Advanced microscopic techniques and nanotechnology, inglese, Microscopy, Medical biotechnology

Advanced microscopic techniques and nanotechnology

Optical microscopy

Resolution limit in traditional optical microscopy:

Light can be used to explore matter in different ways:

• Spectroscopy → we can use a spectrophotometer and see how many light molecules absorb and how many light molecules release.
• Scattering/Diffraction → explore the matter without absorption.
• Imaging → making images and larger images of the matter you’re interested in.

There is a limit to what we can see using optical microscopy, (how small can you go?) because we cannot see anything smaller than 0.2 µm (in practice 0.5 µm). However, there is a lot of stuff we would like to see smaller than that size, for example, pores on the cell’s membrane, synapses…

For a long time, there was a presumed limitation for optical microscopy, that it would never obtain a better resolution than half of the wavelength of light; they circumvented this limitation, bringing optical microscopy to the nanodimension. Now we can see pores.

Things to know about microscopes

• Optic basis → light velocity, wavelength, frequency, reflection index.
• Lens and image formation → principles of reflection and transmission.
• Basic structure of an optical microscope → when we look in a microscope, what we see is a virtual image of the object.

Limit in resolution: what is the matter, what can we see?

We have an infinitesimal point, like a nanoparticle that is shining light, and we create an image of it. We also have a lens: the shining light goes through the lens and forms an image. The image of a point is not a point, but has a size, so we cannot see things that are smaller than that size. Therefore, if we have an object made of details, and we do its image that is still made of details, each detail has a size because they are not points, so the image will be blurry.

Optical resolution

The minimum size that we can resolve (that we can clearly see with a microscope) can be calculated by the formula:

2 λ 0w= πNA

• λ → λ is the wavelength of the light we are using; because we are considering the wavelength of light in air (the wavelength changes when we go in different means).
• NA (Numerical Aperture) → is a number coming from the quality of the objective of the microscope and depends on the wavelength and the quality of the microscope. The NA is written on the objective, next to the magnification (es. 10x). NA is defined as the product of the reflective index (n) of the material that is between the object and objective (air or oil), and the sin of the angle of the light that the object can collect.

NA = n sin α

The larger the angle, the larger the NA, and the smaller is the resolution (w): this means that we can see smaller things, because the object collects a lot of light and we can see better. In order to have a big NA, we need a large numerical index or a large angle. Lenses are not perfect and that can give different quality of image.

What happens when we do an image of a point?

We can consider a profile of intensity of an image of a point; we get something called Airy Disk, in which the central part is the main thing we see, and it is like a peak and then there is a blur around the peak. The Airy disk and Airy pattern are descriptions of the best-focused spot of light that a perfect lens with a circular aperture can make, limited by the diffraction of light. The larger the numerical aperture, the smaller the image of a point, and it is why I can see better, so I can distinguish two points and define details. Resolution is the minimum distance that allows us to distinguish two points. Same magnification but different resolutions allow us to see the difference between objects.

Point spread function

It’s the name of the shape of the image of a point. It tells us the quality of our microscope. It can be:

• Small and symmetric → the microscope is good.
• Large and dirty → it means that the object is not correctly aligned, or there are other problems (like a mosquito on the sample).

Diffraction

Diffraction refers to various phenomena, which occur when a wave encounters an obstacle or a slit. The waves come out as circles that are wider than deep, and this happens because there is something that slows them down. It happens, for example, when the waves want to go across a place where there are holes. We also can see that the waves have a specific direction, and they’re aligned: they have all the maximum together and all the minimum together. They have a specific angle that depends on the wavelength and the distance between holes, and in particular, we need the distance between holes to be larger than the wavelength, λ = sin θ dh

They produce a continuous oscillation between what can pass and what cannot (all, less, nothing, more, everything). Light passes and goes either straight or forms an angle connected to the distance between holes. In addition, also the contrary is valid, because waves converging with a certain angle create a grating with λ = sin θ dh. In fact, because of this concept, using a lens we can obtain the image of the alternation of holes and objects (zebra lines). So we have a periodicity, a sheaf of lines in a particular direction (the angle), and a lens. The lens collects the lines and focuses them back on a screen, and then we have an image. Now if we change the periodicity of lines:

• Make them larger (bigger holes) → the angle becomes smaller.
• Make them closer (more frequent) → the angle becomes larger, and maybe so large that it doesn’t enter in the lens, and then I don’t have the image anymore.

NA is the angle of lines that I’m able to collect in my lens. With a certain lens, I can accept certain angles, but the angles are related to “spatial frequency.” To have diffraction, I need the distance between lines to be larger than the wavelength. The narrowest periodicity accepted is 1.2 λ0 / NA. The larger the angle, the narrower are the zebra lines we can see.

Trick

If I illuminate with tilted light, I can obtain a wave (after the reticulate) less tilted. In order to do it, I have to use a condenser, so I can make the resolution better. The condenser is a system of lenses that illuminates the sample uniformly using lights with different directions. Indeed the complete equation for transmission microscopy is:

1.2 λ0w = NA oss + NA ill

When I tilt, I gain something because I bring some of the directions that were out of the objective inside it.

Summarizing

• The resolution limit is connected to the component of direction that lenses are able to collect.
• The smaller the angle, the worse is the resolution.
• If the periodicity becomes too narrow, the diffraction doesn’t exist. Therefore, we are still limited in the resolution. The details are intrinsically lost in the propagation.

Fourier transform

Every image is composed by an alternation of lines, a series of discontinuous lines, and I can reproduce it by adding sinusoidal waves (with maximum and minimum) to other sinusoidal waves (with different maximum and minimum). The more components you add, the better resolution you obtain. The Fourier transform is a mathematical operation used to determine frequencies in a function. If I have an image and I want to write it using sinusoidal waves, what kind of sinusoidal waves should I put? I can add more components with different inclinations and directions, so at the end I will obtain the image; each direction corresponds to a system of lines. The more I add, the more I gain information, and the more the image will be detailed.

Each image can be decomposed or broken into many systems of lines: in each system, when the light arrives, it generates diffraction and so generates lines with different directions; I can obtain a map of these directions that can be used to form the original image, the Fourier transform. In the Fourier transform: each spot shown represents the direction of the light, and so, it stands for a system of lines with that specific inclination. Each stripe of lines can be identified by a spot in the Fourier transform that indicates the direction, a map of the angles; but we have still to remember that, if the angle is too large, it will not contribute to image formation, so only the angles going inside the lens will contribute to the image. So each image can be divided into a system of stripes, and each stripe can be identified by a point in the Fourier transform, which tells us what the angle is.

Now, let’s consider an image, and the Fourier transform of this image: if we erase the components outside of a circle and we do a reverse transform, what we obtain is the same image as before, but we have lost the components with narrow stripes (small periodicity) in all the directions and we get a blurry image. This operation is irreversible.

Confocal microscopy

Confocal microscopy, however, obeys the resolution limit; it isn’t one of the super resolution techniques, it’s just an advanced technique but it’s still within the resolution limit. Resolution and magnification are two completely different things; they’re connected only because of two reasons:

• Objectives that have a large magnification usually have a large numerical aperture because otherwise it would be senseless to have big magnification without resolution. So when you grow in magnification, you grow in numerical aperture by fact because the object is made in that way.
• All the setups are usually done to provide a connection: when you look into the microscope, usually things are set so that you see a clear image. It would be useless to have a magnification that is too large because you could see things that are not resolved; also, it would not make sense to have a magnification that is too small so you have a lot of details that you could see but don’t see because the magnification is too small. You need to have a balance between the two.

Confocal microscopy practice

If the resolution is the smallest distance that I can recognize, it comes out that it is also the smaller distance I can focus the light into. These are two kinds of complementary concepts. So if I want to illuminate the smallest portion possible of my sample, the lateral size is 0, time divided by the numerical aperture.

How is the shape of this light? There is a lamp, as light becomes to being focused through the sample, it becomes narrow. If you draw it with geometry, it should go to a point but it doesn’t go to a point, it goes to a minimum and then it opens again, so you have an hourglass shape. How long is the section in which the light is compressed? This distance I want to define is:

π λ0 z = 22 NA

While w defines how narrow the beam is.

One attitude of conventional microscopy is that I illuminate the entire sample, I took a lens and I take an image and look at it, I enlarge, etc. With confocal microscopy, you can scan the image, which means that instead of illuminating it all, you can illuminate one point at a time, progressively. The thing is that I cannot really illuminate one point at a time! I use a trick: I have the source of light which is very small (it usually is a source with a screen with a small hole, so light from the other side is only light that comes through the hole); then I use a partially reflective mirror (a lens) and make an image of this hole on the sample. We know that the image of a point is not a point; it has a width.

Then I look back, so I send a light that excites my fluorescent molecules that shine light in all directions; then I look backward: my lens is collecting light and I look at that: what am I getting? The light that I’m receiving comes from all the hourglass shape, from every point that I illuminated. But I would like to illuminate one single point and to get information from it. So in order to get information from one single point, I can put a second small hole (called pinhole) exactly on the same image plane of the centre of the hourglass beam that is coming from my sample. Only light coming from the focal plane can pass through this second pinhole, while if it comes from below or above it will be cut away when it reaches the pinhole. With this technique, I basically do a trick by which light that is coming not exactly from the centre, but from above and from below my focal plane is rejected for the larger part.

Central concept of scanning confocal microscopy

• I illuminate with a source that comes from a very tiny point (that could be a pinhole or a laser) and I do an image on the sample of the small source, which is somewhere in the sample. Then I do another image through the lenses of the same point on another pinhole so that only light coming from the centre can pass while light coming from above or from below is rejected.

Resolution in confocal microscopy

That’s why with confocal microscopy I’m sensitive only where I’m focusing and I’m not sensitive below and above. What kind of resolution does the trick of the two pinholes give me in the z direction (lateral wide resolution)? I’m sensitive to something that in xy direction has the formula:

2 λ0 w = π NA

And in the third direction:

π λ0 z = 22 NA

And the result is a number three times larger that can reach 1-2 μm (while w is about 0.5 μm). So my resolution is about 0.5 μm in xy and it is 1-2 μm in the z direction. So when I’m using normal microscopy, I try to illuminate the whole surface of my sample uniformly; in fact, they have a condenser to have light as uniformly as possible on the whole surface. With confocal microscopy, I try to illuminate the smallest portion that I can, doing an image through a pinhole of a single point: so the information I get from each position is how much light is coming from that position, which is 0.5 μm wide and 2 μm deep.

How can I do confocal microscopy in practice? In practice, it is a little bit more complicated: since I have to illuminate one point at a time, I have to bring this light all around the sample in a very controlled way. The source is typically a laser because it’s easier to put all the light through the pinhole (it’s coherent) and also because lasers are monochromatic (you choose the laser of the color that you need to excite the fluorescent molecule; usually, we use multilasers). The laser goes from a box that moves around the beam, then you have to control what you’re doing, and this is a crucial point because you have to synchronize what you learn with where you’re shining light. Your phototube will tell you in time how much light it has seen, but this is not an image; you have to match information about how much light you’re receiving and the position that you’re illuminating on the sample. So you can create a map of position – intensity. You also need a detector, which is usually a very sensitive camera.

The box that moves the beam has some mirrors that are controlled by piezoelectric movement (a device that is able to control very fast movements). The mirrors that are moving control the xy position, and typically you have the z objective that goes up and down and controls the z position. I want the light to have the same intensity when I move it around the sample (the neck has a greater intensity of light, it’s more concentrated) and it’s complicated because you always want the mirror to enter the objective but with the same angles, or you will have a different intensity; this is why you cannot have just one lens but you need a system of mirrors. So it’s important to control the focal position without altering the enter position in the objective.

Typically, in another box, there are one or more lasers, and you can shine one or more colors at the same time because sometimes it is useful to look at more than one fluorophore at a time; so you need to be able to scan, but you also need to be able to separate by color, so what do you need to do? Instead of just a photomultiplier (PMT, a detector that just measures the light that arrives, no matter what color it is), I put something more to separate the colors. To separate the colors, I just use another box that is able to read the intensity of light as a function of the color because it has inside a diffraction grate. So light arrives and it’s separated in colors and it’s sent all together to the detector, a multianode which is like a system of different eyes/detector, and each detector gets a range of each color. You can do this if you have enough light because you’re illuminating a point in the sample. 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 sensitive. After computing, you have a 3D image because it has xyz.

Multibeam + CCD

Instead of scanning with just one beam, I can scan with many beams together, if I have enough light.