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Advanced optical microscopy
Introduction on the resolution of optical microscopes
Effects of the finite resolution on images
Introduction to confocal microscopy
Optical processes and techniques that can overcome the resolution limit, such as: non linear microscopy, STED,TIRF,PALM, SNOM.

introduction to nanotechnology
Nanoparticles:quantum... Vedi di più

Esame di Advanced microscopic techniques and nanotechnology dal corso del docente Prof. T. Bellini



Typically in another box there are one or more lasers and you can shine one or

more colours at the same time because sometimes is useful to look at more

than one fluorophore at time; so you need to be able of scanning but you also

need to be able to separate that by colour so what do you need to do? Instead

of just a photomultiplier (PMT, detector that just measure the light that arrive,

no matter what colour is it), I put something more to separate the colours.

To separate the colours, I just use another box that is able to read the intensity

of light as function of the colour because it has inside a diffraction grate. So

light arrives and it’s separated in colours and it’s sent all together to the

detector, a multi anode which is like a system of different eyes/detector and

each detector gets a range of each colour. enough light

You can do this if you have

because you’re illuminating a point in the


The question is: when the light goes back how

much light goes back?

Usually you use a PMT because you receive

very little light so you have to be very


After computing you have a 3D image


because it has

Multibeam + CCD

Instead of scanning with just one beam, I can scan with many beams together,

if I have a source of light which is powerful enough.

If the light is powerful I can decide to separate it in more points at the same

time. How do I do that? I can use a Nipkow disc, it’s a wheel with many holes

that rotates.

If the wheel rotate you can see through the holes, and in a complete turn you

had all the holes per line. 9

Then if you have a lamp on the other side and if you can synchronize the things

you could have that your hole is moving and there’s a light here but the light

that gets intense or dim as the hole moves so on your retina you get a line

which is bright-bright-dark-bright dark etc.

If the wheel turn fast enough the light remain on your retina and you have an

image (is like the old TVs before the catotube).

You have a light coming from a laser (you

don’t focus it), you send on the first disk

and this disk has a lot of small lenses

that focus the light on a second disk of

pinholes: the two disks are attached to

each others so they move together.

So when the light encounters the first

disc is divided into different beams, each

lens focuses on a different place on the

disc with the pinholes and goes through

the holes.

Passed the pinholes, you’re exactly in

the situation that you had before

(objective and the sample) but it’s like if

you have different lasers.

The light that goes back from the sample goes through the pinholes as before,

what pass through the pinholes is the light on the focal point of the beam, not

much light from below or from above. Then with a partial reflecting mirror you

can send it on a very sensitive camera (CCD).

By rotating the disc you can move the spots on the sample, so you can see

lines, and as you turn you fill the space, until in one turn you have filled the all


With multi beam confocal microscopy you can go really fast, it is very useful

when you are in a hurry and you have to see something that is happening and

you have to take an image before it goes.

There’s a lot of problem also in communicating data because you can go really

fast but you also have to transfer this data to the computer, the speed of

communication is crucial.

There’re some problems:

- You can go fast but you don’t have enough light

- You can go fast and take a lot of images but it’s not clear where you put

them, so if you want to go really fast you have to use local memories

- Incredible amount of data produced

Intrinsic concept of scanning microscopy

Pixel is a picture element, is the size of unit surface by which I divide an

image. 10

Pixel is an intrinsic unit because when I’m scanning I divide the space in

positions, I don’t have a continuous result. The system says I’m in position 1,

there’s intensity of 10, then the system move to position 2: I’m dividing space

in distinct positions.

So to get an image you have to say position and light intensity in that position.

If it’s in 2D is like a matrix, I’m dividing in squares and each square is called

pixel. xy, z

But here you don’t have only I also have so I have to divide the position in

xy and scan all the positions. So my unit element is not like in the picture a


square, it’s a volume because has and is called Voxel.

This makes impossible to see the image without a computer, because you have

a list of position and a list of intensity.

One thing is how do I divide the space into positions (Voxel) and another thing

is the minimum volume I can see as a resolution: it’s called Resel and, I cannot

distinguish anything inside, because this is the minimum thing that I can see.

Voxel and Resel are not the same thing, one is intrinsic of the optics which is

the minimum volume element I can resolve and the other is how do I decide to

split the space (it can be 100 times larger or 100 times smaller than

resolution), I decide it telling the piezo system where to move the beam.

I want to have Resel and Voxel to coincide so that each position is a resolution

element, but the fact that they coincide is not intrinsic.

Of this cylinder I know how high and how wide it is, it’s not that within I cannot

seen anything and without it’s clearly distinguished. When I shine laser into a

point I can distinguish that my light is coming mainly from the cylinder but is

also coming a little bit from the side too (is a continuous function).

In confocal microscopy I have and overlap of Resels from voxels, each voxel

should contain a Resel but contains also light that is coming from the neighbour

Resels; so the light getting from a position is contaminated a little from the

light of Resels around, because the resolution is not sharp (even if I make

Resels and Voxels coincide).

So what I can do? I can correct a little bit but if I know the shape of my Resel

(which means if I know the shape of my point spread function) I can take this

image, do the Fourier’s transform and then there’s a filter that I can use in the

Fourier’s transform to correct it and then go back to the image.

The problem is that sometimes, pixel or voxel of an image are contaminated by


neighbours and there is trick called that can partly clean this


Confocal microscopy advantages

- You get at the limit of resolution, it’s easy to clean the system but you

don’t go very further other microscopy

You can have 3D images

- (most important aspect) what you get is a

composition of the image.

Doing scanning, if you have light enough you can go faster or you can look at

colours: the output are images where you can get different coloured images;


for example you can get an image where you can split the image in a portion

with a wavelength and a portion with another wavelength.

If you have a system with 2 fluorophores if you put together you’ll see just

black and white, you don’t distinguish colours, or you can split in 2 regions and

you have 2 images and you can give false colours to the fluorescent signals. If

you have fluorophores that are well separated you have a good situation, but

sometimes you have fluorophores that have an emission spectra overlapped

and in this case you need more information, is hard to have a situation in which

you can split the colours.

You can have a system of images and which of this is distinct by different

wavelength: we can have a stack of images, each of these is a different

position of depth for example, but we can also have a stack of images each of

these is a different wavelength, so if you want to put them together you’ll have


a 4 dimension object and .

If you have a signal grey made by red and green fluorophores, if you know the

spectra of the 2, there’s a mathematical procedure by which you can know how

much green and how much red you have. What I get is a mix of the 2 so I need

to unmix them, but to be able to unmix them you need to know the behaviour,

the value as a function of different values, of fluorophores.

I need to separate the colours either because we have very well split

fluorophores and it’s easy or because you have a mix of fluorophores, in that

case you have a stack and for each position you can tell how much you have

green and how much you have red: so for each voxels you can separate the 2


Light Sheet Microscopy

It’s a kind of variant of confocal microscopy.


I can look at the whole picture, as I did before, but now I can illuminate only


a sheet/plane in the direction: so it’s a kind of combination because I’m

looking in 2D but the system is illuminated only on a layer, so I’m getting the z

resolution because I’m illuminating only a plane.

You can illuminate the whole plane or you can use a beam that scans through

the all plane. You illuminate from the side and look through the objective.

Selective Plane Illumination Microscopy (SPIM)

It’s called or Light sheet.

It remains with the resolution limit of all the other microscopy.

L i g h t s h e e t m i c r o s c opy








E In light-sheet microscopy, fluorescence excitation (blue arrow) and detection (green

In light-sheet microscopy, fluorescence excitation (blue arrow) and detection

R arrow) are split into two distinct optical paths.

The illumination axis is orthogonal to the detection axis and is designed to illuminate

(green arrow) are split into two distinct optical paths.

a very thin volume around the focal plane of the detection objective.

Many different implementations of this principle exist, however, the most common

The illumination axis is orthogonal to the detection axis and is designed to

one is the generation of a sheet of laser light that illuminates the sample in the focal

plane from one side.

illuminate a very thin volume around the focal plane of the detection objective.


Many different implementations of this principle exist, however, the most

common one is the generation of a sheet of laser light that illuminates the

sample in the focal plane from one side.

While in confocal you illuminate point by point, through the pinholes, and so

you’re sensitive only on a plane; in light sheet you’re looking all together but

you’re illuminating just one sheet, so the detection is all together on one plane.


- Not complicated as the confocal

- Less photobleaching (you broke the fluorophores only where you’re looking,

in confocal you shine also above and below but you’re not sensitive to these

point). 5 Ottobre 2016

What do you want to avoid with bleaching? You want to illuminate only what

you want to look at. When you use a confocal microscopy you illuminate also

the below and the above portion of what you are focusing on. With the light

sheet microscopy you only illuminate what you look, just the plane of interest

(but you look at the hole system of fluorophore).

Is it possible to overcome the resolution limit set by diffraction?

Both 2D microscopy and scanning microscopy (as confocal) obey the diffraction

resolution limit. image

The resolution applies as we make a linear image of an object. By we

mean that we use a lens to make an image; linear means that the optical

signal you’re looking at, is proportional to the intensity of the light that is

light transmitted or emitted by the molecules in

shining, so it means that the

the sample is proportional to the light that is used to illuminate or excite them.

To overcome the diffraction barrier you have to overcome one of these two

concepts, or both:

By inducing the sample by a proper choice of molecules illumination,

 

non-linear mechanisms of absorption or emission

By replacing the use of optical images with other strategies.

Scanning microscopy

There are several types of scanning microscopy:

Confocal microscopy

- scanning with production of an image

- SEM (Scanning Electron Microscope) scanning with production of an


AFM (Atomic Force Microscopy)

- scanning without making an image


If we want to make something in the middle between confocal and atomic

force, we could think about a stethoscope that makes a sort of a bigger image

of the heartbeat. 13

We could make a stethoscope with light: the NSOM/SNOM (Near field

without the

Scanning Optical Microscopy) is a type of optical scanning

generation of an image.

It’s a capillary with an optical fibre in the centre (70 nm): you can go and put

your fibre tip in the sample that you want to look without making an image,

it doesn’t use lenses but it just collects light from that point of interest.


So the tip goes near to where the light comes out and collects the light from


I have this tip and I can:

- Illuminate the sample and look for the light emitted by the fluorophore in

the sample

- Shine and collect light from the same source locally.

I just have to be able to mechanically bring around the tip: for example I can

touch the membrane of a cell with the tip!

I can go beyond the diffraction limit

So with NSOM/SNOM , because if I don’t

make an image, I can go smaller than the wavelength!!

Two photons excitation microscopy

It’s a kind of not linear microscopy in which you can excite fluorophores with

two photons. In the graph, there are the energetic levels of

molecules (black straights): the molecules have

different levels because of vibration; the lower

level is the electronic ground state.

In violet there is the energy of a molecule which

is excited one time.

During fluorescence you shine light on a molecule

and if the molecule carries enough energy then

the system absorbs this energy (360 nm) and

goes to a higher vibrational state.

But when the vibrations are quenched, the system goes back to a lower state.

If the molecule absorbs 360nm, when it emits light, it will emit at a lower

energy (460nm) because it has lost part of the energy because of vibration.

So in fluorescence molecules absorb a certain quantity of energy and release a


smaller quantity of energy: since the quantity of released energy is smaller

wavelength is longer (460 nm instead of 360 nm).

In the two photons excitation microscopy you can excite the same fluorophores

by using simultaneously two photons that have half of the energy (720nm): the

at the same

photons have to arrive time on the same molecules, or within a

very short time.

We can do the same thing with three photons too.


Normally the absorption is proportional to the intensity (I ). If the photons


ass 0

are two, the amount of energy absorbed is no longer proportional to the

intensity but to the intensity squared (I ), because you need two photons




to be at the same time and hit the same molecule. This means that you need

more photons because they have to be in the

same place at the same moment.

In linear absorption the intensity of excited

fluorophores is proportional to the intensity of

shining light while their number is proportional

to the intensity of energy: the total energy is

but the intensity varies

always the same,

through the hourglass.

number of fluorophores excited is always the same the density is

So the but

greater in the middle. linear absorption.

This is what happens with

The profile of the intensity of the beam is like a

Gaussian and this is also the profile of the intensity of

the excited fluorophores, if the probability is

proportional to the intensity (as a single photon).

In two photons, if the probability is proportional to

the squared of the intensity, the probability of

much larger in the centre

excitation changes: it is

and less in the side, much more

so it becomes

probable to excite the fluorophores in the centre of

the beam.

With double photons emission I’m concentrating the excitation in the centre of

the beam,: with this technique only molecules in the centre of the beam get

excited and so I narrowed the region where I can excite molecules!

lose resolution because I use a bigger wavelength,

However using this method I

using a smaller portion of a larger beam.

What do we gain? When I shine light with linear excitation, I’m exciting photons

everywhere where the beam goes, while if I have two photons I’m just exciting

where the beam is minimum without the

need of having a pinhole (I’m doing a sort of

scanning microscopy!).

The other thing I gain is that I have much

less photobleaching because I’m exciting

only the centre of the beam so I’m not

wasting fluorophores below and upper, so

the fluorescence I produce is just where I’m

looking at. Moreover I use longer

wavelengths so I can penetrate better the



much powerful sources,

For this method we also need to use like a million

times more powerful. It is also possible to use pulsed sources that don’t shine

photons continuously but accumulate photons and the shine them all together

in order to have a very concentrate energy within the pulses.

STED (Stimulated Emission Depletion fluorescence)

In order to have absorption I have to shine light, while to have an emission I

don’t have to shine light.

molecule to emit energy if I shine it whit the

I can convince a

same light that it emits: for example if I shine my molecule in

green but also in red (that is my emission light, as in figure),

the energy decay become faster. Not only I release my light, I

release it in the same direction and with the same maximum

stimulated emission is the phenomenon by

and minimum:

which the rate of emission of an excited molecule increases

proportionally to the intensity of light that it is illuminated by, if

the light is the same wavelength of the fluorescence emission


STED uses two lights:


- One for the excites the fluorophores

stimulated emission

- One for the makes the fluorophores de-excited.

 The number of molecules which

are on level 2 (dn ), the energy


from which we started to get

fluorescence, change in time by

virtue some terms one of that is

proportional to the intensity of

light that shines (h ) times the


difference between level n and


level n .


If level n is more populated than level n light comes and goes down.

2 3

If level n is more populated than level n the light can also go back.

3 2

(formula riquadro rosso).

I can de-excite the fluorophores with light.

So in STED I’m using two beams of two different shapes:

excitation pulse normal

- The is a focus beam

de-excitation pulse donut-shape

- The is a beam darker in the centre and

bright on the side.

So I excite molecules were the beam is, then I turn down the fluorophores

around with the de-excitation beam. 16

Non linearity is used in de-excitation and

to do that you have to shine stronger and


Increasing the power of light, the hole

become smaller and smaller because the

probability to getting de-excitated is not

anymore proportional.

Since the stimulated emission is brought

in a non-linear regime when you increase

a lot the power, the region where the

fluorophores are not de-excited becomes

really small: increasing intensity the light areas become saturated and dark

areas are contracted. We gain much if the turning off is proportional to

the intensity: I have to use non linearity in de-

excitation, so in turning fluorophores off and I can

do this shining stronger, with super powerful pulse.

With this method of increasing power the hole

becomes smaller and smaller: the probability of

being de-excited is proportional to the de-

excitation pulse when this pulse is not very

powerful; because the probability of being de-

excited cannot be more than a limit, when the de-

exciting pulse goes over this limit, all the

molecules become de-excited.

*Dashed lines indicate the percentage of quenched

fluorophores.Upon entering the non- linear regime

the region where we can still have excited

fluorophores shrinks!

The much I increase the power of the de-excitation light, the narrower becomes

the region where I still have fluorophores emitting light


*the dashed blue line represents the 100% quenching level.

This technology is made up of a first green excitation laser and

then a second read beam that has a donut-shape; the size of the

hole is the resolution; the red pulse is much stronger and a little

delayed compared to the green beam. After I’ve de-excited my

fluorophores on the side, I’m able to look the remaining ones at

the centre. scanning technique

At the end what I have is a where I have a

smaller region but with very concentrate fluorophores.


Excitation is intrinsically a stimulation, because electrons absorb energy and

move to the next orbital.

Stimulated emission is instead a new concept: fluorescence life time (the time

the molecule stays excited) can be reduced when the molecule is shined at the

same wavelength it would emit.

This technique uses two beams:

Excitation beam

- normal shape

Quenching beam

- donut shape, with a hole in the centre

The excitation pulse has the same usual shape of a light beam.

Light beam is usually a Gaussian, a peak. It’s

more intense in the centre, less intense in the

sides. The intensity walking along x will start

with low intensity, than it reaches the

maximum at the centre, than it goes off on the

other side. This is a linear excitation because

the number of fluorescent molecules excited is


proportional to the intensity of light. The density, the number of molecule over

volume (for example the number of molecules in a cube of 1μm volume) that


are excited after this pulse, will have the same shape so there will be more

excited molecules in the centre of the area.

If I cut in half the intensity of the beam, the density of the molecules will be


The second beam has the opposite shape:

from zero, it goes up to the maximum, goes

down to zero in the centre and then it goes

up again to maximum and down again. This is

the quenching beam, the stimulated


If it is linear, the fraction of excited molecules

which are quenched is proportional to the

intensity, so it will de-excite more where

there are the peaks at the edge and less where it goes down in the centre.

For example: we have some flourescent molecules and we excite a fraction of

them and then with the de-excitation pulse we quench a fraction of the excited

molecules proportionally to the intensity.

If we double the intensity we also double the number of quenched molecules.

If both beams are linear we don’t gain anything because the width of the

excitation beam peak is the same of the hole in te quenching beam.

If I increase the intensity of the second beam, I increase the fraction of the

excited molecules that are quenched, and if I increase the intesity a lot I can

reach the 100% of the excited molecules quenched. But if from this intensity I

double the power, I won’t double the effect because I can’t go over 100%!

So the pattern of quenched molecules has the same pattern of light as long as

they are proportional: when I have a quench beam that de-excite 100% of the

molecule, if I augment the intensity I will shrink the hole, so I will shrink the

area where the molecules are still excited and the only fluorophores that

survive are the ones in the centre. This is non-linearity.

The blue dash is the line where the 100% of

fluorophores are quenched.

Look at the four profile patterns each one

stronger than the precedent from blue to

violet: assuming that the smallest (1) at the

maximum of the intensity de-excites 100% of

the molecule in that area, if I increase the

intensity (same wavelenght) I can quench

molecules proportionally to the intensity, and

so in a bigger area (because it’s not linear).

In this way I can shrink the area where

molecules are still excited: for each pattern the area where molecules are still

excited is smaller than the area of lower intensity pattern.


Summarize: In order to perform STED I use two beams:

Excitation beam is a pulsed laser with an

 ordinary Gaussian shape

Quenching beam is a pulsed laser that is higher

 in intensity and has a donut shape; the size of

the hole is usual 0,5 m.

The first pulse excites the fluorophores, the second

beam quenches them: if the STED beam has a power

zero, I can see the signal from all the fluorophores

excited. The larger the intensity of the second pulse,

the fewer are the fluorophores that remain excited.

Usually this technique allows to see the 10% of the

fluorophores, while 90% are de-excited: the 10% that

are left are the ones in the centre of the hole.

The shape of the light coming from my fluorophores is

much more narrow so I can move my resolution from

0,5µm (black spike) to 100nm (red spike).

Also you can stain your molecules with two different fluorescence proteins (GFP

and YFP) and you can excite them with the same beam and then quench them

by shooting very hard staying on the same wavelength, then looking at the

emission using a dichroic mirror to recognize the two different emission (paper

– two colours STED...).

So STED is a super-resolved optical scanning microscopy that enables 3D

image formation.

By exploiting a non-linear stimulated emission, STED enables a large

improvement over the resolution limit for linear images.

Moreover by forcing the quenching of fluorophores STED minimizes bleaching

effects: the bleaching of fluorophores is proportional to the time that it stays


Total Internal Reflection microscopy (TIR)

The phenomenon is that when light goes from a

transparent material to another transparent material

and the refractive indexes are different, light that is

going through changes direction and there is


If n is larger than n , than θ has to be smaller than

1 2 1

θ .

2 20

If I go from a material with higher refraction index to one with lower refraction

index (like glass, water or oil to air) and I keep increasing θ I’ll reach the point


where exiting angle (θ ) will be 90° degrees.

2 n 2


sin θ

If θ is 90°, sin θ =1 and then .

2 2 1 n 1

At this angle the exiting beam doesn’t really exit from material 1 and for angled

“exiting beam” will be completely reflected

larger than this one the : so there is

an angle above which the exiting beam doesn’t really exit and the light is

complete reflected without going outside!!

But we know that any point isn’t really a light

but has a width, so for the Snell law we

shouldn’t have light in the point of total

internal reflection in medium two but there is

a little bit of light that is just close to the

surface: if I go really close to the interface I

discover there is a little sheet of light called

evanescent wave that stays close and

doesn’t go far from the interface.

Its intensity falls just as you move away from

the surface: it starts intense and in a short

distance it goes to zero (the distance from the interface where you have this

light is far smaller than a We can use this light to illuminate something


very close to the surface.

If I want to know what are the properties of the evanescent wave, I have to


- z how intense it is

- d what’s its penetration depth (how far does it propagate?).

Both this parameters depends on the angle that light is forming with the

interface on the other side. n 2



There is the critical angle above which I have total internal

1 n 1


When this angle becomes larger intensity decreases so the best angle to have

a strong intensity is just a little higher than critical angle.

The same thing happens for penetration: if you move to larger angles,

penetration becomes narrower and narrower.

a little more the critical angle I can have the maximum of intensity and

So just

penetration; if I keep increasing angle I will get lower intensity and penetration.

It decays exponentially.

If penetration it’s 100 nm it means that d= 100

nm; so when z is equal to d this is exponential to

the which means 1/3 of the starting intensity. So

-1 21

this is the shape of the intensity moving away from the interface when the

penetration depth is 100nm.

So playing with two materials, from one with a higher

refractive index to one with a lower refractive index, you

can create this evanescence light in which the intensity

and the width depends on the angle.

But what can I do with that? I can study a cell wall because

I can illuminate just what is closer to the surface.

The refraction index of the cell is about 1.37-1.38 (1.33 is

one of water and cells have lot of other stuff), so I have to

use a material with higher refractive index (ex. glass slide

with n=1.518) and shine the light trough that.

There are two ways to do it:

External coupling on the other side I have a

 

beam coming that is reflecting so I can look what is

illuminated on the other side of reflection. I

illuminate the sample from below and look from the

above (accoppiamento a prisma).

Through the objective the objective stays

 

below: I want to shine a light on the side of the

objective so when the light comes out, it comes

with an angle tilted enough to do internal

reflection. The maximum angle you can achieve is

the one of NA, so the NA has to be larger than the

reflecting index of the cell. The best objective has


The maximum angle you can achieve is the

maximum angle you can look at and it’s basically

the angle of the NA. So comes out that NA is the refractive index (of the

material between the lense and the sample) times the sin this angle.

So basically (formula) NA has to be larger than refractive index of the

sample you are looking at (typically cell so 1.38).



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Advanced optical microscopy
Introduction on the resolution of optical microscopes
Effects of the finite resolution on images
Introduction to confocal microscopy
Optical processes and techniques that can overcome the resolution limit, such as: non linear microscopy, STED,TIRF,PALM, SNOM.

introduction to nanotechnology
Nanoparticles:quantum dots, nanomag, metallic nanoparticles. General concepts, stability and bioconiugation. Optical tweezers for micro-manipulation
Microfluidics: miniaturization of lab apparatus (Lab-on-a-chip technologies), microfluidic technologies based on flux and droplets. Diffusion and mixing. Notable examples of micro-mechanicals applications.
Atomic force microscopy
Later-free optical Biosensors for the detection of not marked molecules and interactions between not marked molecules. Introduction to SPR based techniques and to methods that use guided light.

Quantitative analysis of images
Introduction to the fundamentals of computer graphics aimed to the comprehension of the informations contained in images with examples taken from microscopy, gel electrophoresis and medical diagnostic.
Colorimetry: color spectrum, Gamut, chromatic coordinates, gamma value of displays, RGB, CMYK.
Digital image types: (es. BMP,TIF,GIF,JPG)
Lossy and lossless compression
Images stacks over space (3D stacks) and time (movies). Movie file types.
Volumes and surface renderings. Tomography.
Introduction to ImageJ software as a tool to:
- extract quantitative information from an image (measurement of bands on a gel electrophoresis image, particle counting, border detection)
- Punctual, local and global filtering
- False color images applied to multi-fluorescence detection.
- Stack visualization and reslicing
- Timelapse and measurements on images over time

Corso di laurea: Corso di laurea magistrale in biotecnologie mediche e medicina molecolare
Università: Milano - Unimi
A.A.: 2017-2018

I contenuti di questa pagina costituiscono rielaborazioni personali del Publisher _ariiel di informazioni apprese con la frequenza delle lezioni di Advanced microscopic techniques and nanotechnology e studio autonomo di eventuali libri di riferimento in preparazione dell'esame finale o della tesi. Non devono intendersi come materiale ufficiale dell'università Milano - Unimi o del prof Bellini Tommaso.

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Lezioni, Fisica