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Super-resolution microscopy techniques

Super-resolution microscopy techniques

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%

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)

∫ABn(r)ds\int_A^B n(r)ds

Fermat’s principle

Light tries to tale minimal travel time Snell’s law:

n1sinθ1=n2sinθ2n_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=(ϵμϵ0μ0)1/2∈C 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) $\theta \approx sin(\theta) \approx tan(\theta)$
1z1+1z2=1ff=R/2m=y2y1=−z2z1 \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

n1z1+n2z2=n2−n1Ry2=−n1n2z2z1y1 \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

θ3=θ1−y/f1f=(n2−n1)(1R1−1R2)1z1+1z2=1fm=−y2y1=−z2z1 \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

∇2u=1v2∂2u∂t2k=2πλω=2πvv=cn \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(iϕ(r))exp(iωt) U (r,t) = a(r)exp(i\phi(r))exp(i\omega t)

Helmholtz equations

  • regardless of time
U(r)=a(r)exp(iϕ(r))∇2U(r)+k2U(r)=0 \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

    k=k0nλ=λ0n \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

U(r)=Arexp(−ikr)r=x2+y2+z2 \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

U(r)=Azexp(−ikz)exp(−ikx2+y2z)∇2U(r)+k2U(r)=0 \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=I1+I2+2I1I2cosΔϕI = | 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
∇T2A(r)=2ik∂A∂z ∇_T^2 A(r) = 2ik\frac{∂A}{∂z}

Gaussian beam

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

A(r)=A1q(z)exp(−ik(x2+y2)2q(z))q(z)=z+iz0 \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
W(z)=W01+(z/z0)2DOF=2z0=2W02πλ \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
q2=q1+d1q1=1R1−iλπW121q2=1R2−iλπW22 \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⋅exp(−j(kxx+kyy+kzz))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

θx=sin−1(λνx)≈λνx\theta_x = sin^{-1}(\lambda\nu_x) \approx \lambda\nu_xθy=sin−1(λνy)≈λνy\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≈λ2 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
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Intro to mechanobiology