The basic idea is to have one first lens that makes an object bigger but inverted, and another lens, called the eyepiece that sees the original part bigger, and in correct shape. With some high school physics is possible to compute how much is the enlargement due to the lens.
Lens Physics
$$ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} $$$$ M = \frac{d_i}{d_o} $$The two magnifications compound with each other, giving a final value of $M = m_{1} + m_{2}$.
The resolution
$$ \Delta x = \frac{1.22 \cdot \lambda}{2NA} $$$$ NA = n \cdot sin(\theta) $$Where $n$ is the index of refraction of the medium, and $\theta$ is the angle of the light cone that enters the lens.
This means we cannot distinguish two objects that are closer than $\Delta x$, and this is the limit of the resolution of the lens.
Looking at the aperture you can observe that if you are closer (wider aperture angle), then you resolution is higher, but less field of view. Sometimes is not very easy to bring the object to the tissue (bone, some 3d structure e.g.).
Measuring resolution
In the lab the resolution of a microscope is measured using small beads and spheres of 100nm, we define the resolution as the width of the blurred dots that are produced by the lens.
Types of microscopy
Different microscopes
Electron Microscopy
We have a wavelength of nanometers, which means the resolution is orders of magnitude better than the light microscopy.
We use magnets as lenses in this case.
Nice thing about scanning electron microscopy is that you can gather 3D information (scattering can be seen at different angles), and the resolution is much better than light microscopy.
Comparison EM vs LM
One cubic millimeter would take thousands of hours. Now we can mimic human segmentation process, and we can build volumetric segmentation.
| Feature | Electron Microscopes | Light Microscopes |
|---|---|---|
| Maximum resolution | $0.5 \text{nm}$ | $200 \text{nm}$ |
| Useful magnification | Up to $250,000\times$ in TEM, $100,000\times$ in SEM | Around $1000\times$ ($1500\times$ at best) |
| Wavelength | $1.0 \text{nm}$ | Between $400-700 \text{nm}$ |
| Image Details | Highly detailed images, and even 3D surface imaging. | See reasonable detail, with true colours. |
| Applications/Specimens | Can see organelles of cells, bacteria and even viruses. | Good for small organisms, invertebrates and whole cells. |
Fluorescence Microscope
We have a dichroic mirror The specimen shines in green light when you send some blue light to the specimen, which is then projected back to the camera lens. Lower energy light is emitted. or emit more photons (super high density of photons in specific space). Red light is less scattered, due to higher wavelength, so it is a little better. This is why it is called two photon microscope, this is localized exitation, which means you get very crisp images.
Lightsheet microscope 🟥
TODO. You substitute first the layers of the sample with transpared molecules.
Then with this special type of microscope you can have nanometer resolution
Superresolution Microscopy
You excite parts of die molecule (sparse manner), hopefully different, many times, and then combine the signals you get from the different images.
This was a light microscopy enhancement, which allows you to get high resolution. They won the nobel prize for this idea. The disadvantage is that it is slow, and cannot be done in vivo, because you need many many images to get the final image.
Functional Microscopy
This entails living cells (Calcium and Voltage images), and functional flourescence indicators. You need to be fast, not like super-resolution one. Calcium is proxy of neural spiking.
Voltage imaging -> something in the neurons that can be processed Another nice thing is that we can extract neuron firing voltage parts from image data. (microscopes create huge datasets).
Synthetic Calcium Indicators
When calcium binds with BAPTA molecule, this changes shape, and can be detected. Nowadays we use GCamp protein, which can create some nice images.