# Super-resolution microscopy techniques

Contents

## 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
• Participation in classroom discussions: 25%
• Midterm: 30%
• Term paper: 45%

## Photonics

### Ray optics

When lenght scale of the instrument i smuch larger than that of light wavelength. Neither wave properties (diffraction, interference) nor photon ones. Optical pathlength = 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 critial angle $\theta_c = sin^{-1}(\frac{n_2}{n_1})$ Used in fiber optics and qsuperresolution microscope.

### Nagative-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 requency-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 proprotional 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}

### Wavefonts

• 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}

Fresnal 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
• Not focused on a single point like in ray optics

### Higher order modes (TEM (l,m))

• Laguerre-Gaussion 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 $\lambda$
• wavenumber $k = \sqrt{k_x^2 + k_y^2 + k_z^2} = \frac{2\pi}{\lambda}$

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 throught an aperture: $\theta = 1.22\frac{f\lambda}{D}$:

#### 4-F imaging system

• Original image -> lens (FT) -> (spatial freqs.) -> lens(iFT) -> perfect image (in theory)
• Filtering of higher spatial freqs: 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): Gaussain 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 • Polariztion-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 (indivisual 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 ranomness with rate = photon flux) • mean = variance • SNR = mean^2 / variance = mean ### Schroedinger wave equation (SWE) • Similar to solve for eigenvalues => discrete solutions => quantitized 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: elcetron jump up in energy level • Photon emmision: Spontaneous vs stimulated (laser) ## Occupation of energy levels • Boltzmann distribution • Pumping enegy: population inversion • Laser stimulated emmision ## 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: same energy (elastic) • Particle size much smaller than the photon wavelength • Reason behind blue sky • vs Mie scatttering particle size comparable to photon wavelength • Raman • Stokes: Loss energy • Ani-Stokes: Gain energy • Molecular signature • Brillouin: acoustic ### Stimulated Raman scattering (SRS) • Label-free microscopy ## Eyes • 380 nm ~ 710 nm • theshold 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 abberation • 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 • Resiolution limit of regular light microscope: 200nm • Clear organnels 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 mircoscope • 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) = numericalaperture (NA) • 2nd: Contrast : object v.s. background (noise) signal strength • 3rd: Magnificaition: 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 • Assymetry 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 wavelengthes • Corrected by • Doubling with a lens with a different material and shape • Achromat: corrected for 2 wavelengths • Apochromat: corrected for at least 3 wavelengths • Flunar (semi-apochromat) ### 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 lengthes 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 scietists' eyes, neck, and shoulder ## Objective • The most important part in a microscope ### Objective class • More corrections, more expensive • Achromat: 1 • Semi-apochromat: 2-3 • Apochromat: 5-10 cost ### Labels on the objective • numerical aperture (NA): resolving power (collected photons) • magnification (e.g. 10x): field of view • colorcorrection: Achromat / Semi-apochromat (Neofluar / fluotar) / Apochromat • gimmersion: 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}$Axial spatial resolution (z): usually worse (~700 nm) ### Depth of field vs depth of focus • Depth of field: moving the object • Depth of focus: moving the image plane ### Brightness • More NA, brighter • More mag, dimmer • Best brightness: NA 1.4 and mag 40x ### Illumination (lamp) • Tungsten: 300-1500nm (reddish), dimmer • Tungsten-halogen lamp: stable spctrum and bright • Mercury lamp: 5 spectral peaks, 200hrs • Meta-halide lamp: same spectral properties as the mercury lamp, latts 2000 hrs • Xenon lamp: more constant illumination across wavelengths, 1000 hrs • LED: small, stable, efficient, intense, multiple colors, quick to switch, long-lasting (10000 hrs) ### Filter • Absorption vs interference (modern) • Neutral-density (equal) vs color filters (specific wavelengths) ### Resolution • Rayleigh’s criterion:$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 techiniques #### Interactions with the specimen • Absorption / transmission / reflection: produce contrast (amplitude objects) • scattering (irregular) / diffraction : edge constrast 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, constrast, 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): birghter 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 metabolsim, 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 • emittedwavelength 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:depdens on the type of fluorophores. e.g. FLIM • Photobleaching: irreversibly destroyed after 10000 - 100000 absorption/emission cycles • FRAP: measuinge diffusion rate • Quenching / blinking • Reversible supression of emission • PALM / STORM (single molecule microscopy) • Emission tail: increased crostalk to others • Efficiency (Birghtness):$\Phi\epsilon_{max}$• Quantum yield (Φ) • Molarextinction coef. ($\epsilon_{max}) • The best one: quantum dots (alos 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 / emssion bands for multiple fluorophores ### Fluorophores • Smaller = better spatial resolution • May disrupt normal cellular function • Lables: 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 • Satuartion • 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-occurence) • 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 • Flurorescent 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 • Techical 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 emmision spetrum 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}$, more resolution, but more power (photobleaching) • Implementation: Pulsed, continous wave, gated • Pulsed: synchronization challenges • continous wave (CW): high background noises • Gated: lower background noises than CW, easier than pulsed, mainstream • Protected STED: less photobleaching using photoswitable dyes • Long-time observation • STED with 4-pi: improved axial(z) resolution by another phase plate #### Fluorescence probes • More restricted • Two color: Long Stoke shift + normal Stoke shift dyes ## Localization microscopy • Tracking the particles central positions from reversing the point spread function (e.g. fittin gthe Gaussian distribution). Only possible with sparse points, thus stochastic. • Reconstruct the whole image from a series of sparse excited dyes. • Switching-based separation is the mainstream of sparse activation ### Photoactivated localization microscopy (PALM) • Less convenient than dSTORM. ### Stochastic optical reconstruction microscopy (STORM) • Direct STORM (dSTORM) currently • Readily implemented on regular wide-field microscopes. • Selected dye (esp. Alexa 647) and imaging buffers. • Cameras instead of PMTs to see the whole field. • Gaussian distributions fitting the intensity of dots to calculate the centroid point. • Labels could have an impact on the measured length (e.g. primaryand secondary antibodies) • Localization precision: more photons, less uncertainty (more precision, up to 5-20 nm), more frames (time) required • Precision estimation is a statistical issue. • FWHM = 2.35 uncertainty ($\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
• 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 phtons at one time indicate multiple molecules = false positive, poorly localized
• Structual 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 illimunation 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