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
Tracking the positions and orientations of single molecules within lipid membranes
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
O. Zhang, W. Zhou, J. Lu, T. Wu, and M. D. Lew, “Resolving the three-dimensional
translational dynamics of single molecules using radially and azimuthally polarized
fluorescence,” Nano Lett.22, 1024 (2022). [Open Scholarship, Article, Data, Summary
PDF, Video abstract]
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
Designing microscopes for optimal multidimensional nanoscale imaging
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.
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
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
Quantum and classical limits on measurement precision and sensitivity
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
O. Zhang and M. D. Lew, “Quantum limits for precisely estimating the orientation and
wobble of dipole emitters,” Phys. Rev. Research2, 033114 (2020). [Article, Summary PDF]
O. Zhang and M. D. Lew, “Single-molecule orientation localization microscopy I:
fundamental limits,” J. Opt. Soc. Am. A38, 277 (2021). [arXiv.org, Article]
O. Zhang and M. D. Lew, “Single-molecule orientation localization microscopy II: a
performance comparison,” J. Opt. Soc. Am. A38, 288 (2021). [arXiv.org, Article]
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)?
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
First demonstration of nanoscale super-resolved imaging with accurate molecular 3D
position and 3D orientation determination over an entire extended object
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
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
First experimental report to quantify the anisotropic rotational diffusion of a single
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
Correction: Appl. Phys. Lett.115, 069901 (2019). [Article]
Optimal design of point spread functions for resolving closely spaced emitters in 3D
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
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. Express30, 37154 (2022). [Article, Data]
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
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
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
T. Wu, P. Lu, M. A. Rahman, X. Li, and M. D. Lew, “Deep-SMOLM: deep learning resolves the
orientations and 2D positions of overlapping single
molecules with optimal nanoscale resolution,” Opt. Express30, 36761 (2022).
Engineering News, Article, Code, Data]
Wasserstein Induced Flux (WIF) for detecting image artifacts and heterogeneity
Any 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
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
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.
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
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]