Model-based aberration corrected microscopy inside a glass tube

Abstract

Microscope objectives achieve near diffraction-limited performance only when used under the conditions they are designed for. In nonstandard geometries, such as thick cover slips or curved surfaces, severe aberrations arise, inevitably impairing high-resolution imaging. Correcting such large aberrations using standard adaptive optics can be challenging: existing solutions are either not suited for strong aberrations, or require extensive feedback measurements, consequently taking a significant portion of the photon budget. We demonstrate that it is possible to precompute the corrections needed for high-resolution imaging inside a glass tube based on a priori information only. Our ray-tracing-based method achieved over an order of magnitude increase in image contrast without the need for a feedback signal.

Keywords: 2PEF; a priori; aberration correction; digital twin; fluorescence; laser scanning; lumen; microscopy; model based; nonlinear; organ‐on‐a‐chip; ray tracing; spatial light modulator; tube; two‐photon; wavefront shaping.

FIGURE 1

(A) Without any correction, focusing inside a tube causes an aberrated focus. This prevents high‐resolution imaging. (B) A model is used in a ray tracing simulation to compute a phase pattern to correct the focus at a specified location. (C) A spatial light modulator is used to display the computed corrections. A sharp focus is formed, enabling high‐resolution imaging.

FIGURE 2

Sensitivity of the computed correction pattern for the bottom of the tube to deviations in the model parameters. For each pattern, the absolute squared overlap coefficient ${|\gamma |}^2$ with the unperturbed pattern is plotted as a blue line with dots. In each plot, solid black vertical lines indicate the unperturbed parameters. Dashed black vertical lines indicate the error margins. Lastly, for a flat phase pattern (i.e. no correction) we found ${|\gamma |}^2=0.047$. This value is indicated with red dashed horizontal lines. (A) Sensitivity to outer radius. (B) Sensitivity to shell thickness. (C) Sensitivity to refractive index of tube. (D) Sensitivity to tube rotation around the optical axis.

FIGURE 3

(A) Bright field image of the capillary glass tube. The tube has an inner diameter of 142 $\mu \mathrm{m}$ and an outer diameter of 573 $\mu \mathrm{m}$. The red rectangle indicates the volume imaged with 2PEF. (B–J) 2PEF images of 0.5 $\mu \mathrm{m}$ fluorescent beads in agar inside a capillary glass tube. All fluorescence images are 99.5‐percentile projections of the imaged volume. The color bar indicates the ${\log }_{10}$ of the signal intensity. (F) Without aberration correction. (B–E, G–J) Aberration corrected images. The circular tube inner cross‐section is clearly visible. Each fluorescence image includes an inset with the corresponding phase correction pattern that was used. Since the optical pathlength difference within each correction pattern greatly exceeds the wavelength, the phase correction pattern is wrapped to $[0,2\pi ]$. The patterns were computed/optimised for various target focus locations, which are marked by a cyan $\times$. (B–E) Correction patterns computed using our model‐based ray tracing (RT) method. (G–J) Correction patterns acquired by scanning two Zernike modes in a feedback‐based brute‐force grid‐search. The color scale indicates the ${\log }_{10}$ of the signal intensity of the photon multiplier tube, and is the same for all images.