Abstract

Fourier ptychographic microscopy (FPM) is a newly developed computational imaging technique that can provide gigapixel images with both high resolution (HR) and wide field of view (FOV). However, there are two possible reasons for position misalignment, which induce a degradation of the reconstructed image. The first one is the position misalignment of the LED array, which can largely be eliminated during the experimental system building process. The more important one is the segment-dependent position misalignment. Note that, this segment-dependent positional misalignment still exists, even after we correct the central coordinates of every small segment. In this paper, we carefully analyze this segment-dependent misalignment and find that this global shift matters more, compared with the rotational misalignments. According to this fact, we propose a robust and fast method to correct the two factors of position misalignment of the FPM, termed as misalignment correction for the FPM misalignment correction (mcFPM). Although different regions in the FOV have different sensitivities to the position misalignment, the experimental results show that the mcFPM is robust with respect to the elimination of each region. Compared with the state-of-the-art methods, the mcFPM is much faster.

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

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References

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  6. N. Chen, J. Yeom, K. Hong, G. Li, and B. Lee, “Fast converging algorithm for wavefront reconstruction based on a sequence of diffracted intensity images,” J. Opt. Soc. Korea 18, 217–224 (2014).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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2018 (1)

A. Zhou, N. Chen, H. Wang, and G. Situ, “Analysis of fourier ptychographic microscopy with half of the captured images,” J. Opt. 20, 095701 (2018).
[Crossref]

2016 (1)

2015 (3)

R. Horstmeyer, X. Ou, G. Zheng, P. Willems, and C. Yang, “Digital pathology with Fourier ptychography,” Comput. Med. Imaging Graph. 42, 38–43 (2015).
[Crossref]

J. Chung, X. Ou, R. P. Kulkarni, and C. Yang, “Counting white blood cells from a blood smear using Fourier ptychographic microscopy,” PLOS One 10, e0133489 (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]

2014 (5)

2013 (3)

2012 (1)

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

2009 (1)

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

2007 (1)

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[Crossref] [PubMed]

2004 (1)

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

1992 (1)

J. M. Rodenburg and R. H. T. Bates, “The theory of super-resolution electron microscopy via wrigner-distribution deconvolution,” Philos. Transactions Royal Soc. A. 339, 521–553 (1992).
[Crossref]

1982 (1)

Ao, Z.

A. Williams, J. Chung, X. Ou, G. Zheng, S. Rawal, Z. Ao, R. Datar, C. Yang, and R. Cote, “Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis,” J. Biomed. Opt. 19, 066007 (2014).
[Crossref] [PubMed]

Bates, R. H. T.

J. M. Rodenburg and R. H. T. Bates, “The theory of super-resolution electron microscopy via wrigner-distribution deconvolution,” Philos. Transactions Royal Soc. A. 339, 521–553 (1992).
[Crossref]

Bian, Z.

Bunk, O.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[Crossref] [PubMed]

Chen, M.

Chen, N.

A. Zhou, N. Chen, H. Wang, and G. Situ, “Analysis of fourier ptychographic microscopy with half of the captured images,” J. Opt. 20, 095701 (2018).
[Crossref]

N. Chen, J. Yeom, K. Hong, G. Li, and B. Lee, “Fast converging algorithm for wavefront reconstruction based on a sequence of diffracted intensity images,” J. Opt. Soc. Korea 18, 217–224 (2014).
[Crossref]

A. Zhou, N. Chen, and G. Situ, “Analysis of fourier ptychographic microscopy with half reduced images,” in 2017 International Conference on Optical Instruments and Technology: Optoelectronic Imaging/Spectroscopy and Signal Processing Technology, vol. 10620 (SPIE, Beijing, China, 2018), p. 10620.

A. Zhou, W. Wang, N. Chen, and G. Situ, “Fast light source misalignment correction of Fourier ptychographic microscopy,” in Imaging and Applied Optics 2018, (Orlando, USA, 2018), p. JTh3A.5.

Chen, Q.

Chung, J.

J. Chung, X. Ou, R. P. Kulkarni, and C. Yang, “Counting white blood cells from a blood smear using Fourier ptychographic microscopy,” PLOS One 10, e0133489 (2015).
[Crossref] [PubMed]

A. Williams, J. Chung, X. Ou, G. Zheng, S. Rawal, Z. Ao, R. Datar, C. Yang, and R. Cote, “Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis,” J. Biomed. Opt. 19, 066007 (2014).
[Crossref] [PubMed]

Cote, R.

A. Williams, J. Chung, X. Ou, G. Zheng, S. Rawal, Z. Ao, R. Datar, C. Yang, and R. Cote, “Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis,” J. Biomed. Opt. 19, 066007 (2014).
[Crossref] [PubMed]

Cullis, A. G.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[Crossref] [PubMed]

Datar, R.

A. Williams, J. Chung, X. Ou, G. Zheng, S. Rawal, Z. Ao, R. Datar, C. Yang, and R. Cote, “Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis,” J. Biomed. Opt. 19, 066007 (2014).
[Crossref] [PubMed]

David, C.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[Crossref] [PubMed]

Dobson, B. R.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[Crossref] [PubMed]

Dong, J.

Dong, S.

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, 023903 (2004).
[Crossref] [PubMed]

Fienup, J. R.

Hong, K.

Horstmeyer, R.

R. Horstmeyer, X. Ou, G. Zheng, P. Willems, and C. Yang, “Digital pathology with Fourier ptychography,” Comput. Med. Imaging Graph. 42, 38–43 (2015).
[Crossref]

X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38, 4845–4848 (2013).
[Crossref] [PubMed]

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

Humphry, M.

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

Hurst, A. C.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[Crossref] [PubMed]

Jefimovs, K.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[Crossref] [PubMed]

Johnson, I.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[Crossref] [PubMed]

Kraus, B.

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

Kulkarni, R. P.

J. Chung, X. Ou, R. P. Kulkarni, and C. Yang, “Counting white blood cells from a blood smear using Fourier ptychographic microscopy,” PLOS One 10, e0133489 (2015).
[Crossref] [PubMed]

Lee, B.

Li, G.

Li, X.

Maiden, A.

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

Maiden, A. M.

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

Ou, X.

R. Horstmeyer, X. Ou, G. Zheng, P. Willems, and C. Yang, “Digital pathology with Fourier ptychography,” Comput. Med. Imaging Graph. 42, 38–43 (2015).
[Crossref]

J. Chung, X. Ou, R. P. Kulkarni, and C. Yang, “Counting white blood cells from a blood smear using Fourier ptychographic microscopy,” PLOS One 10, e0133489 (2015).
[Crossref] [PubMed]

X. Ou, G. Zheng, and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22, 4960–4972 (2014).
[Crossref] [PubMed]

A. Williams, J. Chung, X. Ou, G. Zheng, S. Rawal, Z. Ao, R. Datar, C. Yang, and R. Cote, “Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis,” J. Biomed. Opt. 19, 066007 (2014).
[Crossref] [PubMed]

X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38, 4845–4848 (2013).
[Crossref] [PubMed]

Pfeiffer, F.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[Crossref] [PubMed]

Ramchandran, K.

Rawal, S.

A. Williams, J. Chung, X. Ou, G. Zheng, S. Rawal, Z. Ao, R. Datar, C. Yang, and R. Cote, “Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis,” J. Biomed. Opt. 19, 066007 (2014).
[Crossref] [PubMed]

Rodenburg, J.

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

Rodenburg, J. M.

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

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[Crossref] [PubMed]

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

J. M. Rodenburg and R. H. T. Bates, “The theory of super-resolution electron microscopy via wrigner-distribution deconvolution,” Philos. Transactions Royal Soc. A. 339, 521–553 (1992).
[Crossref]

Sarahan, M.

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

Situ, G.

A. Zhou, N. Chen, H. Wang, and G. Situ, “Analysis of fourier ptychographic microscopy with half of the captured images,” J. Opt. 20, 095701 (2018).
[Crossref]

A. Zhou, N. Chen, and G. Situ, “Analysis of fourier ptychographic microscopy with half reduced images,” in 2017 International Conference on Optical Instruments and Technology: Optoelectronic Imaging/Spectroscopy and Signal Processing Technology, vol. 10620 (SPIE, Beijing, China, 2018), p. 10620.

A. Zhou, W. Wang, N. Chen, and G. Situ, “Fast light source misalignment correction of Fourier ptychographic microscopy,” in Imaging and Applied Optics 2018, (Orlando, USA, 2018), p. JTh3A.5.

Soltanolkotabi, M.

Sun, J.

Tang, G.

Tian, L.

Waller, L.

Wang, H.

A. Zhou, N. Chen, H. Wang, and G. Situ, “Analysis of fourier ptychographic microscopy with half of the captured images,” J. Opt. 20, 095701 (2018).
[Crossref]

Wang, W.

A. Zhou, W. Wang, N. Chen, and G. Situ, “Fast light source misalignment correction of Fourier ptychographic microscopy,” in Imaging and Applied Optics 2018, (Orlando, USA, 2018), p. JTh3A.5.

Willems, P.

R. Horstmeyer, X. Ou, G. Zheng, P. Willems, and C. Yang, “Digital pathology with Fourier ptychography,” Comput. Med. Imaging Graph. 42, 38–43 (2015).
[Crossref]

Williams, A.

A. Williams, J. Chung, X. Ou, G. Zheng, S. Rawal, Z. Ao, R. Datar, C. Yang, and R. Cote, “Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis,” J. Biomed. Opt. 19, 066007 (2014).
[Crossref] [PubMed]

Yang, C.

R. Horstmeyer, X. Ou, G. Zheng, P. Willems, and C. Yang, “Digital pathology with Fourier ptychography,” Comput. Med. Imaging Graph. 42, 38–43 (2015).
[Crossref]

J. Chung, X. Ou, R. P. Kulkarni, and C. Yang, “Counting white blood cells from a blood smear using Fourier ptychographic microscopy,” PLOS One 10, e0133489 (2015).
[Crossref] [PubMed]

X. Ou, G. Zheng, and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22, 4960–4972 (2014).
[Crossref] [PubMed]

A. Williams, J. Chung, X. Ou, G. Zheng, S. Rawal, Z. Ao, R. Datar, C. Yang, and R. Cote, “Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis,” J. Biomed. Opt. 19, 066007 (2014).
[Crossref] [PubMed]

X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38, 4845–4848 (2013).
[Crossref] [PubMed]

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

Yeh, L.-H.

Yeom, J.

Zhang, Y.

Zheng, G.

R. Horstmeyer, X. Ou, G. Zheng, P. Willems, and C. Yang, “Digital pathology with Fourier ptychography,” Comput. Med. Imaging Graph. 42, 38–43 (2015).
[Crossref]

A. Williams, J. Chung, X. Ou, G. Zheng, S. Rawal, Z. Ao, R. Datar, C. Yang, and R. Cote, “Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis,” J. Biomed. Opt. 19, 066007 (2014).
[Crossref] [PubMed]

G. Zheng, “Breakthroughs in photonics 2013: Fourier ptychographic imaging,” IEEE Photonics J. 6, 1–7 (2014).

X. Ou, G. Zheng, and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22, 4960–4972 (2014).
[Crossref] [PubMed]

Z. Bian, S. Dong, and G. Zheng, “Adaptive system correction for robust Fourier ptychographic imaging,” Opt. Express 21, 32400–32410 (2013).
[Crossref]

X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38, 4845–4848 (2013).
[Crossref] [PubMed]

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

G. Zheng, “Fourier ptychographic imaging,” in Photonics Conference (IPC), 2015, (IEEE, 2015), pp. 20–21.

Zhong, J.

Zhou, A.

A. Zhou, N. Chen, H. Wang, and G. Situ, “Analysis of fourier ptychographic microscopy with half of the captured images,” J. Opt. 20, 095701 (2018).
[Crossref]

A. Zhou, N. Chen, and G. Situ, “Analysis of fourier ptychographic microscopy with half reduced images,” in 2017 International Conference on Optical Instruments and Technology: Optoelectronic Imaging/Spectroscopy and Signal Processing Technology, vol. 10620 (SPIE, Beijing, China, 2018), p. 10620.

A. Zhou, W. Wang, N. Chen, and G. Situ, “Fast light source misalignment correction of Fourier ptychographic microscopy,” in Imaging and Applied Optics 2018, (Orlando, USA, 2018), p. JTh3A.5.

Zuo, C.

Appl. Opt. (1)

Biomed. Opt. Express (2)

Comput. Med. Imaging Graph. (1)

R. Horstmeyer, X. Ou, G. Zheng, P. Willems, and C. Yang, “Digital pathology with Fourier ptychography,” Comput. Med. Imaging Graph. 42, 38–43 (2015).
[Crossref]

IEEE Photonics J. (1)

G. Zheng, “Breakthroughs in photonics 2013: Fourier ptychographic imaging,” IEEE Photonics J. 6, 1–7 (2014).

J. Biomed. Opt. (1)

A. Williams, J. Chung, X. Ou, G. Zheng, S. Rawal, Z. Ao, R. Datar, C. Yang, and R. Cote, “Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis,” J. Biomed. Opt. 19, 066007 (2014).
[Crossref] [PubMed]

J. Opt. (1)

A. Zhou, N. Chen, H. Wang, and G. Situ, “Analysis of fourier ptychographic microscopy with half of the captured images,” J. Opt. 20, 095701 (2018).
[Crossref]

J. Opt. Soc. Korea (1)

Nat. Photonics (1)

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

Opt. Express (3)

Opt. Lett. (1)

Philos. Transactions Royal Soc. A. (1)

J. M. Rodenburg and R. H. T. Bates, “The theory of super-resolution electron microscopy via wrigner-distribution deconvolution,” Philos. Transactions Royal Soc. A. 339, 521–553 (1992).
[Crossref]

Phys. Rev. Lett. (2)

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

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[Crossref] [PubMed]

PLOS One (1)

J. Chung, X. Ou, R. P. Kulkarni, and C. Yang, “Counting white blood cells from a blood smear using Fourier ptychographic microscopy,” PLOS One 10, e0133489 (2015).
[Crossref] [PubMed]

Ultramicroscopy (2)

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

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

Other (3)

A. Zhou, N. Chen, and G. Situ, “Analysis of fourier ptychographic microscopy with half reduced images,” in 2017 International Conference on Optical Instruments and Technology: Optoelectronic Imaging/Spectroscopy and Signal Processing Technology, vol. 10620 (SPIE, Beijing, China, 2018), p. 10620.

A. Zhou, W. Wang, N. Chen, and G. Situ, “Fast light source misalignment correction of Fourier ptychographic microscopy,” in Imaging and Applied Optics 2018, (Orlando, USA, 2018), p. JTh3A.5.

G. Zheng, “Fourier ptychographic imaging,” in Photonics Conference (IPC), 2015, (IEEE, 2015), pp. 20–21.

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Figures (9)

Fig. 1
Fig. 1 The imaging process of the FPM.
Fig. 2
Fig. 2 The experimental setup (a) with the installation manual of the LED array on the microscope (b), and the adjust method of the central LED (c) along the optical axis.
Fig. 3
Fig. 3 The reconstructions influenced by the global shift of the LED array in the FPM demonstrated by several segments reconstruction (b)–(e) located at different positions in the original captured image (a).
Fig. 4
Fig. 4 A simulated reconstruction with a global shift in the FPM. Amplitude (a) and phase (b) profiles of the object and the reconstructed amplitude (c) and phase (d) profiles with a global shift.
Fig. 5
Fig. 5 The flow chart of the mcFPM.
Fig. 6
Fig. 6 Experimental results of a USAF resolution target. Two segments (a) and (e), which are the enlargement of the parts within the yellow and blue box in the original captured image (d), and their corresponding reconstructions using the conventional FPM without position correction (b) and (f), and the proposed mcFPM (c) and (g).
Fig. 7
Fig. 7 The reconstructed wide FOV and HR images using the conventional FPM without any position correction (a) and the mcFPM (b).
Fig. 8
Fig. 8 The reconstructed results using FPM without position correction (a), the conventional SA method (b), pcFPM (c), mcFPM I (d), mcFPM II (e), and mcFPM III (f) respectively.
Fig. 9
Fig. 9 The reconstructed results using (a) mcFPM and (b) modified mcFPM.

Tables (2)

Tables Icon

Table 1 Time Cost Comparison of the Methods in Fig. 8

Tables Icon

Table 2 Reconstructed Misalignment Parameters of the Different Segments in Fig. 3, Using Modified mcFPM

Equations (15)

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A o u t p u t ( x , y ) = ( A o b j e c t ( x , y ) e i k x m , n x + i k y m , n y ) h ( x , y ) ,
G o u t p u t ( k x , k y ) = G o b j e c t ( k x k x m , n , k y k y m , n ) H ( k x , k y ) ,
I c a p t u r e d m , n ( x , y ) = | 1 { G o u t p u t ( k x , k y ) } | 2
k x m , n = 2 π λ x o x m , n ( x o x m , n ) 2 + ( y o y m , n ) 2 + s 2 , k y m , n = 2 π λ y o y m , n ( x o x m , n ) 2 + ( y o y m , n ) 2 + s 2 ,
x 0 x m , n = x i / M m d Δ x , y 0 y m , n = y i / M n d Δ y ,
ψ j m , n ( k x , k y ) = O j ( k x k x m , n , k y k y m , n ) P j ( k x , k y ) ,
ϕ j m , n ( x , y ) = I c a p t u r e d m , n ( x , y ) | ψ j m , n ( x , y ) | 2 ψ j m , n ( x , y ) ,
ψ j m , n ( x , y ) = 1 { ψ j m , n ( k x , k y ) } .
Φ ( k x , k y ) = { ϕ j m , n ( x , y ) } .
{ O j + 1 ( k x , k y ) = O j ( k x , k y ) + | P j ( k x + k x m , n , k y + k y m , n ) | P j * ( k x + k x m , n , k y + k y m , n ) | P j ( k x , k y ) | m a x ( | P j ( k x + k x m , n , k y + k y m , n ) | 2 + δ 1 ) Δ 1 , P j + 1 ( k x , k y ) = P j ( k x , k y ) + | O j ( k x k x m , n , k y k y m , n ) | O j * ( k x k x m , n , k y k y m , n ) | O j ( k x , k y ) | m a x ( | O j ( k x k x m , n , k y k y m , n ) | 2 + δ 2 ) Δ 2 ,
{ Δ 1 = Φ ( k x + k x m , n , k y + k y m , n ) O j ( k x , k y ) P j ( k x + k x m , n , k y + k y m , n ) , Δ 2 = Φ ( k x , k y ) O j ( k x k x m , n , k y k y m , n ) P j ( k x , k y ) .
E 1 = min Δ k x m , n , Δ k y m , n x , y | I c a p t u r e d m , n ( x , y ) | ψ j m , n ( x , y , Δ k x m , n , Δ k y m , n ) | 2 | 2
{ k x m , n = k x m , n + Δ k x m , n , k y m , n = k y m , n + Δ k y m , n .
{ k x m , n = 2 π λ x i / M m d Δ x ( x i / M m d Δ x ) 2 + ( y i / M n d Δ y ) 2 + s 2 , k y m , n = 2 π λ y i / M n d Δ y ( x i / M m d Δ x ) 2 + ( y i / M n d Δ y ) 2 + s 2 .
E 2 = min Δ x , Δ y m , n x , y | I c a p t u r e d m , n ( x , y ) I F P M m , n ( x , y , Δ x , Δ y ) | 2 ,

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