Abstract

Fourier ptychography captures intensity images with varying source patterns (illumination angles) in order to computationally reconstruct large space-bandwidth-product images. Accurate knowledge of the illumination angles is necessary for good image quality; hence, calibration methods are crucial, despite often being impractical or slow. Here, we propose a fast, robust, and accurate self-calibration algorithm that uses only experimentally collected data and general knowledge of the illumination setup. First, our algorithm makes a fast direct estimate of the brightfield illumination angles based on image processing. Then, a more computationally intensive spectral correlation method is used inside the iterative solver to further refine the angle estimates of both brightfield and darkfield images. We demonstrate our method for correcting large and small misalignment artifacts in 2D and 3D Fourier ptychography with different source types: an LED array, a galvo-steered laser, and a high-NA quasi-dome LED illuminator.

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

Full Article  |  PDF Article
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References

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2017 (5)

J. Dou, Z. Gao, J. Ma, C. Yuan, Z. Yang, and L. Wang, “Iterative autofocusing strategy for axial distance error correction in ptychography,” Opt. Lasers Eng. 98, 56–61 (2017).
[Crossref]

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22, 096005 (2017).
[Crossref]

S. Kang, P. Kang, S. Jeong, Y. Kwon, T. D. Yang, J. H. Hong, M. Kim, K.-D. Song, J. H. Park, J. H. Lee, M. J. Kim, K. H. Kim, and W. Choi, “High-resolution adaptive optical imaging within thick scattering media using closed-loop accumulation of single scattering,” Nat. Commun. 8, 2157 (2017).
[Crossref]

J. Sun, C. Zuo, L. Zhang, and Q. Chen, “Resolution-enhanced Fourier ptychographic microscopy based on high-numerical-aperture illuminations,” Sci. Rep. 7, 1187 (2017).
[Crossref]

J. Liu, Y. Li, W. Wang, H. Zhang, Y. Wang, J. Tan, and C. Liu, “Stable and robust frequency domain position compensation strategy for Fourier ptychographic microscopy,” Opt. Express 25, 28053–28067 (2017).
[Crossref]

2016 (9)

J. Chung, J. Kim, X. Ou, R. Horstmeyer, and C. Yang, “Wide field-of-view fluorescence image deconvolution with aberration-estimation from Fourier ptychography,” Biomed. Opt. Express 7, 352–368 (2016).
[Crossref]

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Efficient positional misalignment correction method for Fourier ptychographic microscopy,” Biomed. Opt. Express 7, 1336–1350 (2016).
[Crossref]

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Sampling criteria for Fourier ptychographic microscopy in object space and frequency space,” Opt. Express 24, 15765–15781 (2016).
[Crossref]

R. Horstmeyer, J. Chung, X. Ou, G. Zheng, and C. Yang, “Diffraction tomography with Fourier ptychography,” Optica 3, 827–835 (2016).
[Crossref]

S. Sen, I. Ahmed, B. Aljubran, A. A. Bernussi, and L. G. de Peralta, “Fourier ptychographic microscopy using an infrared-emitting hemispherical digital condenser,” Appl. Opt. 55, 6421–6427 (2016).
[Crossref]

M. Chen, L. Tian, and L. Waller, “3D differential phase contrast microscopy,” Biomed. Opt. Express 7, 3940–3950 (2016).
[Crossref]

L. Bian, G. Zheng, K. Guo, J. Suo, C. Yang, F. Chen, and Q. Dai, “Motion-corrected Fourier ptychography,” Biomed. Opt. Express 7, 4543–4553 (2016).
[Crossref]

J. Chung, H. Lu, X. Ou, H. Zhou, and C. Yang, “Wide-field Fourier ptychographic microscopy using laser illumination source,” Biomed. Opt. Express 7, 4787–4802 (2016).
[Crossref]

G. Satat, B. Heshmat, D. Raviv, and R. Raskar, “All photons imaging through volumetric scattering,” Sci. Rep. 6, 33946 (2016).
[Crossref]

2015 (7)

2014 (6)

2013 (4)

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]

2011 (1)

2009 (1)

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

2008 (2)

1997 (1)

C. Dammer, P. Leleux, D. Villers, and M. Dosire, “Use of the Hough transform to determine the center of digitized x-ray diffraction patterns,” Nucl. Instrum. Methods Phys. Res. Sect. B 132, 214–220 (1997).
[Crossref]

1993 (1)

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[Crossref]

Ahmed, I.

Aljubran, B.

Barbastathis, G.

Bean, R.

Benk, M.

A. Shanker, A. Wojdyla, G. Gunjala, J. Dong, M. Benk, A. Neureuther, K. Goldberg, and L. Waller, “Off-axis aberration estimation in an EUV microscope using natural speckle,” in Imaging and Applied Optics (Optical Society of America, 2016), paper ITh1F.2.

Berenguer, F.

Bernussi, A. A.

Bian, L.

Bian, Z.

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).

Bunk, O.

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

Cauchie, J.

J. Cauchie, V. Fiolet, and D. Villers, “Optimization of an Hough transform algorithm for the search of a center,” Pattern Recognit. 41, 567–574 (2008).
[Crossref]

Chen, B.

Chen, F.

Chen, M.

Chen, Q.

Choi, W.

S. Kang, P. Kang, S. Jeong, Y. Kwon, T. D. Yang, J. H. Hong, M. Kim, K.-D. Song, J. H. Park, J. H. Lee, M. J. Kim, K. H. Kim, and W. Choi, “High-resolution adaptive optical imaging within thick scattering media using closed-loop accumulation of single scattering,” Nat. Commun. 8, 2157 (2017).
[Crossref]

Chung, J.

Cremer, C.

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[Crossref]

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]

Dai, Q.

Dammer, C.

C. Dammer, P. Leleux, D. Villers, and M. Dosire, “Use of the Hough transform to determine the center of digitized x-ray diffraction patterns,” Nucl. Instrum. Methods Phys. Res. Sect. B 132, 214–220 (1997).
[Crossref]

Dan, D.

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22, 096005 (2017).
[Crossref]

Dasari, R. R.

Davies, E.

E. Davies, Machine Vision: Theory, Algorithms and Practicalities, 3rd ed. (Morgan Kauffmann, 2004).

de Peralta, L. G.

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, 338–343 (2009).
[Crossref]

Dong, J.

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]

A. Shanker, A. Wojdyla, G. Gunjala, J. Dong, M. Benk, A. Neureuther, K. Goldberg, and L. Waller, “Off-axis aberration estimation in an EUV microscope using natural speckle,” in Imaging and Applied Optics (Optical Society of America, 2016), paper ITh1F.2.

Dong, S.

Dosire, M.

C. Dammer, P. Leleux, D. Villers, and M. Dosire, “Use of the Hough transform to determine the center of digitized x-ray diffraction patterns,” Nucl. Instrum. Methods Phys. Res. Sect. B 132, 214–220 (1997).
[Crossref]

Dou, J.

J. Dou, Z. Gao, J. Ma, C. Yuan, Z. Yang, and L. Wang, “Iterative autofocusing strategy for axial distance error correction in ptychography,” Opt. Lasers Eng. 98, 56–61 (2017).
[Crossref]

Eckert, R.

R. Eckert, L. Tian, and L. Waller, “Algorithmic self-calibration of illumination angles in Fourier ptychographic microscopy,” in Imaging and Applied Optics (Optical Society of America, 2016), paper CT2D.3.

Z. Phillips, R. Eckert, and L. Waller, “Quasi-dome: A self-calibrated high-NA LED illuminator for Fourier ptychography,” in Imaging and Applied Optics (Optical Society of America, 2017), paper IW4E.5.

Fan, Q.

Fiolet, V.

J. Cauchie, V. Fiolet, and D. Villers, “Optimization of an Hough transform algorithm for the search of a center,” Pattern Recognit. 41, 567–574 (2008).
[Crossref]

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]

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]

Gao, Z.

J. Dou, Z. Gao, J. Ma, C. Yuan, Z. Yang, and L. Wang, “Iterative autofocusing strategy for axial distance error correction in ptychography,” Opt. Lasers Eng. 98, 56–61 (2017).
[Crossref]

Gesell, L. H.

T. M. Turpin, L. H. Gesell, J. Lapides, and C. H. Price, Theory of the Synthetic Aperture Microscope (1995), Vol. 2566, pp. 1–11.

Goldberg, K.

A. Shanker, A. Wojdyla, G. Gunjala, J. Dong, M. Benk, A. Neureuther, K. Goldberg, and L. Waller, “Off-axis aberration estimation in an EUV microscope using natural speckle,” in Imaging and Applied Optics (Optical Society of America, 2016), paper ITh1F.2.

Gunjala, G.

A. Shanker, A. Wojdyla, G. Gunjala, J. Dong, M. Benk, A. Neureuther, K. Goldberg, and L. Waller, “Off-axis aberration estimation in an EUV microscope using natural speckle,” in Imaging and Applied Optics (Optical Society of America, 2016), paper ITh1F.2.

Guo, K.

Hell, S.

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[Crossref]

Heshmat, B.

G. Satat, B. Heshmat, D. Raviv, and R. Raskar, “All photons imaging through volumetric scattering,” Sci. Rep. 6, 33946 (2016).
[Crossref]

Hong, J. H.

S. Kang, P. Kang, S. Jeong, Y. Kwon, T. D. Yang, J. H. Hong, M. Kim, K.-D. Song, J. H. Park, J. H. Lee, M. J. Kim, K. H. Kim, and W. Choi, “High-resolution adaptive optical imaging within thick scattering media using closed-loop accumulation of single scattering,” Nat. Commun. 8, 2157 (2017).
[Crossref]

Horstmeyer, R.

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]

Illingworth, J.

H. K. Yuen, J. Princen, J. Illingworth, and J. Kittler, “A comparative study of Hough transform methods for circle finding,” in Proceedings of the 5th Alvey Vision Conference, Reading, August31, 1989, pp. 169–174.

Jacobson, M.

M. Jacobson, “Absolute orientation MATLAB package,” in MATLAB Central File Exchange (2015).

Jeong, S.

S. Kang, P. Kang, S. Jeong, Y. Kwon, T. D. Yang, J. H. Hong, M. Kim, K.-D. Song, J. H. Park, J. H. Lee, M. J. Kim, K. H. Kim, and W. Choi, “High-resolution adaptive optical imaging within thick scattering media using closed-loop accumulation of single scattering,” Nat. Commun. 8, 2157 (2017).
[Crossref]

Jiang, H.

Kang, P.

S. Kang, P. Kang, S. Jeong, Y. Kwon, T. D. Yang, J. H. Hong, M. Kim, K.-D. Song, J. H. Park, J. H. Lee, M. J. Kim, K. H. Kim, and W. Choi, “High-resolution adaptive optical imaging within thick scattering media using closed-loop accumulation of single scattering,” Nat. Commun. 8, 2157 (2017).
[Crossref]

Kang, S.

S. Kang, P. Kang, S. Jeong, Y. Kwon, T. D. Yang, J. H. Hong, M. Kim, K.-D. Song, J. H. Park, J. H. Lee, M. J. Kim, K. H. Kim, and W. Choi, “High-resolution adaptive optical imaging within thick scattering media using closed-loop accumulation of single scattering,” Nat. Commun. 8, 2157 (2017).
[Crossref]

Kim, J.

Kim, K. H.

S. Kang, P. Kang, S. Jeong, Y. Kwon, T. D. Yang, J. H. Hong, M. Kim, K.-D. Song, J. H. Park, J. H. Lee, M. J. Kim, K. H. Kim, and W. Choi, “High-resolution adaptive optical imaging within thick scattering media using closed-loop accumulation of single scattering,” Nat. Commun. 8, 2157 (2017).
[Crossref]

Kim, M.

S. Kang, P. Kang, S. Jeong, Y. Kwon, T. D. Yang, J. H. Hong, M. Kim, K.-D. Song, J. H. Park, J. H. Lee, M. J. Kim, K. H. Kim, and W. Choi, “High-resolution adaptive optical imaging within thick scattering media using closed-loop accumulation of single scattering,” Nat. Commun. 8, 2157 (2017).
[Crossref]

Kim, M. J.

S. Kang, P. Kang, S. Jeong, Y. Kwon, T. D. Yang, J. H. Hong, M. Kim, K.-D. Song, J. H. Park, J. H. Lee, M. J. Kim, K. H. Kim, and W. Choi, “High-resolution adaptive optical imaging within thick scattering media using closed-loop accumulation of single scattering,” Nat. Commun. 8, 2157 (2017).
[Crossref]

Kittler, J.

H. K. Yuen, J. Princen, J. Illingworth, and J. Kittler, “A comparative study of Hough transform methods for circle finding,” in Proceedings of the 5th Alvey Vision Conference, Reading, August31, 1989, pp. 169–174.

Kolner, C.

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]

Kuang, C.

Kwon, Y.

S. Kang, P. Kang, S. Jeong, Y. Kwon, T. D. Yang, J. H. Hong, M. Kim, K.-D. Song, J. H. Park, J. H. Lee, M. J. Kim, K. H. Kim, and W. Choi, “High-resolution adaptive optical imaging within thick scattering media using closed-loop accumulation of single scattering,” Nat. Commun. 8, 2157 (2017).
[Crossref]

Lapides, J.

T. M. Turpin, L. H. Gesell, J. Lapides, and C. H. Price, Theory of the Synthetic Aperture Microscope (1995), Vol. 2566, pp. 1–11.

Lee, J.

Lee, J. H.

S. Kang, P. Kang, S. Jeong, Y. Kwon, T. D. Yang, J. H. Hong, M. Kim, K.-D. Song, J. H. Park, J. H. Lee, M. J. Kim, K. H. Kim, and W. Choi, “High-resolution adaptive optical imaging within thick scattering media using closed-loop accumulation of single scattering,” Nat. Commun. 8, 2157 (2017).
[Crossref]

Lei, M.

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22, 096005 (2017).
[Crossref]

Leleux, P.

C. Dammer, P. Leleux, D. Villers, and M. Dosire, “Use of the Hough transform to determine the center of digitized x-ray diffraction patterns,” Nucl. Instrum. Methods Phys. Res. Sect. B 132, 214–220 (1997).
[Crossref]

Li, X.

Li, Y.

Liu, C.

Liu, J.

Liu, S.

Z. Liu, L. Tian, S. Liu, and L. Waller, “Real-time brightfield, darkfield, and phase contrast imaging in a light-emitting diode array microscope,” J. Biomed. Opt. 19, 106002 (2014).
[Crossref]

Liu, Z.

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]

Z. Liu, L. Tian, S. Liu, and L. Waller, “Real-time brightfield, darkfield, and phase contrast imaging in a light-emitting diode array microscope,” J. Biomed. Opt. 19, 106002 (2014).
[Crossref]

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Ma, J.

J. Dou, Z. Gao, J. Ma, C. Yuan, Z. Yang, and L. Wang, “Iterative autofocusing strategy for axial distance error correction in ptychography,” Opt. Lasers Eng. 98, 56–61 (2017).
[Crossref]

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Maiden, A.

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[Crossref]

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Nanda, P.

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A. Shanker, A. Wojdyla, G. Gunjala, J. Dong, M. Benk, A. Neureuther, K. Goldberg, and L. Waller, “Off-axis aberration estimation in an EUV microscope using natural speckle,” in Imaging and Applied Optics (Optical Society of America, 2016), paper ITh1F.2.

Ou, X.

Pan, A.

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22, 096005 (2017).
[Crossref]

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S. Kang, P. Kang, S. Jeong, Y. Kwon, T. D. Yang, J. H. Hong, M. Kim, K.-D. Song, J. H. Park, J. H. Lee, M. J. Kim, K. H. Kim, and W. Choi, “High-resolution adaptive optical imaging within thick scattering media using closed-loop accumulation of single scattering,” Nat. Commun. 8, 2157 (2017).
[Crossref]

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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]

Peterson, I.

Pfeiffer, F.

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

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Z. Phillips, R. Eckert, and L. Waller, “Quasi-dome: A self-calibrated high-NA LED illuminator for Fourier ptychography,” in Imaging and Applied Optics (Optical Society of America, 2017), paper IW4E.5.

Phillips, Z. F.

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]

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T. M. Turpin, L. H. Gesell, J. Lapides, and C. H. Price, Theory of the Synthetic Aperture Microscope (1995), Vol. 2566, pp. 1–11.

Princen, J.

H. K. Yuen, J. Princen, J. Illingworth, and J. Kittler, “A comparative study of Hough transform methods for circle finding,” in Proceedings of the 5th Alvey Vision Conference, Reading, August31, 1989, pp. 169–174.

Ramchandran, K.

Raskar, R.

G. Satat, B. Heshmat, D. Raviv, and R. Raskar, “All photons imaging through volumetric scattering,” Sci. Rep. 6, 33946 (2016).
[Crossref]

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G. Satat, B. Heshmat, D. Raviv, and R. Raskar, “All photons imaging through volumetric scattering,” Sci. Rep. 6, 33946 (2016).
[Crossref]

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S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[Crossref]

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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]

Rodenburg, J. M.

Rulison, J. J.

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]

Sadras, N.

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]

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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]

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G. Satat, B. Heshmat, D. Raviv, and R. Raskar, “All photons imaging through volumetric scattering,” Sci. Rep. 6, 33946 (2016).
[Crossref]

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Shanker, A.

A. Shanker, A. Wojdyla, G. Gunjala, J. Dong, M. Benk, A. Neureuther, K. Goldberg, and L. Waller, “Off-axis aberration estimation in an EUV microscope using natural speckle,” in Imaging and Applied Optics (Optical Society of America, 2016), paper ITh1F.2.

Shiradkar, R.

So, P. T. C.

Soltanolkotabi, M.

Song, K.-D.

S. Kang, P. Kang, S. Jeong, Y. Kwon, T. D. Yang, J. H. Hong, M. Kim, K.-D. Song, J. H. Park, J. H. Lee, M. J. Kim, K. H. Kim, and W. Choi, “High-resolution adaptive optical imaging within thick scattering media using closed-loop accumulation of single scattering,” Nat. Commun. 8, 2157 (2017).
[Crossref]

Stelzer, E. H. K.

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[Crossref]

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Sun, W.

Suo, J.

Switz, N. 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]

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Tang, G.

Thibault, P.

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

Tian, L.

M. Chen, L. Tian, and L. Waller, “3D differential phase contrast microscopy,” Biomed. Opt. Express 7, 3940–3950 (2016).
[Crossref]

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]

L. Tian and L. Waller, “Quantitative differential phase contrast imaging in an LED array microscope,” Opt. Express 23, 11394–11403 (2015).
[Crossref]

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]

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]

L. Tian, X. Li, K. Ramchandran, and L. Waller, “Multiplexed coded illumination for Fourier ptychography with an LED array microscope,” Biomed. Opt. Express 5, 2376–2389 (2014).
[Crossref]

L. Tian, J. Wang, and L. Waller, “3D differential phase-contrast microscopy with computational illumination using an LED array,” Opt. Lett. 39, 1326–1329 (2014).
[Crossref]

Z. Liu, L. Tian, S. Liu, and L. Waller, “Real-time brightfield, darkfield, and phase contrast imaging in a light-emitting diode array microscope,” J. Biomed. Opt. 19, 106002 (2014).
[Crossref]

R. Eckert, L. Tian, and L. Waller, “Algorithmic self-calibration of illumination angles in Fourier ptychographic microscopy,” in Imaging and Applied Optics (Optical Society of America, 2016), paper CT2D.3.

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T. M. Turpin, L. H. Gesell, J. Lapides, and C. H. Price, Theory of the Synthetic Aperture Microscope (1995), Vol. 2566, pp. 1–11.

Vila-Comamala, J.

Villers, D.

J. Cauchie, V. Fiolet, and D. Villers, “Optimization of an Hough transform algorithm for the search of a center,” Pattern Recognit. 41, 567–574 (2008).
[Crossref]

C. Dammer, P. Leleux, D. Villers, and M. Dosire, “Use of the Hough transform to determine the center of digitized x-ray diffraction patterns,” Nucl. Instrum. Methods Phys. Res. Sect. B 132, 214–220 (1997).
[Crossref]

Waller, L.

M. Chen, L. Tian, and L. Waller, “3D differential phase contrast microscopy,” Biomed. Opt. Express 7, 3940–3950 (2016).
[Crossref]

L. Tian and L. Waller, “Quantitative differential phase contrast imaging in an LED array microscope,” Opt. Express 23, 11394–11403 (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]

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

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]

Z. Liu, L. Tian, S. Liu, and L. Waller, “Real-time brightfield, darkfield, and phase contrast imaging in a light-emitting diode array microscope,” J. Biomed. Opt. 19, 106002 (2014).
[Crossref]

L. Tian, X. Li, K. Ramchandran, and L. Waller, “Multiplexed coded illumination for Fourier ptychography with an LED array microscope,” Biomed. Opt. Express 5, 2376–2389 (2014).
[Crossref]

L. Tian, J. Wang, and L. Waller, “3D differential phase-contrast microscopy with computational illumination using an LED array,” Opt. Lett. 39, 1326–1329 (2014).
[Crossref]

A. Shanker, A. Wojdyla, G. Gunjala, J. Dong, M. Benk, A. Neureuther, K. Goldberg, and L. Waller, “Off-axis aberration estimation in an EUV microscope using natural speckle,” in Imaging and Applied Optics (Optical Society of America, 2016), paper ITh1F.2.

R. Eckert, L. Tian, and L. Waller, “Algorithmic self-calibration of illumination angles in Fourier ptychographic microscopy,” in Imaging and Applied Optics (Optical Society of America, 2016), paper CT2D.3.

Z. Phillips, R. Eckert, and L. Waller, “Quasi-dome: A self-calibrated high-NA LED illuminator for Fourier ptychography,” in Imaging and Applied Optics (Optical Society of America, 2017), paper IW4E.5.

Wang, J.

Wang, L.

J. Dou, Z. Gao, J. Ma, C. Yuan, Z. Yang, and L. Wang, “Iterative autofocusing strategy for axial distance error correction in ptychography,” Opt. Lasers Eng. 98, 56–61 (2017).
[Crossref]

Wang, W.

Wang, Y.

Wang, Z.

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22, 096005 (2017).
[Crossref]

Wojdyla, A.

A. Shanker, A. Wojdyla, G. Gunjala, J. Dong, M. Benk, A. Neureuther, K. Goldberg, and L. Waller, “Off-axis aberration estimation in an EUV microscope using natural speckle,” in Imaging and Applied Optics (Optical Society of America, 2016), paper ITh1F.2.

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M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).

Yang, C.

J. Chung, H. Lu, X. Ou, H. Zhou, and C. Yang, “Wide-field Fourier ptychographic microscopy using laser illumination source,” Biomed. Opt. Express 7, 4787–4802 (2016).
[Crossref]

R. Horstmeyer, J. Chung, X. Ou, G. Zheng, and C. Yang, “Diffraction tomography with Fourier ptychography,” Optica 3, 827–835 (2016).
[Crossref]

L. Bian, G. Zheng, K. Guo, J. Suo, C. Yang, F. Chen, and Q. Dai, “Motion-corrected Fourier ptychography,” Biomed. Opt. Express 7, 4543–4553 (2016).
[Crossref]

J. Chung, J. Kim, X. Ou, R. Horstmeyer, and C. Yang, “Wide field-of-view fluorescence image deconvolution with aberration-estimation from Fourier ptychography,” Biomed. Opt. Express 7, 352–368 (2016).
[Crossref]

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

R. Horstmeyer, X. Ou, J. Chung, G. Zheng, and C. Yang, “Overlapped Fourier coding for optical aberration removal,” Opt. Express 22, 24062–24080 (2014).
[Crossref]

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

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

G. Zheng, C. Kolner, and C. Yang, “Microscopy refocusing and dark-field imaging by using a simple LED array,” Opt. Lett. 36, 3987–3989 (2011).
[Crossref]

Yang, T. D.

S. Kang, P. Kang, S. Jeong, Y. Kwon, T. D. Yang, J. H. Hong, M. Kim, K.-D. Song, J. H. Park, J. H. Lee, M. J. Kim, K. H. Kim, and W. Choi, “High-resolution adaptive optical imaging within thick scattering media using closed-loop accumulation of single scattering,” Nat. Commun. 8, 2157 (2017).
[Crossref]

Yang, Z.

J. Dou, Z. Gao, J. Ma, C. Yuan, Z. Yang, and L. Wang, “Iterative autofocusing strategy for axial distance error correction in ptychography,” Opt. Lasers Eng. 98, 56–61 (2017).
[Crossref]

Yao, B.

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22, 096005 (2017).
[Crossref]

Yaqoob, Z.

Yeh, L.-H.

Yuan, C.

J. Dou, Z. Gao, J. Ma, C. Yuan, Z. Yang, and L. Wang, “Iterative autofocusing strategy for axial distance error correction in ptychography,” Opt. Lasers Eng. 98, 56–61 (2017).
[Crossref]

Yuen, H. K.

H. K. Yuen, J. Princen, J. Illingworth, and J. Kittler, “A comparative study of Hough transform methods for circle finding,” in Proceedings of the 5th Alvey Vision Conference, Reading, August31, 1989, pp. 169–174.

Zhang, F.

Zhang, H.

Zhang, L.

J. Sun, C. Zuo, L. Zhang, and Q. Chen, “Resolution-enhanced Fourier ptychographic microscopy based on high-numerical-aperture illuminations,” Sci. Rep. 7, 1187 (2017).
[Crossref]

Zhang, P.

Zhang, Y.

Zhao, J.

Zhao, T.

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22, 096005 (2017).
[Crossref]

Zheng, G.

R. Horstmeyer, J. Chung, X. Ou, G. Zheng, and C. Yang, “Diffraction tomography with Fourier ptychography,” Optica 3, 827–835 (2016).
[Crossref]

L. Bian, G. Zheng, K. Guo, J. Suo, C. Yang, F. Chen, and Q. Dai, “Motion-corrected Fourier ptychography,” Biomed. Opt. Express 7, 4543–4553 (2016).
[Crossref]

K. Guo, S. Dong, P. Nanda, and G. Zheng, “Optimization of sampling pattern and the design of Fourier ptychographic illuminator,” Opt. Express 23, 6171–6180 (2015).
[Crossref]

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

R. Horstmeyer, X. Ou, J. Chung, G. Zheng, and C. Yang, “Overlapped Fourier coding for optical aberration removal,” Opt. Express 22, 24062–24080 (2014).
[Crossref]

S. Dong, Z. Bian, R. Shiradkar, and G. Zheng, “Sparsely sampled Fourier ptychography,” Opt. Express 22, 5455–5464 (2014).
[Crossref]

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

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

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

G. Zheng, C. Kolner, and C. Yang, “Microscopy refocusing and dark-field imaging by using a simple LED array,” Opt. Lett. 36, 3987–3989 (2011).
[Crossref]

Zhong, J.

Zhou, H.

Zhou, R.

Zuo, C.

Appl. Opt. (2)

Biomed. Opt. Express (6)

J. Biomed. Opt. (2)

Z. Liu, L. Tian, S. Liu, and L. Waller, “Real-time brightfield, darkfield, and phase contrast imaging in a light-emitting diode array microscope,” J. Biomed. Opt. 19, 106002 (2014).
[Crossref]

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22, 096005 (2017).
[Crossref]

J. Microsc. (1)

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[Crossref]

Nat. Commun. (1)

S. Kang, P. Kang, S. Jeong, Y. Kwon, T. D. Yang, J. H. Hong, M. Kim, K.-D. Song, J. H. Park, J. H. Lee, M. J. Kim, K. H. Kim, and W. Choi, “High-resolution adaptive optical imaging within thick scattering media using closed-loop accumulation of single scattering,” Nat. Commun. 8, 2157 (2017).
[Crossref]

Nat. Photonics (1)

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

Nucl. Instrum. Methods Phys. Res. Sect. B (1)

C. Dammer, P. Leleux, D. Villers, and M. Dosire, “Use of the Hough transform to determine the center of digitized x-ray diffraction patterns,” Nucl. Instrum. Methods Phys. Res. Sect. B 132, 214–220 (1997).
[Crossref]

Opt. Express (11)

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Sampling criteria for Fourier ptychographic microscopy in object space and frequency space,” Opt. Express 24, 15765–15781 (2016).
[Crossref]

K. Guo, S. Dong, P. Nanda, and G. Zheng, “Optimization of sampling pattern and the design of Fourier ptychographic illuminator,” Opt. Express 23, 6171–6180 (2015).
[Crossref]

L. Tian and L. Waller, “Quantitative differential phase contrast imaging in an LED array microscope,” Opt. Express 23, 11394–11403 (2015).
[Crossref]

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

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, 13592–13606 (2013).
[Crossref]

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

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

S. Dong, Z. Bian, R. Shiradkar, and G. Zheng, “Sparsely sampled Fourier ptychography,” Opt. Express 22, 5455–5464 (2014).
[Crossref]

R. Horstmeyer, X. Ou, J. Chung, G. Zheng, and C. Yang, “Overlapped Fourier coding for optical aberration removal,” Opt. Express 22, 24062–24080 (2014).
[Crossref]

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]

J. Liu, Y. Li, W. Wang, H. Zhang, Y. Wang, J. Tan, and C. Liu, “Stable and robust frequency domain position compensation strategy for Fourier ptychographic microscopy,” Opt. Express 25, 28053–28067 (2017).
[Crossref]

Opt. Lasers Eng. (1)

J. Dou, Z. Gao, J. Ma, C. Yuan, Z. Yang, and L. Wang, “Iterative autofocusing strategy for axial distance error correction in ptychography,” Opt. Lasers Eng. 98, 56–61 (2017).
[Crossref]

Opt. Lett. (3)

Optica (3)

Pattern Recognit. (1)

J. Cauchie, V. Fiolet, and D. Villers, “Optimization of an Hough transform algorithm for the search of a center,” Pattern Recognit. 41, 567–574 (2008).
[Crossref]

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).
[Crossref]

Sci. Rep. (2)

G. Satat, B. Heshmat, D. Raviv, and R. Raskar, “All photons imaging through volumetric scattering,” Sci. Rep. 6, 33946 (2016).
[Crossref]

J. Sun, C. Zuo, L. Zhang, and Q. Chen, “Resolution-enhanced Fourier ptychographic microscopy based on high-numerical-aperture illuminations,” Sci. Rep. 7, 1187 (2017).
[Crossref]

Ultramicroscopy (2)

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[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. Illumination angles are calibrated by analyzing Fourier spectra. (a) A cheek cell is illuminated at angle α and imaged with NA obj . (b) Brightfield images contain overlapping circles in their Fourier spectra; darkfield images do not. (c) We perform a fast and efficient brightfield calibration in preprocessing, then extrapolate the correction to darkfield images, and, finally, iteratively calibrate angles inside the FPM algorithm using a spectral correlation calibration.
Fig. 2.
Fig. 2. Circular edge detection on brightfield images finds circle centers, giving illumination angle calibration. (a), (b) Comparison of uncalibrated (red) and calibrated (black) illumination k i . The blue box in (b) indicates the search range for k i . (c), (d)  I ˜ i along radial lines, f ( r , ϕ n ) , and derivatives with respect to r . (e), (f)  E 1 and E 2 , sums of the derivatives at known radii R and R + σ , peak near the correct center. Boxes show uncalibrated (red) and calibrated (black) k i centers.
Fig. 3.
Fig. 3. BF calibration uses a fast preprocessing step to estimate illumination angles; then SC calibration iteratively refines them within the FPM solver. (a) Algorithm block diagram. (b) Uncalibrated (red) and BF + SC calibrated (green) illumination angle map. Insets are example search spaces, showing local convexity. (c) FPM convergence plot for different methods.
Fig. 4.
Fig. 4. Experimental results with an LED array microscope, comparing reconstructions with no calibration (average reconstruction time 132 s), simulated annealing (3453 s), our BF calibration (156 s), and our BF + SC calibration (295 s). (a) Amplitude reconstructions of a USAF target in a well-aligned system. (b) Amplitude reconstructions of the same USAF target with a drop of oil placed on top of the sample to simulate sample-induced aberrations. (c) Phase reconstructions of a human cheek cell with computationally misaligned illumination. (d) A Siemens star phase target with experimentally misaligned illumination.
Fig. 5.
Fig. 5. Experimental angle calibration in laser and high-NA quasi-dome illumination systems. (a) Laser illumination is steered by a dual-axis galvanometer. The angled beam is relayed to the sample by 4 in., 80 mm focal length lenses. (b) Our calibration method removes low-frequency reconstruction artifacts. (c) The quasi-dome illuminator enables up to 0.98 NA illum using programmable LEDs. (d) Our 1.23 NA reconstruction provides isotropic 425 nm resolution with BF + SC calibration.
Fig. 6.
Fig. 6. Even small calibration errors degrade 3D FPM resolution severely when defocus distances are large. (a) Experiment schematic for a USAF target placed at varying defocus distances. (b) Measured reconstruction resolution degrades with defocus distance; our calibration algorithm reduces this error significantly. (c) Amplitude reconstructions for selected experimental defocus distances, with and without calibration of the illumination angles.
Fig. 7.
Fig. 7. Our calibration methods are robust to large mismatches between estimated and actual LED array position. Simulation of misaligned illumination by (a) rotation, (b) shift, and (c) scale. Our calibration recovers the illumination with < 0.005 NA error for rotations of 45 ° to 45°, shifts of 0.1 to 0.1 NA, and scalings of 0.5 × to 1.75 × before diverging.

Tables (1)

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Algorithm 1 Brightfield Calibration

Equations (7)

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I i ( r ) = | O ( r ) e i 2 π k i r * P ( r ) | 2 = | F 1 ( O ˜ ( k k i ) P ˜ ( k ) ) | 2 ,
I ˜ i ( k ) = F ( | O ( r ) e i 2 π k i r * P ( r ) | 2 ) = O ˜ ( k k i ) P ˜ ( k ) O ˜ ( k k i ) P ˜ ( k ) ,
E 1 ( R , d i , θ i ) = n = 1 N f ( r = R , ϕ n , d i , θ i ) .
f ( r , ϕ n , d i , θ i ) = rect ( r 2 R ) * 1 2 π σ e r 2 2 σ 2 .
E 2 ( R + σ , d i , θ i ) = n = 1 N f ( r = R + σ , ϕ n , d i , θ i ) ,
R = NA obj λ p s * M mag ,
argmin n I i | O ( m + 1 ) e i 2 π ( k i ( m ) + n Δ k ) r * P ( m + 1 ) | 2 2 2 subject to n = ( n x , n y ) , ( n x , n y ) [ 1 , 0 , 1 ] .

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