More Design Research | Lew Lab at Washington University in St. Louis

• Fundamental limits of measuring wobble accurately
• Quantum and classical limits on measurement precision and sensitivity
• Polarized vortex dipole-spread function
• Tri-spot dipole-spread function
• Crescent point-spread function

Challenge:

• Any measurement noise, e.g., Poisson shot noise, causes the apparent rotation of a fluorescent molecule to appear more constrained than it actually is.
• For 1000 signal photons and 30 background photons per pixel, a single molecule diffusing within a cone of half-angle 78° is indistinguishable from a molecule that is completely free to rotate (half-angle of 90°).

We developed a mathematical model to characterize the accuracy of measuring rotational diffusion, comparing popular and state-of-the-art 2D and 3D methods:

• 2D and 3D methods will perceive the same 3D orientation changes (molecular “wobble”) differently, depending on how far a molecule is oriented out of plane on average.
• In-plane (perpendicular to optical axis) and out-of-plane molecules will exhibit different measurement errors for various measurement techniques.
• The standard PSF has a comparatively large measurement bias for out-of-plane molecules.
• The Tri-spot PSF exhibits consistent performance for both in-plane and out-of-plane molecules.

Read:

• New, fundamental limit to ‘seeing and believing’ in imaging - The Source
• O. Zhang and M. D. Lew, “Fundamental Limits on Measuring the Rotational Constraint of Single Molecules using Fluorescence Microscopy,” Phys. Rev. Lett. 122, 198301 (2019). [The Source - Washington University, arXiv.org, Article, Summary PDF]

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How sensitive or precise can an imaging system be for measuring the orientation of a single molecule? What are the fundamental limits on making the best-possible measurement?

• The Quantum Cramér-Rao bound (QCRB) is a fundamental bound on the best-possible measurement variance that any imaging system can achieve.
• We computed the QCRB for molecules fixed in orientation and propose an interferometric imaging system whose measurements can theoretically achieve this limit.
• For molecules that “wobble” during a camera frame, we found that their average orientations and degree of “wobble” cannot be measured with optimal QCRB-limited precision simultaneously. That is, a scientist must choose which parameter they most care about and make a tradeoff: use an imaging system optimized for that specific task.

Read:

• O. Zhang and M. D. Lew, “Quantum limits for precisely estimating the orientation and wobble of dipole emitters,” Phys. Rev. Research 2, 033114 (2020). [Article, Summary PDF]
• O. Zhang and M. D. Lew, “Single-molecule orientation localization microscopy I: fundamental limits,” J. Opt. Soc. Am. A 38, 277 (2021). [arXiv.org, Article]
  
• O. Zhang and M. D. Lew, “Single-molecule orientation localization microscopy II: a performance comparison,” J. Opt. Soc. Am. A 38, 288 (2021). [arXiv.org, Article]
  

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Challenges in single-molecule orientation-localization microscopy:

• Poor sensitivity to polar orientation (in and out of the imaging plane): Can we design a method with dramatically improved sensitivity?
• 3D molecular wobble: Existing techniques can only measure rotational diffusion as an average across all directions. Can we discern wobble fully in 3 dimensions, with perhaps more in one direction versus another?

We developed the polarized vortex dipole-spread function:

• Measures the 2D position, 3D orientation, and 3D rotational diffusion of single molecules
• Improved sensitivity using two orthogonally polarized imaging channels
• Chemical sensing in lipid membranes: Observed the wobble anisotropies of Nile red molecules changing with cholesterol concentration in the membrane
• Detected unique orientation signatures of amyloid aggregates: Nile red exhibits unique orientational behaviors when bound to amyloid fibrils, oligomers, and fibrillar tangles.
• First experimental report to quantify the anisotropic rotational diffusion of a single molecule

Read:

T. Ding and M. D. Lew, “Single-Molecule Localization Microscopy of 3D Orientation and Anisotropic Wobble Using a Polarized Vortex Point Spread Function,” J. Phys. Chem. B 125, 12718 (2021). [Journal cover, Open Scholarship, Article, Data, Summary PDF]

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Challenges when measuring orientational parameters of dipole-like emitters

• Fluorophore brightness: need to resolve orientation and “wobble” of molecules without spreading their photons over too many measurements
• Measurement degeneracy: using existing techniques, certain orientations produce similar images and cannot be resolved

We developed the Tri-spot dipole-spread function for improved:

• Temporal resolution: 3D orientational parameters of molecules in a large field of view are measured simultaneously using one camera frame
• Orientation resolvability: each orientation produces a unique image
• Near-optimal SNR: least number of measurements required to resolve all possible orientational second moments
• High precision: optimized sensitivity towards all orientational parameters

Read:

O. Zhang, J. Lu, T. Ding, and M. D. Lew, “Imaging the three-dimensional orientation and rotational mobility of fluorescent emitters using the Tri-spot point spread function,” Appl. Phys. Lett. 113, 031103 (2018). [Open Scholarship, Article, Summary PDF]
Correction: Appl. Phys. Lett. 115, 069901 (2019). [Article]

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Most methods for 3D super-resolution imaging focus on single-emitter localization as a performance metric, ignoring the important task of resolving and localizing overlapping emitters in 3D.

How can we express the joint task of resolving overlapping emitters mathematically? Is there a globally optimal point spread function (PSF) that achieves the best possible performance? Are there general design principles that are optimal for this task?

We discover that there are two types of PSFs that achieve high performance. One PSF is very similar to the existing Tetrapod PSFs; the other is a rotating single-spot PSF which we call the crescent PSF. The crescent PSF:

• Exhibits excellent performance for localizing single emitters throughout a 1-μm focal volume (localization precisions of 7.3 nm in x, 7.7 nm in y, and 18.3 nm in z using 1000 detected photons)
• Distinguishes between one and two closely spaced emitters with superior accuracy (25-53% lower error rates than the best-performing Tetrapod PSF, averaged throughout a 1-µm focal volume)

Read:

J. M. Jusuf and M. D. Lew, “Towards optimal point spread function design for resolving closely spaced emitters in three dimensions,” Opt. Express 30, 37154 (2022). [Article, Data]

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