How to define and calculate the efficiency of optical microscope
1. Numerical aperture
Numerical aperture is abbreviated as NA. Numerical aperture is the main technical parameter of objective lens and condenser lens, and it is an important symbol to judge the performance of both (especially for objective lens). The size of its numerical value is respectively marked on the casing of the objective lens and condenser lens.
Numerical aperture (NA) is the product of the refractive index (n) of the medium between the front lens of the objective lens and the object to be inspected and the sine of the half of the aperture angle (u). The formula is as follows: NA=nsinu/2
Aperture angle, also known as "mirror mouth angle", is the angle formed by the object point on the optical axis of the objective lens and the effective diameter of the front lens of the objective lens. The larger the aperture angle, the larger the light flux entering the objective lens, which is proportional to the effective diameter of the objective lens and inversely proportional to the distance of the focal point.
When observing with a microscope, if you want to increase the NA value, the aperture angle cannot be increased. The only way is to increase the refractive index n value of the medium. Based on this principle, water immersion objective lenses and oil immersion objective lenses are produced. Because the refractive index n value of the medium is greater than 1, the NA value can be greater than 1.
The maximum numerical aperture is 1.4, which has reached the limit both theoretically and technically. At present, bromonaphthalene with a high refractive index is used as a medium. The refractive index of bromonaphthalene is 1.66, so the NA value can be greater than 1.4.
It must be pointed out here that in order to give full play to the role of the numerical aperture of the objective lens, the NA value of the condenser lens should be equal to or slightly greater than that of the objective lens during observation.
Numerical aperture is closely related to other technical parameters, and it almost determines and influences other technical parameters. It is proportional to the resolution, proportional to the magnification, and inversely proportional to the depth of focus. As the NA value increases, the width of the field of view and the working distance will decrease accordingly.
2. Resolution
The resolution of the microscope refers to the minimum distance between two object points that can be clearly distinguished by the microscope, also known as the "discrimination rate". Its calculation formula is σ=λ/NA
Where σ is the minimum resolution distance; λ is the wavelength of light; NA is the numerical aperture of the objective lens. The resolution of the visible objective lens is determined by two factors: the NA value of the objective lens and the wavelength of the illumination source. The larger the NA value, the shorter the wavelength of the illumination light, and the smaller the σ value, the higher the resolution.
To increase the resolution, i.e. reduce the value of σ, the following measures can be taken:
1. Reduce the wavelength λ value and use a short-wavelength light source.
2. Increase the medium n value to increase the NA value (NA=nsinu/2).
3. Increase the aperture angle u value to increase the NA value.
4. Increase the contrast between light and dark.
3. Magnification and effective magnification
Due to the two magnifications of the objective lens and the eyepiece, the total magnification Γ of the microscope should be the product of the objective lens magnification β and the eyepiece magnification Γ1:
Γ=βΓ1
Obviously, compared with the magnifying glass, the microscope can have a much higher magnification, and the magnification of the microscope can be easily changed by exchanging the objective lens and eyepiece with different magnifications.
Magnification is also an important parameter of the microscope, but one cannot blindly believe that the higher the magnification, the better. The limit of microscope magnification is the effective magnification.
Resolution and magnification are two different but related concepts. Relational formula: 500NA<Γ<1000NA
When the numerical aperture of the selected objective lens is not large enough, that is, the resolution is not high enough, the microscope cannot distinguish the fine structure of the object. At this time, even if the magnification is excessively increased, the obtained image can only be an image with a large outline but unclear details. , called the invalid magnification. Conversely, if the resolution meets the requirements but the magnification is insufficient, the microscope has the ability to resolve, but the image is still too small to be clearly seen by human eyes. Therefore, in order to give full play to the resolving power of the microscope, the numerical aperture should be reasonably matched with the total magnification of the microscope.
4. Depth of focus
Depth of focus is the abbreviation of depth of focus, that is, when using a microscope, when the focus is on a certain object, not only all points on the plane of this point can be seen clearly, but also within a certain thickness above and below the plane, To be clear, the thickness of this clear part is the depth of focus. If the depth of focus is large, you can see the entire layer of the object under inspection, while if the depth of focus is small, you can only see a thin layer of the object under inspection. The depth of focus has the following relationship with other technical parameters:
1. The depth of focus is inversely proportional to the total magnification and the numerical aperture of the objective lens.
2. The depth of focus is large, and the resolution is reduced.
Due to the large depth of field of the low magnification objective lens, it is difficult to take pictures with the low magnification objective lens. This will be described in more detail in photomicrographs.
5. Field of view diameter (FieldOfView)
When observing a microscope, the bright circular area seen is called the field of view, and its size is determined by the field diaphragm in the eyepiece.
The diameter of the field of view is also called the width of the field of view, which refers to the actual range of the inspected object that can be accommodated in the circular field of view seen under the microscope. The larger the diameter of the field of view, the easier it is to observe.
There is the formula:
F=FN/β
In the formula, F - the diameter of the field of view;
FN - field number (FieldNumber, abbreviated as FN, marked on the outside of the eyepiece barrel);
β - the magnification of the objective lens.
It can be seen from the formula:
1. The diameter of the field of view is proportional to the number of fields of view.
2. Increasing the multiple of the objective lens reduces the diameter of the field of view. Therefore, if you can see the whole picture of the inspected object under the low power lens, and change to a high power objective lens, you can only see a small part of the inspected object.
6. Poor coverage
The optical system of the microscope also includes the coverslip. Due to the non-standard thickness of the cover glass, the optical path of the light after entering the air from the cover glass is changed, resulting in a phase difference, which is poor coverage. The generation of poor coverage affects the sound quality of the microscope.
According to international regulations, the standard thickness of the cover glass is 0.17mm, and the allowable range is 0.16-0.18mm. The difference in this thickness range has been calculated in the manufacture of the objective lens. The 0.17 marked on the objective lens housing indicates the thickness of the cover glass required by the objective lens.
7. Working distance WD
The working distance is also called the object distance, which refers to the distance from the surface of the front lens of the objective lens to the object to be inspected. During microscope inspection, the object to be inspected should be between one and two times the focal length of the objective lens. Therefore, it and the focal length are two concepts. What is usually called focusing is actually adjusting the working distance.
In the case of a certain numerical aperture of the objective lens, the working distance is short and the aperture angle is large.
High magnification objective lens with large numerical aperture and small working distance
