# Fundamental concepts

Here are a few basic concepts one should know before starting your acquisition:

## Objective lens

The objective lens is one of the most important pieces of equipment of your microscope, it will determine the size of your **field of view**, your **resolution**, your **sampling** and depending of the quality of your objective, it will help with some **optical correction**.

Key parameters that you can see on the markings on the barrel of an objective lens:

### Numerical aperture

It is the angular aperture of objective NA given as:

Where *θ* is the half-angle of the cone of specimen light accepted by the objective lens, and *n* is the refractive index of the medium between the lens and the specimen.

The **higher the NA,** the more diffracted rays are collected from the specimen and then the **higher the spatial resolution** you could expect.

### Magnification

A higher magnification will not give you a higher resolution; however, the magnification is critical for **sampling** (see below) while working with a camera. Moreover, the ratio of numerical aperture to magnification determines the light-gathering power of a lens and hence the **image brightness** B:

(epi-illumination mode)

Where M is the magnification and NA is the numerical aperture.

Finally, you should keep in mind that a higher magnification will yield a smaller **field of view**.

### Immersion medium

As we have seen before, in the equation the NA is directly proportional to *n* then the higher the refractive index of the immersion medium, the higher the resolution you could have. However, if the immersion refractive index of the objective does not match the refractive index of the medium surrounding the sample, we get spherical aberration. This is a phenomenon whereby the PSF becomes asymmetrical at increasing depth, and the blur becomes worse. **Therefore, matching the refractive indices of the immersion and embedding media is often strongly preferable to using the highest NA objective available.**

For example, for fixed cells, if you use ProLong® Gold Antifade Mountant, which has a refractive index of 1.47, an oil (*n* = 1.52) objective will be great or, if you have the option, a glycerol (*n* = 1.47) objective would be perfect. For live cells, you will probably be working with a live cell imaging solution (more info on how to prepare your sample) with a reflective index and therefore should work with a water objective.

### Optical correction

This is more or less an indication of the quality (and the price) of your objective. It is indicative of the amount of colors that are corrected for spherical and chromatic aberration as well as if the objective provide flat-field correction, here is table that summarize the different optical correction available:

Objective Type | Spherical Aberration | Chromatic Aberration | Field Curvature |
---|---|---|---|

Achromat | 1 Color | 2 Colors | No |

Plan Achromat | 1 Color | 2 Colors | Yes |

Fluorite | 2-3 Colors | 2-3 Colors | No |

Plan Fluorite | 3-4 Colors | 2-4 Colors | Yes |

Plan Apochromat | 3-4 Colors | 4-5 Colors | Yes |

## Spatial resolution and sampling

### Spatial resolution

The *spatial resolution* of the microscope is defined by the smallest resolvable distance between two points in an image.

*XY* resolution

Which define the *Rayleigh criterion* where *d* is the minimum resolved distance (in other words, your *XY* resolution), and NA is the numerical aperture of the objective lens. It's also the radius of the central diffraction disk also known at the ** Airy disk** (see figure bellow).

*Z* resolution

Where n is refractive index of the immersion medium.

### Sampling

Sampling is the process of converting the continuous analog signals out of the objective into a numeric digital sequence. According to the **Nyquist sampling theorem**, in order to preserve the spatial resolution, the radius of the *Airy disk* (*d*) should be covered by a minimum of 2 adjacent pixels.

Concretely, what does that mean? Let's assume that you are working with an objective with , and with a the *resolvable power* of you objective is:

If you are working with a sCMOS camera, which typically have a physical pixel size, after magnification, your pixel size is:

, which will then give you a good sampling as illustrated is figure bellow:

## Dynamic Range

The number of resolvable steps of light intensity, gray-level steps ranging from black to white, is called the dynamic range.

Ideally, especially if you plan in doing any image quantitation/measurements, **the larger the number of gray levels the more accurate your measurement would be** and also the easier the extraction of information will be.

### Bit depth

After digitization (by an analogue to digital converter(ADC)) in the computer, the photon signal is displayed as shades of gray ranging from black (no signal) to white (saturating signal) on the monitor. The ADC are described in terms of their bit depth. Since a computer bit can only be in one of two possible stated (0 or 1), the bit depth is described as 2^{x} number of steps. Therefore, an 8 bit processor can encode 2^{8} steps or 256 gray levels and a 16 bit processor can encode 2^{1}6 steps or 65536 gray levels.

### Laser power

Here the advice is relatively simple: **"Use the lowest laser power to give an acceptable image"**. This is true especially working with live cells, too much laser power will be phototoxic to cells and will alter their behavior. Moreover, using low laser power will prevent photobleaching of your fluorophores.

**What is an acceptable image?** It's an image you acquire for quantification and chevk for signal-to-noise level.

### Gain

Gain is a relative measure of the amplification one applies to the photon detection system. On a traditional PMT the signal voltage is amplified by multiplication by a factor, while on a camera, increasing the electronic gain reduces the number of photoelectrons that are assigned per gray level. In either case, increasing gain will result in brighter images. Particularly, **gain does not make camera more sensitive**. It boosts the noise as well as the signal and at some point as gain is increased (and the overall image gets brighter), the signal/noise ratio (S/N) starts to decrease. The overall aim is to get the highest S/N, **not** the brightest image.

### Offset

Offset is an electron adjustment that shift the signal positively or negatively. In cameras, offset has to be adjusted to prevent the ADC to hit 0.