison, H. S. Patel, N. Sadras, A. V. Gande, N. A. Switz, D. A. Fletcher, and L. Waller, “Multi-contrast imaging and digital refocusing on a mobile microscope with a domed led array,” PLoS One 10, e0124938 (2015).
[Crossref] [PubMed]

L.-H. Yeh, J. Dong, J. Zhong, L. Tian, M. Chen, G. Tang, M. Soltanolkotabi, and L. Waller, “Experimental robustness of fourier ptychography phase retrieval algorithms,” Opt. Express 23, 33214–33240 (2015).
[Crossref]

L. Tian, Z. Liu, L.-H. Yeh, M. Chen, J. Zhong, and L. Waller, “Computational illumination for high-speed in vitro fourier ptychographic microscopy,” Optica 2, 904–911 (2015).
[Crossref]

C. Zuo, J. Sun, J. Zhang, Y. Hu, and Q. Chen, “Lensless phase microscopy and diffraction tomography with multi-angle and multi-wavelength illuminations using a led matrix,” Opt. Express 23, 14314–14328 (2015).
[Crossref] [PubMed]

W. Luo, A. Greenbaum, Y. Zhang, and A. Ozcan, “Synthetic aperture-based on-chip microscopy,” Light-Sci. Appl. 4, e261 (2015).
[Crossref]

M. Sanz, J. A. Picazo-Bueno, J. García, and V. Micó, “Improved quantitative phase imaging in lensless microscopy by single-shot multi-wavelength illumination using a fast convergence algorithm,” Opt. Express 23, 21352–21365 (2015).
[Crossref] [PubMed]

L. Tian and L. Waller, “3d intensity and phase imaging from light field measurements in an led array microscope,” Optica 2, 104–111 (2015).
[Crossref]

C. Kuang, Y. Ma, R. Zhou, J. Lee, G. Barbastathis, R. R. Dasari, Z. Yaqoob, and P. T. So, “Digital micromirror device-based laser-illumination fourier ptychographic microscopy,” Opt. Express 23, 26999–27010 (2015).
[Crossref] [PubMed]

2014 (4)

2013 (3)

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

X. Pan, C. Liu, and J. Zhu, “Single shot ptychographical iterative engine based on multi-beam illumination,” Appl. Phys. Lett. 103, 171105 (2013).
[Crossref]

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68 (2013).
[Crossref] [PubMed]

2012 (3)

A. M. Maiden, M. J. Humphry, and J. Rodenburg, “Ptychographic transmission microscopy in three dimensions using a multi-slice approach,” J. Opt. Soc. Am. A 29, 1606–1614 (2012).
[Crossref]

S. B. Kim, H. Bae, K.-i. Koo, M. R. Dokmeci, A. Ozcan, and A. Khademhosseini, “Lens-free imaging for biological applications,” J. Lab. Autom. 17, 43–49 (2012).
[Crossref] [PubMed]

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, 889–895 (2012).
[Crossref] [PubMed]

2010 (3)

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, 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, 11181–11191 (2010).
[Crossref] [PubMed]

L. Waller, S. S. Kou, C. J. Sheppard, and G. Barbastathis, “Phase from chromatic aberrations,” Opt. Express 18, 22817–22825 (2010).
[Crossref] [PubMed]

2009 (2)

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
[Crossref] [PubMed]

K. Matsushima and T. Shimobaba, “Band-limited angular spectrum method for numerical simulation of free-space propagation in far and near fields,” Opt. Express 17, 19662–19673 (2009).
[Crossref] [PubMed]

2008 (1)

2004 (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 Process. 13, 600–612 (2004).
[Crossref] [PubMed]

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

2001 (1)

L. Allen and M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199, 65–75 (2001).
[Crossref]

Allen, L.

L. Allen and M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199, 65–75 (2001).
[Crossref]

Allier, C.

C. Allier, S. Morel, R. Vincent, L. Ghenim, F. Navarro, M. Menneteau, T. Bordy, L. Hervé, O. Cioni, X. Gidrol, Y. Usson, and J.-M. Dinten, “Imaging of dense cell cultures by multiwavelength lens-free video microscopy,” Cytom. Part A 91, 433–442 (2017).
[Crossref]

Antipa, N.

Bae, H.

S. B. Kim, H. Bae, K.-i. Koo, M. R. Dokmeci, A. Ozcan, and A. Khademhosseini, “Lens-free imaging for biological applications,” J. Lab. Autom. 17, 43–49 (2012).
[Crossref] [PubMed]

Barbastathis, G.

Bian, Z.

Y. Zhou, J. Wu, Z. Bian, J. Suo, G. Zheng, and Q. Dai, “Fourier ptychographic microscopy using wavelength multiplexing,” J. Biomed. Opt. 22, 066006 (2017).
[Crossref]

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, 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, 11181–11191 (2010).
[Crossref] [PubMed]

Bordy, T.

C. Allier, S. Morel, R. Vincent, L. Ghenim, F. Navarro, M. Menneteau, T. Bordy, L. Hervé, O. Cioni, X. Gidrol, Y. Usson, and J.-M. Dinten, “Imaging of dense cell cultures by multiwavelength lens-free video microscopy,” Cytom. Part A 91, 433–442 (2017).
[Crossref]

Bostan, E.

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 Process. 13, 600–612 (2004).
[Crossref] [PubMed]

Chen, M.

Chen, Q.

Chung, J.

Chung, P.-L.

A. Greenbaum, Y. Zhang, A. Feizi, P.-L. Chung, W. Luo, S. R. Kandukuri, and A. Ozcan, “Wide-field computational imaging of pathology slides using lens-free on-chip microscopy,” Sci. Transl. Med. 6, 267 (2014).
[Crossref] [PubMed]

Cioni, O.

C. Allier, S. Morel, R. Vincent, L. Ghenim, F. Navarro, M. Menneteau, T. Bordy, L. Hervé, O. Cioni, X. Gidrol, Y. Usson, and J.-M. Dinten, “Imaging of dense cell cultures by multiwavelength lens-free video microscopy,” Cytom. Part A 91, 433–442 (2017).
[Crossref]

Cohen, O.

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, 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, 11181–11191 (2010).
[Crossref] [PubMed]

Cui, H.

D’Ambrosio, M. V.

Z. F. Phillips, M. V. D’Ambrosio, L. Tian, J. J. Rulison, H. S. Patel, N. Sadras, A. V. Gande, N. A. Switz, D. A. Fletcher, and L. Waller, “Multi-contrast imaging and digital refocusing on a mobile microscope with a domed led array,” PLoS One 10, e0124938 (2015).
[Crossref] [PubMed]

Dai, Q.

Z. Zhang, Y. Zhou, S. Jiang, K. Guo, K. Hoshino, J. Zhong, J. Suo, Q. Dai, and G. Zheng, “Invited article: Mask-modulated lensless imaging with multi-angle illuminations,” APL Photonics 3, 060803 (2018).
[Crossref]

Y. Zhou, J. Wu, Z. Bian, J. Suo, G. Zheng, and Q. Dai, “Fourier ptychographic microscopy using wavelength multiplexing,” J. Biomed. Opt. 22, 066006 (2017).
[Crossref]

Dasari, R. R.

Dinten, J.-M.

C. Allier, S. Morel, R. Vincent, L. Ghenim, F. Navarro, M. Menneteau, T. Bordy, L. Hervé, O. Cioni, X. Gidrol, Y. Usson, and J.-M. Dinten, “Imaging of dense cell cultures by multiwavelength lens-free video microscopy,” Cytom. Part A 91, 433–442 (2017).
[Crossref]

Dokmeci, M. R.

S. B. Kim, H. Bae, K.-i. Koo, M. R. Dokmeci, A. Ozcan, and A. Khademhosseini, “Lens-free imaging for biological applications,” J. Lab. Autom. 17, 43–49 (2012).
[Crossref] [PubMed]

Dong, J.

Dong, S.

Egami, R.

Faulkner, H. M.

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

Feizi, A.

W. Luo, Y. Zhang, A. Feizi, Z. Göröcs, and A. Ozcan, “Pixel super-resolution using wavelength scanning,” Light-Sci. Appl. 5, e16060 (2016).
[Crossref]

A. Greenbaum, Y. Zhang, A. Feizi, P.-L. Chung, W. Luo, S. R. Kandukuri, and A. Ozcan, “Wide-field computational imaging of pathology slides using lens-free on-chip microscopy,” Sci. Transl. Med. 6, 267 (2014).
[Crossref] [PubMed]

Fienup, J. R.

Fletcher, D. A.

Z. F. Phillips, M. V. D’Ambrosio, L. Tian, J. J. Rulison, H. S. Patel, N. Sadras, A. V. Gande, N. A. Switz, D. A. Fletcher, and L. Waller, “Multi-contrast imaging and digital refocusing on a mobile microscope with a domed led array,” PLoS One 10, e0124938 (2015).
[Crossref] [PubMed]

Gande, A. V.

Z. F. Phillips, M. V. D’Ambrosio, L. Tian, J. J. Rulison, H. S. Patel, N. Sadras, A. V. Gande, N. A. Switz, D. A. Fletcher, and L. Waller, “Multi-contrast imaging and digital refocusing on a mobile microscope with a domed led array,” PLoS One 10, e0124938 (2015).
[Crossref] [PubMed]

García, J.

Ghenim, L.

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Zhou, Y.

Z. Zhang, Y. Zhou, S. Jiang, K. Guo, K. Hoshino, J. Zhong, J. Suo, Q. Dai, and G. Zheng, “Invited article: Mask-modulated lensless imaging with multi-angle illuminations,” APL Photonics 3, 060803 (2018).
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Y. Zhou, J. Wu, Z. Bian, J. Suo, G. Zheng, and Q. Dai, “Fourier ptychographic microscopy using wavelength multiplexing,” J. Biomed. Opt. 22, 066006 (2017).
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Zhu, J.

X. He, C. Liu, and J. Zhu, “Single-shot fourier ptychography based on diffractive beam splitting,” Opt. Lett. 43, 214–217 (2018).
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X. Pan, C. Liu, and J. Zhu, “Single shot ptychographical iterative engine based on multi-beam illumination,” Appl. Phys. Lett. 103, 171105 (2013).
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Zuo, C.

Annu. Rev. Biomed. Eng. (1)

A. Ozcan and E. McLeod, “Lensless imaging and sensing,” Annu. Rev. Biomed. Eng. 18, 77–102 (2016).
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APL Photonics (1)

Z. Zhang, Y. Zhou, S. Jiang, K. Guo, K. Hoshino, J. Zhong, J. Suo, Q. Dai, and G. Zheng, “Invited article: Mask-modulated lensless imaging with multi-angle illuminations,” APL Photonics 3, 060803 (2018).
[Crossref]

Appl. Optics (1)

P. Li and A. Maiden, “Lensless led matrix ptychographic microscope: problems and solutions,” Appl. Optics 57, 1800–1806 (2018).
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Appl. Phys. Lett. (2)

X. Pan, C. Liu, and J. Zhu, “Single shot ptychographical iterative engine based on multi-beam illumination,” Appl. Phys. Lett. 103, 171105 (2013).
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J. M. Rodenburg and H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004).
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Biomed. Opt. Express (5)

Cytom. Part A (1)

C. Allier, S. Morel, R. Vincent, L. Ghenim, F. Navarro, M. Menneteau, T. Bordy, L. Hervé, O. Cioni, X. Gidrol, Y. Usson, and J.-M. Dinten, “Imaging of dense cell cultures by multiwavelength lens-free video microscopy,” Cytom. Part A 91, 433–442 (2017).
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IEEE Trans. Image Process. (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
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J. Biomed. Opt. (1)

Y. Zhou, J. Wu, Z. Bian, J. Suo, G. Zheng, and Q. Dai, “Fourier ptychographic microscopy using wavelength multiplexing,” J. Biomed. Opt. 22, 066006 (2017).
[Crossref]

J. Lab. Autom. (1)

S. B. Kim, H. Bae, K.-i. Koo, M. R. Dokmeci, A. Ozcan, and A. Khademhosseini, “Lens-free imaging for biological applications,” J. Lab. Autom. 17, 43–49 (2012).
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J. Opt. Soc. Am. A (1)

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, 1417–1428 (2010).
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Light-Sci. Appl. (3)

W. Luo, A. Greenbaum, Y. Zhang, and A. Ozcan, “Synthetic aperture-based on-chip microscopy,” Light-Sci. Appl. 4, e261 (2015).
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W. Luo, Y. Zhang, A. Feizi, Z. Göröcs, and A. Ozcan, “Pixel super-resolution using wavelength scanning,” Light-Sci. Appl. 5, e16060 (2016).
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Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light-Sci. Appl. 7, 17141 (2018).
[Crossref]

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, 889–895 (2012).
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Nat. Photonics (1)

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution fourier ptychographic microscopy,” Nat. Photonics 7, 739 (2013).
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Nature (1)

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68 (2013).
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Opt. Commun. (1)

L. Allen and M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199, 65–75 (2001).
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Opt. Express (10)

M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express 16, 7264–7278 (2008).
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C. Zuo, J. Sun, J. Zhang, Y. Hu, and Q. Chen, “Lensless phase microscopy and diffraction tomography with multi-angle and multi-wavelength illuminations using a led matrix,” Opt. Express 23, 14314–14328 (2015).
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R. Horisaki, R. Egami, and J. Tanida, “Single-shot phase imaging with randomized light (spiral),” Opt. Express 24, 3765–3773 (2016).
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L. Waller, S. S. Kou, C. J. Sheppard, and G. Barbastathis, “Phase from chromatic aberrations,” Opt. Express 18, 22817–22825 (2010).
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M. Sanz, J. A. Picazo-Bueno, J. García, and V. Micó, “Improved quantitative phase imaging in lensless microscopy by single-shot multi-wavelength illumination using a fast convergence algorithm,” Opt. Express 23, 21352–21365 (2015).
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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, 11181–11191 (2010).
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K. Matsushima and T. Shimobaba, “Band-limited angular spectrum method for numerical simulation of free-space propagation in far and near fields,” Opt. Express 17, 19662–19673 (2009).
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Opt. Lett. (1)

Optica (6)

PLoS One (1)

Z. F. Phillips, M. V. D’Ambrosio, L. Tian, J. J. Rulison, H. S. Patel, N. Sadras, A. V. Gande, N. A. Switz, D. A. Fletcher, and L. Waller, “Multi-contrast imaging and digital refocusing on a mobile microscope with a domed led array,” PLoS One 10, e0124938 (2015).
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Sci. Transl. Med. (1)

A. Greenbaum, Y. Zhang, A. Feizi, P.-L. Chung, W. Luo, S. R. Kandukuri, and A. Ozcan, “Wide-field computational imaging of pathology slides using lens-free on-chip microscopy,” Sci. Transl. Med. 6, 267 (2014).
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Ultramicroscopy (1)

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
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Other (2)

Y. Wu, Y. Rivenson, Y. Zhang, H. Gunaydin, X. Lin, and A. Ozcan, “Extended depth-of-field in holographic image reconstruction using deep learning based auto-focusing and phase-recovery,” arXiv preprint arXiv:1803.08138 (2018).

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Figures (9)

Fig. 1
Fig. 1 The schematic of the proposed single-shot lensless imaging system: (a) the optical setup and (b) the corresponding forward model expression. The mathematical representation of the single-shot measurement Idetected is presented. The coordinate r in equations is omitted for simplicity.
Fig. 2
Fig. 2 The flow chart shows one iteration of the reconstruction algorithm, which includes N inner iterations. Particularly, PSF = Fresnel ( d ) = 1 { exp ( j k 0 2 k x 2 k y 2 d ) }, where −1{·} represents the inverse Fourier transform and d is the propagation distance. The conj(·) is the conjugate operator. 5 to 10 iterations are generally needed for the recovery. The coordinate r is omitted in above equations.
Fig. 3
Fig. 3 Simulation results of a complex object using 10 iterations. (a) Results of the multi-acquisition lensless imaging and our single-shot scheme. (b) Results using direct split method [24] with different split ratios. A loss of details and periodic artifacts are introduced, especially in recovered phase. Among them, results with SSIM or RMSE in yellow are of best performance. (c) SSIM and RMSE curves of recovered results. Our method achieves similar performance as the multi-acquisition case.
Fig. 4
Fig. 4 (a) is the real setup of our single-shot scheme. (b) is the single-shot illumination pattern and (c) shows the corresponding single-shot measurement. (d) and (e) are recovered results of a USAF-1951 resolution chart. Although with some artifacts, the group 6-5 of resolution chart can be distinguished, achieving 4.92 μm half-pitch resolution.
Fig. 5
Fig. 5 (a) includes illumination patterns and corresponding 4 measurements of the 4-frame scheme. (b) is the close-up of one raw image. (c) and (d) are recovered results of the USAF-1951 resolution chart. As shown in (d), the group 7-2 can be distinguished, indicating about 3.48 μm half-pitch resolution.
Fig. 6
Fig. 6 Recovered amplitude images of a lilium ovary cross section. (a) is the result using the single-shot scheme, while (b) is the result of the 4-frame scheme with the same region cropped from the full FOV image (c), marked by the red dashed box. Some close-ups of both schemes are presented in the left bottom correspondingly. Lineouts are shown to demonstrate the differences. The result of 4-frame scheme has over 4 times FOV and better details.
Fig. 7
Fig. 7 Recovered complex images of a meiosis of grasshopper section. (a1) and (b1) are the amplitude and phase images of the single-shot scheme, while (a2) and (b2) are some close-up images. (c1) and (d1) are the results of the 4-frame scheme with the same region, while the close-ups are shown in (c2) and (d2). Different details are emphasized by blue and red arrows. The cropped areas are marked by blue and red dashed boxes in images (e) and (f) correspondingly, which occupy about 1/4 of the full FOV. More close-up images of the results using the 4-frame scheme are shown in the right.
Fig. 8
Fig. 8 Simulation of the single-shot scheme with a varying object-to-sensor distance d2. A smaller d2 causes heavier crosstalk and results in bad reconstruction quality (larger RMSE). We use d2 ≈ 5 mm in reality (since the RMSE curve of the amplitude almost converges) to balance the crosstalk and the number of pixels in use.
Fig. 9
Fig. 9 Simulation results to show the effect of the partial coherence of illumination to both schemes based on real parameters. We use a Siemens star target to evaluate the resolution, as shown in (a). The spectrum curves of illumination before and after the spectral filter are shown in (b). Simulation results corresponding to different partially coherent conditions are presented in (c). The ’Setup 1’ in the upper half of (c) refers to the single-shot scheme, while the ’Setup 2’ in the bottom half refers to the 4-frame scheme. In comparison, the latter has better resolution and less artifacts due to the less crosstalk among diffraction patterns. Recovered results in the same rows of the blue dashed box (column 1 and column 2) and of the green dashed box (column 4 and column 5) respectively have similar performance. This indicates that the effect of the partial temporal coherence has been mostly eliminated, as a spectral filter and ∼ 5 mm object-to-sensor distance in use. Comparing the results of column 1 and column 4, the spatial size of LED (the partial spatial coherence) leads to artifacts.

Tables (2)

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Table 1 Parameters in experiments of single-shot scheme.

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Table 2 Parameters in experiments of 4-frame scheme.

Equations (5)

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U ¯ 2 ( k ) = exp ( j k 0 2 k x 2 k y 2 d 1 ) U ¯ 1 ( k ) ,
I i ( r ) = | U 4 ( r ) | 2 = | PSF 2 ( r ) { PSF 1 ( r ) [ P i ( r ) P M ( r ) ] O ( r ) } | 2 .
I detected ( r ) = i L s I i ( r ) = i L s | PSF 2 ( r ) { PSF 1 ( r ) [ P i ( r ) P M ( r ) ] O ( r ) } | 2 ,
min O ( r ) , P M ( r ) | I detected ( r ) ( i L s | PSF 2 ( r ) { PSF 1 ( r ) [ P i ( r ) P M ( r ) ] O ( r ) } | 2 + b ) | 2 , s . t . I detected ( r ) b 0 ,
W FOV 2 × ( z 1 + R p ) ,

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