Abstract

Fourier ptychographic microscopy (FPM) is a newly developed super-resolution technique, which employs angularly varying illuminations and a phase retrieval algorithm to surpass the diffraction limit of a low numerical aperture (NA) objective lens. In current FPM imaging platforms, accurate knowledge of LED matrix’s position is critical to achieve good recovery quality. Furthermore, considering such a wide field-of-view (FOV) in FPM, different regions in the FOV have different sensitivity of LED positional misalignment. In this work, we introduce an iterative method to correct position errors based on the simulated annealing (SA) algorithm. To improve the efficiency of this correcting process, large number of iterations for several images with low illumination NAs are firstly implemented to estimate the initial values of the global positional misalignment model through non-linear regression. Simulation and experimental results are presented to evaluate the performance of the proposed method and it is demonstrated that this method can both improve the quality of the recovered object image and relax the LED elements’ position accuracy requirement while aligning the FPM imaging platforms.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref] [PubMed]
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2015 (4)

2014 (4)

2013 (5)

2012 (1)

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

2011 (2)

A. Shenfield and J. M. Rodenburg, “Evolutionary determination of experimental parameters for ptychographical imaging,” J. Appl. Phys. 109(12), 124510 (2011).
[Crossref]

A. E. Tippie, A. Kumar, and J. R. Fienup, “High-resolution synthetic-aperture digital holography with digital phase and pupil correction,” Opt. Express 19(13), 12027–12038 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (2)

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref] [PubMed]

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. Garcia-Martinez, and J. Garcia, “Synthetic aperture superresolution with multiple offaxis holograms,” J. Opt. Soc. Am. A 23(12), 3162–3170 (2006).
[Crossref]

2004 (2)

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

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

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.

Bean, R.

Beckers, M.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[Crossref] [PubMed]

Berenguer, F.

Bian, L.

Bian, Z.

Bowers, C. W.

Brueck, S. R.

Bunk, O.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

Chen, B.

Chen, F.

Chen, M.

Chen, Q.

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).

Dai, Q.

Dean, B. H.

Di, J.

Diaz, A.

Dierolf, M.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

Dong, S.

Fan, Q.

Faulkner, H. M. L.

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

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

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.

Garcia, J.

Garcia-Martinez, P.

Giewekemeyer, K.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[Crossref] [PubMed]

Gonsalves, R. A.

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

Gorniak, T.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[Crossref] [PubMed]

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.

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).

Humphry, M. J.

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

Jiang, H.

Kraus, B.

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

Kumar, A.

Kuznetsova, Y.

Li, X.

Liang, R.

Liu, Z.

Maiden, A. M.

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. 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(10), 1256–1262 (2009).
[Crossref] [PubMed]

Menzel, A.

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.

Peterson, I.

Pfeiffer, F.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

Ramchandran, K.

Robinson, I. K.

Rodenburg, J. M.

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21(11), 13592–13606 (2013).
[Crossref] [PubMed]

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

A. Shenfield and J. M. Rodenburg, “Evolutionary determination of experimental parameters for ptychographical imaging,” J. Appl. Phys. 109(12), 124510 (2011).
[Crossref]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref] [PubMed]

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

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.

Rosenhahn, A.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[Crossref] [PubMed]

Salahieh, B.

Salditt, T.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[Crossref] [PubMed]

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]

Sarahan, M. C.

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

Schwarz, C. J.

Seber, G. A. F.

G. A. F. Seber and C.J. Wild, “Nonlinear regression,” WileyNew York770, 376–385 (1989).

Senkbeil, T.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[Crossref] [PubMed]

Shenfield, A.

A. Shenfield and J. M. Rodenburg, “Evolutionary determination of experimental parameters for ptychographical imaging,” J. Appl. Phys. 109(12), 124510 (2011).
[Crossref]

Shiradkar, R.

Situ, G.

Sun, 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).

Sun, W.

Suo, J.

Thibault, P.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

Tian, L.

Tippie, A. E.

Vila-Comamala, J.

Waller, L.

Wild, C.J.

G. A. F. Seber and C.J. Wild, “Nonlinear regression,” WileyNew York770, 376–385 (1989).

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, 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, 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)

Appl. Phys. Lett. (1)

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

Biomed. Opt. Express (2)

J. Appl. Phys. (1)

A. Shenfield and J. M. Rodenburg, “Evolutionary determination of experimental parameters for ptychographical imaging,” J. Appl. Phys. 109(12), 124510 (2011).
[Crossref]

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]

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 (6)

Opt. Lett. (6)

Optica (1)

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 (4)

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

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref] [PubMed]

Other (1)

G. A. F. Seber and C.J. Wild, “Nonlinear regression,” WileyNew York770, 376–385 (1989).

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Figures (8)

Fig. 1
Fig. 1 An example of the segments in the FOV which are very sensitive to the positional misalignment in the FPM platform. (a) the frequency apertures’ positions in the Fourier domain; (b1)–(b3) are the captured LR image, the recovered HR intensity image, and the recovered HR phase distribution without positional misalignment; (c1)–(c3) are the captured LR image, the recovered HR intensity image, and the recovered HR phase distribution with positional misalignment.
Fig. 2
Fig. 2 The diagram of a misaligned FPM setup.
Fig. 3
Fig. 3 Block diagram of the pcFPM method.
Fig. 4
Fig. 4 The reconstruction results for different segments in the FOV using ordinary FPM. (a1) and (a2) are the ideal HR intensity and phase profiles; (b1)–(b4) show the recovered HR intensity and phase profiles, the central parts of the recovered frequency spectrum and the frequency apertures’ positions respectively with positional misalignment when the recovered segment in in the center of the FOV; (c1)–(c4) show the recovered HR intensity and phase profiles, the central parts of the recovered frequency spectrum and the frequency apertures’ positions respectively with the same misalignment condition when the recovered segment is away from the center of the FOV with (100µm,200µm) shifting along x-axis and y-axis.
Fig. 5
Fig. 5 The recovered results using pcFPM under the same misalignment condition as in Fig. 4(c). (a)–(d) show the recovered HR intensity and phase profiles, the recovered frequency spectrum and the frequency apertures’ positions respectively with the same misalignment condition.
Fig. 6
Fig. 6 The performance of pcFPM under different noise conditions. (a)–(d) show the RMSE of four position factors (θxy,h) during correcting iterations of pcFPM, under five noise conditions with standard deviation σ = 0,0.01,0.02,0.04,0.08; (e) and (f) show the RMSE of the reconstructed intensity and phase profiles (I and ϕ) under four reconstruction situations with noise increasing.
Fig. 7
Fig. 7 Experimental results of two segments in a USAF target recovered with conventional FPM and pcFPM. (a) presents the FOV of the USAF resolution board recorded by the camera; (b1)–(b3) show the the enlargements of one small segment, the reconstructed HR intensity images with conventional FPM and pcFPM respectively; (c1)–(c3) show the the enlargements of another small segment, the reconstructed HR intensity images with conventional FPM and pcFPM respectively.
Fig. 8
Fig. 8 Experimental results of two segments in a sample of stained human kidney vessel cells reconstructed with conventional FPM and pcFPM. (a) presents the FOV of the specimen recorded by the camera; (b1)–(b3) show the the enlargements of one small segment, the reconstructed HR complex images with conventional FPM and pcFPM respectively; (c1)–(c3) show the the enlargements of another small segment, the reconstructed HR complex images with conventional FPM and pcFPM respectively.

Equations (9)

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x m , n i = d L E D [ cos ( θ ) m + sin ( θ ) n ] + Δ x , y m , n i = d L E D [ sin ( θ ) m + cos ( θ ) n ] + Δ x ,
u m , n = 2 π λ x o x m , n i ( x o x m , n i ) 2 + ( y o y m , n i ) 2 + h 2 , v m , n = 2 π λ y o y m , n i ( x o x m , n i ) 2 + ( y o y m , n i ) 2 + h 2 ,
S j = { { ( m , n ) | m = 2 , , 2 , n = 2 , , 2 } j 9 { ( m , n ) | m = 7 , , 7 , n = 7 , , 7 } else .
O r , j , m , n e ( u , v ) = O j ( u ( u m , n + Δ u r , m , n ) , v ( v m , n + Δ v r , m , n ) ) P j ( u , v ) ,
E ( r ) = x , y ( | o r , j , m , n e ( x , y ) | 2 I m , n c ( x , y ) ) 2 .
s = argmin [ E ( r ) ] , u m , n u = u m , n + Δ u s , m , n , v m , n u = v m , n + Δ v s , m , n .
Δ O m , n ( u , v ) = { I m , n c ( x , y ) o s , j , m , n e ( x , y ) | o s , j , m , n e ( x , y ) | } o s , j , m , n e ( u , v ) .
O j ( u u m , n , v v m , n ) = O j ( u u m , n u , v v m , n u ) + | P j ( u , v ) | P j * ( u , v ) | P j ( u , v ) | max ( | P j ( u , v ) | 2 + δ 1 ) Δ O m , n ( u , v ) , P j ( u , v ) = P j ( u , v ) + | O j ( u u m , n u , v v m , n u ) | O j * ( u u m , n u , v v m , n u ) | O j ( u u m , n u , v v m , n u ) | max ( | O j ( u u m , n u , v v m , n u ) | 2 + δ 2 ) Δ O m , n ( u , v ) .
Q ( θ , Δ x , Δ y , h ) = m , n [ ( u m , n ( θ , Δ x , Δ y , h ) u m , n u ) 2 + ( v m , n ( θ , Δ x , Δ y , h ) v m , n u ) 2 ] , ( θ , Δ x , Δ y , h ) u = argmin [ Q ( θ , Δ x , Δ y , h ) ] ,

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