high resolution

Magnification formula

M=v/u

Why is the resolution not infinite in a perfect light

microscope?

Light can be seen as waves

What is resolution

The absolute boundary of where two separate points can still be

distinguished

What is Rayleigh’s criterion

The images of two point sources are just

resolved when the central maximum of one

Airy pattern coincides with the first dark ring

of the other Airy pattern. d = 0.61 * lambda/(NA). NA is numerical aperture and NA = nsin(alpha) where n is the refractive index

Why is Fluorescence useful

It can highlight different proteins and allows targeting of specific ones. It can also give better resolution

Whats huygens principle

every point on a wavefront can be seen as a source of a secondary wavelet

What affect does an aperture hav on a point source

Bigger apperture → narrower spread, different wavelenghts of light give different spreads. The size of the aperture decide the smallest details

What are some tools to target biological strucutres for flourescense. What challenges are there

genetic modification of proteins, nanobots. The challenge is to introduce label without disturbing the system.

What is flourescence, how are the photon energies before and after

Molecules absorb light → excited → emitts photon. Due to stokes shift (energy loss due to vibrations) the emitted spectrum has a lower energy than the absrobed one.

How and why do Microscope seperates excitation and emission photons

Dichroic mirrors are used to seperate escitation and emission photons so that we only se the emission. The use of filters is also inmplemented to target specific parts for instance bandpass. The filters depend on what color you want to se.

What problems can there be when imaging multiple fluorophores sequentially

Excitation bleedthrough: overlap of excitation spectra causes both fluorophores to be excited simultaneously

Emission bleedthrough: overlap of emission spectrum causes both fluorophores to be detected at the same wavelength

Fluorophore interactions: emission from one fluorophore excites second fluorophore, FRET or quenching

What advantages are there with an inverted microscope

The objective is closer to the specimen which is hard to achieve with normal, easier to exchange fluids, the center of ggravity is lower so it isnt as sensitive to vibrations

What is the best strategy to maximize fluorescence signal?

A. Get the molecule to emit many photons.

B. Collect and detect as many emitted photons as you can.

C. Minimize photons from everything else

What is the efficency of fluorophores

The time from absorbtion to emission is called a duty cycle and is 1-5 ns so max photons per second is the inverse. Excited tripel state may interfere and make it take longer. Exctinction coefficient (how likely a molecule is to absob a photon) plays a role as well as quantum yield (fraction of excited molecules that will emit a photon)

How many percent of photons do we detect

High numerical apertures detect 5-10% in the focal plane, sensitive cameras can collect 90-95%, so in total we collect about 5-10%

How does the environment affect detection

The environment is a solvent that surrounds the molecule, this solvent causess scattering of the light, limiting the amount of solvent is therefore important, as well as cleaning dirt particels

What is the basic idea behind confocal microscopy

An ideal microscope detects the light scattered or absorbed by each point of a specimen. But if

we make measurements of each point at the same time, then every focal image point will be

clouded by scattered light rays of neighboring points. There is no way to eliminate every

possible such ray, but it is easy to remove all rays not initially aimed at the focal point

Whats the difference between Widefield and scanning confocal microscopy, what are there advantages/disadvantages

Widefield microscopy: acquisition of image points in parallel by imaging onto pixilated detector

Widefield:

• has uniform illumination

• uses an image sensor for

parallel imaging

• is fast

• has poor optical

sectioning

Scanning microscopy: acquisition of image points sequentially by scanning focused laser beam relative to sample

Confocal:

• has single spot

illumination

• uses a scanner for

sequential imaging

• is slow

• has good optical

sectioning

• SNR depends on the size

of the pinhole

What is STED

Stimulated emission depletion, it adds a donut-shaped depletion laser to the confocal microscope to reduce the effective laser scanning spot size. incident photon knock out molecules in excited states. you have an excited spot and add the donut depletion spot around it. Best resolution when we increase the power of the depletion laser.

Whats the concept behind Single-molecule localization microscopy (SMLM)

Include information about the intensity profile of a single molecule

into the estimation process! (Prior knowledge is power

What is noteabel about the size of fluorescence images

The fluorescence image of a single molecule is

many times bigger than biological structures. Diffraction limmit makes resolving small structures hard. We want to seperate spatial info of a single fluorophore in time. Accomplish by making the fluorophoes blink

How do we get flourophores to blink?

PALM - 50 nm res, live cell compatible. excites molecules so that they switch cromoform

STORM - 20nm res, uses organic dyes, have to puncure cells (kills) so not compatible with life

DNA-Paint - blinking by binding and unbinding with molecules, modifiable blinking. Wash sample → target dissapears → many colors

For blinking Why is it good/bad if the "off"-time gets

smaller?

A. Single molecule spots start to overlap. That's bad.

C. Measurement time gets shorter. That's good

What is shot noise

Light is composed of discrete quanta (photons)

• Number of detected photons p in a fixed time interval is a

stochastic variable

• Photon count p follows Poisson distribution

What is readout noise

Caused by reading the contents of the CCD wells and transferring the result off-chip.

• Solution: slow-scan rates (< 1 MHz) and good electronics.

• Root-Mean-Square error (RMS) ≈ 0 to 40 electrons / pixel

What is the rule of thumb for localization unceartainy?

Position estimate by each photon with standard deviation

N: photons, s: size PSF, a: pixel size, b: background noise

Independent estimates for Nph photons

The overall standard deviation is then:

Combines ray picture (NA of lens), wave picture () and particle picture (SNR of photon

count) in one formula

What is nyquist sampling

A function is band limited (frequencies over B have function zero), Perfect reconstruction possible for nyquist sampling: deltaX <= 1/(2B). So for microscopy: B = 2NA/lambda → deltaX <= lambda/(4NA)

Stage drift

Every bit of drift is a problem

What problems are there with 3D localization

PSF elongates in z, better focus near the actual position → no information on z position

What 3D Localization techniques are there

Astigmatism - add cylindrical lens → x and y have different focal points → PSF asymetric

Biplane - Add beam splitter + extra camera → delay in one of the paths → different focal points (one more blurry) → can decide if object is closer to which focal point → map back to calibration

What is light sheet microscopy, what are the advantages

Light kills cells → limit light, send light from the side and illuminate the sheet from the side, there are different types of light sheet.

Static light sheet:

- Simple and minimal optics

- Edges of sheet are non-uniform

Scanning beam:

- Active scanning hardware

- Very homogeneous intensity profile

Advantages:

* Not very high resolution, but unlimited imaging time!

• Uses very low illumination dose, compatible with outside sunshine

• Imaging of whole embryos for days possible

• Biggest hit in developmental biology

how can Illumination patterns be used for resolution increase, Structured Illumination Microscopy (SIM)

If two emitters are close by then you might be unable to distinguish between the two because of overlap in PSF. To fix this we can use illumination patterns so that the two emitters gets different amount of light. Shift sinusoidal pattern to illuminate the other one and you get multiple images with shifted pattern → combine in computer.

Offers 2x increased resolution with good signal transfer of all spatial

frequencies.

• Works in 3D! Can increase axial resolution too. Only need more patterns in

3D.

• Compatible with any fluorophore/labeling, no special biochemistry needed!

• To make it work, there are many practical problems:

• projected pattern positions on the sample must be known with nm accuracy

• multiple acquisitions with different pattern positions must be acquired

• the digital reconstruction adds “structured noise

what is the Moire effect

* Overlay of periodic patterns gives image with larger period

• Can be used to “magnify” small structures

• “Structured Illumination Microscopy

What is stimulated emission depletion (STED)

Resolution ~ 50 nm.

• Relies on narrow

seperation of

fluorophore

excitation and

emission

• Dyes require special

characteristics

• Complex

instrumentation

What is MINFLUX

can doughnut spot over region ~𝐿

• triangulation based on photon counts

• precision scales as ∆𝑥~ 𝐿/sqrt(𝑁)

• not as 𝜆/(𝑁𝐴)

Advantages:

Gives better localization precision for same number of photons as in

traditional localization

• Reason: Include information about the beam position into the

estimation process! (Prior knowledge is power)

• About 10x less photons needed for same loc. precision

• Allows very fast tracking of one single molecule emitter with very high

precision

What is SIMFLUX

Like minflux but instead of doughnut beam use SIM-pattern (horisontal or vertical lines) , you can have 2 pattern directions but 3 phases

What can you do to improve resolution

Increase n or sinα (NA)

Decrease λ

Ensure sparsity (source distance > d)

Non-linear effects

What is atomic resolution and how can it be achieved

When you can see patterns of atoms. Use electrons instead of photons. However electrons have small penetartion but high scattering. We want to limit scattering, so we work in vaccums

What is the difference between widefield and scanning

Widefield:

1. Illuminate area on sample

2. Detect signal from area

3. Obtain image, all pixels at once

Scanning:

1. Illuminate spot on sample

2. Detect signal from spot = pixel

3. Move to next spot

4. Repeat for all pixels

What is the time it takes for an image to be imaged

Time per image = dwell time (time per pixel) x number of pixels. Typical times are dwell time=1 micro s, number of pixels = 10^6 → time per image = 1s

How does the probe size affect the resolution, in what way does it contribute

1. diffraction (like with light) d=lambda/(2 alpha)

2. spherical abberation d = C_s alpha³

3. Chromatic aberation d = C_c deltaE/E0 * alpha

4. Source size d = M_T d

for gaussian distribution add up all the squares for d². However in EM its typically not gaussian distribution

How do you get the electrons for the beam

Extract electrons and project them in a beam in vacuum

Electrons can be pulled out of a material

if we supply sufficient energy:

• Strong electric field

• Electric field enhancement: sharp tip /

Field Emission Gun)

• Heating

• Photo-emission (only used in very specific

applications)

What is the difference between current and brightness

Brightness = dI/(dA dOMEGA V)

Reduced Brightness:

Current dI passing through area

dA in solid angle dΩ at voltage V

Reduced brightness is a

conserved quantity

What is coherens

Coherens is important in phase related imaging. There are two types temporal (related to delta E) and spatial (related to source size, alpha and Brightness)

What are the components of a basic mircoscope

radiation source (light), a system of lenses and other components (from source to sample), a sample, another lens/components system (from sample to detector), detector

why was electron microscopes developed

To circumvent the diffraction limit of light microscopes.

What differences are there between electrons and photons

Electrons have mass and charge. This makes it so electrons interact differently with the sample, we also have to handle them differently in the microscope. Electrons interacts more with particles → scatter → electron microscope operate in vacuum → special sample preparation. Interaction with sample may also cause charging of sample.

How do lenses for electrons work

First you can use electric field to extert a force on the electrons (colomb force). The sample is biased in comparison to the microscope, the electrons from microscope are decelerated towards the sample. This gives less chromatic aberations. Backscattered electrons are accelerated.

We also use magnetic filed (loprentz force). The electrons start to rotate in the optical axis plane. For lower energies the rotation time gets smaller. This seperates the secondry electrons. The working distance is short for this type.

You can combine both. This makes the SE2 oscillations increase.

The signal increase for electrical immersion because SE2 miss electrons, the energy of SE2 increases→more signal, electrons are focused towards detector→ higher contrast and signal to noise → easier to see features and shorter image time

What are some practical conciderations for electron microscopes

There may be strong E and B field → dont have magnetic or magnetizable materials in the microscope. Materials which have an electric or magnetic field will cause abberations. External fields will also affect the electron beam. Electron lenses are much bulkier than those for light which more easily leads to imperfections. The E and B field are also hard to control and always lead to abberations

Whats the difference in acceleration voltage between SEM and TEM

SEM: potential difference of about 30kV

TEM: 80-300 kV

What is the basic layout of a SEM microscope

A source, a first condenser lens, aperture, second condenser lens, another aperture (variable size), objective lens and scan deflectors (this part is where the field can be). The scan deflectors provide the deflection for moving the beam over the sample surface

What is the main purpose of apertures in SEM

to regulate beam waist and/or beam opening angle and thereby the current in the beam. Next to this, the apertures also allow the different parts of the electron column to be of different vacuum levels. Due to the presence of apertures, the current in the column is not constant

What advantages and disadvantages are there to a high current is SEM

it tells us how many electrons arrive at the sample in a certain amount of time, which in turn determines the amount of signal generated. Current and dwell time are thus intricately linked and increasing the probe current may allow reducing the dwell time and thereby lead to lower overall measurement time. However, as we will see later, increasing the current may lead to a larger probe size and thus lower resolution

How does colomb repulsion affect the performance of SEM

• The repulsion between electrons can lead to a force component in the direction perpendicular to the beam axis, i.e. a lateral movement of the electrons. This then leads to broadening of the beam and blurring of the focus.

• The repulsion between electrons can lead to a force component in the direction parallel to the beam axis. This leads to some electrons being accelerated and others being decelerated. As a result, the energy dispersion in the beam increases, leading to more chromatic aberrations.

For SEM how are the beam opening angles concidered

The opening angles are very small compared to light microscopes. This is due to the electrons already having large focal depht

What is astigmatism

it is one of the most prominent abberations in electron microscopes. It is caused by the lens operation being stringer in one of the lateral directions, this causes the beam to experience a stronger lens field in either x or y direction and thus having different focus depending on direction. The optimal focus will then be inbetween the two, but it will be blurry in both directions.

What are:

transmitted electron

elastically scattered electron

backscattered electron

inelastically scattered electron

transmitted electron: is an electron that has passed through the sample without any change in direction

elastically scattered electron: will have changed direction and momentum but will not have lost any energy

backscattered electron: is an elastically scattered electron where the scattering angle is larger than 90 degrees. These thus leave the sample on the same side facing the incoming electron beam.

inelastically scattered electron: is an electron that did loose energy on its way through the sample. This is mostly due to collisions and energy transfer with other electrons in the orbits in the sample material. The energy lost in the inelastic scattering process is transferred to electrons in the material and thus leads to low energy electrons in the material

Can a primary electron experience multiple scattering events

Yes due to amount of energy lost in a single inelastic scattering event is in most cases relatively small

Why may a fraction of the backscattered electrons have an energy slightly lower than the primary beam energy

Because they experienced inelastic scattering before or after their elastic scattering

Why and how do we sometimes need electrons that are coherent after interacting with the sample.

For applications where we want to exploit the electron wave character for imaging, e.g. phase contrast imaging in TEM and electron diffraction, we can only use electrons that have preserved coherence after interacting with the sample.

Inelastic scattered electrons are incoherent but transmitted electrons are coherent, as well as electrons that have only undergone elestic scattering

Which types of electrons exist that interact or exut the sample

We have the incident primary beam of electrons, back scattered electrons (BSE) that have either undergone elastic or inelastic scattering, secondry electrons from the sample (SE), transmitted electron beam, elastic and inelastic electrons (not backscattered). The elastically scattered electrons can be either coherent or not.

For thick or bulk samples, can you use SEM or TEM

SEM, since electrons travelling through the sample will scatter multiple times until they lose al their energy

What is the mean free path of an elctron

the average distance an electron can travel before it undergoes a scattering event

What is the formula for the radius of elastic scattering for different sized atoms

r_elas = Ze/(deltaV Theta), Z=atomic number, deltaV the potential difference at which the electron has been accelerated and Theta the angle at which the electron has been scattered.

How are secondry electrons produced, what typical energy do they have

A primary electron from the beam inelasticaly scatters of an orbital electron in the sample, this transfers energy to the orbital electron, if the energy is sufficent the orbital electron is ejected into the material.

Typically these electrons have relatively low energy: electrons with energy between 0 and 50eV are called secondary electrons but the majority has an energy between 0 and 20eV with a peak in the energy distribution close to 0eV.

One primary electron can create multiple secondry electrons, most of which never leave the sample

Backscattered electrons (come back to this)p0o00o

What is beam damage in SEM

The damage done to the sample as a result of irradiation with the electron beam. Chemical reactions of low energy electrons are the main contributor to sample damage. Other factors that may contribute are (local) heating, (local) electric fields due to charging or separation of charges in the material, and, at high (>100keV) incoming electron energy, direct displacement of an atom, so-called knock-on damage. In organic materials, chemical bond breakage can lead to the release of small hydrocarbon fragments and conjugation of carbon-carbon bonds. Beam damage may thus lead to chemical and structural changes evidenced for instance in atomic and molecular rearrangements, sample shrinkage, and mass loss.

In SEM why does xray and photon emission happen

Inner-shell ionization leaves an unoccupied electron level relatively close to the atom nucleus. Such a vacancy will be rapidly filled by an electron from a higher shell, bringing the electron to a more stable (but still ionized) state. The energy lost by the electron decaying from the higher shell to the inner shell vacancy is released in the form of an X-ray photon. This X-ray photon thus has an energy exactly equal to the energy difference between the two shells. As energy levels are unique for each atomic element, the X-ray energy bears a unique signature of the atom that was ionized. Thus, the overall energy spectrum of X-rays emitted from the sample provides information about the elemental composition of the sample. The energy of emitted X-rays is in the order of keVs.

A special type of X-ray emission that is not due to atom-specific interactions is Brehmsstrahlung. Brehmsstrahlung (German for ‘braking radiation’) originates from the deceleration of primary electrons upon interaction with the sample. Upon interaction with an atomic nucleus, the primary electron besides being deflected may loose some energy in the process. This energy is lost by emission of an X-ray photon. The energy range can thus span the entire X-ray window from about 0eV up to the primary beam energy. Brehmsstrahlung thus gives a near continuous background in the EDX spectrum.

In SEM what are interaction volume and escape depths

The interaction volume is the entire volume in the sample in which electron scattering interactions may take place upon electron irradiation.

In electron microscopy what is charging

During electron microscopy, the electron beam injects electrons in the sample. As a result of the interactions of the primary electrons, secondary and back-scattered electrons may escape from the sample. For thin samples, electrons may also leave the sample at the bottom surface. If there is an imbalance between total number of electrons injected into the sample and the total number of electrons leaving the sample, the sample may gradually charge up during irradiation. This (im)balance can be expressed in term of primary beam current and the secondary and back-scatter electrons yields of the sample.

This means that we need to ground our sample. However most biological samples arent conductive so if the sample is charged (-) incoming electrons will be decelerated and deflected. If the sample is charged (+) higher enrgy SE will be attracted back to the sample which creates black spots.

In case of weakly conducting or insulating samples, a thin conductive coating (e.g. a sputter-coated gold film) may prevent the occurrence of artefacts. In this case, the coating will screen the electron beam from any electric field generated by charges in the sample. However, the coating itself may impact the visibility of high-resolution features in the sample. Alternatively, careful consideration of the imaging conditions (beam energy, current, dwell time, line or frame integration) may prevent the occurrence of artefacts.

How should the thickness of biological samples be for EM

TEM: thin samples (not only for primary electrons but also thin in respect to mean free path of inelastic scattering to avoid damage), use sectioning to make a thick sample thin. An advantage of sectioning is that it provides access to the cell or sample interior, and, by collecting serially cut sections, can allow for volume reconstruction

SEM: Can use thin samples but not limited to it, Whole cells, thicker tissues, or even small organisms can be mounted in the vacuum chamber of the SEM

What are the challenges and goals of EM sample preparation

Challenges of sample preparation:

• Samples must be thin

• Vacuum in the microscope

• Radiation damage (inelastic scattering)

• Signal-to-noise (elastic scattering ~ Z)

• Charging

Goal of sample preparation:

• Preserve biological specimen in a native state such that it

will give maximum contrast at the lowest possible dose

What are the steps in sample preparation for EM with chemical fixation

1. Fixation: fixation can be done either chemically or by rapid cooling, so called cryo-fixation.

   Chemical fixation: Fixation with aldehydes (glutaraldehyde, para-formaldehyde) followed by dehydration with a graded ethanol series and further fixation with osmium tetroxide. Used for: cells, tissues (incl human tissue), organs/organoids, small organisms.

2. Embedding: in plastic, typically an epoxy or an acrylic polymer resin (e.g. Epon, HM20, Durcupan are known resin materials)

3. Sectioning: with a microtome or ultramicrotome using either a glass knife or a diamond knife

4. Staining: or labelling to enhance contrast in the sample. Staining is crucial as the native elements present in the sample (mostly carbohydrates) hardly provide intensity contrast in either back-scatter or transmission detection. smium is an important element in the chemical fixation workflow as it is a strong fixative but also functions as a stain providing contrast to membranes and thus allowing visibility of the biological ultrastructure. Further staining, either with additional rounds of osmium or using other metal salts, e.g. with uranyl, lead, neodymium, can be done on the resin block or after sectioning in which case we speak of post-staining. When applying a staining agent to an entire resin block, homogeneous infiltration is a concern that may need additional measures to be taken as an inhomogeneous stain distribution may give rise to artificial contrast variations or low contrast images from sections obtained from deeper in the bloc

Describe Cryo-EM Sample Preparation

Cryo-electron microscopy requires samples to be kept at cryogenic temperatures throughout imaging. The overarching goal is to preserve the biological specimen in a state as close to its native, hydrated condition as possible while making it compatible with the high-vacuum environment of the electron microscope. This is achieved by vitrification, the conversion of liquid water into amorphous (vitreous) ice rather than allowing crystalline ice to form, which would disrupt and destroy biological ultrastructure. Once vitrified, samples must be transferred and handled under liquid nitrogen temperatures at all times to prevent devitrification (recrystallisation) or ice contamination.

It is mainly used for small samples:

macromolecules, viruses, cells, thin tissues (HPF)

How should you consider the imageing time when you chose pixel size

!mportant to properly choose pixel size based on

needed image resolution and Nyquist theorem, 3x larger pixel size, 9x faster imaging

What is special about TEM and how does it work

TEM lets us see the internal architecture of matter at the molecular scale. By transmitting a beam of electrons through a thin specimen, TEM produces images that reflect differences in how strongly different parts of the sample scatter electrons. In biological applications, this means we can directly visualise macromolecular assemblies, membrane organization, and organelle architecture with a resolution measured in Ångströms rather than micrometers

What is the advantage of TEM in structural biology

TEM has the additional advantage that specimens do not need to form the macroscopic crystals required for conventional X-ray crystallography. In cryogenic electron microscopy, biological material can be vitrified and examined in a hydrated, close-to-native state. Single-particle cryo-EM determines structures by combining 2D projection images of many copies of the same macromolecule, while cryogenic electron tomography (cryo-ET) can examine individual cellular regions and non-repeating structures in three dimensions. Together, these approaches have made TEM central to modern structural biology, from near-atomic-resolution structures of proteins to the organization of macromolecules within cells.

What parts are there in the TEM column

the illumination system, the specimen stage, and the imaging system.

What is usually used as the electron gun for TEM, what energies

TEM usually use a field emission gun, they are highly coherent, bright and low energy spread. Usually 80-300keV

In TEM what illumination system is used

a series of condenser lenses (C1 and C2, sometimes C3) shape the beam before it reaches the specimen

Why does biological TEMs typically use an objective aperture positioned in the back focal plane of the objective

This aperture blocks electrons scattered to large angles, which are incoherent relative to the direct beam and would otherwise add noise and reduce contrast. The aperture size controls the effective resolution and the contribution of amplitude contrast.

What objective lens is used in TEM

a strong magnetic lens that surrounds the specimen and forms the first, most-magnified intermediate image. Because this lens governs the final image quality, minimising its aberrations (especially spherical aberration ) is the central engineering challenge of TEM design.

* The C1 lens determines the spot size of the source on the specimen

• The C2 lens controls the illumination of the specime

What kind of images does TEM produce

A TEM image is the projection of a 3D object