Abstract

Estimation of optical aberrations from volumetric intensity images is a key step in sensorless adaptive optics for 3D microscopy. Recent approaches based on deep learning promise accurate results at fast processing speeds. However, collecting ground truth microscopy data for training the network is typically very difficult or even impossible thereby limiting this approach in practice. Here, we demonstrate that neural networks trained only on simulated data yield accurate predictions for real experimental images. We validate our approach on simulated and experimental datasets acquired with two different microscopy modalities and also compare the results to non-learned methods. Additionally, we study the predictability of individual aberrations with respect to their data requirements and find that the symmetry of the wavefront plays a crucial role. Finally, we make our implementation freely available as open source software in Python.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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2020 (4)

2019 (2)

A. Barbotin, S. Galiani, I. Urbančič, C. Eggeling, and M. J. Booth, “Adaptive optics allows STED-FCS measurements in the cytoplasm of living cells,” Opt. Express 27(16), 23378–23395 (2019).
[Crossref]

L. Möckl, P. N. Petrov, and W. E. Moerner, “Accurate phase retrieval of complex 3d point spread functions with deep residual neural networks,” Appl. Phys. Lett. 115(25), 251106 (2019).
[Crossref]

2018 (5)

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15(12), 1090–1097 (2018).
[Crossref]

P. Zhang, S. Liu, A. Chaurasia, D. Ma, M. J. Mlodzianoski, E. Culurciello, and F. Huang, “Analyzing complex single-molecule emission patterns with deep learning,” Nat. Methods 15(11), 913–916 (2018).
[Crossref]

Y. Jin, Y. Zhang, L. Hu, H. Huang, Q. Xu, X. Zhu, L. Huang, Y. Zheng, H.-L. Shen, W. Gong, and K. Si, “Machine learning guided rapid focusing with sensor-less aberration corrections,” Opt. Express 26(23), 30162–30171 (2018).
[Crossref]

A. Aristov, B. Lelandais, E. Rensen, and C. Zimmer, “ZOLA- 3D allows flexible 3D localization microscopy over an adjustable axial range,” Nat. Commun. 9(1), 2409 (2018).
[Crossref]

T. L. Liu, S. Upadhyayula, D. E. Milkie, V. Singh, K. Wang, I. A. Swinburne, K. R. Mosaliganti, Z. M. Collins, T. W. Hiscock, J. Shea, A. Q. Kohrman, T. N. Medwig, D. Dambournet, R. Forster, B. Cunniff, Y. Ruan, H. Yashiro, S. Scholpp, E. M. Meyerowitz, D. Hockemeyer, D. G. Drubin, B. L. Martin, D. Q. Matus, M. Koyama, S. G. Megason, T. Kirchhausen, and E. Betzig, “Observing the cell in its native state: Imaging subcellular dynamics in multicellular organisms,” Science 360(6386), eaaq1392 (2018).
[Crossref]

2017 (2)

2015 (1)

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, “Direct wavefront sensing for high-resolution in vivo imaging in scattering tissue,” Nat. Commun. 6(1), 1–6 (2015).
[Crossref]

2014 (1)

M. J. Booth, “Adaptive optical microscopy: the ongoing quest for a perfect image,” Light: Sci. Appl. 3(4), e165 (2014).
[Crossref]

2012 (2)

N. Ji, T. R. Sato, and E. Betzig, “Characterization and adaptive optical correction of aberrations during in vivo imaging in the mouse cortex,” Proc. Natl. Acad. Sci. 109(1), 22–27 (2012).
[Crossref]

X. Tao, J. Crest, S. Kotadia, O. Azucena, D. C. Chen, W. Sullivan, and J. Kubby, “Live imaging using adaptive optics with fluorescent protein guide-stars,” Opt. Express 20(14), 15969–15982 (2012).
[Crossref]

2010 (1)

J.-W. Cha, J. Ballesta, and P. T. So, “Shack-hartmann wavefront-sensor-based adaptive optics system for multiphoton microscopy,” J. Biomed. Opt. 15(4), 046022 (2010).
[Crossref]

2009 (2)

D. Débarre, E. J. Botcherby, T. Watanabe, S. Srinivas, M. J. Booth, and T. Wilson, “Image-based adaptive optics for two-photon microscopy,” Opt. Lett. 34(16), 2495–2497 (2009).
[Crossref]

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. 106(9), 2995–2999 (2009).
[Crossref]

2007 (1)

M. J. Booth, “Adaptive optics in microscopy,” Philos. Trans. R. Soc., A 365(1861), 2829–2843 (2007).
[Crossref]

2006 (1)

K. Willig, J. Keller, M. Bossi, and S. W. Hell, “Sted microscopy resolves nanoparticle assemblies,” New J. Phys. 8(6), 106 (2006).
[Crossref]

2004 (1)

2003 (1)

1982 (1)

1976 (1)

Agard, D. A.

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase retrieval for high-numerical-aperture optical systems,” Opt. Lett. 28(10), 801–803 (2003).
[Crossref]

P. Kner, L. Winoto, D. A. Agard, and J. W. Sedat, “Closed loop adaptive optics for microscopy without a wavefront sensor,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XVII, vol. 7570 (International Society for Optics and Photonics, 2010), p. 757006.

Alalouf, O.

Aristov, A.

A. Aristov, B. Lelandais, E. Rensen, and C. Zimmer, “ZOLA- 3D allows flexible 3D localization microscopy over an adjustable axial range,” Nat. Commun. 9(1), 2409 (2018).
[Crossref]

Azucena, O.

Ba, J.

D. Kingma and J. Ba, “Adam: A method for stochastic optimization,” Int. Conf. on Learn. Represent. (ICLR) (2015).

Ballesta, J.

J.-W. Cha, J. Ballesta, and P. T. So, “Shack-hartmann wavefront-sensor-based adaptive optics system for multiphoton microscopy,” J. Biomed. Opt. 15(4), 046022 (2010).
[Crossref]

Barbotin, A.

Betzig, E.

T. L. Liu, S. Upadhyayula, D. E. Milkie, V. Singh, K. Wang, I. A. Swinburne, K. R. Mosaliganti, Z. M. Collins, T. W. Hiscock, J. Shea, A. Q. Kohrman, T. N. Medwig, D. Dambournet, R. Forster, B. Cunniff, Y. Ruan, H. Yashiro, S. Scholpp, E. M. Meyerowitz, D. Hockemeyer, D. G. Drubin, B. L. Martin, D. Q. Matus, M. Koyama, S. G. Megason, T. Kirchhausen, and E. Betzig, “Observing the cell in its native state: Imaging subcellular dynamics in multicellular organisms,” Science 360(6386), eaaq1392 (2018).
[Crossref]

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, “Direct wavefront sensing for high-resolution in vivo imaging in scattering tissue,” Nat. Commun. 6(1), 1–6 (2015).
[Crossref]

N. Ji, T. R. Sato, and E. Betzig, “Characterization and adaptive optical correction of aberrations during in vivo imaging in the mouse cortex,” Proc. Natl. Acad. Sci. 109(1), 22–27 (2012).
[Crossref]

Bi, C.

F. Xu, D. Ma, K. P. MacPherson, S. Liu, Y. Bu, Y. Wang, Y. Tang, C. Bi, T. Kwok, A. A. Chubykin, P. Yin, S. Calve, G. E. Landreth, and F. Huang, “Three-dimensional nanoscopy of whole cells and tissues with in situ point spread function retrieval,” Nat. Methods 17(5), 531–540 (2020).
[Crossref]

Biteen, J. S.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. 106(9), 2995–2999 (2009).
[Crossref]

Booth, M.

Booth, M. J.

Boothe, T.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15(12), 1090–1097 (2018).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics7th ed., (Cambridge University1999).

Bossi, M.

K. Willig, J. Keller, M. Bossi, and S. W. Hell, “Sted microscopy resolves nanoparticle assemblies,” New J. Phys. 8(6), 106 (2006).
[Crossref]

Botcherby, E. J.

Broaddus, C.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15(12), 1090–1097 (2018).
[Crossref]

Bu, Y.

F. Xu, D. Ma, K. P. MacPherson, S. Liu, Y. Bu, Y. Wang, Y. Tang, C. Bi, T. Kwok, A. A. Chubykin, P. Yin, S. Calve, G. E. Landreth, and F. Huang, “Three-dimensional nanoscopy of whole cells and tissues with in situ point spread function retrieval,” Nat. Methods 17(5), 531–540 (2020).
[Crossref]

Calve, S.

F. Xu, D. Ma, K. P. MacPherson, S. Liu, Y. Bu, Y. Wang, Y. Tang, C. Bi, T. Kwok, A. A. Chubykin, P. Yin, S. Calve, G. E. Landreth, and F. Huang, “Three-dimensional nanoscopy of whole cells and tissues with in situ point spread function retrieval,” Nat. Methods 17(5), 531–540 (2020).
[Crossref]

Cha, J.-W.

J.-W. Cha, J. Ballesta, and P. T. So, “Shack-hartmann wavefront-sensor-based adaptive optics system for multiphoton microscopy,” J. Biomed. Opt. 15(4), 046022 (2010).
[Crossref]

Chaurasia, A.

P. Zhang, S. Liu, A. Chaurasia, D. Ma, M. J. Mlodzianoski, E. Culurciello, and F. Huang, “Analyzing complex single-molecule emission patterns with deep learning,” Nat. Methods 15(11), 913–916 (2018).
[Crossref]

Chen, D. C.

Chollet, F.

F. Chollet, “Keras,” https://keras.io (2015).

Chubykin, A. A.

F. Xu, D. Ma, K. P. MacPherson, S. Liu, Y. Bu, Y. Wang, Y. Tang, C. Bi, T. Kwok, A. A. Chubykin, P. Yin, S. Calve, G. E. Landreth, and F. Huang, “Three-dimensional nanoscopy of whole cells and tissues with in situ point spread function retrieval,” Nat. Methods 17(5), 531–540 (2020).
[Crossref]

Collins, Z. M.

T. L. Liu, S. Upadhyayula, D. E. Milkie, V. Singh, K. Wang, I. A. Swinburne, K. R. Mosaliganti, Z. M. Collins, T. W. Hiscock, J. Shea, A. Q. Kohrman, T. N. Medwig, D. Dambournet, R. Forster, B. Cunniff, Y. Ruan, H. Yashiro, S. Scholpp, E. M. Meyerowitz, D. Hockemeyer, D. G. Drubin, B. L. Martin, D. Q. Matus, M. Koyama, S. G. Megason, T. Kirchhausen, and E. Betzig, “Observing the cell in its native state: Imaging subcellular dynamics in multicellular organisms,” Science 360(6386), eaaq1392 (2018).
[Crossref]

Crest, J.

Culley, S.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15(12), 1090–1097 (2018).
[Crossref]

Culurciello, E.

P. Zhang, S. Liu, A. Chaurasia, D. Ma, M. J. Mlodzianoski, E. Culurciello, and F. Huang, “Analyzing complex single-molecule emission patterns with deep learning,” Nat. Methods 15(11), 913–916 (2018).
[Crossref]

Cumming, B. P.

Cunniff, B.

T. L. Liu, S. Upadhyayula, D. E. Milkie, V. Singh, K. Wang, I. A. Swinburne, K. R. Mosaliganti, Z. M. Collins, T. W. Hiscock, J. Shea, A. Q. Kohrman, T. N. Medwig, D. Dambournet, R. Forster, B. Cunniff, Y. Ruan, H. Yashiro, S. Scholpp, E. M. Meyerowitz, D. Hockemeyer, D. G. Drubin, B. L. Martin, D. Q. Matus, M. Koyama, S. G. Megason, T. Kirchhausen, and E. Betzig, “Observing the cell in its native state: Imaging subcellular dynamics in multicellular organisms,” Science 360(6386), eaaq1392 (2018).
[Crossref]

Dambournet, D.

T. L. Liu, S. Upadhyayula, D. E. Milkie, V. Singh, K. Wang, I. A. Swinburne, K. R. Mosaliganti, Z. M. Collins, T. W. Hiscock, J. Shea, A. Q. Kohrman, T. N. Medwig, D. Dambournet, R. Forster, B. Cunniff, Y. Ruan, H. Yashiro, S. Scholpp, E. M. Meyerowitz, D. Hockemeyer, D. G. Drubin, B. L. Martin, D. Q. Matus, M. Koyama, S. G. Megason, T. Kirchhausen, and E. Betzig, “Observing the cell in its native state: Imaging subcellular dynamics in multicellular organisms,” Science 360(6386), eaaq1392 (2018).
[Crossref]

Débarre, D.

Dibrov, A.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15(12), 1090–1097 (2018).
[Crossref]

Drubin, D. G.

T. L. Liu, S. Upadhyayula, D. E. Milkie, V. Singh, K. Wang, I. A. Swinburne, K. R. Mosaliganti, Z. M. Collins, T. W. Hiscock, J. Shea, A. Q. Kohrman, T. N. Medwig, D. Dambournet, R. Forster, B. Cunniff, Y. Ruan, H. Yashiro, S. Scholpp, E. M. Meyerowitz, D. Hockemeyer, D. G. Drubin, B. L. Martin, D. Q. Matus, M. Koyama, S. G. Megason, T. Kirchhausen, and E. Betzig, “Observing the cell in its native state: Imaging subcellular dynamics in multicellular organisms,” Science 360(6386), eaaq1392 (2018).
[Crossref]

Eggeling, C.

Ferdman, B.

Fienup, J. R.

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21(15), 2758–2769 (1982).
[Crossref]

S. W. Paine and J. R. Fienup, “Smart starting guesses from machine learning for phase retrieval,” in Space Telescopes and Instrumentation 2018: Optical, Infrared, and Millimeter Wave, vol. 10698H. A. MacEwen, M. Lystrup, G. G. Fazio, N. Batalha, E. C. Tong, and N. Siegler, eds. (SPIE, 2018), p. 210.
[Crossref]

Forster, R.

T. L. Liu, S. Upadhyayula, D. E. Milkie, V. Singh, K. Wang, I. A. Swinburne, K. R. Mosaliganti, Z. M. Collins, T. W. Hiscock, J. Shea, A. Q. Kohrman, T. N. Medwig, D. Dambournet, R. Forster, B. Cunniff, Y. Ruan, H. Yashiro, S. Scholpp, E. M. Meyerowitz, D. Hockemeyer, D. G. Drubin, B. L. Martin, D. Q. Matus, M. Koyama, S. G. Megason, T. Kirchhausen, and E. Betzig, “Observing the cell in its native state: Imaging subcellular dynamics in multicellular organisms,” Science 360(6386), eaaq1392 (2018).
[Crossref]

Galiani, S.

Gong, W.

Goodman, J.

J. Goodman, Introduction to Fourier Optics2nd ed., (MaGraw-Hill1996).

Göröcs, Z.

Gu, M.

Günaydin, H.

Gustafsson, M. G.

Hanser, B. M.

Harvey, B. K.

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, “Direct wavefront sensing for high-resolution in vivo imaging in scattering tissue,” Nat. Commun. 6(1), 1–6 (2015).
[Crossref]

Hell, S. W.

K. Willig, J. Keller, M. Bossi, and S. W. Hell, “Sted microscopy resolves nanoparticle assemblies,” New J. Phys. 8(6), 106 (2006).
[Crossref]

Henriques, R.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: pushing the limits of fluorescence microscopy,” Nat. Methods 15(12), 1090–1097 (2018).
[Crossref]

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Supplementary Material (1)

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» Supplement 1       Supplemental Notes, Tables, and Figures

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Figures (4)

Fig. 1.
Fig. 1. Overview of our approach: We train a CNN (PHASENET) with synthetic PSFs ${\textrm{h}_{\textrm{synth}}}$ (${\textrm{n}_\textrm{z}}$ axial planes) generated from randomly sampled amplitudes of Zernike modes ${\textrm{a}_\textrm{i}}{\; }$. The trained network is then used to predict the amplitudes $\widetilde {{\textrm{a}_\textrm{i}}}$ from experimental bead images ${\textrm{h}_{\textrm{real}}}$. The predicted amplitudes $\widetilde {{\textrm{a}_\textrm{i}}}$ are then used to reconstruct the wavefront.
Fig. 2.
Fig. 2. Measurement of single Zernike mode aberrations for Point Scanning data: a) PHASENET predictions on images with experimentally introduced oblique astigmatism ${\textrm{Z}_5}$ (see Fig. S2 in Supplement 1 for modes ${\textrm{Z}_6}{\; } - {\; }{\textrm{Z}_{15}}$). Shown are ground truth vs. the predicted amplitude ${\textrm{a}_5}$ (black dots), perfect prediction (solid black line), and the upper/lower bounds of amplitudes used during training (gray arrow). The inset shows the distribution of predicted non-introduced modes $({{\textrm{a}_6},{\; } \cdots ,{\; }{\textrm{a}_{15}}} )$. Scalebar 500 nm. b) RMSE for PHASENET and compared methods (GS and ZOLA) on all images. Boxes show interquartile range (IQR), lines signify median, and whiskers extend to 1.5 IQR.
Fig. 3.
Fig. 3. Results for Widefield data with mixed-modes aberrations: a) Predictions for lower order modes $({{\textrm{Z}_5}{\; } - {\; }{\textrm{Z}_{10}}} ):$ We show the ground truth (GT) wavefront, lateral (XY) and axial (XZ) midplanes of the experimental 3D image, the reconstructed wavefront and their GT difference for all methods (Gerchberg-Saxton/GS [11], ZOLA, PHASENET), and the reconstructed image from the PHASENET prediction. We further depict the RMSE for all n = 50 experimental PSFs. Boxes show interquartile range (IQR), lines signify median, and whiskers extend to 1.5 IQR. b) Same results but including higher order modes ${\textrm{Z}_5}{\; } - {\; }{\textrm{Z}_{15}}$. Scalebar: 500 nm.
Fig. 4.
Fig. 4. Results for varying number of input planes ${\textrm{n}_\textrm{z}}$: a) Ground truth vs. the predicted amplitude ${\textrm{a}_5}$ (oblique astigmatism) for single mode data Point Scanning and using PHASENET models with ${\textrm{n}_\textrm{z}}{ = \; 1,\; 2,\; 32}$. b) The same for ${\textrm{a}_7}$ (vertical coma). c) Prediction error (RMSE) on Widefield data (50 images) for PHASENET models trained with different ${\textrm{n}_\textrm{z}}$. We show the RMSE for odd (orange) and even (blue) Zernike modes separately. Boxes depict interquartile range (IQR), lines signify median, and whiskers extend to 1.5 IQR.

Tables (1)

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Table 1. Runtime of all methods for aberration estimation from a single (n = 1) and multiple (n = 50) PSFs of size 32×32×32.

Equations (2)

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φ ( k x , k y ) = i a i Z i ( k x , k y )
h synth n ( x, y, z )  =  | [ P ( k x , k y ) e 2 π i φ n ( k x , k y ) / λ e 2 π i z n 0 2 λ 2 k x 2 k y 2 ] | 2