8. Light Microscopy

Focal length f

• Distance between the lense and the focus (the point where parallel light beams passing through the lense converge)

Magnification

• Factor by which the object is enlarged by the lense

generally:

• In a microscope, the total magnification is the product of object lense magnification and eyepiece magnification.

  M(obj)*M(eye)=M(total)

Numerical Aperture

Real images are locations in the light beam where light rays converge. If you would put a piece of paper there, you would see the image.

Virtual images are where extensions of diverging light rays meet. It is basically where your eye thinks the object is.

Magnification, resolution, contranst

Spherical aberrations are defects in lenses: The light rays passing through the lense at different positions do not meet perfectly at one focal point but are spread over a certain area:

This issue can be resolved by combining concave and convex lenses:

or by using aspherical lenses:

The refractive index of the lense differs for different wavelengths, resulting in different focus points for different wavelengths.

There are two types of chromatic aberrations:

• axial: focus points at different distances from the lense

• transverse: focus points at different locations in the focal plane

Chromatic aberrations can be resolved by using lenses made of multiple materials, correcting the different refractive indices for the different wavelengths.

Or add “diffractive optical elements” to the lense:

Or use flourite-containing glass with less chromatic aberrations.

Resolution limit: minimal distance at which two separate features can be distinguished.

Resolution is limited because of diffraction and aberrations, imperfect lenses, etc.

Result: Airy disks (refractive rings around bright central spot)

n refers to the refractive index of the medium between the sample and the lense.

NA refers to the numerical aperture of the microscope, which characterizes the range of angles over which the system can accept or emit light (the “acceptance cone” of an objective) - the wider the angle and the higher the refractive index, the higher the maximal resolution).

Rayleigh criterion:

theta: angular resolution

Two objects are just resolvable when the center of the diffraction pattern of one is directly over the first minimum of the diffraction pattern of the other.

a) The resolution power of the microscope is given by

leading to a minimal distance x of 0,529 μm.

b) Use a higher NA Objective (with immersion fluid), use a smaller wavelength

c) fObj= ftubelens/mObj= 3.333 mm

d) As it does not move with the sample, we can eliminate the sample or coverslip, it has to be in one of the conjugate planes of the sample, so within (or at the back end of) the eyepiece, around the lamp field Diaphragm, or on the camera chip

Contrast: The ability to destinguish between different objects or an object and its background based on their relative intensities.

Contrast depends on even illumination of the sample.

• Köhler illumination: based on a condensor which gathers the light from the microscope’s light source and focuses it into a proper cone

• —> even illumination of the sample and the conjugate image plane

• Staining

• Contrast-enhancing illumination:

  • Phase contrast microscopy

  • Differential interference microscopy (DIC)

  • Darkfield illumination

Image formation

When passes through a sample, the light wave is not only altered in amplitude (which we can see as reduced intensity), but also undergoes a phase shift which is undetectable for our eyes.

Part of the light passes through the sample undisturbed (sourround wave S) and some is diffracted (diffracted wave D). Both are detected in the objective, their interference generates a particle wave (P).

We only detect S and P wave. When the D wave has low amplitude (as is the case for biological samples), we can hardly detect a difference between S and P wave —> the contrast is low.

To increase the contrast between background and sample, the S wave is advanced in phase and reduced in amplitude leading to interference.

There are two types of phase contrast:

• In positive phase contrast, the S wave is advanced by lamda/4 which results in a total phase difference between S and D wave of lamda/2

  —> destructive interference

  —> objects with higher n appear dark

  —> objects can have bright halos from diffracted light

• In negative phase contrast, the S wave is retarded by lamda/4 which results in overlap of the S and D wave

• —> constructive interference

—> high contrast through brightness

The goal is to eliminate all non-diffracted light from the image. This is achieved by using an illumination anulus as in phase contrast microscopy - the resulting light circle is focused on the sample. However, the numerical aperture of the illumination source is higher than the one of the objective. Therefore, non-diffracted S-wave light is not observed. The light diffracted by the sample, which is spread in all directions, is observed by the microscope.

translates gradients in optical pathlengths into contrast changes (instead of absolute optical pathlength differences as in phase contrast)

This method depends on birefringent materials which have different refractive indices depending on their orientation, and change the polarization of the light passing through them.

If your sample happens to be birefringent, you can directly analyze it with a microscope with two polarizers, illuminating with polarized light and detecting only light with a polarization perpendicular to the initial light:

If this is not the case, instead, optical path differences are converted into changes in polarization which are then translated into contrast.

This is achieved using so-called Wallaston prisms (on the right) which consist of two wedges of a crystal in perpendicular orientation:

Wallaston prism I splits the light beam into two rays with perpendicular polarization and a slight shear (phase shift). When they pass through the sample, they pass through slightly different areas. If one of the area is, for example, thicker than the other one, it induces another phase shift. Wallaston prism II reunites the two rays back to one, reversing the splitting of the first. If the two rays do not have the original phase offset, they are combined to an eliptically polarized wave. The analyzer removes the original polarized light - you only see something if one of the split rays has passed through the sample and the other has not.

Be careful when looking at DIC images! Sometimes, things look like there is a topological difference, but in fact you only see optical path gradients!

Be mindful about the effect of your sample! The sample’s orientation is important! Also, birefringent samples/sample containers (e.g., plastic petri dishes) can interfere with the measurement.

—> high contrast through perceived 3D topology

If the second DIC prism (Wolaston II) is removed from the light path, a reversal of the actions of the first prism does not occur, meaning the shear and rotation of the O-and E-ray are not reversed. Therefore, most of the light will pass through the analyzer and the image will resemble a standard bright field image.

Only excites fluorophores within 100 nm from a reflection surface. It has a particularly high contrast and signal-to-noise ratio and causes less photodamage than widefield imaging.

In TIRF, the sample is illuminated with a light beam with a small angle relative to the sample surface (reflection angles > 62°) so that the light beam is deflected at the surface.

However, while reflecting, the light causes a standing wave (evanescent wave) that is directed inside the sample and excites nearby fluorophors.

The penetration depth decreases with increasing refection angles and smaller wavelengths!

Result:

Confocal Laser Scanning Microscopy allows optional sectioning of samples along the optical axis of the microscope (“vertically”).

This is achieved with a detector with a small pinhole. Only light from a specific focal plane in the sample can pass through the hole.

The resolution depends on the wavelength, numerical aperture, and the size of the pinhole - the smaller, the higher the resolution.

Similar principle as Confocal Laser Scanning Microscopy. But:

• faster

• lower resolution

Instead of a single pinhole, two rotating disks of several thousand pinholes are used, illuminating the sample with several distinct small focus points (ideally no crosstalk) at the same time.

Advantages:

• better signal-to-noise ratio (because we can use CCD cameras)

• less bleaching and less phototoxicity (because we are faster)

• live cell imaging and movies possible (because we are faster)

Disadvantages:

• lower axial resolution (because the pinhole size is fixed)

• generally less flexibility to adjust components depending on the sample

D: diffusion constant

Method to determine

• diffusion coefficients

• average concentrations

• association/dissociation constants

of fluorescence labelled samples.

The method requires a Confocal Microscope.

The beam of the microscope is focused in an area of interest. When a labeled particle passes through the confocal volume, its intensity is measured and with the help of an autocorrelation function, the overall fluorescence fluctuation over time can be determined

—> info about molecular dynamics

This only works with very dilute samples!

Depends on

• dipole orientation of the fluorophors

• distance between donor and acceptor

generall principle: RESOLFT - reversible saturable optical fluorescence transitions

—> fluorescing molecules are reversibly “turned off” so that they cannot respond to activation

—> higher resolution possible

SMLM: Single Molecule Localization Microscopy

STED: Stimulated Emission Depletion

GSD: Ground-State Depletion

SIM: Structured Illumination Microscopy

SMLM: Single Molecule Localization Microscopy

Principle: When the Point Spread Functions (PSFs) of two fluorophors do not overlap, we can determine their precise position. The overlap of the Point Spread Functions is avoided by separating the fluorescence of different molecules in time via photoswitching.

Whether one particular fluorophor is switched “on” or “off” is a stochastic event. Under suitable conditions (e.g., low intensity activation beam, certain buffers), only a small number of molecules will be ON and, hence, appear as spatially isolated, non-overlapping PSFs. The “off”/”on”/”off” switching leads to fluorophore ‘blinking’. By taking a large number of wide-field images, we statistically observe all fluorescing particles without their PSFs overlapping, and an image where all fluorophors are “on” can be assembled.

Nuclear pore complex in a conventional microscope:

Nuclear pore complexes after SMLM:

STORM: stochastic optical reconstruction microscopy

• uses fluorescence dyes that can photoswitch in certain buffers

PALM: Photoactivated Localization Microscopy

• uses fluorescence dyes that can be activated with an activation beam (UV)

https://doi.org/10.1038/s43586-021-00038-x

STED: Stimulated Emission Depletion

This method uses fluorescence dyes that can be activated and deactivated with a laser. The dye is activated with a short excitation pulse. A ring-shaped STED beam, quenching the fluorescing molecules in its range (-> stimulated emission), is used directly afterwards.

This allows engineering of the dyes’ Point Spread Functions, avoiding overlap and therefore increasing resolution.

Result of STED:

GSD: Ground-State Depletion

SIM: Structured Illumination Microscopy

This method is based on Moiré patterns: large-scale interference patterns that appear when two similar ruled patterns are overlain with a slight rotation/displacement.

In SIM, you use your sample as the first pattern and a known mask (illumination structure) as the second. From the observed Moiré pattern and the known mask, one can receive a sample image in high resolution.

The concept behind SIM can be explained by a simile with Moiré fringes. If two patterns with fine details are superposed multiplicatively, a third, coarser pattern will appear (Fig. 3a). If only one of the fine patterns and the superposed pattern is known, the other fine pattern can be calculated. Translating this idea to microscopy shows how imaging is performed. One of the fine patterns is the spatial distribution of the fluorescent dye, that needs to be imaged. The other fine pattern is the structured excitation light intensity. The superposed pattern is given by these two and can be observed with the microscope setup.

(from Huszka, G., Gijs, M.A.M., Super-resolution optical imaging: A comparison, Micro and Nano Engineering, 2, 2019, pp 7-28, https://doi.org/10.1016/j.mne.2018.11.005)

https://www.youtube.com/watch?v=DbWtjTFSV-0&ab_channel=RiceProfELEC571

Alexa Fluor 488:

• C) as excitation filter

  • generally, difficult to get a wavelength that is in the emission range of the dye because the Mercury lamp does not really have a peak there

• B) as emission filter

  • does not overlap with C and is in the range of the dye’s emission

Alexa Fluor 549:

• B) as excitation filter

• A) as emission filter

Pacific Blue:

• D) as excitation filter

• C) as emission filter

The pinhole and the tiltable dichromatic mirror.

Wavelength, Objective NA and pinhole diameter

Advantage of Spinning Disk Confocal

• faster

• better SNR

• less photobleaching

Disadvantage

• pinhole size is not adjustable

• less axial resolution

Standard epifluorescent microscope:

• since a normal fluorescence microscope has a resolution of about 200 to 300 nm, one would most likely be able to distinguish five seperate blobs. One would not be able to say for sure which letters are there (except for L, maybe).

STORM:

• resolution of about 50 nm

• possible to make out the letters, but not all individual fluorophors

• overlapping image

STED:

• 20-50 nm resolution

• ideally able to make out individual fluorophors

• line-for-line scanning, overlapping images give final complete image

STORM und STED final images are comparable (just not the seperate images)

FRET

d.

The evanescent wave energy is a function of the excitation wavelength.

c.