Super-resolution microscopy technique

Course notes of Super-resolution microscopy.

Course information¶

Lecturer: Tony Yang
Time: 789 (W)
Location: MD225
Reference books
Bahaa Saleh and Malvin Teich, Fundamental of Photonics, 2nd ed. Wiley, New York, 2007.
Erfle, Holger, Super-Resolution Microscopy: Methods and Protocols, Humana Press, 2017
Grading:
Participation in classroom discussions: 25%
Midterm: 30%
Term paper: 45%
G drive: https://drive.google.com/drive/u/1/folders/1sTXB5tplkqXRCZ05VJYFFkjfPJ-hs43I

Photonics¶

Ray optics¶

When length scale of the instrument is much larger than that of light wavelength.
Neither wave properties (diffraction, interference) nor photon ones.
Optical path length = line integral from one point to another, with respect to refraction index (n)
$\(\int_A^B n(r)ds$\)

Fermat's principle¶

Light tries to tale minimal travel time
Snell's law:
$\(n_1sin\theta_1 = n_2sin\theta_2$\)

Huygen's principle¶

Wavefront and wavelets: explains refraction, diffraction and interference

Total internal reflection¶

Dense material to loose material.
With little energy loss (<0.1%) as evanescent wave, penetration depth about 100-200 nm.
When incidence angle $\theta >$ the critical angle $\theta_c = sin^{-1}(\frac{n_2}{n_1})$
Used in fiber optics and superresolution microscope.

Negative-index metamaterials¶

\[ n = \left( \frac{\epsilon\mu}{\epsilon_0\mu_0} \right)^{1/2} \in \mathbb{C} \]

Superlensing breaking through the diffraction limit.
n is frequency-dependent

Spherical mirrors¶

Approximation of the 'perfect' parabolic mirror at small angles
For small angles (paraaxial) $\theta \approx sin(\theta) \approx tan(\theta)$

\[ \begin{aligned} \frac{1}{z_1} &+ \frac{1}{z_2} = \frac{1}{f} \cr f &= R/2 \cr m &= \frac{y_2}{y_1} = \frac{-z_2}{z_1} \end{aligned} \]

Spherical boundaries of different refractive indices¶

\[ \begin{aligned} \frac{n_1}{z_1} &+ \frac{n_2}{z_2} = \frac{n_2 - n_1}{R} \cr y_2 &= \frac{-n_1}{n_2} \frac{z_2}{z_1} y_1 \end{aligned} \]

Thin lens from two spherical surfaces¶

\[ \begin{aligned} \theta_3 &= \theta_1 - y / f \cr \frac{1}{f} &= (n_2-n_1)(\frac{1}{R_1} - \frac{1}{R_2}) \cr \frac{1}{z_1} &+ \frac{1}{z_2} = \frac{1}{f} \cr m &= \frac{-y_2}{y_1} = \frac{-z_2}{z_1} \end{aligned} \]

Transformation in matrix forms¶

Light rays as 2-component vector
Components as 2 by 2 matrix.

Wave optics¶

Considerations¶

Diffraction (+), polarization (-), Fraunhofer (+), Fresnal (+)
Maxwell equations: EM (E and B) vector fields
optic phase is the central quantity.
phase match at boundaries

Wave equation¶

2nd derivative of space proportional to that of time
u: space; t: time; v: phase velocity; k: wave number; $\omega$: angular frequency; n: refractive index

\[ \begin{aligned} \nabla^2u &= \frac{1}{v^2}\frac{\partial^2u}{\partial t^2} \cr k &= \frac{2\pi}{\lambda} \cr \omega &= 2\pi v \cr v &= \frac{c}{n} \end{aligned} \]

Linear equations => superposition possible
Complex notation by Euler's formula
a: amplitude, ϕ(r): phase, ω: angular velocity
periodic both in time and space
the real part = physical quantity

\[ U (r,t) = a(r)exp(i\phi(r))exp(i\omega t) \]

Helmholtz equations¶

regardless of time

\[ \begin{aligned} U (r) = a(r)exp(i\phi(r)) \cr \nabla^2U (r) + k^2U (r) = 0 \cr \end{aligned} \]

Waterfronts¶

surfaces of constant phase (等相位面)
Plane waves in media with refractive index n
$$
\begin{aligned}
k &= k_0n \cr
λ &= \frac{λ_0}{n}
\end{aligned}
$$

Bigger the n, higher in spatial frequency (shorter in wavelength). The same time frequency.

Spherical waves¶

\[ \begin{aligned} U (r) &= \frac{A}{r}exp(-ikr) \cr r &= \sqrt{x^2 + y^2 + z^2} \end{aligned} \]

Fresnel Approximation: Paraaxial ($z^2 >> (x^2 + y^2)$): Spherical -> paraboloidal -> planar wave

\[ \begin{aligned} U (r) &= \frac{A}{z}exp(-ikz) exp \left( -ik \frac{x^2 + y^2}{z} \right) \cr \nabla^2U (r) &+ k^2U (r) = 0 \cr \end{aligned} \]

Reflection, Refraction¶

Results are similar to ray optics at planar surfaces for planar waves
Plane wave through thin lens -> paraboloidal waves
Intensity = $| U(r) |^2$

Interference¶

By superposition of two rays

\[I = | U(r) |^2 = I_1 + I_2 + 2\sqrt{I_1I_2} cosΔϕ\]

Paraxial waves¶

Slowly varying envelope: slow change in amplitude
Paraxial Helmholtz equation

\[ ∇_T^2 A(r) = 2ik\frac{∂A}{∂z} \]

Gaussian beam¶

https://en.wikipedia.org/wiki/Gaussian_beam

\[ \begin{aligned} A(r) &= \frac{A_1}{q(z)}exp \left( \frac{-ik(x^2 + y^2)}{2q(z)} \right) \cr q(z) &= z + iz_0 \end{aligned} \]

q(z): q-parameter
A solution to the paraxial Helmholtz equation
The best we can do in real situations
Cannot avoid spreading, but Gaussian beam's angular divergence in minimal.
Inside the waist (the narrowest part of the beam) is similar to planar wave
Long wavelength and thin beam waist -> more divergence
Depth of focus

\[ \begin{aligned} W(z) &= W_0 \sqrt{1 + (z / z_0)^2} \cr DOF &= 2z_0 = 2 \frac{W_0^2 \pi}{\lambda} \end{aligned} \]

Calculate the divergence by the q parameter and complex distance

\[ \begin{aligned} q_2 &= q_1 + d \cr \frac{1}{q_1} &= \frac{1}{R_1} - \frac{iλ}{πW_1^2} \cr \frac{1}{q_2} &= \frac{1}{R_2} - \frac{iλ}{πW_2^2} \cr \end{aligned} \]

Beam quality: M-square factor >=1, the smaller the better.
Through thin lens
Change in phase -> wavefront is bent
Radius is unchanged
Not focused on a single point like in ray optics

Higher order modes (TEM (l,m))¶

Laguerre-Gaussian beams -> important in superresolution.

Fourier Optics¶

Any wave = sum (superpositions) of plane waves
Important properties: angles and spatial frequencies
Optical components: linear functions with frequency response
Impulse (with all frequencies) => Impulse response function
Inputs of various freq. => Transfer function

Propagation of light in free space¶

Angles => spatial frequencies in the x-y plane

\[U(x,y,z) = A \cdot exp(-j(k_xx+k_yy+k_zz))\]

Where
* wave vector $\textbf{k} = (k_x, k_y, k_z)$
* wave length $\lambda$
* wave number $k = \sqrt{k_x^2 + k_y^2 + k_z^2} = \frac{2\pi}{\lambda}$

For paraxial waves

\[\theta_x = sin^{-1}(\lambda\nu_x) \approx \lambda\nu_x\]

\[\theta_y = sin^{-1}(\lambda\nu_y) \approx \lambda\nu_y\]

Optical Fourier Transform¶

Spatial frequencies at different angles
A lens could do Fourier transform at the focal plane

Fraunhofer Far Field Approximation¶

Far field: $d \gg \frac{b^2}{\lambda} , \frac{a^2}{\lambda}$
Near field ($d \approx \lambda$): superresolution (~nm) due to little distortion
Far field image (diffraction pattern) is the Fourier transform of the original image
Smaller the scale (higher spatial frequencies), larger the distortion (wider aura)
Diffraction: is everywhere, but best demonstrated in the pinhole(aperture) experiment

Rectangular aperture¶

expressed as cardinal sine (sinc) function
Angular divergence (first zero value): $\theta_x = \frac{\lambda}{D_x}$

Circular aperture¶

Bessel function, Airy pattern
$\theta = 1.22\frac{\lambda}{D}$: angle of the Airy disk
Focused optical beam through an aperture: $\theta = 1.22\frac{f\lambda}{D}$:

4-F imaging system¶

Original image -> lens (FT) -> (spatial frequencies) -> lens(iFT) -> perfect image (in theory)
Filtering of higher spatial frequencies: less detailed image, less noise
Spatial filtering: cleaning laser beams

Transfer function of free space¶

Higher freq. => real exponent => attenuate rapidly (evanescent wave)

Polarization¶

Electric-field as a vector
Polarization ellipse: looking at the xy plane from the z axis.
Phase difference: $\varphi$
Linearly polarized: $\varphi = 0 $ or $\pi$
Circularly polarized $\varphi = \pm \pi /2 $ and $a_x = a_y$$
Linear polarizer : only passed a certain linearly polarized light
Wave retarder: changes $\varphi$ to change polarization pattern

Fiber optics¶

Low-loss
Light could bend inside it
Single-mode fiber (small core): Gaussian wave only
Multimode fiber (larger core): higher order light source
Relation to numerical aperture (NA)
Acceptance angle of the fiber: $\theta_a = sin^{-1}(NA)$
Larger NA: more higher order information, more noise
Smaller NA: $V = 2\pi\frac{a}{\lambda_0}NA < 2.405$. Gaussian wave only
Polarization-maintaining fibers

Quantum optics¶

Quantum electrodynamics (QED)
Energy carried by a photon: $E = h\nu = \hbar\omega$
Typical light source: more than trillion photons per second
$E (eV) = \frac{1.24}{\lambda_0(\mu m)}$
Momentum carried by a photon: $p = hk$
Probability of photon position or the squared magnitude of the SWE (individual behavior) is directly proportional to light intensity (group behavior)
At smaller n : the interference pattern looks random (randomness of photon flow)
At larger n: the interference pattern is more similar to what we see in the macroscale
Poisson distribution (discrete randomness with rate = photon flux)
mean = variance
SNR = mean^2 / variance = mean

Schrodinger wave equation (SWE)¶

Similar to solve for eigenvalues => discrete solutions => quantized energy levels
Particle in a well / atoms with a single electron => standing wave (discrete solutions)
Multi-electron: no analytical solutions

Photons and matter¶

Photon absorption and release: jumping in energy levels
Rotational : microwave to far-infrared
Vibrational : IR e.g. CO2 laser
Electronic : visible to UV
Photon absorption: electron jump up in energy level
Photon emission: Spontaneous vs stimulated (laser)

Occupation of energy levels¶

Boltzmann distribution
Pumping energy: population inversion
Laser stimulated emission

Luminescence¶

Cathodo- (CRT)
Sono- (ultrasound)
Chemi- (lightsticks)
Bio- (firefly)
Electro- (LED)
Photo- (Laser, Fluorescence, Phosphorescence)

Photoluminescence¶

In fact emitting a range of wavelengths (many sub-energy levels)
Fluorescence (spin-allowed, shorter lifetime) vs phosphorescence (spin-forbidden, longer lifetime)

Multiphoton¶

Absorption of 2 lower energy photons => emission of 1 higher energy photon
Multiphoton fluorescence

Light scattering¶

Photoluminescence: real excited states (resonant)
Scattering: virtual excited states (non-resonant)
Rayleigh scattering: same energy (elastic)
- Particle size much smaller than the photon wavelength
- Reason behind blue sky
- vs Mie scattering particle size comparable to photon wavelength
Raman scattering
- Stokes: Loss energy
- Ani-Stokes: Gain energy
- Molecular signature
Brillouin: acoustic

Stimulated Raman scattering (SRS)¶

Label-free microscopy

Eyes¶

380 nm ~ 710 nm
threshold of vision: 10 photons (a cluster of rod cells)
Logarithmic perception: Weber-Fechner Law (like hearing)
Single lens: spherical and chromatic aberration inevitable
Astigmatism: directional aberration
Pupil (Aperture)
Small pupil: less spherical and chromatic aberration (paraxial), less brightness and more diffraction
Large pupil: more brightness, more spherical and chromatic aberration
Optimum: 3mm
Viewing angle: the perceived size

Length scale of microscopes¶

Resolution limit of regular light microscope: 200nm
Clear organelles structure: 30nm

Geometrical optics of a thin lens¶

Lens equation: $\frac{1}{f} = \frac{1}{a} + \frac{1}{b}$
Magnification factor: $M = \frac{b}{a}$
Virtual image: divergent rays forming a real image on the retina due to the lens
Compound microscope: M = $M_{obj}$ * $M_{eye}$
*

Infinity-corrected microscope¶

Object on the focal plane of the objective lens
Parallel rays from the objective is converged by the tube lens
Magnification: reference tube length (160-200mm) divided by the focal length of the objective
shorter focal length = larger magnification
1.5mm => 100x

Microscope anatomy and design¶

The most important: resolving power (distinguish between two points) = numerical aperture (NA)
2nd: Contrast : object v.s. background (noise) signal strength
3rd: Magnification: $M_{obj}$ * $M_{eye}$

Anatomy¶

Light source: Koehler illumination to see the sample, not the light source
Diaphragm
Field: field of view
Condenser / aperture: resolution + brightness (open, larger angle) vs contrast + depth of view (closed, smaller angle)
Condenser
Objective
Eyepiece / camera

Different types of microscopic design¶

Transmitted light
Bright field
Dark field
Phase contrast
DIC
Polarization
Reflected light: objective = condenser (most common in modern microscopes)
Fluorescence
Upright vs inverted

Optical aberrations¶

Spherical aberrations¶

Paraxial and peripheral rays have different focal planes
Asymmetry in unfocused images
Corrected by
2 plano-convex lenses facing each other
meniscus lenses
lenses with different radii
doubling with another lens with opposing degree of spherical aberration

Chromatic aberrations¶

Different refractive index for different wavelengths
Corrected by
Doubling with a lens with a different material and shape
Achromat: corrected for 2 wavelengths
Apochromatic: corrected for at least 3 wavelengths
Flunar (semi-apochromatic)

Astigmatism¶

Different directional plane, different foci
Not in perfect alignment (off-axis) / curvature of field
Esp. in high NA lens
Caused / corrected vy a plano-cylindrical lens

Coma¶

Comet tail
Off-axis aberration (misalignment)

Field Curvature¶

Thin flat object -> image with edges curving towards lens
Cause: difference of lengths of light paths
Esp. in high NA
Planar view objectives correct this

Distortion¶

non-linear aberrations
different magnification across the field of view

Transverse chromatic aberration¶

Chromatic difference of magnification

Testing for aberrations¶

Color shift between channels
Fluorescent beads

Anti-vibration tables¶

Vibrations
Ground (low freq. 0.1 - 5 Hz)
Acoustic
Direct vibration from the components (10-100 Hz)
Solution:
Air isolators
Active control

Ergonomics¶

Protect scientists' eyes, neck, and shoulder

Objective¶

The most important part in a microscope

Objective class¶

More corrections, more expensive
Achromat: 1
Semi-apochromatic: 2-3
Apochromatic: 5-10 cost

Labels on the objective¶

numerical aperture (NA): resolving power (collected photons)
magnification (e.g. 10x): field of view
color correction: Achromat / Semi-apochromat (Neofluar / fluotar) / Apochromat
immersion: air / water / oil
free working distance
cover slip thickness (usually 170 μm)

Numerical aperture¶

NA = nsinα

Oil immersion¶

no air gap causing total internal reflection (loss of photon information)
NA up to 1.4

Abbe's law¶

Lateral spatial resolution (xy):

\[ d \approx \frac{\lambda}{2} \]

Axial spatial resolution (z): usually worse (~700 nm)

Depth of field vs depth of focus¶

Depth of field: moving the object
Depth of focus: moving the image plane

Brightness¶

More NA, brighter
More mag, dimmer
Best brightness: NA 1.4 and mag 40x

Illumination (lamp)¶

Tungsten: 300-1500nm (reddish), dimmer
Tungsten-halogen lamp: stable spectrum and bright
Mercury lamp: 5 spectral peaks, 200hrs
Meta-halide lamp: same spectral properties as the mercury lamp, lasts 2000 hrs
Xenon lamp: more constant illumination across wavelengths, 1000 hrs
LED: small, stable, efficient, intense, multiple colors, quick to switch, long-lasting (10000 hrs)

Filter¶

Absorption vs interference (modern)
Neutral-density (equal) vs color filters (specific wavelengths)

Resolution¶

Rayleigh's criterion: $d = \frac{0.61 \lambda}{NA}$
Sparrow's (astrophysics): $d = \frac{0.47 \lambda}{NA}$
Abbe's: $d = \frac{0.5 \lambda}{NA}$
Interpreted as spatial freq. response of a transfer function (low-pass filter)

Contrast¶

Signal strength of object vs background
Human eye limit: 2% (dynamic range = 50x, 5-6 bits)
Improved by staining (including fluorescence) and lighting techniques

Interactions with the specimen¶

Absorption / transmission / reflection: produce contrast (amplitude objects)
scattering (irregular) / diffraction : edge contrast enhancement
Refraction: difference in refractive index (n)
Polarization: DIC (differential interference contrast) with two coherent beam and Wollaston prisms
Phase change: phase contrast (shifting phases)/ phase interference
Fluorescence: achieves superresolution
Absorption and release of photons (time scale of 1fs to 1ns)
Great resolution, contrast, sensitivity and specificity
Live cell imaging
Various labels (with different wavelength)

Bright vs Dark field¶

Bright field : darker specimen than the background, lower contrast
Dark field (by oblique illumination): brighter specimen than the background, higher contrast
transmitted light fall outside the objective, scattered light only

Fluorescence microscopy¶

Finally the main point of superresolution microscopy
high-contrast (clean labeling)
sensitive: single molecule imaging (single photon)
specific: labeling agent dependent
multiple labeling at once with different wavelength
versatile
Live imaging: cell metabolism, protein kinetics
Molecular interaction: FRET
Relatively cheap and safe

Quantum processes¶

Driving photon: kick electrons to an upper electronic state
Fluorescence: electrons falling back to the ground state
Some relaxation by vibrational energy levels (Strokes shift), or non-photogenic energy shifts
Absorb / emit a range of wavelengths with abs. peak
emitted wavelength is usually longer than absorbed
Time scale: 1fs to 1ns
Phosphorescence: singlet -> triplet -> singlet electron (spin-forbidden), much longer time scale (in seconds)

Fluorophore¶

Conjugated pi bonds providing the electronic energy levels from UV to IR
Fluorescence lifetime:depend on the type of fluorophores. e.g. FLIM
Photobleaching: irreversibly destroyed after 10000 - 100000 absorption/emission cycles
FRAP: measuring diffusion rate
Quenching / blinking
Reversible suppression of emission
PALM / STORM (single molecule microscopy)
Emission tail: increased crosstalk to others
Efficiency (Brightness): $\Phi\epsilon_{max}$
Quantum yield (Φ)
Molar extinction coef. ($\epsilon_{max}$)
The best one: quantum dots (also the most versatile)

Fluorescence microscope¶

epi illumination is more suitable for biology
Object = condenser
Increased contrast (reduced background)
transmitted light are outside field of view (only see fluorescence photons)
Filter sets: one for excitation + one for emission + one dichromic mirror
May need to design excitation / emission bands for multiple fluorophores

Fluorophores¶

Smaller = better spatial resolution
May disrupt normal cellular function
Labels: organic dye (1 nm), protein (3 nm), quantum dots (10 nm), gold particles (100 nm)
Specificity molecules: Antibody (15 nm), Fab, Streptavidin, Nanobody (3 nm)
May have secondary ones (making the entire dot even bigger)
Absorption / emission wavelengths
Stokes shift
Molar extinction coefficient / quantum yield = brightness
Toxicity
Saturation
Environment (pH)

Fluorescent protein: e.g. GFP¶

Introduced by transfection: not always successful (transfection and cell viability)
Others: CFP (cyan), mCherry, mOrange, ...

Photoactive fluorescent protein e.g. mCherry¶

State transitions by activating photons
photoactivable
photoconvertible
photoswitchable

Quantum dots¶

Bright and resistant to photobleaching
Blinking under continuous activation
Bigger (10 nm)
Broad excitation and narrow emission spectra

Autofluoresence¶

e.g. Tryptophan, NAD(P)(H) in the cell
Label-free imaging
Background

Issues of fluorescence microscopy¶

Blurring
Bleaching
Bleed-through

Blurring in fluorescence microscopy¶

Limited depth of field compared to specimen thickness
Reduce the SNR (out-of-focus blurred images)
Solution: optical sectioning

Confocal¶

Pinhole: block out-of-focus light. Aperture in Airy Units (AU), optimal is 1
Raster scanning with mirrors and a laser: point-by-point
Phototoxicity issues: Time-lapse possible, but even higher phototoxicity
photon detection
PMT: high gain, low quantum efficiency(QE) (1/8)
CCD: higher QE (65%), higher background noise (lower SNR)
ScMOS: QE~95%
Avalanche photodiode (APD): QE~80%, higher SNR
Imaging parameters: no absolute rules, always trade-offs
Resolution: slightly better than wide field (1.4x spatial freq., by FWHM of the PSF)

Spinning disc¶

Faster imaging (parallel scans) and lower phototoxicity
Spinning microlens array + pinholes
Thinner optical slice of 800nm (traditional confocal: 1000nm)

Point spread function¶

Point -> psf -> Airy disk
After Fourier transform: Optical transfer function (OTF)

Convolution¶

Lens: finite aperture, could not capture higher spatial frequencies of the object
A way to understand and calculate blurring. Image = object * psf
Simplified to multiplication in the frequency domain by Fourier transform
Optical transfer function (OTF) = F{PSF}

Point spread function (PSF)¶

Hour-glass shape (sharper xy and less z resolution) due to the orientation of the objective
Confocal pinhole open at 1 AU: less spreading of the PSF

Deconvolution¶

Computational iterative process: deblurring, restorative
Only makes good image better

Total Internal Reflection Fluorescence (TIRF)¶

An illumination method for bottom 200nm (extent of evanescent field)
Improves axial resolution (up to ~100 nm) and contrast

Colocalization¶

spatial overlap between two (or more) different fluorescent labels
Pearson correlation coefficient
Spatial colocalization doe snot mean interaction (just the same pixel: co-occurrence)
Software analysis: ImageJ
Mander's Colocalization coefficients
Noise leads to underestimation of colocalization

Spectral Overlap¶

Bleed-through
Crossover
Cross-talk
Managed by tweaking light sources and filters

Resolution limit¶

Abide to physical laws
Abbe limit: 0.5 * wavelength / numerical aperture, from Fourier optics
Electron microscope (EM): 2nm. But cells need to be fixed and processed
Fluorescent microscopy: 200 nm. Multiple labeling methods. Multiple strategies to enhance the resolution.

Super-resolution light microscopy (SRLM) (precisely nanoscopy)¶

Cost, specimen prep, and operational complexity are in the middle between confocal and EM.

Near field microscopy¶

Evanescent waves (before the light diffracts)
5-10 nm axial resolution, 30-100 nm lateral resolution
Practically zero working distance

4-pi microscopy¶

Two opposing objectives improves z resolution
Technical difficulties

PALM, STED, STROM¶

Using non-linear properties of the fluorophores (turing they on / off)

Stimulated emission depletion microscopy (STED)¶

Donut-shaped induced depletion laser (high power)
At the tail of emission spectrum to avoid cross-talk
Donut-shape via a vortex phase plate
Diffraction-limited. But combining another diffraction-limited excitation laser to achieve super-resolution
Higher labels and samples preparation requirements, and optical alignment (vibration sensitive)
Depletion efficiency: $p_{STED} = exp(-\frac{I_{STED}}{I_{sat}})$
Resolution by the factor of $\sqrt{1 + \frac{I_{STED}}{I_{sat}}}$
More $I_{STED}$, more resolution, but more power (photobleaching)
Implementation: Pulsed, continuous wave, gated
Pulsed: synchronization challenges
continuous wave (CW): high background noises
Gated: lower background noises than CW, easier than pulsed, mainstream
Protected STED: less photobleaching using photoswitchable dyes
Long-time observation
STED with 4-pi: improved axial(z) resolution by another phase plate

Fluorescence probes¶

More restricted
Two color: Long Stoke shift + normal Stoke shift dyes

Localization microscopy¶

Tracking the particles central positions from reversing the point spread function (e.g. fitting the Gaussian distribution). Only possible with sparse points, thus stochastic.
Reconstruct the whole image from a series of sparse excited dyes.
Switching-based separation is the mainstream of sparse activation

Photoactivated localization microscopy (PALM)¶

Less convenient than dSTORM.

Stochastic optical reconstruction microscopy (STORM)¶

Direct STORM (dSTORM) currently
Readily implemented on regular wide-field microscopes.
Selected dye (esp. Alexa 647) and imaging buffers.
Cameras instead of PMTs to see the whole field.
Gaussian distributions fitting the intensity of dots to calculate the centroid point.
Labels could have an impact on the measured length (e.g. primary and secondary antibodies)
Localization precision: more photons, less uncertainty (more precision, up to 5-20 nm), more frames (time) required
Precision estimation is a statistical issue.
FWHM = 2.35 uncertainty ($\sigma_{loc}$)
Imaging buffer: together with activation laser, determines the state (active, vs dark) of dyes
More fluorophores could be reactivated when the signal gets too weak by the activation laser (typically UV).
But not too strong to ruin the single molecule signals.
To avoid cross-talk (activating multiple types of dyes at once) and photobleaching by stronger activation photons,
starting activating with far-red (long-wavelength) dyes
Irradiation density
Too high: no single molecule anymore, poor localization quality
Too low: more time required and more background noise
Threshold for signal detection and rejection criteria
Too strict: wasted the real signal
Too loose: more noise
Too many photons at one time indicate multiple molecules = false positive, poorly localized
Structural averaging: reducing noise by a series of images (time info. -> spatial info.)
Pair correlation analysis and molecular cluster analysis (not randomly distributed particles)
Single molecule tracking
3D localization by encoding z information into the optic system
Bi-plane
Dual helix
Astigmatism

Structured illumination microscopy¶

SIM for short
Grating pattern for structured illumination (stripes) encoding high frequency information
Indicated by Fourier optics (extension of optical transfer function (OTF))
Multiple images by superimposing illumination stripes in different angles
Increasing resolving power by 2x
Even more resolution improvement by non-linear optics (saturation SIM)

Light sheet microscopy¶

Orthogonal illumination
Improved z axis and optical section
Low laser intensity for live cell imaging, minimal phototoxicity
Scanning beam / lattice for even illumination and more z resolution