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Multi-scale sensorless adaptive optics: application to stimulated emission depletion microscopy

Jacopo Antonello, Aurélien Barbotin, Ee Zhuan Chong, Jens Rittscher, and Martin J. Booth

Open Access Open Access

Abstract

Sensorless adaptive optics is commonly used to compensate specimen-induced aberrations in high-resolution fluorescence microscopy, but requires a bespoke approach to detect aberrations in different microscopy techniques, which hinders its widespread adoption. To overcome this limitation, we propose using wavelet analysis to quantify the loss of resolution due to the aberrations in microscope images. By examining the variations of the wavelet coefficients at different scales, we are able to establish a multi-valued image quality metric that can be successfully deployed in different microscopy techniques. To corroborate our arguments, we provide experimental verification of our method by performing aberration correction experiments in both confocal and STED microscopy using three different specimens.

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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Data Availability

The research materials supporting this publication can be accessed at https://doi.org/10.5287/bodleian:7RzzNpw4P.

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Figures (9)
Fig. 1.
Fig. 1. Comparison of the Fourier and wavelet analyses of an image. (a) 2D STED image (raw photon counts; $400 \times 400$ pixels; HeLa cell nucleus); (b) magnitude of the Fourier spectrum of the image in logarithmic scale. (c) and (d) wavelet coefficients at scales of 100 and 800 nm, respectively. Linear scale.

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Fig. 2.
Fig. 2. Simulation results showing the sensitivity of vector $\mathbf {m}$ to the residual aberration $c$ . For each value of $c$ , an aberrated image is generated (see Section 3) and the corresponding value of $\mathbf {m}$ is computed. (a)–(c) elements of $\mathbf {m}$ corresponding to scales 75.2, 150.3, and 300.6 nm; (d) evolution of $\mathbf {m}$ as $c$ varies between −1 and 1. The scalebar on the right indicates the residual rms, i.e., $|c|$ . As $|c|$ increases, the finer scales elements $m_1$ and $m_2$ decrease whereas the coarse scale element $m_3$ increases.

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Fig. 3.
Fig. 3. Fits of the elements of $\mathbf {m}$ obtained from one iteration of the generalised $PN$ algorithm applied to correct coma (Noll index 7). The markers denote experimental data and the lines show the fits. The corresponding wavelet scales are reported on the right. The optimal correction to apply is computed as a linear combination of the extrema of each fit (see Section 4), and is indicated with a dashed line. This correction was obtained in our experiments in Section 6, see the STED correction in Fig. 7.

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Fig. 4.
Fig. 4. Layout of the adaptive STED microscope described in detail in Section 5. Legend: L lens; P pinhole; ${\lambda} /2$ half-wave plate; ${\lambda} /4$ quarter-wave plate; A aperture; C CMOS camera; PBS polarising beam splitter; D dichroic beam splitter; Q quad-band beam splitter; F emission filter; BS beam splitter; MMF multi-mode fibre; R resonant mirror; G galvanometer mirror; M flat mirror; W achromatic quarter-wave plate; $\varnothing$ conjugate pupil planes.

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Fig. 5.
Fig. 5. Maximum projections of CA1 pyramidal neurons filled with Alexa 594 in an organotypic hippocampal slice imaged at a depth of approximately 8 ${\mu}$ m. The projections are computed by summing the raw photon counts of a $20 \times 20 \times 4$ ${\mu}$ m $^3$ volume ( $400 \times 400 \times 80$ pixels). (a) and (b) $xy$ projections acquired in confocal and Z-STED mode, respectively; (c) and (d) $xz$ projections; (e) profiles of the lines marked in the $xy$ projections, computed using cubic interpolation; (f) profiles of the lines marked in the $xz$ projections. Static aberrations have been corrected.

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Fig. 6.
Fig. 6. Maximum projections of CA1 pyramidal neurons imaged in Z-STED mode before and after AO at a depth of approximately 14 ${\mu}$ m. The projections are obtained from the raw photon counts of a $20 \times 20 \times 4$ ${\mu}$ m $^3$ volume ( $200 \times 200 \times 80$ pixels). (a) and (b) $xy$ projections before and after AO, respectively; (c) and (d) $xz$ projections; (e) profiles of the lines marked in the $xy$ projections; (f) profiles of the lines marked in the $xz$ projections; (g) Zernike aberrations corrected in confocal mode. The coefficients are enumerated and normalised according to Noll [23], and given in units of nm; (h) Zernike aberrations corrected in Z-STED mode, obtained using the preceding confocal correction as an initial condition.

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Fig. 7.
Fig. 7. Maximum projections of actin labelled with silicon rhodamine in COS-7 cells imaged in Z-STED mode before and after AO at a depth of approximately 6 ${\mu}$ m. The projections are obtained from the raw photon counts of a $20 \times 20 \times 5$ ${\mu}$ m $^3$ volume ( $500 \times 500 \times 120$ pixels). (a) and (b) $xy$ projections before and after AO, respectively; (c) and (d) $xz$ projections; (e) profiles of the lines marked in the $xy$ projections; (f) profiles of the lines marked in the $xz$ projections; (g) Zernike aberrations corrected in confocal mode; (h) Zernike aberrations corrected in Z-STED mode, obtained using the preceding confocal correction as an initial condition.

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Fig. 8.
Fig. 8. Comparison before and after the correction reported in Fig. 7. (a) $20 \times 20$ ${\mu}$ m $^2$ $xy$ cross section ( $500 \times 500$ pixels) imaged in 3D STED mode before AO; (b) same as in (a) after AO; (c) $20 \times 5$ ${\mu}$ m $^2$ $xz$ cross section ( $500 \times 120$ pixels) imaged in Z-STED mode before AO; (d) same as in (c) after AO. (e) profiles of the lines marked in (a) and (b); (f) profiles of the lines marked in (c) and (d).

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Fig. 9.
Fig. 9. HeLa cell nucleus in mid S-phase with replication sites labelled by a short EdU pulse and detected with Alexa Fluor 594. The imaging mode is Z-STED. (a) $20 \times 8$ ${\mu}$ m $^2$ $xz$ cross section ( $400 \times 160$ pixels) before AO; (b) same as (a) after AO; (c) profiles marked in the cross sections; (d) Zernike aberrations corrected in confocal mode; (e) Zernike aberrations corrected in Z-STED mode, obtained using the preceding confocal correction as an initial condition.

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Equations (4)

Equations on this page are rendered with MathJax. Learn more.

a j = h ↑ j − 1 ∗ a j − 1 , d j = a j − 1 − a j ,
m ′ := [ ∑ k | ( d 1 ) k | 2 ⋮ ∑ k | ( d J ) k | 2 ] ,
m := m ′ / | m ′ | ,
C := ( Π + H T H ) − 1 H T ,
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