Abstract

Fourier ptychographic microscopy (FPM) is a new computational super-resolution approach, which can obtain not only the correct object function, but also the pupil aberration, the LED misalignment, and beyond. Although many state-mixed FPM techniques have been proposed to achieve higher data acquisition efficiency and recovery accuracy in the past few years, little is known that their reconstruction performance highly depends on the data redundancy in both object and frequency domains. Generally, at least 35% aperture overlapping percentage in the Fourier domain is needed for a successful reconstruction using ordinary FPM method. However, the data redundancy requirements for those state-mixed FPM schemes are largely remained unexplored until now. In this paper, we explore the spatial and spectrum data redundancy requirements for the FPM recovery process to introduce sampling criteria for the conventional and state-mixed FPM techniques in both object and frequency space. Moreover, an upsampled FPM method is proposed to solve the pixel aliasing problem, and an alternative illumination-angle subsampled FPM scheme is introduced to get rid of the complexity of decoherence and achieve the expected recovery quality with reduced data quantity. All the proposed methods and sampling criteria are validated with both simulations and experiments, and our results show that state-mixed techniques cannot provide a significant performance advantage since they are much more sensitive to data redundancy. This paper provides both the guidelines for designing the most suitable FPM platform and the insights for the capabilities and limitations of the FPM approach.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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2016 (1)

2015 (3)

2014 (6)

2013 (5)

Z. Bian, S. Dong, and G. Zheng, “Adaptive system correction for robust Fourier ptychographic imaging,” Opt. Express 21(26), 32400–32410 (2013).
[Crossref]

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494(7435), 68–71 (2013).
[Crossref] [PubMed]

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[Crossref]

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

X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38(22), 4845–4848 (2013).
[Crossref] [PubMed]

2011 (1)

2010 (2)

2008 (3)

2006 (2)

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture fourier holographic optical microscopy,” Phys. Rev. Lett. 97(16), 168102 (2006).
[Crossref] [PubMed]

V. Mico, Z. Zalevsky, P. Garcła-Martłnez, and J. Garcła, “Synthetic aperture superresolution with multiple offaxis holograms,” J. Opt. Soc. Am. A 23(12), 3162–3170 (2006).
[Crossref]

2004 (1)

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]

2003 (2)

2001 (1)

L. Allen and M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1), 65–75 (2001).
[Crossref]

1993 (1)

1982 (1)

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 215829 (1982).
[Crossref]

Alexandrov, S. A.

T. Gutzler, T. R. Hillman, S. A. Alexandrov, and D. D. Sampson, “Coherent aperture-synthesis, wide-field, high-resolution holographic microscopy of biological tissue,” Opt. Lett. 35(8), 1136–1138 (2010).
[Crossref] [PubMed]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture fourier holographic optical microscopy,” Phys. Rev. Lett. 97(16), 168102 (2006).
[Crossref] [PubMed]

Allen, L.

L. Allen and M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1), 65–75 (2001).
[Crossref]

Bao, P.

Batey, D. J.

D. J. Batey, T. B. Edo, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Reciprocal-space up-sampling from real-space oversampling in x-ray ptychography,” Phys. Rev. A 89(4), 043812 (2014).
[Crossref]

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref] [PubMed]

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[Crossref]

Bian, Z.

Bowers, C. W.

Brueck, S. R.

Chen, M.

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]

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).

Claus, D.

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref] [PubMed]

Dean, B. H.

Di, J.

Dong, S.

Edo, T. B.

D. J. Batey, T. B. Edo, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Reciprocal-space up-sampling from real-space oversampling in x-ray ptychography,” Phys. Rev. A 89(4), 043812 (2014).
[Crossref]

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[Crossref]

Fan, Q.

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]

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).

Fienup, J. R.

Garcla, J.

Garcla-Martlnez, P.

Gonsalves, R. A.

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 215829 (1982).
[Crossref]

Granero, L.

Guizar-Sicairos, M.

Gutzler, T.

T. Gutzler, T. R. Hillman, S. A. Alexandrov, and D. D. Sampson, “Coherent aperture-synthesis, wide-field, high-resolution holographic microscopy of biological tissue,” Opt. Lett. 35(8), 1136–1138 (2010).
[Crossref] [PubMed]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture fourier holographic optical microscopy,” Phys. Rev. Lett. 97(16), 168102 (2006).
[Crossref] [PubMed]

Hillman, T. R.

T. Gutzler, T. R. Hillman, S. A. Alexandrov, and D. D. Sampson, “Coherent aperture-synthesis, wide-field, high-resolution holographic microscopy of biological tissue,” Opt. Lett. 35(8), 1136–1138 (2010).
[Crossref] [PubMed]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture fourier holographic optical microscopy,” Phys. Rev. Lett. 97(16), 168102 (2006).
[Crossref] [PubMed]

Horstmeyer, R.

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

X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38(22), 4845–4848 (2013).
[Crossref] [PubMed]

Hu, Y.

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).

Jiang, H.

Kumar, A.

Kuznetsova, Y.

Li, X.

Liang, R.

Liu, Z.

Maiden, A. M.

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[Crossref]

Menzel, A.

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494(7435), 68–71 (2013).
[Crossref] [PubMed]

Mic, V.

Mico, V.

Milster, T.

Nanda, P.

Osten, W.

Ou, X.

Oxley, M.

L. Allen and M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1), 65–75 (2001).
[Crossref]

Pacheco, S.

Pedrini, G.

Pešic, Z. D.

D. J. Batey, T. B. Edo, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Reciprocal-space up-sampling from real-space oversampling in x-ray ptychography,” Phys. Rev. A 89(4), 043812 (2014).
[Crossref]

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[Crossref]

Ramchandran, K.

Rau, C.

D. J. Batey, T. B. Edo, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Reciprocal-space up-sampling from real-space oversampling in x-ray ptychography,” Phys. Rev. A 89(4), 043812 (2014).
[Crossref]

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[Crossref]

Rodenburg, J. M.

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref] [PubMed]

D. J. Batey, T. B. Edo, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Reciprocal-space up-sampling from real-space oversampling in x-ray ptychography,” Phys. Rev. A 89(4), 043812 (2014).
[Crossref]

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[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]

Rodriguez, J. J.

Salahieh, B.

Sampson, D. D.

T. Gutzler, T. R. Hillman, S. A. Alexandrov, and D. D. Sampson, “Coherent aperture-synthesis, wide-field, high-resolution holographic microscopy of biological tissue,” Opt. Lett. 35(8), 1136–1138 (2010).
[Crossref] [PubMed]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture fourier holographic optical microscopy,” Phys. Rev. Lett. 97(16), 168102 (2006).
[Crossref] [PubMed]

Schwarz, C. J.

Shiradkar, R.

Sun, J.

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]

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, W.

Thibault, P.

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494(7435), 68–71 (2013).
[Crossref] [PubMed]

Tian, L.

Tippie, A. E.

Wagner, U.

D. J. Batey, T. B. Edo, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Reciprocal-space up-sampling from real-space oversampling in x-ray ptychography,” Phys. Rev. A 89(4), 043812 (2014).
[Crossref]

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[Crossref]

Waigh, T. A.

D. J. Batey, T. B. Edo, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Reciprocal-space up-sampling from real-space oversampling in x-ray ptychography,” Phys. Rev. A 89(4), 043812 (2014).
[Crossref]

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[Crossref]

Waller, L.

Yang, C.

Yeh, L. H.

Zalevsky, Z.

Zhang, F.

Zhang, J.

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, P.

Zhang, Y.

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]

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).

Zhao, J.

Zheng, G.

Zhong, J.

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).
[Crossref]

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).

Appl. Opt. (3)

Biomed. Opt. Express (3)

J. Opt. Soc. Am. A (2)

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]

Nature (1)

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494(7435), 68–71 (2013).
[Crossref] [PubMed]

Opt. Commun. (1)

L. Allen and M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1), 65–75 (2001).
[Crossref]

Opt. Eng. (1)

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 215829 (1982).
[Crossref]

Opt. Express (5)

Opt. Lett. (5)

Optica (1)

Phys. Rev. A (2)

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[Crossref]

D. J. Batey, T. B. Edo, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, and J. M. Rodenburg, “Reciprocal-space up-sampling from real-space oversampling in x-ray ptychography,” Phys. Rev. A 89(4), 043812 (2014).
[Crossref]

Phys. Rev. Lett. (2)

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture fourier holographic optical microscopy,” Phys. Rev. Lett. 97(16), 168102 (2006).
[Crossref] [PubMed]

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]

Proc. SPIE (1)

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).

Ultramicroscopy (1)

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref] [PubMed]

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Figures (12)

Fig. 1
Fig. 1 Simulations of the pixel aliasing problem in the ordinary FPM method.
Fig. 2
Fig. 2 Comparison of the ordinary FPM, subsampled FPM, upsampled FPM schemes using simulations.
Fig. 3
Fig. 3 Experimental results of the ordinary FPM, subsampled FPM, upsampled FPM schemes.
Fig. 4
Fig. 4 Comparison of the recovery qualities with different spatial-sampling-ratio Rcam and aperture-overlapping-rate Roverlap using simulations.
Fig. 5
Fig. 5 Experimental recovered results of a USAF target with different spatial-sampling-ratio Rcam and aperture-overlapping-rate Roverlap.
Fig. 6
Fig. 6 Comparison of the illumination-angle multiplexed FPM with differnt multiplexing strategies and the illumination-angle subsampled FPM with different aperture-overlapping-rate Roverlap using simulations.
Fig. 7
Fig. 7 Experimental results a USAF target recovered using the illumination-angle multiplexed FPM with differnt multiplexing strategies and the illumination-angle subsampled FPM with different aperture-overlapping-rate Roverlap respectively.
Fig. 8
Fig. 8 Simulation results of the ordinary wavelength multiplexed FPM and corrected wavelength multiplexed FPM.
Fig. 9
Fig. 9 Comparison of the corrected wavelength multiplexed FPM and the illumination-angle subsampled FPM with different aperture-overlapping-rate Roverlap using simulations.
Fig. 10
Fig. 10 Experimental results a sample of stained human kidney vessel cells recovered using the corrected wavelength multiplexed FPM and the illumination-angle subsampled FPM with different aperture-overlapping-rate Roverlap respectively.
Fig. 11
Fig. 11 Diagrams of the definitions of Rcam and Roverlap and examples of different Roverlap and Roverlap.
Fig. 12
Fig. 12 Diagrams of the FPM platform and different illumination-angle subsampling conditions.

Equations (3)

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R c a m = f c a m f o b j = λ N A M a g 2 Δ x c a m .
R L E D = f o b j f L E D = N A ( D L E D ) 2 + h 2 D L E D .
R overlap = { 1 π [ 2 a r c c o s ( 1 2 R L E D ) 1 R L E D 1 ( 1 2 R L E D ) 2 ] , R L E D > 1 2 0 , else .

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