Washington University in St Louis

The Preston M. Green Department of
Electrical & Systems Engineering


Single-Molecule Localization Microscopy of 3D Orientation and Anisotropic Wobble Using a Polarized Vortex Point Spread Function
J. Phys. Chem. B Vol. 125, Iss. 46 (2021). Image credit: Tianben Ding

Since the earliest invention of telescopes, microscopes, and eyeglasses, imaging systems have been designed to help humans visualize the world around us – big and small, near and far. These imaging systems collect the light reflected or emitted from an object and focus it onto our eyes or a camera. The design of these systems dictates that their images only contain two-dimensional (2D) information about an object and that their 2D images are blurred if the object is out of focus. We build imaging systems with new capabilities that surpass these shortcomings.

Super-resolution is a key feature of many of our imaging systems–the ability to overcome the resolution limit of wave physics, called the diffraction limit, in order to visualize the nanoscale world. Single-molecule imaging is also a central theme of our research–enabling our technology to see individual molecules as they drive biological and chemical dynamics at the nanoscale.

Our research

Video vignettes

6D single-molecule imaging using a multi-view reflector microscope [WEBM - 13.0 MB]

Deep-SMOLM: deep learning resolves the 3D orientations and 2D positions of overlapping single molecules with optimal nanoscale resolution [MP4 - 3.97 MB]
Resolving the three-dimensional rotational and translational dynamics of single molecules using radially and azimuthally polarized fluorescence [MP4 - 4.08 MB]
“Elucidating the nanoscale architecture of amyloid aggregates using a polarized donut point spread function” [MP4 - 54 MB]

“pixOL: pixel-wise point spread function engineering for measuring the 3D orientation and 3D location of dipole-like emitters” [MP4 - 38 MB]
“Robustly Detecting Imaging Model Mismatches and Reconstruction Artifacts in Single-Molecule Localization Microscopy” [MP4 - 57 MB]

Learn more

Sensing biological and chemical environments

Detecting chemical composition and enzyme activity within lipid membranes

Polar angle and wobble maps of Nile red molecules in lipid nanodomains
3D orientations of single fluorescent molecules reveal lipid nanodomains

Can the orientations of fluorescent probes be used to sense and image the surrounding chemical environment?

Using points accumulation for imaging in nanoscale topography (PAINT), our engineered Tri-spot PSF, and our Robust Statistical Estimation (RoSE) algorithm capable of measuring molecular orientations, we have characterized how the orientations of Nile red, merocyanine, DiI, and other lipid probes interact with lipid membranes. SMOLM resolves cholesterol concentration, lipid-ordered and liquid-disordered domains, and enzyme activity that cannot be resolved by localization alone.

Single-molecule orientation localization microscopy in lipid bilayers


[Back to top]

Tracking the positions and orientations of single molecules within lipid membranes

A radially and azimuthally polarized microscope resolves rotational dynamics of Nile red within lipid bilayers

How can we measure the translational and rotational dynamics of single molecules simultaneously with nanoscale precision?

Measuring radially and azimuthally polarized light enables high detection and estimation performance in single-molecule orientation-localization microscopy (SMOLM). This microscope reveals two interesting complementary phenomena: Nile red simultaneously exhibits large orientational motions but be motionless in the lateral direction within cholesterol-poor model lipid membranes. Nile red also shows dramatic jump diffusion while also being rotationally fixed in cholesterol-rich membranes.


[Back to top]

Imaging the nanoscale organization of amyloid aggregates

Locations of blinking Nile red molecules are combined to create a TAB super-resolution image of amyloid fibrils. [WebM - 3.29 MB]

How can we visualize how amyloid aggregates are organized at the nanoscale?

Using Transient Amyloid Binding (TAB), a polarization-sensitive fluorescence microscope, and our Robust Statistical Estimation (RoSE) algorithm capable of measuring molecular orientation, we have demonstrated SMOLM for resolving the positions and orientations of Nile red (NR) molecules on the surfaces of amyloid aggregates. SMOLM resolves disordered NR orientations that may represent heterogeneous beta-sheet assemblies in amyloid fibrils that cannot be resolved by localization alone.

“Flyover” animation of single-molecule orientation localization microscopy [WebM - 20.3 MB]. See more animations and interactive demos.


[Back to top]

Transient Amyloid Binding (TAB)

Locations of blinking ThT molecules create a TAB super-resolution image of amyloid fibrils. [WebM - 4.24 MB]

How can we visualize amyloid aggregation at nanometer resolution with minimum perturbation over extended time periods?

Amyloid aggregates are signatures of neurodegenerative disorders such as Alzheimer’s disease. We developed Transient Amyloid Binding (TAB) super-resolution microscopy to resolve amyloid structures using the standard probe, Thioflavin T (ThT), without the need for covalent modification or immunostaining of amyloids. Spontaneous binding and corresponding bursts of ThT fluorescence on amyloids are used to reconstruct super-resolution images of native amyloid structures.


[Back to top]

Designing microscopes for optimal multidimensional nanoscale imaging


Images of a rotating dipole using a polarized microscope

The orientations and rotations of fluorescent molecules have been used to study the movements of molecular motors along microtubules, the stretching and bending of DNA, the dynamics and composition of lipid membranes, and the spatial and temporal organization of various soft materials. However, current technologies have trouble distinguishing and resolving these dynamics, e.g., neighboring molecules that are fixed in space vs. one molecule that is translationally fixed but rotating over time. We are designing optimal imaging systems and point spread functions (PSFs) for measuring molecular positions and orientations. Such technologies leverage 1) how molecules are excited by polarized illumination, 2) the polarization of fluorescence light emitted by the molecules, and 3) the radiation pattern of the fluorescence emitted by the molecules.

Explore how we design new imaging capabilities:

Fundamental limits on measurement accuracy


Bias in measurements of rotational diffusion [MP4 - 7.62 MB]
  • 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.


[Back to top]

Quantum and classical limits on measurement precision and sensitivity

An interferometric imaging system for achieving the Quantum Cramer-Rao Bound 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.


  • 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]

[Back to top]

Multi-view reflector microscope

The multi-view reflector (MVR) imaging architecture enables us to measure molecular orientation robustly in 3D. [MP4 - 2.1 MB]
How can new optical architectures boost imaging performance?

  • Extremely little light is collected from individual blinking molecules.
  • Measuring a molecule's 3D position and 3D orientation simultaneously with isotropic, nanoscale resolution is a formidable challenge.

The MVR microscope localizes the 3D positions and 3D orientations of Nile red accurately and precisely. [MP4 - 2.6 MB]
The multi-view reflector (MVR) architecture:

  • Measures the 3D positions and 3D orientations of single molecules with 10.9 nm and 2.0° precisions, respectively, over a 1.5 µm depth range.
  • Accurately resolves spherical lipid bilayers despite refractive-index mismatch.
  • Resolves the infiltration of lipid membranes by amyloid-beta oligomers by measuring the rotational dynamics of Nile red fluorophores.
  • Detects heterogeneities in the fluidity of cellular membranes via 6D imaging of merocyanine 540 fluorophores.

The MVR microscope measures the morphology and fluidity of HEK-293T cell membranes with nanoscale resolution in 6D. [MP4 - 1.0 MB]

[Back to top]

pixOL: Dipole-spread function engineering

The pixOL microscope resolves lipid morphology and organization in 3D Challenges in 6D single-molecule orientation-localization microscopy:

  • Spatial and angular information are mixed within the image of a fluorescent molecule, called its dipole-spread function (DSF).
  • How can we optimize a phase mask to optimally encode 6D molecular information: 3D position (x, y, and z)and 3D orientation (polar angle θ, azimuthal angle ϕ, and rotational “wobble” solid angle Ω)?

Single-molecule detection using the pixOL microscope [MP4 - 6.7 MB]
We demonstrate the pixOL microscope:

  • Uses a pixel-wise optimization algorithm to engineer the Green's tensor of a microscope--the dipole extension of point-spread function engineering
  • Achieves optimal precision to simultaneously measure the 3D orientation and 3D location of a single molecule, i.e., 4.1° orientation, 0.44 sr wobble angle, 23.2 nm lateral localization, and 19.5 nm axial localization precisions over a 700 nm depth range using 2500 detected photons
  • First demonstration of nanoscale super-resolved imaging with accurate molecular 3D position and 3D orientation determination over an entire extended object


3D view of 6D single-molecule orientation-localization microscopy (SMOLM) of Nile red within spherical supported lipid bilayers consisting of (top) DPPC plus cholesterol (chol) and (bottom) DPPC-only [MP4 - 6.9 MB]. See more animations.

[Back to top]

The vortex dipole-spread function

The polarized vortex PSF resolves single-molecule wobble in 3D 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?

SMOLM reconstruction of an amyloid fiber from blinking Nile red molecules collected by the vortex microscope [MP4 - 19.0 MB]
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


“Flyover” animation of 3D single-molecule orientation localization microscopy [MP4 - 23.0 MB]. See more animations and interactive demos.

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]

[Back to top]

The Tri-spot dipole-spread function

Tri-spot PSF concept art 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


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]

[Back to top]

Optimal design of point spread functions for resolving closely spaced emitters in 3D

Towards optimal point spread function design for resolving closely spaced emitters in three dimensionsMost 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?

Translating tetrapod-like PSF and rotating crescent PSF
Encoding 3D emitter position into optical PSFs. Left: A tetrapod-like PSF contracts and expands as an emitter moves through focus. Right: The crescent PSF rotates as an emitter moves through focus. Scalebar: 1 µm.

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)


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]

[Back to top]

Building multidimensional image analysis algorithms robust against bias and noise

Deep-SMOLM resolves the 3D orientations and 2D positions of single molecules, even when their images overlap

Demonstration of SM detection and position-orientation estimation using Deep-SMOLM. [MP4 - 3.6 MB]

Severe shot noise, overlapping images of blinking molecules, and simultaneously fitting high-dimensional information—both orientation and position—greatly complicates image analysis in single-molecule orientation-localization microscopy (SMOLM).

How can we design an SMOLM image analysis algorithm that is precise, computationally efficient, and robust against these effects?

Deep-SMOLM is a deep-learning based estimator that:

  • Achieves superior 3D orientation and 2D position measurement precision above and beyond traditional iterative approaches, within 3% of the theoretical limit
  • Demonstrates state-of-the-art estimation performance when molecule images overlap, e.g., achieving 95% accuracy for emitters separated by 139 nm, corresponding to a 43% image overlap
  • Accurately and precisely reconstructs 5D images of both simulated biological fibers and experimental amyloid fibrils at a speed ˜10 times faster than iterative estimators


[Back to top]

Wasserstein Induced Flux (WIF) for detecting image artifacts and heterogeneity

WIF effectively denoises inaccurate fits from any localization softwareAny image analysis algorithm (both physics-based methods and data-driven deep learning techniques) uses an internal model of the imaging system to estimate the parameters of interest (e.g., the position of a single molecule). How can we detect if the model is incorrect for some or all of the observed data without knowing the ground truth?

“Quantifying and Maximizing Imaging Accuracy in Single-Molecule Super-Resolution Microscopy,” Invited talk at ISBI 2020 [MP4 - 184 MB]

WIF is a technique that tests the stability of a localization under a controlled computational perturbation and measures the consistency of any computational imaging model to explain the observed raw microscope images. We demonstrate WIF's ability to detect localization errors stemming from overlapping images, dipole emission patterns, and optical aberrations. WIF also quantifies heterogeneities in the observed single-molecule images that arise from different molecular orientations.


[Back to top]

Robust Statistical Estimation (RoSE) software

RoSE demonstration [MP4 - 2.40 MB]

How can we estimate the likelihood that a fluorescent molecule is emitting light from each pixel within an object domain? And how can we estimate the likelihood that a molecule within a pixel belongs to an unknown target structure?

RoSE works for arbitrary 3D point spread functions (PSFs) and biological structures. It calculates the likelihood that each image pixel contains a molecule, and not background light, by leveraging spatial sparsity. Further, by analyzing blinking statistics, it can also calculate the confidence of each pixel in truly representing the target structure. RoSE thereby minimizes false localizations that cause bias and artifacts in super-resolution microscopy.


  1. H. Mazidi, J. Lu, A. Nehorai, and M. D. Lew, “Minimizing Structural Bias in Single-Molecule Super-Resolution Microscopy,” Sci. Rep. 8, 13133 (2018). [Article, Data, Summary PDF]
  2. H. Mazidi, E. S. King, O. Zhang, A. Nehorai, and M. D. Lew, “Dense Super-Resolution Imaging of Molecular Orientation via Joint Sparse Basis Deconvolution and Spatial Pooling,” 2019 IEEE 16th International Symposium on Biomedical Imaging (ISBI 2019), 325 (2019). [arXiv.org, Article]

Try our software

Check out our repositories on GitHub. Contact us if you need any assistance.

[Back to top]