Volumetric nanoscale localization using engineered point spread functions in light sheet microscopy

Technical Summary: Volumetric Nanoscale Localization Using Engineered Point Spread Functions in Light Sheet Microscopy

Problem Statement
Nanoscale three-dimensional localization across large biological volumes remains a significant challenge in optical microscopy. Existing approaches typically face a trade-off between imaging speed, volumetric field of view (FOV), and localization precision. While engineered point spread functions (ePSFs) enable 3D localization without mechanical sectioning, extending their axial range often degrades localization precision and necessitates sparse labeling to avoid emitter overlap. Conversely, methods capable of handling high emitter densities often remain confined to small axial ranges (approximately 8 µm or less). Consequently, achieving simultaneous nanometer-scale precision and extended volumetric imaging has been a persistent limitation, restricting super-resolution mapping to isolated optical sections rather than entire cellular or multicellular systems.

Methodology
The authors address this challenge by integrating a twin Airy engineered point spread function (ePSF) with two-photon light sheet fluorescence microscopy (LSFM). The experimental setup utilizes an open-top geometry with a femtosecond-pulsed Gaussian illumination beam (860 nm for beads, 790 nm for biological samples) scanned to form a light sheet with a 4.7 µm full-width half-maximum thickness and a 150 µm Rayleigh range.

Key methodological innovations include:

• Twin Airy ePSF: A spatial light modulator (SLM) positioned in the Fourier plane of the collection arm modulates the fluorescence emission to generate a twin Airy PSF. This design allows the axial ($z$) position of an emitter to be inferred directly from the displacement of two principal Airy beams, offering an intuitive route to 3D localization.
• Broadband Propagation Modeling: Unlike many ePSF implementations that rely on narrowband assumptions, the authors developed a broadband propagation model to account for the spectral width of biological fluorophores (spanning ~150 nm). This model explicitly incorporates the broadband emission characteristics to ensure accurate localization under realistic conditions.
• Zero-Order Preservation: The study demonstrates that preserving the zero-order light from the SLM (rather than filtering it out via spectral or spatial filtering) does not adversely affect localization precision. This approach maintains a high photon flux and space-bandwidth product, avoiding the performance degradation associated with spectral filtering required to eliminate the zero order in broadband applications.
• Optimization: The twin Airy phase mask was optimized using Cramér-Rao lower bound (CRLB) analysis combined with the propagation model, yielding an optimal scale factor ($\alpha$) of 5.35 for the specific light sheet geometry.

Key Contributions

• Scalable Volumetric Imaging: The framework successfully decouples instantaneous emitter density from the total imaging volume. By confining fluorescence generation to a thin light sheet, the system limits the number of emitters per frame, suppressing PSF overlap without requiring complex computational multi-emitter recovery algorithms.
• Broadband Compatibility: The explicit incorporation of broadband fluorescence emission characteristics into the PSF design and modeling ensures robust performance with standard biological fluorophores, avoiding the photon budget losses associated with narrowband spectral filtering.
• Hardware Integration: The study shows that this approach can be implemented as a straightforward modification to existing LSFM systems by adding an SLM to the collection path, facilitating the transition to single-emitter localization in light sheet microscopy.

Results
The system was validated using fluorescent bead phantoms and live mammalian oocytes:

• Localization Precision: The system achieved lateral localization precisions of $\Delta x = 19$ nm and $\Delta y = 16$ nm, and an axial precision of $\Delta z = 42$ nm. These values were obtained over a field of view of 295 µm $\times$ 330 µm and an axial range of 100 µm.
• Theoretical Limits: Theoretical CRLB analysis suggested potential precisions of $\Delta x = 2.72$ nm, $\Delta y = 3.28$ nm, and $\Delta z = 9.54$ nm, indicating that current experimental performance is primarily limited by mechanical vibrations and thermal drift rather than the intrinsic performance of the ePSF.
• Biological Application: The method successfully localized fluorescent beads injected into murine oocytes (approx. 80 µm in diameter) throughout the oocyte volume. The bead localizations were overlaid onto conventional LSFM images of Phalloidin-stained transzonal projections, demonstrating the platform's ability to provide structural context in biologically complex environments.
• Comparison: The approach surpasses previous ePSF-based localization microscopy in terms of accessible imaging volume (several orders of magnitude increase) while maintaining comparable localization precision. It also offers lower computational demands compared to high-density volumetric methods that rely on deep learning or deconvolution to disentangle overlapping emitters.

Significance and Claims
The paper claims to establish a scalable strategy for localization-based super-resolution imaging across biologically relevant volumes, effectively bridging the gap between nanoscale precision and large-scale volumetric microscopy. The authors assert that by shifting the burden of emitter separability from computational post-processing to optical control at the point of acquisition, the method enables nanoscale mapping throughout extended biological volumes without requiring complex multi-emitter fitting.

The authors note that current performance limits are driven by mechanical stability rather than theoretical bounds. They project that in the absence of mechanical vibrations, the system could achieve sub-10-nm localization precision over millimeter-scale imaging volumes. The work positions this approach as a complementary alternative to high-density computational methods, offering a path toward 3D super-resolution microscopy that is both optically efficient and computationally tractable.