Accurate Phase Retrieval of Complex 3D Point Spread Functions with Deep Residual Neural Networks

Overview

Journal Appl Phys Lett

Date 2020 Mar 5

PMID 32127719

Citations 19

Authors

Leonhard Mockl

Petar N Petrov

W E Moerner

Affiliations

Soon will be listed here.

Abstract

Phase retrieval, i.e., the reconstruction of phase information from intensity information, is a central problem in many optical systems. Imaging the emission from a point source such as a single molecule is one example. Here, we demonstrate that a deep residual neural net is able to quickly and accurately extract the hidden phase for general point spread functions (PSFs) formed by Zernike-type phase modulations. Five slices of the 3D PSF at different focal positions within a two micrometer range around the focus are sufficient to retrieve the first six orders of Zernike coefficients.

Citing Articles

Deep-blur: Blind identification and deblurring with convolutional neural networks.

Debarnot V, Weiss P Biol Imaging. 2025; 4():e13.

PMID: 39776610 PMC: 11704139. DOI: 10.1017/S2633903X24000096.

X-ray lens figure errors retrieved by deep learning from several beam intensity images.

Sanchez Del Rio M, Celestre R, Reyes-Herrera J J Synchrotron Radiat. 2024; 31(Pt 5):1001-1009.

PMID: 39042577 PMC: 11371063. DOI: 10.1107/S1600577524004958.

Universal inverse modeling of point spread functions for SMLM localization and microscope characterization.

Liu S, Chen J, Hellgoth J, Muller L, Ferdman B, Karras C Nat Methods. 2024; 21(6):1082-1093.

PMID: 38831208 DOI: 10.1038/s41592-024-02282-x.

Using Diffraction Deep Neural Networks for Indirect Phase Recovery Based on Zernike Polynomials.

Yuan F, Sun Y, Han Y, Chu H, Ma T, Shen H Sensors (Basel). 2024; 24(2).

PMID: 38276390 PMC: 10819540. DOI: 10.3390/s24020698.

Aberration Estimation for Synthetic Aperture Digital Holographic Microscope Using Deep Neural Network.

Jeon H, Jung M, Lee G, Hahn J Sensors (Basel). 2023; 23(22).

PMID: 38005665 PMC: 10674498. DOI: 10.3390/s23229278.

References

Guo H, Korablinova N, Ren Q, Bille J . Wavefront reconstruction with artificial neural networks. Opt Express. 2009; 14(14):6456-62. DOI: 10.1364/oe.14.006456. View

Paine S, Fienup J . Machine learning for improved image-based wavefront sensing. Opt Lett. 2018; 43(6):1235-1238. DOI: 10.1364/OL.43.001235. View

Facomprez A, Beaurepaire E, Debarre D . Accuracy of correction in modal sensorless adaptive optics. Opt Express. 2012; 20(3):2598-612. DOI: 10.1364/OE.20.002598. View

Siemons M, Hulleman C, Thorsen R, Smith C, Stallinga S . High precision wavefront control in point spread function engineering for single emitter localization. Opt Express. 2018; 26(7):8397-8416. DOI: 10.1364/OE.26.008397. View

Yan T, Richardson C, Zhang M, Gahlmann A . Computational correction of spatially variant optical aberrations in 3D single-molecule localization microscopy. Opt Express. 2019; 27(9):12582-12599. DOI: 10.1364/OE.27.012582. View

von Diezmann A, Lee M, Lew M, Moerner W . Correcting field-dependent aberrations with nanoscale accuracy in three-dimensional single-molecule localization microscopy. Optica. 2016; 2(11):985-993. PMC: 4782984. DOI: 10.1364/OPTICA.2.000985. View

Nishizaki Y, Valdivia M, Horisaki R, Kitaguchi K, Saito M, Tanida J . Deep learning wavefront sensing. Opt Express. 2019; 27(1):240-251. DOI: 10.1364/OE.27.000240. View

Shechtman Y, Sahl S, Backer A, Moerner W . Optimal point spread function design for 3D imaging. Phys Rev Lett. 2014; 113(13):133902. PMC: 4381866. DOI: 10.1103/PhysRevLett.113.133902. View

Petrov P, Shechtman Y, Moerner W . Measurement-based estimation of global pupil functions in 3D localization microscopy. Opt Express. 2017; 25(7):7945-7959. PMC: 5810908. DOI: 10.1364/OE.25.007945. View

10.

Moomaw B . Camera technologies for low light imaging: overview and relative advantages. Methods Cell Biol. 2013; 114:243-83. DOI: 10.1016/B978-0-12-407761-4.00011-7. View

11.

Quirin S, Pavani S, Piestun R . Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions. Proc Natl Acad Sci U S A. 2012; 109(3):675-9. PMC: 3271897. DOI: 10.1073/pnas.1109011108. View

12.

von Diezmann L, Shechtman Y, Moerner W . Three-Dimensional Localization of Single Molecules for Super-Resolution Imaging and Single-Particle Tracking. Chem Rev. 2017; 117(11):7244-7275. PMC: 5471132. DOI: 10.1021/acs.chemrev.6b00629. View

13.

Mortensen K, Churchman L, Spudich J, Flyvbjerg H . Optimized localization analysis for single-molecule tracking and super-resolution microscopy. Nat Methods. 2010; 7(5):377-81. PMC: 3127582. DOI: 10.1038/nmeth.1447. View

14.

Zhang P, Liu S, Chaurasia A, Ma D, Mlodzianoski M, Culurciello E . Analyzing complex single-molecule emission patterns with deep learning. Nat Methods. 2018; 15(11):913-916. PMC: 6624853. DOI: 10.1038/s41592-018-0153-5. View

15.

Ouyang W, Aristov A, Lelek M, Hao X, Zimmer C . Deep learning massively accelerates super-resolution localization microscopy. Nat Biotechnol. 2018; 36(5):460-468. DOI: 10.1038/nbt.4106. View

16.

Debarre D, Booth M, Wilson T . Image based adaptive optics through optimisation of low spatial frequencies. Opt Express. 2009; 15(13):8176-90. DOI: 10.1364/oe.15.008176. View

17.

Wang W, Ye F, Shen H, Moringo N, Dutta C, Robinson J . Generalized method to design phase masks for 3D super-resolution microscopy. Opt Express. 2019; 27(3):3799-3816. DOI: 10.1364/OE.27.003799. View

18.

Backer A, Moerner W . Extending single-molecule microscopy using optical Fourier processing. J Phys Chem B. 2014; 118(28):8313-29. PMC: 4317050. DOI: 10.1021/jp501778z. View

19.

Lew M, Moerner W . Azimuthal polarization filtering for accurate, precise, and robust single-molecule localization microscopy. Nano Lett. 2014; 14(11):6407-13. PMC: 4245985. DOI: 10.1021/nl502914k. View

20.

Goy A, Arthur K, Li S, Barbastathis G . Low Photon Count Phase Retrieval Using Deep Learning. Phys Rev Lett. 2019; 121(24):243902. DOI: 10.1103/PhysRevLett.121.243902. View