Abstract

We present a learning-based Shack-Hartmann wavefront sensor (SHWS) to achieve the high-order aberration detection without image segmentation or centroid positioning. Zernike coefficient amplitudes of aberrations measured from biological samples are referred and expanded to generate the training datasets. With one SHWS pattern inputted, up to 120th Zernike modes could be predicted within 10.9 ms with 95.56% model accuracy by a personal computer. The statistical experimental results show that compared with traditional modal-based SHWS, the root mean squared error in phase residuals of this method is reduced by ∼40.54% and the Strehl ratio of the point spread functions is improved by ∼27.31%. The aberration detection performance of this method is also validated on a mouse brain slice with 300 µm thickness and the median improvement of peak-to-background ratio of this method is ∼30% to 40% compared with traditional SHWS. With the high detection accuracy, simple processes, fast prediction speed and good compatibility, this work offers a potential approach to improve the wavefront sensing ability of SHWS, which could be combined with an existing adaptive optics system and be further applied in biological applications.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (4)

X. Zhu, L. Huang, Y. Zheng, Y. Song, Q. Xu, J. Wang, K. Si, S. Duan, and W. Gong, “Ultrafast optical clearing method for three-dimensional imaging with cellular resolution,” Proc. Natl. Acad. Sci. U. S. A. 116(23), 11480–11489 (2019).
[Crossref]

J. Mompean, J. L. Aragon, P. M. Prieto, and P. Artal, “GPU-based processing of Hartmann-Shack images for accurate and high-speed ocular wavefront sensing,” Futur. Gener. Comp. Syst. 91, 177–190 (2019).
[Crossref]

Y. Nishizaki, M. Valdivia, R. Horisaki, K. Kitaguchi, M. Saito, J. Tanida, and E. Vera, “Deep learning wavefront sensing,” Opt. Express 27(1), 240–251 (2019).
[Crossref]

Y. Zhang, C. Wu, Y. Song, K. Si, Y. Zheng, L. Hu, J. Chen, L. Tang, and W. Gong, “Machine learning based adaptive optics for doughnut-shaped beam,” Opt. Express 27(12), 16871–16881 (2019).
[Crossref]

2018 (4)

S. W. Paine and J. R. Fienup, “Machine learning for improved image-based wavefront sensing,” Opt. Lett. 43(6), 1235–1238 (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]

Z. Q. Li and X. Y. Li, “Centroid computation for Shack-Hartmann wavefront sensor in extreme situations based on artificial neural networks,” Opt. Express 26(24), 31675–31692 (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)

Q. Li, M. Reinig, D. Kamiyama, B. Huang, X. Tao, A. Bardales, and J. Kubby, “Woofer–tweeter adaptive optical structured illumination microscopy,” Photonics Res. 5(4), 329–334 (2017).
[Crossref]

N. Ji, “Adaptive optical fluorescence microscopy,” Nat. Methods 14(4), 374–380 (2017).
[Crossref]

2016 (1)

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), 7276 (2015).
[Crossref]

2014 (1)

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11(6), 625–628 (2014).
[Crossref]

2013 (2)

M. Thier, R. Paris, T. Thurner, and G. Schitter, “Low-Latency Shack-Hartmann Wavefront Sensor Based on an Industrial Smart Camera,” IEEE Trans. Instrum. Meas. 62(5), 1241–1249 (2013).
[Crossref]

M. Shaw, K. O’Holleran, and C. Paterson, “Investigation of the confocal wavefront sensor and its application to biological microscopy,” Opt. Express 21(16), 19353–19362 (2013).
[Crossref]

2011 (3)

2009 (1)

2007 (1)

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

2006 (1)

2004 (1)

M. Schwertner, M. J. Booth, M. A. A. Neil, and T. Wilson, “Measurement of specimen-induced aberrations of biological samples using phase stepping interferometry,” J. Microsc. 213(1), 11–19 (2004).
[Crossref]

2003 (1)

2001 (1)

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J Refract Surg 17(5), S573–S577 (2001).
[Crossref]

1997 (1)

1979 (1)

1977 (1)

Antonello, J.

J. Antonello, “Optimisation-based wavefront sensorless adaptive optics for microscopy,” (Ph. D. thesis (Delft University of Technology), 2014).

Aragon, J. L.

J. Mompean, J. L. Aragon, P. M. Prieto, and P. Artal, “GPU-based processing of Hartmann-Shack images for accurate and high-speed ocular wavefront sensing,” Futur. Gener. Comp. Syst. 91, 177–190 (2019).
[Crossref]

Artal, P.

J. Mompean, J. L. Aragon, P. M. Prieto, and P. Artal, “GPU-based processing of Hartmann-Shack images for accurate and high-speed ocular wavefront sensing,” Futur. Gener. Comp. Syst. 91, 177–190 (2019).
[Crossref]

J. L. Fuentes, E. J. Fernández, P. M. Prieto, and P. Artal, “Interferometric method for phase calibration in liquid crystal spatial light modulators using a self-generated diffraction-grating,” Opt. Express 24(13), 14159–14171 (2016).
[Crossref]

Azucena, O.

Ba, J.

D. Kingma and J. Ba, “Adam: A Method for Stochastic Optimization,” https://arxiv.org/abs/1412.6980 .

Bardales, A.

Q. Li, M. Reinig, D. Kamiyama, B. Huang, X. Tao, A. Bardales, and J. Kubby, “Woofer–tweeter adaptive optical structured illumination microscopy,” Photonics Res. 5(4), 329–334 (2017).
[Crossref]

Barwick, S.

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), 7276 (2015).
[Crossref]

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11(6), 625–628 (2014).
[Crossref]

Bille, J.

Booth, M. J.

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

M. Schwertner, M. J. Booth, M. A. A. Neil, and T. Wilson, “Measurement of specimen-induced aberrations of biological samples using phase stepping interferometry,” J. Microsc. 213(1), 11–19 (2004).
[Crossref]

Bronner, M. E.

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11(6), 625–628 (2014).
[Crossref]

Chen, D. C.

Chen, J.

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]

Copland, J.

D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann wavefront sensor precision and accuracy,” in Advanced Characterization Techniques for Optical, Semiconductor, and Data Storage Components, A. Duparre and B. Singh, eds. (Spie-Int Soc Optical Engineering, Bellingham, 2002), pp. 148–160.

Crest, J.

Cubalchini, R.

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]

Daria, V. R.

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]

Duan, S.

X. Zhu, L. Huang, Y. Zheng, Y. Song, Q. Xu, J. Wang, K. Si, S. Duan, and W. Gong, “Ultrafast optical clearing method for three-dimensional imaging with cellular resolution,” Proc. Natl. Acad. Sci. U. S. A. 116(23), 11480–11489 (2019).
[Crossref]

Engerer, P.

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11(6), 625–628 (2014).
[Crossref]

Eriksen, R. L.

Fernandez, B.

Fernández, E. J.

Fienup, J. R.

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]

Fried, D. L.

Fu, M.

Fuentes, J. L.

Garcia, D.

Gavel, D.

Gluckstad, J.

Gong, W.

Graham, B.

B. Graham, “Fractional max-pooling,” https://arxiv.org/abs/1412.6071 .

Guo, H.

Hara, K.

K. Hara, D. Saito, and H. Shouno, “Analysis of function of rectified linear unit used in deep learning,” in 2015 International Joint Conference on Neural Networks (IJCNN), (IEEE, 2015), 1–8.

Hardy, J. W.

J. W. Hardy, Adaptive optics for astronomical telescopes (Oxford University, 1998), Vol. 16.

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), 7276 (2015).
[Crossref]

Hinton, G. E.

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “ImageNet Classification with Deep Convolutional Neural Networks,” in International Conference on Neural Information Processing Systems, (Curran Associates, Inc., 2012), 1097–1105.

Hiscock, T. W.

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]

Hockemeyer, 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]

Horisaki, R.

Hu, L.

Huang, B.

Q. Li, M. Reinig, D. Kamiyama, B. Huang, X. Tao, A. Bardales, and J. Kubby, “Woofer–tweeter adaptive optical structured illumination microscopy,” Photonics Res. 5(4), 329–334 (2017).
[Crossref]

Huang, H.

Huang, L.

X. Zhu, L. Huang, Y. Zheng, Y. Song, Q. Xu, J. Wang, K. Si, S. Duan, and W. Gong, “Ultrafast optical clearing method for three-dimensional imaging with cellular resolution,” Proc. Natl. Acad. Sci. U. S. A. 116(23), 11480–11489 (2019).
[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]

Ji, N.

N. Ji, “Adaptive optical fluorescence microscopy,” Nat. Methods 14(4), 374–380 (2017).
[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), 7276 (2015).
[Crossref]

Jin, Y.

Kamiyama, D.

Q. Li, M. Reinig, D. Kamiyama, B. Huang, X. Tao, A. Bardales, and J. Kubby, “Woofer–tweeter adaptive optical structured illumination microscopy,” Photonics Res. 5(4), 329–334 (2017).
[Crossref]

Kingma, D.

D. Kingma and J. Ba, “Adam: A Method for Stochastic Optimization,” https://arxiv.org/abs/1412.6980 .

Kirchhausen, T.

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IEEE Trans. Instrum. Meas. (1)

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J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

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Figures (6)

Fig. 1.
Fig. 1. The experimental optical system setup for learning based Shack-Hartmann wavefront sensor. P, linear polarizer plate; BS, beam splitter; SLM, spatial light modulator; BB, beam blocker; L1-L6, relay lenses; FS1-FS2, field stop; M1-M2, mirror; OBJ1-OBJ2, objective lenses; G, glass coverslip; BSP, beam splitter plate, 50:50 (R:T); CMOS, complementary metal oxide semiconductor camera; SHWS, Shack-Hartmann wavefront sensor, consists of a micro-lens array and a CMOS camera. The black dotted line indicates the conjugate plane of the SLM along the beam path.
Fig. 2.
Fig. 2. The architecture of the neural network and the processes of model training and testing. (a) The neural network architecture. (b) Processes of model training and testing. (c) Comparison of mode amplitude of Zernike coefficients between aberration and predicted wavefront in (b).
Fig. 3.
Fig. 3. Comparison of wavefront sensing capability of TSHWS and LSHWS. (a) Distorted SHWS pattern. (b) SHWS pattern compensated by the wavefront detected by TSHWS. (c) SHWS pattern compensated by the wavefront detected by LSHWS. Scale bar is 1 mm. (d) Comparison of numbered spots in (a), (b) and (c). Scale bar is 100 µm. (e) ‘I’, ‘II’ and ‘III’ represent the aberration wavefront, TSHWS detected wavefront and LSHWS detected wavefront, respectively. (f) Comparison of spots intensity profiles in (a), (b) and (c), the direction of profiles is indicated with green arrows in (a). The black dotted lines indicate the ideal centers of the spots. All the intensity distributions are normalized.
Fig. 4.
Fig. 4. Comparison of PSF before and after wavefront compensation. (a-b) Two groups of wavefront compensation results. In each group, the quiver plots of the SHWS spots, PSF patterns and their corresponding wavefront after compensation are presented. Scale bar in PSF pattern is 2 µm. (c-d) Comparison of the differences in detected amplitudes of Zernike mode coefficients in (a) and (b). (e-f) Comparison of central intensity profiles of PSF in (a) and (b). (g) RMS error of phase residuals of TSHWS and LSHWS from 100 testing datasets. Gray arrows indicate the datasets shown in (a) and (b). All the intensity distributions are normalized.
Fig. 5.
Fig. 5. Experimental validation on 300 µm mouse brain slice. (a-c) Three groups of wavefront compensation results. Scale bars in SHWS pattern and PSF pattern are 1 mm and 2 µm, respectively. (d) Comparison of central intensity profiles of PSF. ‘I’, ‘II’, and ‘III’ present the profiles in (a), (b) and (c) respectively. All the intensity distributions are normalized. (e) Comparison of detected amplitudes of Zernike mode coefficients in (b). The corresponding detected wavefronts are inserted in the sub-graphs.
Fig. 6.
Fig. 6. The PBR of corrected foci with two methods on 300 µm mouse brain tissue. (a) Thirty groups of wavefront compensation results. The dots in the figure present the PBR of corrected foci. (b) Statistic results of the improvements of PBR of LSHWS over TSHWS. The data sets shown in Figs. 5(a)–5(c) are corresponding to the 7th, 2rd, 12th test data in (a).

Tables (2)

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Table 1. Coefficient amplitude ranges of 2nd to 120th Zernike modes for datasets generating

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Table 2. The correlation coefficient of SHWS patterns and the Strehl ratio of PSFs (20 data sets)