How to find the resolution of a microscope. Microscope magnification and resolution

Item h placed slightly further than the front focus of the lens. The lens gives real, inverse, augmented image H’ , located between the front focus of the eyepiece and the optical center of the eyepiece. This intermediate image is viewed through the eyepiece as if through a magnifying glass. The eyepiece gives imaginary, direct, magnified image H, which is located at the distance of best vision S ≈ 25 cm from the optical center of the eye.

We look at this image with our eyes and it forms on its retina. real, inverse, reduced image.

Microscope Magnification– the ratio of the dimensions of the virtual image to the dimensions of the object viewed through the microscope:
. Multiply the numerator and denominator by the size of the intermediate image H’ :
. Thus, the magnification of the microscope is equal to the product of the objective magnification and the eyepiece magnification. Lens magnification can be expressed in terms of the characteristics of the microscope using the similarity of right triangles
, Where L  optical tube length: the distance between the back focus of the lens and the front focus of the eyepiece (we assume that L >> F about). Eyepiece magnification
. Therefore, the magnification of the microscope is:
.

4. Resolution and resolution limit of the microscope. Diffraction phenomena in a microscope, the concept of Abbe's theory.

Microscope resolution limitz - this is the smallest distance between two points of an object viewed through a microscope, when these points are still perceived separately. The resolution limit of a conventional biological microscope lies in the range of 3-4 microns. Resolution microscope is the ability to provide a separate image of two closely located points of the object under study, that is, this is the reciprocal of the resolution limit.

Diffraction of light imposes a limit on the ability to distinguish the details of objects when they are observed through a microscope. Since light does not propagate rectilinearly, but bends around obstacles (in this case, the objects in question), images of small details of objects turn out blurry.

E. Abbe suggested diffraction theory of microscope resolution. Let the object that we want to examine through a microscope be a diffraction grating with a period d. Then the minimum detail of the object that we must distinguish will be precisely the lattice period. Light diffraction occurs on the grating, but the diameter of the microscope objective is limited, and at large diffraction angles, not all the light passing through the grating enters the objective. In reality, light from an object propagates to the lens in a certain cone. The resulting image is closer to the original, the more maxima involved in the formation of the image. Light from an object propagates to the lens from a condenser in the form of a cone, which is characterized by angular aperture u- the angle at which the lens is visible from the center of the object under consideration, that is, the angle between the outer rays of the conical light beam entering the optical system. According to E. Abbe, to obtain an image of a grating, even the most fuzzy one, rays of any two orders of the diffraction pattern must enter the lens, for example, rays forming the central and at least the first diffraction maximum. Let us recall that for the oblique incidence of rays on a diffraction grating, its main formula has the form: . If the light comes at an angle , and the diffraction angle for first maximum equals
, then the formula takes the form
. The resolution limit of the microscope should be taken as the constant of the diffraction grating, then
, where  is the wavelength of light.

As can be seen from the formula, one way to reduce the resolution limit of a microscope is to use light with a shorter wavelength. In this regard, an ultraviolet microscope is used, in which microobjects are examined in ultraviolet rays. The basic optical design of such a microscope is similar to that of a conventional microscope. The main difference is the use of optical devices that are transparent to UV light and the image registration features. Since the eye does not perceive ultraviolet radiation (in addition, it burns the eyes, i.e. is dangerous for the organ of vision), photographic plates, fluorescent screens or electro-optical converters are used.

If a special liquid medium called immersion, then the resolution limit also decreases:
, Where n– absolute refractive index of immersion, A – lens numerical aperture. Water is used as immersion ( n = 1.33), cedar oil ( n= 1.515), monobromonaphthalene ( n = 1.66), etc. For each type of immersion, a special lens is made, and it can only be used with this type of immersion.

Another way to reduce the resolution limit of a microscope is to increase the aperture angle. This angle depends on the size of the lens and the distance from the subject to the lens. However, the distance from the object to the lens cannot be changed arbitrarily; it is constant for each lens and the object cannot be brought closer. In modern microscopes, the aperture angle reaches 140 o (respectively, u/2 = 70 o). With this angle, maximum numerical apertures and minimum resolution limits are obtained.

The data is given for an oblique incidence of light on an object and a wavelength of 555 nm, to which the human eye is most sensitive.

Please note that the eyepiece does not affect the resolution of the microscope at all, it only creates a magnified image of the lens.

System expansion– an important factor, which is based on the choice of one or another microscope, depending on the solution of the necessary problems. We are all accustomed to the fact that it is necessary to inspect semiconductor elements on an inspection microscope with a magnification of 1000x or more, we can study insects by working with a 50x stereo microscope, 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 lenses have values ​​of 2000x, 5000x? What does this 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, calculating the current magnification of the system is not difficult. It is necessary to multiply the magnification of all optical components of the system. Typically, in the case of a stereo microscope, this is the objective, zoom lens 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 a magnification or reduction factor (especially common with older models of Leitz microscopes). Also, additional optical components, be it 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 lens 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 emerging from the optical system into 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 image of the segment formed by the optical system, perpendicular to the axis of the optical system, to the length of the segment itself

Geometric system magnification

In the case when the system does not have eyepieces, and the enlarged image is formed by a camera on a monitor screen, for example, as on a microscope, one should move on to the term geometric magnification of the optical system.
The geometric magnification of a microscope is the ratio of the linear size of the image of an object on the monitor to the real size of the object being studied.
You can get the geometric magnification value by multiplying the following values: optical magnification of the lens, optical magnification of the camera adapter, 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 system magnification = 50x0.5x(14/0.4) = 875x.
Although the optical magnification 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. This concept should not be confused with optical zoom.

Microscope resolution

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

The resolution of the microscope depends on the numerical value of the objective aperture, as well as on the wavelength of the illumination 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 lens, R is the resolution of the optical system.

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

As can be seen from the circuit diagram of a light microscope, eyepieces magnify the actual image of an object. If, for example, you increase the magnification factor 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

Let's assume that we have two options for building a simple laboratory microscope. We will build the first one using a 40x NA 0.65 objective and 10x eyepieces. The second one will use a 20x NA 0.4 objective and 20x eyepieces.

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

A microscope is designed to observe small objects with greater magnification and greater resolution than a magnifying glass provides. The optical system of a microscope consists of two parts: a lens and an eyepiece. The microscope lens forms a true magnified inverse image of the object in the front focal plane of the eyepiece. The eyepiece acts like a magnifying glass and forms a virtual image at the best viewing distance. In relation to the entire microscope, the object in question is located in the front focal plane.

Microscope Magnification

The action of a microlens is characterized by its linear magnification: V ob = -Δ/F\" ob * F\" ob - focal length of the microlens * Δ - distance between the rear focus of the lens and the front focus of the eyepiece, called the optical interval or optical length of the tube.

The image created by the microscope objective at the front focal plane of the eyepiece is viewed through the eyepiece, which acts as a magnifying glass with visible magnification:

G ok =¼ F ok

The overall magnification of a microscope is determined as the product of the objective magnification and the eyepiece magnification: G=V about *G approx

If the focal length of the entire microscope is known, then its apparent magnification can be determined in the same way as for a magnifying glass:

As a rule, the magnification of modern microscope lenses is standardized and amounts to a series of numbers: 10, 20, 40, 60, 90, 100 times. Eyepiece magnifications also have very specific values, for example 10, 20, 30 times. All modern microscopes have a set of objectives and eyepieces that are specially designed and manufactured to fit together so that they can be combined to achieve different magnifications.

Field of view of the microscope

The field of view of the microscope depends on the angular field of the eyepiece ω , within which an image of fairly good quality is obtained: 2y=500*tg(ω)/G * G - microscope magnification

For a given angular field of the eyepiece, the linear field of the microscope in object space is smaller, the greater its apparent magnification.

Microscope exit pupil diameter

The exit pupil diameter of a microscope is calculated as follows:
where A is the front aperture of the microscope.

The diameter of the exit pupil of a microscope is usually slightly smaller than the diameter of the pupil of the eye (0.5 - 1 mm).

When observing through a microscope, the pupil of the eye must be aligned with the exit pupil of the microscope.

Microscope resolution

One of the most important characteristics of a microscope is its resolution. According to Abbe's diffraction theory, the linear resolution limit of a microscope, that is, the minimum distance between points of an object that are imaged as separate, depends on the wavelength and numerical aperture of the microscope:
The maximum achievable resolution of an optical microscope can be calculated based on the expression for the microscope aperture. If we take into account that the maximum possible value of the sine of the angle is unity, then for the average wavelength we can calculate the resolution of the microscope:

There are two ways to increase the resolution of a microscope: * By increasing the objective aperture, * By decreasing the wavelength of light.

Immersion

In order to increase the aperture of the lens, the space between the object in question and the lens is filled with the so-called immersion liquid - a transparent substance with a refractive index greater than one. Water, cedar oil, glycerin solution and other substances are used as such a liquid. The apertures of high magnification immersion objectives reach the value , then the maximum achievable resolution of an immersion optical microscope will be.

Application of ultraviolet rays

To increase the resolution of a microscope, the second method uses ultraviolet rays, the wavelength of which is shorter than that of visible rays. In this case, special optics must be used that are transparent to ultraviolet light. Since the human eye does not perceive ultraviolet radiation, it is necessary either to resort to means that convert the invisible ultraviolet image into a visible one, or to photograph the image in ultraviolet rays. At the wavelength, the resolution of the microscope will be.

In addition to increased resolution, the ultraviolet light observation method has other advantages. Typically, living objects are transparent in the visible region of the spectrum, and therefore are pre-stained before observation. But some objects (nucleic acids, proteins) have selective absorption in the ultraviolet region of the spectrum, due to which they can be “visible” in ultraviolet light without staining.

Light microscopy

Light microscopy provides magnification up to 2-3 thousand times, a color and moving image of a living object, the possibility of micro-filming and long-term observation of the same object, assessment of its dynamics and chemistry.

The main characteristics of any microscope are resolution and contrast. Resolution is the minimum distance at which two points are located, demonstrated separately by a microscope. The resolution of the human eye in the best vision mode is 0.2 mm.

Image contrast is the difference in brightness between the image and the background. If this difference is less than 3 - 4%, then it cannot be caught either by the eye or by a photographic plate; then the image will remain invisible, even if the microscope resolves its details. Contrast is influenced both by the properties of the object, which change the luminous flux compared to the background, and by the ability of the optics to capture the resulting differences in the properties of the beam.

The capabilities of a light microscope are limited by the wave nature of light. The physical properties of light - color (wavelength), brightness (wave amplitude), phase, density and direction of wave propagation change depending on the properties of the object. These differences are used in modern microscopes to create contrast.

The magnification of a microscope is defined as the product of the objective magnification and the magnification of the eyepiece. Typical research microscopes have an eyepiece magnification of 10, and an objective magnification of 10, 45 and 100. Accordingly, the magnification of such a microscope ranges from 100 to 1000. Some microscopes have a magnification of up to 2000. Even higher magnification does not make sense, since resolution does not improve. On the contrary, the image quality deteriorates.

Numerical aperture is used to express the resolving power of an optical system or the aperture ratio of a lens. Lens aperture is the light intensity per unit area of ​​the image, approximately equal to the square of NA. The NA value is approximately 0.95 for a good lens. The microscope is usually sized so that its total magnification is about 1000 NA. If a liquid (oil or, more rarely, distilled water) is introduced between the objective and the sample, an “immersion” objective is obtained with an NA value as high as 1.4 and a corresponding improvement in resolution.

Light microscopy methods

Light microscopy methods (illumination and observation). Microscopy methods are selected (and provided constructively) depending on the nature and properties of the objects being studied, since the latter, as noted above, affect the image contrast.

Bright field method and its varieties

The bright field method in transmitted light is used to study transparent preparations with absorbing (light-absorbing) particles and parts included in them. These can be, for example, thin colored sections of animal and plant tissues, thin sections of minerals, etc. In the absence of a preparation, a beam of light from the condenser, passing through the lens, produces a uniformly illuminated field near the focal plane of the eyepiece. If there is an absorbent element in the preparation, partial absorption and partial scattering of the light incident on it occurs, which causes the appearance of the image. It is also possible to use the method when observing non-absorbing objects, but only if they scatter the illuminating beam so strongly that a significant part of it does not fall into the lens.

The oblique lighting method is a variation of the previous method. The difference between them is that the light is directed at the object at a large angle to the direction of observation. Sometimes this helps to reveal the “relief” of an object due to the formation of shadows.

The bright field method in reflected light is used when studying opaque objects that reflect light, such as polished sections of metals or ores. The preparation is illuminated (from an illuminator and a translucent mirror) from above, through a lens, which simultaneously plays the role of a condenser. In the image created in a plane by the lens together with the tube lens, the structure of the preparation is visible due to the difference in the reflectivity of its elements; In the bright field, inhomogeneities that scatter the light incident on them also stand out.

Dark field method and its variations

The dark-field microscopy method is used to obtain images of transparent, non-absorbent objects that cannot be seen using the bright-field method. Often these are biological objects. Light from the illuminator and mirror is directed onto the preparation by a specially designed condenser - the so-called. dark field condenser. Upon exiting the condenser, the main part of the light rays, which did not change their direction when passing through the transparent preparation, forms a beam in the form of a hollow cone and does not enter the lens (which is located inside this cone). The image in the microscope is formed using only a small part of the rays scattered by microparticles of the drug located on the slide into the cone and passing through the lens. Dark-field microscopy is based on the Tyndall effect, a famous example of which is the detection of dust particles in the air when illuminated by a narrow beam of sunlight. In the field of view against a dark background, light images of the structural elements of the drug are visible, which differ from the surrounding environment in their refractive index. Large particles have only bright edges that scatter light rays. Using this method, it is impossible to determine from the appearance of the image whether the particles are transparent or opaque, or whether they have a higher or lower refractive index compared to the surrounding medium.

Conducting a dark-field study

Slides should be no thicker than 1.1-1.2 mm, coverslips 0.17 mm, without scratches or dirt. When preparing the drug, you should avoid the presence of bubbles and large particles (these defects will be visible with a bright glow and will not allow you to observe the drug). For dark-field, more powerful illuminators and maximum lamp intensity are used.

Setting up darkfield lighting is basically as follows:

Install the light according to Koehler;

Replace the bright-field condenser with a dark-field one;

Immersion oil or distilled water is applied to the upper condenser lens;

Raise the condenser until it touches the bottom surface of the slide;

A low magnification lens is focused on the specimen;

Using centering screws, a light spot (sometimes having a darkened central area) is transferred to the center of the field of view;

By raising and lowering the condenser, the darkened central area disappears and a uniformly illuminated light spot is obtained.

If this cannot be done, then you need to check the thickness of the glass slide (this phenomenon is usually observed when using too thick glass slides - the cone of light is focused in the thickness of the glass).

After setting the light correctly, install a lens of the required magnification and examine the specimen.

The ultramicroscopy method is based on the same principle - preparations in ultramicroscopes are illuminated perpendicular to the direction of observation. With this method, it is possible to detect (but not literally “observe”) extremely small particles, the sizes of which lie far beyond the resolution of the most powerful microscopes. With the help of immersion ultramicroscopes, it is possible to register the presence in a preparation of particles × particles up to 2 × 10 to the -9th degree m in size. But the shape and exact dimensions of such particles cannot be determined using this method. Their images appear to the observer in the form of diffraction spots, the dimensions of which depend not on the size and shape of the particles themselves, but on the aperture of the lens and the magnification of the microscope. Since such particles scatter very little light, extremely strong light sources, such as a carbon electric arc, are required to illuminate them. Ultramicroscopes are used mainly in colloid chemistry.

Phase contrast method

The phase contrast method and its variety - the so-called. The “anoptral” contrast method is designed to obtain images of transparent and colorless objects that are invisible when observed using the bright field method. These include, for example, living, undyed animal tissues. The essence of the method is that even with very small differences in the refractive indices of different elements of the preparation, the light wave passing through them undergoes different changes in phase (acquires the so-called phase relief). Not perceived directly by either the eye or the photographic plate, these phase changes are converted with the help of a special optical device into changes in the amplitude of the light wave, i.e., into changes in brightness (“amplitude relief”), which are already visible to the eye or recorded on the photosensitive layer. In other words, in the resulting visible image, the distribution of brightness (amplitude) reproduces the phase relief. The image obtained in this way is called phase contrast.

The phase contrast device can be installed on any light microscope and consists of:

A set of lenses with special phase plates;

Condenser with rotating disk. It contains annular diaphragms corresponding to the phase plates in each of the lenses;

An auxiliary telescope for adjusting phase contrast.

The phase contrast setting is as follows:

Replace the lenses and condenser of the microscope with phase ones (indicated by the letters Ph);

Install a low magnification lens. The hole in the condenser disk must be without an annular diaphragm (indicated by the number "0");

Adjust the light according to Koehler;

Select a phase lens of appropriate magnification and focus it on the specimen;

Turn the condenser disk and install the annular diaphragm corresponding to the lens;

As you know, a person receives the bulk of information about the world around him through 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 changes from purple to red.

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

Usually, when talking about the resolution of a particular 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 arc minute. In this case, the eye can distinguish two point objects located 25–30 cm away from it only when the distance between these objects is more than 0.075 mm. This is quite comparable to the resolution of a conventional computer scanner. In fact, 600 dpi resolution means the scanner can distinguish dots as close as 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 their operating principle is the same. The optical microscope made it possible to push the resolution limit 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 established 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 lens, which characterizes both the microscope and the substance that is located 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 that 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 reaches 1.78. Whatever the angle u, the value sin u cannot be more than one. Thus, the resolution of an optical microscope does not exceed a fraction of the wavelength of light.

The resolution is generally considered to be half the wavelength.

Intensity, resolution and magnification of an object are different things. You can make it so that the distance between the centers of images of objects that are located 10 nm from each other will be 1 mm. This would correspond to an increase of 100,000 times. However, it will not be possible to distinguish whether it 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. We will further, for simplicity, consider light sources. A typical image of a point light source obtained using an optical microscope is shown in Figure 2. The intensity of the light rings is much less than that of the 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 this intensity distribution is called the point spread function. This function does not depend on 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 continue to merge. This kind of magnification is often said to be useless - larger images will simply be blurrier. 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 made it possible to store images. The human eye was supplemented first by film cameras and films, and then by cameras based on digital devices that convert the light falling on them into electrical signals. The most common of these devices are CCD matrices (CCD stands for charge-coupled device). The number of pixels in digital cameras continues to increase, but this alone cannot improve the resolution of optical microscopes.

Even 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 exactly the path that the creators of electron and X-ray microscopes took. Despite the numerous advantages of such microscopes, the problem of using light to view nanoobjects remained. There were many reasons for this: convenience and ease of working with objects, the short time required to obtain an image, known methods for coloring samples, and much more. Finally, after years of hard work, it became possible to view nanoscale objects using an optical microscope. The greatest progress in this direction has been achieved in the field of fluorescence microscopy. Of course, no one has canceled the diffraction limit, but they managed to get around it. Currently, there are various optical microscopes that make it possible to examine objects whose dimensions 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 it is.

From what has already been said about the diffraction limit of resolution, it is clear that seeing a point source is not that difficult. If this source is of 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 a point object, you can determine exactly where the object is located. The accuracy of determining the coordinates of such an object is quite high. This can be illustrated by Figure 5. The coordinates of a point object can be determined 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. The closest other point source must be so far away that the researcher knows for sure that the image being processed corresponds to one source. It is clear that this is a distance l must satisfy the condition. In this case, image analysis can provide very precise 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 from each other at distances much smaller than . If these sources shine simultaneously, then it will be impossible to say anything about where exactly 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, one can find out what their relative positions are. This means that information has been obtained about the shape and size of the object, which is presented as a set of point sources. In other words, in this case, you can examine 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 a 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 take a closer look at it.

If you carefully study the conditions that are implied when talking about the diffraction limit, you will find that the distances from objects to lenses are much greater than the wavelength of light. At distances comparable to and smaller than this wavelength, the picture is different. Near any object caught in the electromagnetic field of a light wave, there is an alternating electromagnetic field, the frequency of change of which is the same as the frequency of change of the field in the light wave. Unlike a light wave, this field quickly decays as it moves away from the nanoobject. The distance at which the intensity decreases, e.g. e times, comparable to the size of the object. Thus, the electromagnetic field of optical frequency turns out to be concentrated in a volume of space, the size of which is much smaller than the wavelength of light. Any nanoobject that falls into this area will interact in one way or another with the concentrated field. If the object with the help of which this field concentration is carried out is sequentially moved along any trajectory along the nanoobject being studied 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 was concentrated. And this, in turn, is determined by the size of the object with the help of which this field is concentrated.

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

The essence of the second group of methods comes down to the following. Instead of making nearby nanoobjects 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, you can determine the position of each object, and then create a single picture. This is very similar to what is shown in Figure 5, only the colors will be different for the three images.

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 “turned off” using specially selected light. Such switchings occur statistically. In other words, if there are many switchable nanoobjects, then by selecting the wavelength of light and its intensity, you can force only part of these objects to “turn off”. The remaining objects will continue to shine, and an image can be obtained from them. After this, you need to “turn on” all the sources and “turn off” some of them again. The set of sources that remain “on” will be different from the set that remained “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 proportion 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.

Super-resolution optical microscopy is currently developing rapidly. It is safe to assume that this area will attract an increasing number of researchers in the coming years, and we hope that the readers of this article will be among them.