Superresolution
fluorescence microscopy
Leonid Keselman, Daniel Fernandes

Overview
1.What is “super-resolution”
a. Diffraction
b. STORM

2.Compressed Sensing
a. Applied to STORM

3.Light Sheet Imaging
a. Lattice-Light SheetsNatural Resolution Limits: Diffraction

sources: Wikipedia (6wavelength=slitwidthblue.gif, Single_Slit_Diffraction_(english).svg, Beugungsscheibchen.k.720.jpg)

Natural Resolution Limits: Diffraction*

sources: font-awesome fa-bicycle=

Natural Resolution Limits: Diffraction
For typical cameras
𝑑 = 1.22 ∗ 𝜆 ∗ 𝑓#Raleigh Criterion

For microscopes𝑑=𝜆𝜆=2𝑛 sin 𝜃 2 𝑁𝐴

Abbe diffraction limit
NA is typically 0.1-0.4 for common lenses in air, up to 1.0-1.5 for oil lenses.

iPhone 7:=1.22 * 650nm * f/1.8=1.4 μm
pixels are only 1.22 μm!

Typical Limit:= 500nm/(2 * 1.25)= 0.2 μm = 200nm
Microtubules are ~24nm

STORM: Stochastic Optical Reconstruction Microscopy
Rust, Bates, Zhuang. "Stochastic optical reconstruction microscopy (STORM)
provides sub-diffraction-limit image resolution." Nature Methods 3.10 (2006)

All pixels “on”:

Random 1% ofpixels “on”

Random 1% of
pixels “on”

Random 1% of
pixels “on”

STORM: Stochastic Optical Reconstruction Microscopy
Rust, Bates, Zhuang. "Stochastic optical reconstruction microscopy (STORM)
provides sub-diffraction-limit image resolution." Nature Methods 3.10 (2006)

All pixels “on”:

1 reading

100 readings

1000 readings

STORM: Stochastic Optical Reconstruction Microscopy
Bates, Blosser, Zhuang. "Short-range spectroscopic ruler based on asingle-molecule optical switch." Physical review letters 94.10 (2005)

STORM: Stochastic Optical Reconstruction Microscopy
Bates, Blosser, Zhuang. "Short-range spectroscopic ruler based on asingle-molecule optical switch." Physical review letters 94.10 (2005)

STORM: Stochastic Optical Reconstruction Microscopy
Wolter, Steve, et al. "Real‐time computation of subdiffraction‐resolution
fluorescence images." Journal of microscopy 237.1 (2010)

Compressed Sensing (a.k.a. Sparse Sampling)
If your data is “compressible”, you can take just a handful of randommeasurements, and, using “simple” math, you can reconstruct your data(with minimal error and high probability)
Emmanuel Candes and Terence Tao. "Near-optimal signal recovery fromrandom projections: Universal encoding strategies?." arXiv:math/0410542(2004)

Compressed Sensing (a.k.a. Sparse Sampling)
1

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Compressed Sensing (a.k.a. Sparse Sampling)
1

2

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Compressed Sensing (a.k.a. Sparse Sampling)

Davenport, Duarte, Eldar, Kutynoik , Introduction to Compressed SensingCompressed Sensing
Duarte, et al. Single-Pixel Imaging via Compressive Sampling. (2008)Compressed Sensing
Real Picture(65,536 pixels)

CS Reconstruction(3,300 samples)

CS Reconstruction(1,300 samples)

CS Reconstruction(6,500 samples)Faster STORM using compressed sensing
Zhu, et al."Faster STORM using compressed sensing." Nature Methods (2012)
1. Acquire PSF

2. Get Image

3. Increase Grid

4. Solve CS problem

Faster STORM using compressed sensing
Zhu, et al."Faster STORM using compressed sensing." Nature Methods (2012)Denser Images!

Many times denser

More precise

Faster imaging

Faster STORM using compressed sensing

Faster STORM using compressed sensing
40% pixels on

40% on, CS Solve

CS50 readings
4% Density

https://github.com/leonidk/cs371

Classic
1000 readings~0.8% Density

Quantitative Comparison
Sage, Daniel, et al. "Quantitative evaluation of software packages for
single-molecule localization microscopy." Nature Methods 12.8 (2015)

https://github.com/hrouault/Brecs

Extra Slides

Faster STORM using compressed sensing
Solve
𝑤0+ ⋯ + 𝑤205

+ ⋯+ 𝑤819+⋯=Withmin 𝐰 1

Gives𝐰 ∈ ℝ1024

𝐰 ∈ ℝ32x32𝐰=

DAOSTORM
Stetson, Peter B. "DAOPHOT: A computer
program for crowded-field stellarphotometry." Publications of the Astronomical
Society of the Pacific 99.613 (1987).

FALCON
Min, Junhong, et al. "FALCON: fast and unbiased
reconstruction of high-density super-resolution
microscopy data." Scientific reports 4 (2014)

STORM: Stochastic Optical Reconstruction Microscopy
Bates, Blosser, Zhuang. "Short-range spectroscopic ruler based on a single-molecule opticalswitch." Physical review letters 94.10 (2005)

STORM: Stochastic Optical Reconstruction Microscopy
Rust, Bates, Zhuang. "Stochastic optical reconstruction microscopy(STORM) provides sub-diffraction-limit image resolution." Naturemethods 3.10 (2006)

STORM: Stochastic Optical Reconstruction Microscopy
Rust, Bates, Zhuang. "Stochastic optical reconstruction microscopy(STORM) provides sub-diffraction-limit image resolution." Naturemethods 3.10 (2006)