According to the definition of the English physicist Rayleigh, the resolution of an optical system is minimum distance between two points the image it creates, while they are still visible separately. Rayleigh showed that the maximum resolution of a lens (i.e. the minimum distance d between two adjacent image points) is directly proportional to the length of the light wave used l and inversely proportional to the refractive index of the medium n, as well as the opening angle a:

Wavelength l equal to the product of the speed of light v for the period of oscillation T. Refractive index n defined as the ratio of the speed of light in a vacuum (300,000 km/sec) to the speed of light v in this environment. For air, the refractive index is 1.0, for water - 1.3, for cedar oil - 1.5. Opening angle a characterizes the ability of a lens to collect light rays. It is defined as the angle between the two lines connecting the edge of the lens to the point of its front focus and therefore depends on the diameter of the lens and its curvature (Fig. 3). Maximum value a for modern lenses reaches 138 o.

Rice. 3. Lens opening a

It also follows from the Rayleigh formula that the resolution of a microscope can be increased in three ways:

1) a decrease in wavelength l(this method is implemented in ultraviolet and electron microscopes);

2) an increase in the refractive index of the medium n(immersion lenses);

3) an increase in the diameter of the objective lenses (i.e. an increase in the angle a).

In order to make it convenient to compare the resolution of different lenses, Abbe separated the denominator of the Rayleigh formula into a separate indicator - the numerical aperture NA, after which the formula took the following form:

Numerical aperture of the objective NA = n * sin(a/2) characterizes its resolution, regardless of the design and wavelength used. The introduction of an averaging factor of 0.61 reflects the fact that the maximum resolution is provided only by the edge rays with the maximum angle a, while the rays close to the central give a resolution two times lower (Fig. 3). NA of air lenses is always less than 1
(n = 1, sin a < 1), но иммерсионные объективы могут иметь NA и больше 1. Величина численной апертуры объектива гравируется на его корпусе, что позволяет легко вычислить его номинальное разрешение, используя формулу Рэлея-Аббе. В этих расчетах обычно принимают, что средняя длина волны дневного света составляет 550 нм. Численная апертура современных иммерсионных объективов достигает значений 1.3 – 1.4. Рекорд в этой области принадлежит объективу фирмы Карл Цейсс с апертурой 1.45, который способен формировать изображения микроструктур размером 170 нм.

In addition to resolution in the preparation plane d(field resolution), the microscope objective also has depth resolution dz(Young, 1998).

Depth resolution (depth of focus) plays a special role in confocal microscopy, where three-dimensional reconstructions of microstructures are created on the basis of optical sections and where the thickness of the optical section strongly affects the quality of the reconstruction. Therefore, special hardware and software are provided in confocal microscopes to reduce the depth of focus. As follows from the Young formula for a conventional microscope, the depth of focus is dz almost does not differ from the field resolution d.

The second most important indicator of lenses and eyepieces is the magnification, which is also always indicated on their frames. As a general rule, the higher the magnification of a lens, the greater its numerical aperture (i.e. resolution). However, this dependence is not always observed - there are lenses of the same magnification with different and even adjustable apertures, and lenses with a high aperture may have a reduced magnification. In this regard, distinguish useful and useless increase, meaning that useful magnification is related to resolution and useless magnification is not. Essentially useless magnification is the scaling of the image, in which the amount of information received remains the same or even decreases. However, it may be necessary, for example, when matching the size of the field of view of a microscope and the CCD array of a digital camera.

The total magnification of a microscope is equal to the product of the magnification of the objective and the eyepiece. In some microscopes, the magnification of additional lenses built into the binocular attachment should also be taken into account. In microscopes equipped with television cameras or digital cameras, an electronic zoom is added to the optical zoom. Since the overall magnification of the microscope in this case will depend on many factors, it is customary in scientific publications to indicate the brand of the microscope, as well as the magnification and aperture of the objective used (for example, Zeiss Axiolab, x100/1.25).

Microscope calibration . If it is intended to measure the size of cells and other microstructures, the microscope must be calibrated. The microscope is calibrated using a special preparation - an object-micrometer. It is a glass slide, in the center of which there is a scale with divisions of 10 µm (Fig. 4). There are also object-micrometers in the form of a metal plate with a hole in the center, where glass is fixed with a light scale on a dark background. However, they are less convenient due to the difficulty of focusing on the scale, especially when there is a lack of light at high magnifications.

To determine the size of micro-objects, a special measuring eyepiece (eyepiece-micrometer), which also has a scale. The principle of calibration is to determine the division value of the eyepiece-micrometer scale by combining it with the scale
micrometer object. Knowing the division value of the object-micrometer and the number of its divisions per a certain number of divisions of the eyepiece-micrometer, it is possible, by dividing the first by the second, to obtain calibration factor. Multiplying the calibration factor by the measurement results
eyepiece-micrometer will allow you to bring them to the absolute value, expressed in micrometers. To improve the accuracy of measurements, improved eyepiece micrometers are also used, which are equipped with a micrometric screw that moves the pointer in the field of view.

If the microscope has a built-in camera or digital camera, its calibration is carried out as follows:

1. Install the object-micrometer in the microscope in such a way that its divisions occupy a strictly vertical position.

2. Focus the lens on the scale of the object-micrometer and take its digital picture (Fig. 4).

3. Using the image processing program Scion Image (or similar), a strictly horizontal brightness profile along the scale is obtained.

4. The number of pixels (raster elements) is measured in a segment connecting two scale divisions that are sufficiently far apart from each other.

5. Calculate the calibration factor by dividing the length of the segment (µm) by the number of pixels measured in it.

Rice. four. The object-micrometer scale (left) and its brightness profile (right).

Objective x10, division value 10 microns. The scale additionally shows the brightness profile line. The distance between the extreme divisions along this line is 400 µm or 265 pixels. The calibration factor is 1.509 (400/265).

This method of microscope calibration is fast and highly accurate (less than 1% error). Naturally, calibration must be done for each lens separately, even if they have the same nominal magnification.

Measurement of the resolution of a microscope. The Rayleigh-Abbe formula allows you to calculate only the nominal (i.e. theoretically expected) resolution of the lens. The actual resolution of the lens (and the microscope as a whole) may differ significantly from the nominal.

If the microscope is equipped with a TV camera or a digital camera, measuring its actual resolution is not a big problem. To do this, however, it is necessary to consider in more detail the principle of its operation.

The Fresnel diffraction described above in the form of concentric circular rings (Fig. 1) occurs only if the light wave has complete coherence. A partially coherent microscope illumination system will form a diffraction pattern without pronounced rings. Moreover, due to the imperfection of the optics, the inverse Fourier transform will also give an image that is smoothed compared to the original one. Consequently, the microscope introduces an error into the imaging process, which leads to a decrease in its resolution. To assess this error in microscopy, point spread function (P oint S pread F union, PSF) and optical transmission function (O ptical T ransfer F union, OTF).

Rice. 5. Point spread function ( PSF) and the optical transmission function ( OTF). OTF is the Fourier transform of PSF.

Essentially, PSF is the microscopic image of a circular hole of minimum diameter, which is illuminated by incoherent light, and OTF is its Fourier transform (Fig. 5). The smaller the PSF (and the larger the OTF associated with it), the higher the resolution. Thus, the task of measuring the resolution of a microscope is reduced to determining its PSF (or OTF).

There are many different ways to directly and indirectly estimate the PSF value. For example, it can be calculated by examining the shape of the brightness drops in the vicinity of the boundaries of microobjects. In practice, however, the simplest and most accurate way to estimate the maximum resolution of a microscope is to analyze its OTF rather than its PSF.

In order to measure the resolution of a microscope at a given OTF magnification, you must:

1. Get a digital photograph of a cytological preparation.

2. To be able to apply the fast Fourier transform algorithm, cut out a square section from it, the side of which L(in pixels) is a power of 2 (128,256,512, etc.).

3. Perform a direct Fourier transform of this section using the Scion Image program (or similar) and obtain the OTF of the microscope.

4. Measure the OTF diameter ( D) in pixels (Fig. 5).

5. Using the obtained parameters L and D, as well as cell dimensions of the camera matrix C in µm, camera adapter magnification Ma and lens magnification Mo,calculate the maximum resolution of the microscope d in nm according to the formula:

Rice. 6. Anaphase image of mitosis (256x256) and its Fourier image.

A digital photograph of an onion root cell dividing by mitosis (Fig. 6, left) was taken using a Zeiss Axiolab microscope, x100/1.25 lens, Axiocam MR camera with x0.63 adapter, CCD-matrix cell size 6.7 µm (specified in the specification). The Fourier image of this image (Fig. 6, right) was obtained in the Scion Image program after cropping with a 256x256 frame. The diameter of the OTF measured using the Scion Image program is 129 pixels, and the resolution of the microscope calculated using the above formula is 211 nm.

The accuracy of this method of measuring microscope resolution depends mainly on the correct determination of the OTF diameter. However, as can be seen from the OTF brightness profile (Fig. 7), its boundary gradually decreases to the level of random noise, which makes it difficult to measure D.

One way to improve the objectivity of determining the diameter of an OTF is to measure it (or the radius of the OTF, which is denoted as HWHM) at half the maximum signal brightness. In this case, the microscope resolution estimate will be somewhat lower than the maximum value.

Another way is to use special preparations prepared from diatoms and containing small regular structures at the limit of microscope resolution. In this case, contrasting reflections appear in the Fourier image, which greatly facilitate the accurate measurement of the OTF diameter.

Rice. 7. OTF brightness profile from center to periphery. HWHM- OTF radius at the level of half of its maximum ( H alpha W idth on H alpha M aximum).

PSF and OTF are directly related to the Rayleigh-Abbe formula. In an aberration-free microscope, PSF has circular symmetry and is given by

where h(r) is the PSF J1 is the Bessel function of the first kind, a = 2pNA/l.

Thus, at least in the ideal case, the shape of the PSF is determined by only two parameters - the wavelength l and the numerical aperture of the objective NA. The analytical description of the PSF can be used to increase the resolution of the microscope by additional image processing on a computer.

Microscopes are used to detect and study microorganisms. Light microscopes are designed to study microorganisms that are at least 0.2 microns in size (bacteria, protozoa, etc.) and electronic microscopes to study smaller microorganisms (viruses) and the smallest structures of bacteria.
Modern light microscopes- These are complex optical devices, the handling of which requires certain knowledge, skills and great accuracy.
Light microscopes are divided into student, working, laboratory and research, differing in design and optics. Domestic microscopes (Biolam, Bimam, Mikmed) have designations indicating which group they belong to (C - student, R - workers, L - laboratory, I - research), the equipment is indicated by a number.

A microscope is divided into mechanical and optical parts.
To mechanical part include: a tripod (consisting of a base and a tube holder) and a tube mounted on it with a revolver for mounting and changing lenses, an object table for the preparation, devices for attaching a condenser and light filters, as well as mechanisms built into the tripod for coarse (macromechanism, macroscrew) and fine
(micromechanism, microscrew) for moving the object stage or tube holder.
Optical part The microscope is represented by objectives, eyepieces and an illumination system, which in turn consists of an Abbe condenser located under the object stage, a mirror having a flat and concave side, as well as a separate or built-in illuminator. The objectives are screwed into the revolver, and the corresponding eyepiece, through which the image is observed, is installed on the opposite side of the tube. There are monocular (having one eyepiece) and binocular (having two identical eyepieces) tubes.

Schematic diagram of the microscope and illumination system

1. Light source;
2. Collector;
3. Iris field diaphragm;
4. Mirror;
5. Iris aperture diaphragm;
6. Condenser;
7. Drug;
7". Enlarged actual intermediate image of the preparation, formed; by the objective;
7"". Enlarged virtual final image of the preparation, observed in the eyepiece;
8. Lens;
9. output lens icon;
10. Field aperture of the eyepiece;
11. Eyepiece;
12. Eye.

Plays a major role in image acquisition lens. It builds an enlarged, real and inverted image of the object. Then this image is further enlarged when viewed through an eyepiece, which, similarly to a conventional magnifier, gives an enlarged virtual image.
Increase microscope can be roughly determined by multiplying the magnification of the objective by the magnification of the eyepiece. However, magnification does not determine image quality. Image quality, its clarity, is determined microscope resolution, i.e., the ability to distinguish separately two closely spaced points. Resolution limit- the minimum distance at which these points are still visible separately - depends on the wavelength of light that illuminates the object, and the numerical aperture of the objective. The numerical aperture, in turn, depends on the angular aperture of the objective and the refractive index of the medium between the front lens of the objective and the preparation. Angular aperture is the maximum angle at which rays passing through an object can enter the lens. The larger the aperture and the closer the refractive index of the medium between the lens and the preparation is to the refractive index of glass, the higher the resolution of the lens. If we consider the aperture of the condenser equal to the aperture of the objective, then the resolution formula has the following form:

where R is the resolution limit; - wavelength; NA - numerical aperture.

Distinguish useful and useless increase. Useful magnification is usually equal to the numerical aperture of the objective magnified by 500-1000 times. Higher ocular magnification does not bring out new details and is useless.
Depending on the medium that is between the lens and the preparation, there are "dry" lenses of small and medium magnification (up to 40x) and immersion lenses with a maximum aperture and magnification (90-100x). A “dry” lens is a lens with air between the front lens and the specimen.

A feature of immersion lenses is that an immersion liquid is placed between the front lens of such an objective and the preparation, which has a refractive index the same as glass (or close to it), which ensures an increase in the numerical aperture and resolution of the lens. Distilled water is used as an immersion liquid for water immersion lenses, and cedar oil or a special synthetic immersion oil is used for oil immersion lenses. The use of synthetic immersion oil is preferable, since its parameters are more accurately normalized, and, unlike cedar oil, it does not dry out on the surface of the front lens of the objective. For lenses operating in the ultraviolet region of the spectrum, glycerin is used as an immersion liquid. In no case should you use substitutes for immersion oil and, in particular, vaseline oil.
**The image obtained with lenses has various disadvantages: spherical and chromatic aberrations, curvature of the image field, etc. In lenses consisting of several lenses, these disadvantages are corrected to some extent. Depending on the degree of correction of these shortcomings, achromatic lenses and more complex apochromatic lenses are distinguished. Accordingly, lenses in which the curvature of the image field is corrected are called plan achromats and plan apochromats. The use of these lenses produces a sharp image across the entire field, while the image obtained with conventional lenses does not have the same sharpness in the center and at the edges of the field of view. All characteristics of the lens are usually engraved on its frame: own magnification, aperture, lens type (APO - apochromat, etc.); water immersion lenses have the designation VI and a white ring around the frame in its lower part, oil immersion lenses have the designation MI and a black ring.
All objectives are designed to work with a 0.17mm cover slip.
The thickness of the coverslip especially affects image quality when working with strong dry systems (40x). When working with immersion objectives, cover slips thicker than 0.17 mm should not be used because the thickness of the cover slip may be greater than the working distance of the objective, and in this case, when trying to focus the objective on the specimen, the front lens of the objective may be damaged.
Eyepieces consist of two lenses and also come in several types, each of which is used with a specific type of lens, further eliminating image imperfections. The type of eyepiece and its magnification are marked on its frame.
The condenser is designed to focus the light from the illuminator on the preparation, directed by the mirror of the microscope or illuminator (in the case of using an attached or built-in illuminator). One of the details of the condenser is the aperture diaphragm, which is essential for proper illumination of the specimen.
The illuminator consists of a low-voltage incandescent lamp with a thick filament, a transformer, a collector lens and a field diaphragm, the opening of which determines the diameter of the illuminated field on the specimen. The mirror directs the light from the illuminator into the condenser. In order to maintain the parallelism of the beams coming from the illuminator to the condenser, it is necessary to use only the flat side of the mirror.

Setting the illumination and focusing of the microscope

Image quality also depends to a large extent on proper lighting. There are several different ways of illuminating a specimen under microscopy. The most common way is lighting installations according to Köhler, which is as follows:
1) set the illuminator against the microscope mirror;
2) turn on the illuminator lamp and direct the light onto a flat (!) microscope mirror;
3) place the preparation on the microscope stage;
4) cover the microscope mirror with a sheet of white paper and focus the image of the lamp filament on it by moving the lamp socket in the illuminator;
5) remove a sheet of paper from the mirror;
6) close the aperture diaphragm of the condenser. By moving the mirror and slightly moving the lamp socket, the image of the filament is focused on the aperture diaphragm. The distance of the illuminator from the microscope should be such that the image of the lamp filament is equal to the diameter of the aperture diaphragm of the condenser (the aperture diaphragm can be observed using a flat mirror placed on the right side of the microscope base).
7) open the aperture diaphragm of the condenser, reduce the opening of the field diaphragm of the illuminator and significantly reduce the incandescence of the lamp;
8) at low magnification (10x), looking into the eyepiece, a sharp image of the preparation is obtained;
9) slightly turning the mirror, the image of the field diaphragm, which looks like a bright spot, is transferred to the center of the field of view. Lowering and raising the condenser, one achieves a sharp image of the edges of the field diaphragm in the plane of the preparation (a colored border can be seen around them);
10) open the field diaphragm of the illuminator to the edges of the field of view, increase the incandescence of the lamp filament and slightly (by 1/3) reduce the opening of the aperture diaphragm of the condenser;
11) When changing the lens, you need to check the light setting.
After completing the adjustment of the light according to Koehler, it is impossible to change the position of the condenser and the opening of the field and aperture diaphragms. The illumination of the preparation can only be adjusted with neutral light filters or by changing the incandescence of the lamp using a rheostat. Excessive opening of the aperture diaphragm of the condenser can lead to a significant decrease in image contrast, and insufficient opening can lead to a significant deterioration in image quality (the appearance of diffraction rings). To check the correct opening of the aperture diaphragm, it is necessary to remove the eyepiece and, looking into the tube, open it so that it covers the luminous field by one third. For correct illumination of the preparation, when working with low magnification lenses (up to 10x), it is necessary to unscrew and remove the upper lens of the condenser.
Attention! When working with lenses that give high magnification - with strong dry (40x) and immersion (90x) systems, in order not to damage the front lens, when focusing, they use the following technique: observing from the side, lower the lens with a macro screw almost to contact with the preparation, then, looking into the eyepiece, the macroscrew very slowly raises the lens until the image appears, and with the help of the microscrew the final focusing of the microscope is performed.

Microscope care

When working with a microscope, do not use great effort. Do not touch the surfaces of lenses, mirrors and filters with your fingers.
To protect the internal surfaces of the objectives, as well as the prisms of the tube from dust, you must always leave the eyepiece in the tube. When cleaning the outer surfaces of the lenses, remove dust from them with a soft brush washed in ether. If necessary, gently wipe the lens surfaces with a well-washed, soap-free linen or cambric cloth lightly moistened with clean gasoline, ether, or a special mixture for cleaning optics. It is not recommended to wipe the lens optics with xylene, as this may cause them to stick.
From mirrors with external silvering, you can only remove dust by blowing it off with a rubber bulb. You cannot wipe them. It is also impossible to unscrew and disassemble the lenses yourself - this will lead to their damage. Upon completion of work on the microscope, it is necessary to carefully remove the remnants of immersion oil from the front lens of the objective in the manner described above. Then lower the stage (or condenser in microscopes with a fixed stage) and cover the microscope with a cover.
To preserve the appearance of the microscope, it is necessary to periodically wipe it with a soft cloth slightly soaked in acid-free Vaseline and then with a dry, soft, clean cloth.

In addition to conventional light microscopy, there are microscopy methods that allow you to study unstained microorganisms: phase contrast , darkfield and luminescent microscopy. To study microorganisms and their structures, the size of which is less than the resolution of a light microscope, use

System enlargement- an important factor, which is based on the choice of one or another microscope, depending on the solution of the necessary tasks. We are all used to the fact that it is necessary to carry out control of semiconductor elements on an inspection microscope with a magnification of 1000x or more, insects can be studied by working with a 50x stereomicroscope, and we studied onion scales stained with iodine or brilliant green at school on a monocular microscope, when the concept of magnification was not yet familiar to us.

But how to interpret the concept of magnification when we have a digital or confocal microscope in front of us, and the values ​​​​of 2000x, 5000x are on the objectives? What does it mean, will 1000x magnification on an optical microscope produce an image similar to a 1000x digital microscope? You will learn about this in this article.

Optical zoom system

When we work with a laboratory or stereoscopic microscope, it is not difficult to calculate the current magnification of the system. It is necessary to multiply the magnification of all optical components of the system. Usually, in the case of a stereo microscope, this is an objective, zoom or magnifying drum and eyepieces.
In the case of a conventional laboratory microscope, the situation is even simpler - the total magnification of the system = the magnification of the eyepieces multiplied by the magnification of the lens installed in the working position. It is important to remember that sometimes there are specific models of microscope tubes that have an increase or decrease factor (especially common for older models of Leitz microscopes). Also, additional optical components, whether it be a coaxial illumination source in a stereo microscope or an intermediate camera adapter located under the tube, may have an additional magnification factor.

For example, a stereo microscope with 10x eyepieces, a 2x objective, a zoom at 8x and a coaxial illumination unit with a factor of 1.5x will have a total optical magnification of 10x2x8x1.5 = 240x.

In this case, optical magnification (G) should be understood as the ratio of the tangent of the angle of inclination of the beam that emerged from the optical system into the image space to the tangent of the angle of the beam conjugate to it in the space of objects. Or the ratio of the length of the segment formed by the optical system of the image, perpendicular to the axis of the optical system, to the length of the segment itself

Geometric increase of the system

In the case when the system does not have eyepieces, and the enlarged image is formed by the camera on the monitor screen, for example, as on a microscope, one should proceed to the term of geometric magnification of the optical system.
The geometric magnification of the microscope is the ratio of the linear size of the image of the object on the monitor to the real size of the object under study.
You can get the value of the geometric magnification by multiplying the following values: the optical zoom of the lens, the optical zoom of the camera adapter, the ratio of the monitor diagonal to the diagonal of the camera matrix.
For example, when working on a laboratory microscope with a 50x objective, a 0.5x camera adapter, a 1/2.5” camera and displaying the image on a 14” laptop monitor, we will get a geometric magnification of the system = 50x0.5x(14/0.4) = 875x.
Although the optical magnification in this case will be equal to 500x in the case of 10x eyepieces.

Digital microscopes, confocal profilometers, electron microscopes and other systems that form a digital image of an object on a monitor screen operate with the concept of geometric magnification. Do not confuse this concept with optical zoom.

Microscope resolution

There is a widespread misconception that the resolution of a microscope and its magnification are interconnected by a rigid relationship - the higher the magnification, the smaller objects we can see in it. This is not true. The most important factor is always permission optical system. After all, an increase in an unresolved image will not give us new information about it.

The resolution of a microscope depends on the numerical value of the objective aperture, as well as on the wavelength of the light source. As you can see, there is no system increase parameter in this formula.

where λ is the average wavelength of the light source, NA is the numerical aperture of the objective, R is the resolution of the optical system.

When using an objective with NA 0.95 on a laboratory microscope with a halogen source (average wavelength of about 500 nm), we get a resolution of about 300 nm.

As can be seen from the concept of a light microscope, eyepieces magnify the actual image of an object. If, for example, we increase the magnification of the eyepieces by 2 times (insert 20x eyepieces into the microscope), then the total magnification of the system will double, but the resolution will remain the same.

Important note

Suppose we have two options for building a simple laboratory microscope. The first one is built using a 40x NA 0.65 objective and 10x eyepieces. The second will use a 20x NA 0.4 objective with 20x eyepieces.

The magnification of microscopes in both versions will be the same= 400x (simple multiplication of objective magnification and eyepieces). But resolution in the first option will be higher, than in the second, since the numerical aperture of the 40x objective is larger. In addition, do not forget about the field of view of the eyepieces, in 20x this parameter is 20-25% lower.

Image quality determined microscope resolution, i.e. the minimum distance at which the optics of a microscope can distinguish separately two closely spaced points. the resolution depends on the numerical aperture of the objective, the condenser, and the wavelength of the light that illuminates the preparation. The numerical aperture (opening) depends on the angular aperture and the refractive index of the medium located between the front lens of the objective and the condenser and the preparation.

Angular lens aperture- this is the maximum angle (AOB) at which the rays that have passed through the preparation can enter the lens. Numerical aperture of the lens is equal to the product of the sine of half the angular aperture and the refractive index of the medium located between the glass slide and the front lens of the objective. N.A. = n sinα where, N.A. - numerical aperture; n is the refractive index of the medium between the preparation and the objective; sinα - the sine of the angle α equal to half the angle AOB in the diagram.

Thus, the aperture of dry systems (between the frontal lens of the objective and the preparation-air) cannot be more than 1 (usually no more than 0.95). The medium placed between the preparation and the objective is called immersion liquid or immersion, and the lens designed to work with immersion liquid is called immersion. Due to immersion with a higher refractive index than air, it is possible to increase the numerical aperture of the objective and hence the resolving power.

The numerical aperture of objectives is always engraved on their frames.
The resolution of the microscope also depends on the aperture of the condenser. If we consider the condenser aperture equal to the lens aperture, then the resolution formula is R=λ/2NA, where R is the resolution limit; λ - wavelength; N.A - numerical aperture. From this formula it can be seen that when observed in visible light (green part of the spectrum - λ=550nm), the resolution (resolution limit) cannot be > 0.2 µm

The effect of the numerical aperture of a microscope objective on image quality

Ways to improve optical resolution

High light cone angle selection, both lens side and light source side. Due to this, it is possible to collect more refracted light rays from very thin structures in the lens. Thus, the first way to increase resolution is to use a condenser whose numerical aperture matches the numerical aperture of the objective.

The second way is to use an immersion liquid between the front lens of the objective and the cover slip. So we act on the refractive index of the medium n, described in the first formula. Its optimal value recommended for immersion liquids is 1.51.

Immersion liquids

Immersion liquids are necessary to increase the numerical aperture and, accordingly, the resolution of immersion objectives specially designed for working with these liquids and marked accordingly. Immersion liquids placed between the objective and the preparation have a higher refractive index than air. Therefore, the rays of light deflected by the smallest details of the object do not scatter, leaving the preparation, and enter the lens, which leads to an increase in resolution.

There are lenses for water immersion (marked with a white ring), oil immersion (black ring), glycerine immersion (yellow ring), monobromonaphthalene immersion (red ring). In light microscopy of biological preparations, objectives of water and oil immersion are used. Special quartz lenses of glycerin immersion transmit short-wave ultraviolet radiation and are designed for ultraviolet (not to be confused with luminescent) microscopy (that is, for studying biological objects that selectively absorb ultraviolet rays). Monobromonaphthalene immersion objectives are not used in microscopy of biological objects.

Distilled water is used as an immersion liquid for the lens of water immersion, natural (cedar) or synthetic oil with a certain refractive index is used for oil immersion.

Unlike other immersion liquids oil immersion is homogeneous because it has a refractive index equal to or very close to that of glass. Usually this refractive index (n) is calculated for a certain spectral line and a certain temperature and is indicated on the bottle of oil. So, for example, the refractive index of immersion oil for working with a cover glass for the spectral line D in the sodium spectrum at a temperature of = 20 ° C is 1.515 (nD 20 = 1.515), for working without a cover glass (nD 20 = 1.520).

To work with apochromat lenses, dispersion is also normalized, that is, the difference in refractive indices for different lines of the spectrum.

The use of synthetic immersion oil is preferable, since its parameters are more accurately normalized, and, unlike cedar oil, it does not dry out on the surface of the front lens of the objective.

Given the above, in no case should you use substitutes for immersion oil and, in particular, vaseline oil. In some microscopy techniques, to increase the aperture of the condenser, an immersion liquid (usually distilled water) is placed between the condenser and the specimen.

As you know, a person receives the main share of information about the world around him with the help of vision. The human eye is a complex and perfect device. This device created by nature works with light - electromagnetic radiation, the wavelength range of which is between 400 and 760 nanometers. The color that a person perceives at the same time changes from purple to red.

Electromagnetic waves corresponding to visible light interact with the electron shells of the atoms and molecules of the eye. The result of this interaction depends on the state of the electrons of these shells. Light can be absorbed, reflected or scattered. What exactly happened to the light can tell a lot about the atoms and molecules it interacted with. The size range of atoms and molecules is from 0.1 to tens of nanometers. This is many times smaller than the wavelength of light. However, objects of precisely this size - let's call them nano-objects - are very important to see. What needs to be done for this? Let's discuss first what the human eye can see.

Usually, when talking about the resolution of an optical device, they operate with two concepts. One is angular resolution and the other is linear resolution. These concepts are interrelated. For example, for the human eye, the angular resolution is approximately 1 arcminute. In this case, the eye can distinguish two point objects that are 25–30 cm away from it only when the distance between these objects is greater than 0.075 mm. This is quite comparable to the resolution of a conventional computer scanner. Indeed, a resolution of 600 dpi means that the scanner can distinguish between dots that are 0.042 mm apart.

In order to be able to distinguish objects located at even smaller distances from each other, an optical microscope was invented - a device that increases the resolution of the eye. These devices look different (as can be seen from Figure 1), but they have the same principle of operation. The optical microscope made it possible to move the resolution limit down to fractions of a micron. Already 100 years ago, optical microscopy made it possible to study micron-sized objects. However, at the same time it became clear that it was impossible to achieve a further increase in resolution by simply increasing the number of lenses and improving their quality. The resolution of an optical microscope turned out to be limited by the properties of light itself, namely its wave nature.

At the end of the century before last, it was found that the resolution of an optical microscope is . In this formula, λ is the wavelength of light, and n sin u- the numerical aperture of the microscope objective, which characterizes both the microscope and the substance that is between the object of study and the microscope lens closest to it. Indeed, the expression for the numerical aperture includes the refractive index n environment between the object and the lens, and the angle u between the optical axis of the lens and the outermost rays that exit the object and can enter this lens. The refractive index of vacuum is equal to unity. For air, this indicator is very close to unity, for water it is 1.33303, and for special liquids used in microscopy to obtain maximum resolution, n comes to 1.78. Whatever the angle u, sin u cannot be greater than one. Thus, the resolution of an optical microscope does not exceed a fraction of the wavelength of light.

The resolution is usually considered to be half the wavelength.

Intensity, resolution and magnification of an object are two different things. You can make it so that the distance between the image centers of objects that are 10 nm apart will be 1 mm. This would correspond to a magnification of 100,000 times. However, it will not be possible to distinguish whether this is one object or two. The fact is that images of objects whose dimensions are very small compared to the wavelength of light will have the same shape and size, independent of the shape of the objects themselves. Such objects are called point objects - their sizes can be neglected. If such a point object glows, then an optical microscope will depict it as a light circle surrounded by light and dark rings. Let us further, for simplicity, consider the light sources. A typical image of a point source of light obtained using an optical microscope is shown in Figure 2. The intensity of light rings is much less than that of a circle, and decreases with distance from the center of the image. Most often, only the first light ring is visible. The diameter of the first dark ring is . The function that describes such an intensity distribution is called the point spread function. This function is independent of what the magnification is. The image of several point objects will be precisely circles and rings, as can be seen from Figure 3. The resulting image can be enlarged, however, if the images of two neighboring point objects merge, they will merge further. Such an increase is often called useless - large images will simply be more blurry. An example of useless magnification is shown in Figure 4. The formula is often called the diffraction limit, and it is so famous that it was carved on the monument to the author of this formula, the German optical physicist Ernst Abbe.

Of course, over time, optical microscopes began to be equipped with a variety of devices that allow you to store images. The human eye was supplemented first by film cameras and film cameras, and then by cameras based on digital devices that convert the light that hits them into electrical signals. The most common of these devices are CCDs (CCD stands for charge-coupled device). The number of pixels in digital cameras continues to grow, but this alone cannot improve the resolution of optical microscopes.

Twenty-five years ago, it seemed that the diffraction limit was insurmountable and that, in order to study objects whose dimensions are many times smaller than the wavelength of light, it was necessary to abandon light as such. This is the way the creators of electron and X-ray microscopes went. Despite the numerous advantages of such microscopes, the problem of using light to view nanoobjects remained. There were many reasons for this: the convenience and ease of working with objects, the short time it takes to obtain an image, known methods for staining samples, and much more. Finally, after many years of hard work, it became possible to view nano-objects with an optical microscope. The greatest progress in this direction has been achieved in the field of luminescence microscopy. Of course, no one canceled the diffraction limit, but it was possible to bypass it. Currently, there are various optical microscopes that allow you to view objects that are much smaller than the wavelength of the very light that creates images of these objects. All these devices share one common principle. Let's try to explain which one.

From what has already been said about the diffraction limit of resolution, it is clear that it is not so difficult to see a point source. If this source has sufficient intensity, its image will be clearly visible. The shape and size of this image, as already mentioned, will be determined by the properties of the optical system. At the same time, knowing the properties of the optical system and being sure that the object is point, it is possible to determine exactly where the object is located. The accuracy of determining the coordinates of such an object is quite high. Figure 5 can serve as an illustration of this. The coordinates of a point object can be determined the more accurately, the more intensely it glows. Back in the 80s of the last century, using an optical microscope, they were able to determine the position of individual luminous molecules with an accuracy of 10–20 nanometers. A necessary condition for such an accurate determination of the coordinates of a point source is its loneliness. Another point source closest to it should be so far away that the researcher knows for sure that the image being processed corresponds to one source. It is clear that this distance l must satisfy the condition. In this case, image analysis can provide very accurate data on the position of the source itself.

Most objects whose dimensions are much smaller than the resolution of an optical microscope can be represented as a set of point sources. The light sources in such a set are located at distances from each other that are much smaller than . If these sources shine simultaneously, then it will be impossible to say anything about exactly where they are located. However, if you can make these sources shine in turn, then the position of each of them can be determined with high accuracy. If this accuracy exceeds the distance between the sources, then, having knowledge of the position of each of them, you can find out what their relative position is. And this means that information about the shape and size of the object has been obtained, which is presented as a set of point sources. In other words, in this case, it is possible to consider an object with an optical microscope whose dimensions are smaller than the diffraction limit!

Thus, the key point is to obtain information about different parts of the nanoobject independently of each other. There are three main groups of methods to do this.

The first group of methods purposefully makes one or another part of the object under study shine. The best known of these methods is near-field scanning optical microscopy. Let's consider it in more detail.

If one carefully examines the conditions that are implied when talking about the diffraction limit, it will be found that the distances from objects to lenses are much greater than the wavelength of light. At distances comparable to or shorter than this wavelength, the picture is different. Near any object that has fallen into the electromagnetic field of a light wave, there is an alternating electromagnetic field, the frequency of which is the same as the frequency of the field in the light wave. Unlike a light wave, this field rapidly decays with distance from the nanoobject. The distance over which the intensity decreases, e.g. e times comparable to the size of the object. Thus, the electromagnetic field of optical frequency is concentrated in a volume of space, the size of which is much smaller than the wavelength of light. Any nano-object that enters this area will somehow interact with the concentrated field. If the object with which this field concentration is carried out is successively moved along some trajectory along the nanoobject under study and the light emitted by this system is recorded, then an image can be constructed from individual points lying on this trajectory. Of course, at each point the image will look as shown in Figure 2, but the resolution will be determined by how much the field has been concentrated. And this, in turn, is determined by the size of the object with which this field is concentrated.

The most common way to concentrate the field this way is to make a very small hole in the metal screen. Typically, this hole is located at the end of a pointed, metal-coated light guide (a light guide is often called an optical fiber and is widely used for long-distance data transmission). Now it is possible to produce holes with diameters from 30 to 100 nm. The resolution is the same. Devices that work on this principle are called near-field scanning optical microscopes. They appeared 25 years ago.

The essence of the second group of methods is as follows. Instead of making neighboring nano-objects shine in turn, you can use objects that glow in different colors. In this case, with the help of light filters that transmit light of one color or another, it is possible to determine the position of each of the objects, and then to compose a single picture. This is very similar to what is shown in Figure 5, only the colors for the three images will be different.

The last group of methods that make it possible to overcome the diffraction limit and examine nanoobjects uses the properties of the luminous objects themselves. There are sources that can be "turned on" and "off" with the help of specially selected light. Such switching occurs statistically. In other words, if there are many switchable nano-objects, then, by choosing the wavelength of light and its intensity, it is possible to make only a part of these objects “turn off”. The remaining objects will continue to shine, and you can get an image from them. After that, you need to “turn on” all the sources and again “turn off” some of them. The set of sources that remain "on" will be different from the set that was left "on" the first time. By repeating this procedure many times, you can get a large set of images that differ from each other. By analyzing such a set, it is possible to locate a large fraction of all sources with very high accuracy, well above the diffraction limit. An example of super resolution obtained in this way is shown in Figure 6.

At present, super-resolution optical microscopy is developing rapidly. It is safe to assume that in the coming years this area will attract an increasing number of researchers, and I would like to believe that readers of this article will be among them.