Resolution of optical instruments. Great encyclopedia of oil and gas
Using even an ideal optical system (one without defects and aberrations), it is impossible to obtain a stigmatic image of a point source, which is explained by the wave nature of light. The image of any luminous point in monochromatic light is a diffraction pattern, that is, the point source is displayed as a central bright spot surrounded by alternating dark and light rings.
According to Rayleigh criterion, images of two nearby identical point sources or two nearby spectral lines with equal intensities and identical symmetrical contours are resolvable (separated for perception) if the central maximum of the diffraction pattern from one source (line) coincides with the first minimum of the diffraction pattern from another (Fig. 265, a). When the Rayleigh criterion is met, the intensity of the “dip” between the maxima is 80% of the intensity at the maximum, which is sufficient to resolve the lines 1 and 2. If the Rayleigh criterion is violated, then one line is observed (Fig. 265, b).
1. Lens resolution. If light from two distant point sources falls on the lens S 1 and S 2 (for example, stars) with some angular distance , then, due to the diffraction of light waves at the edges of the diaphragm limiting the lens, in its focal plane, instead of two points, maxima are observed, surrounded by alternating dark and light rings (Fig. 266). It can be proven that two nearby stars observed in the lens in monochromatic light are resolvable , if the angular distance between them
where is the wavelength of light, D- lens diameter.
Resolving power (resolving power) of the lens is called the quantity
Where - the smallest angular distance between two points at which they are still resolved by an optical device.
According to the Rayleigh criterion, images of two identical points are resolvable when the central maximum of the diffraction pattern for one point coincides with the first minimum of the diffraction pattern for the other (Fig. 266). It follows from the figure that when the Rayleigh criterion is met, the angular distance between points should be equal , i.e., taking into account (183.1)
Therefore, the lens resolution
i.e., it depends on its diameter and the wavelength of light.
From formula (183.2) it is clear that to increase the resolution of optical instruments, it is necessary either to increase the diameter of the lens or to reduce the wavelength. Therefore, to observe the finer details of an object, ultraviolet radiation is used, and the resulting image is in this case observed using a fluorescent screen or recorded on a photographic plate. Even greater resolution could be obtained using x-rays, but it has a high penetrating power and passes through matter without refraction; therefore, in this case it is impossible to create refractive lenses. Electron streams (at certain energies) have approximately the same wavelength as X-rays. That's why electron microscope has a very high resolution.
The resolution of a spectral device is a dimensionless quantity
Where - absolute value the minimum difference in wavelengths of two adjacent spectral lines at which these lines are recorded separately.
2. Resolution of the diffraction grating. Let the maximum T- th order for wavelength 2 is observed at an angle , i.e., according to (180.3), d sin =m 2 . When moving from a maximum to an adjacent minimum, the path difference changes to /N(see (180.4)), where N- number of grid slits. Therefore, the minimum 1 observed at an angle min , satisfies the condition d sin min = m 1 + 1 /N. According to the Rayleigh criterion, = min , i.e. m 2 =m 1 + 1 /N or 2 / ( 2 – 1)=mN. Tax as 1 and 2 are close to each other, i.e. 2 – 1 = then, according to (183.3),
Thus, the resolution of a diffraction grating is proportional to the order m spectrum and number N slots, i.e. when given number gaps increase when moving to large values order m interference. Modern diffraction gratings have a fairly high resolution (up to 210 5).
Dispersion of Light
As already mentioned, light passing through a triangular prism is refracted and, when leaving the prism, deviates from its original direction towards the base of the prism. The amount of beam deflection depends on the refractive index of the prism material, and, as experiments show, the refractive index depends on the frequency of light. The dependence of the refractive index of a substance on the frequency (wavelength) of light is called dispersion. It is very easy to observe the phenomenon of dispersion when passing white light through a prism (Fig. 102). Upon leaving the prism White light decomposes into seven colors: red, orange, yellow, green, blue, indigo, violet. Red light deviates the least, violet light deviates the most. This suggests that glass has the highest refractive index for violet light, and the lowest for red light. Light with different wavelengths propagates in a medium with at different speeds: purple with the smallest, red with the largest, since n= c/v ,
As a result of the passage of light through a transparent prism, an ordered arrangement of monochromatic electromagnetic waves optical range - range.
All spectra are divided into spectra emissions and spectra absorption. The emission spectrum is created by luminous bodies. If a cold, non-emitting gas is placed in the path of the rays incident on the prism, then dark lines appear against the background of the continuous spectrum of the source.
In this case, we obtain the absorption spectrum of the gas. The German physicist G. Kirchhoff (1824-1887) discovered the law according to which the spectral composition of light, which is emitted by bodies in a hot state, is absorbed by them in a cold state (atoms of this element absorb those wavelengths that are emitted at high temperatures).
The emission spectra are divided into solid, lined And striped. A continuous spectrum is produced by hot solids and liquids. A line spectrum is a collection of specific spectral lines (on a black background). This spectrum is produced by excited gases in the atomic state. Isolated atoms of a given chemical element emit strictly defined wavelengths. The banded spectrum consists of individual spectral bands separated by dark spaces. Unlike line spectra, striped spectra are created not by atoms, but by molecules that are not bound or weakly bound to each other.
ELECTRONIC THEORY OF LIGHT DISPERSION
From Maxwell’s macroscopic electromagnetic theory it follows that the absolute refractive index of the medium
where is the dielectric constant of the medium, - magnetic permeability. In the optical region of the spectrum for all substances 1, therefore
From formula (186.1) some contradictions with experiment are revealed: the quantity n, being a variable, remains at the same time equal to a certain constant . In addition, the values n, obtained from this expression, do not agree with the experimental values. The difficulties of explaining the dispersion of light from the point of view of Maxwell's electromagnetic theory are eliminated by Lorentz's electronic theory. In Lorentz's theory, light dispersion is considered as a result of the interaction of electromagnetic waves with charged particles that are part of the substance and perform forced oscillations in the alternating electromagnetic field of the wave.
Let us apply the electronic theory of light dispersion for a homogeneous dielectric, formally assuming that light dispersion is a consequence of the dependence from frequency light waves. The dielectric constant of a substance, by definition (see (88.6) and (88.2)), is equal to
Where { - dielectric susceptibility of the medium, 0 - electrical constant, R - instantaneous polarization value. Hence,
those. depends on R. In this case, electronic polarization is of primary importance, i.e. forced oscillations of electrons under the influence of the electric component of the wave field, since for the orientational polarization of molecules the frequency of oscillations in the light wave is very high ( 10 15 Hz).
To a first approximation, we can assume that forced vibrations are performed only by the external electrons most weakly associated with the nucleus - optical electrons. For simplicity, we consider the vibrations of only one optical electron. The induced dipole moment of an electron performing forced oscillations is equal to p=ex, Where e- electron charge, X - displacement of an electron under the influence of the electric field of a light wave. If the concentration of atoms in a dielectric is equal to n 0, then the instantaneous polarization value
From (186.2) and (186.3) we obtain
Consequently, the task comes down to determining the displacement X electron under the influence external field E. We will consider the field of the light wave to be a function of frequency , i.e., varying according to harmonic law: E = E 0cos t.
The equation of forced oscillations of an electron (see §147) for the simplest case (without taking into account the resistance force that determines the absorption of the energy of the incident wave) will be written in the form
Where T, - weight i- th charge.
From expressions (186.8) and (186.9) it follows that the refractive index n depends on frequency external field, i.e., the obtained dependences actually confirm the phenomenon of light dispersion, albeit under the above assumptions, which must be eliminated in the future. From expressions (186.8) and (186.9) it follows that in the region from = 0 to = 0 n 2 is greater than one and increases with increasing (normal variance); at = 0 n 2 = ±; in the area from = 0 to = n 2 is less than one and increases from – to 1 (normal variance). Moving from n 2 k n, we find that the dependence graph n from has the form shown in Fig. 270. This behavior n close 0 - the result of the assumption that there are no resistance forces during electron oscillations. If we take this circumstance into account, then the graph of the function n( ) near 0 will be given by the dashed line AB. Region AB - area of anomalous dispersion ( n decreases as it increases ), other parts of the dependence n from describe the normal variance ( n increases with increasing ).
Russian physicist D. S. Rozhdestvensky (1876-1940) contributed a classic work on the study of anomalous dispersion in sodium vapor. He developed the interference method for very precise measurement refractive index of vapors and experimentally showed that formula (186.9) correctly characterizes the dependence n from , and also introduced a correction to it that takes into account the quantum properties of light and atoms.
Page 1
Resolution optical instruments and, in particular, microscopes are limited by the phenomenon of diffraction. Particle image smaller sizes will have the form of a diffraction circle, the shape of which is practically independent of the shape of the particles. At in a special way By observing these diffraction patterns, however, they can be noticed and, therefore, the fact of the existence of particles, their position and movement can be established. The observation and study of such small particles in colloidal solutions and aerosols constitute the subject of ultramicroscopy.
Limitations in the resolution of optical instruments are associated with diffraction phenomena and aberrations of elements optical systems.
In addition to the resolution of the eye, the resolution of an optical device is affected by the degree of correction of the system.
What determines the resolution of optical instruments?
On increasing the resolution of optical instruments: Dokl.
Usually, the resolution of an optical device is understood as the ability to distinguish (resolve) two close elements in the image of an object - two close luminous points in a conventional optical device or two close monochromatic lines in the spectrum obtained using a spectral device.
What is meant by the resolution of an optical device and what it depends on.
Why does the phenomenon of diffraction limit the resolution of optical instruments, such as a telescope?
According to the Rayleigh criterion, the maximum resolution of an optical device corresponds to the condition when the main maximum of the diffraction pattern from one point object exactly coincides with the first minimum of the diffraction pattern from another point object close to the first. This condition is met by the minimum angular resolution of the optical device.
From formula (183.2) it is clear that to increase the resolution of optical instruments it is necessary either to increase the diameter of the lens or to reduce the length of the lens. Therefore, to observe the finer details of an object, ultraviolet radiation is used, and the resulting image in this case is observed using a fluorescent screen or recorded on a photographic plate. Even greater resolution could be obtained using x-rays, but it has a high penetrating power and passes through matter without refraction; therefore, in this case it is impossible to create refractive lenses. Electron streams (at certain energies) have approximately the same wavelength as X-rays.
From formula (183.2) it is clear that to increase the resolution of optical instruments, it is necessary either to increase the diameter of the lens or to reduce the wavelength. Therefore, to observe the finer details of an object, ultraviolet radiation is used, and the resulting image in this case is observed using a fluorescent screen or recorded on a photographic plate. Even greater resolution could be obtained using x-rays, but it has a high penetrating power and passes through matter without refraction; therefore, in this case it is impossible to create refractive lenses. Electron streams (at certain energies) have approximately the same wavelength as X-rays.
Another interest Ask, very important from a technical point of view: what is the resolution of optical instruments. When we create a microscope, we want to see the entire object that is in our field of vision. This means, for example, that when we look at a bacterium that has two spots on its sides, we want to distinguish both spots in a magnified image. They may think that for this you only need to get sufficient magnification, because you can always add more lenses and achieve higher magnification, and if the designer is dexterous, he will eliminate spherical and chromatic aberrations; there seems to be no reason why not enlarge the desired image to any size. But the limit of the microscope's capabilities is not due to the fact that it is impossible to achieve magnification of more than 2000 times.
RESOLUTION(resolving power) of optical devices is a value characterizing the ability of these devices to provide a separate image of two points of an object close to each other. The smallest linear (or angular) distance between two points, starting from which their images merge and cease to be distinguishable, called. linear (or angular) resolution limit. Its reciprocal value serves as a quantitative measure of R. s. optical devices. An ideal image of a point as an element of an object can be obtained from a spherical wave. surfaces. Real optical systems have entrance and exit pupils (see. Diaphragm ) of finite dimensions, limiting the wave surface. Thanks to light diffraction, even in the absence
aberrations of optical systems and manufacturing errors, optical the system depicts a point in monochromatic. light in the form of a light spot surrounded by alternately dark and light rings.
Using the theory, you can calculate naim. distance allowed by optical system, if it is known at what illumination distributions the receiver (eye, photo layer) perceives the image separately. In accordance with the condition introduced by J. W. Rayleigh (1879), images of two points can be seen separately if the center of the diffraction the spots of each of them intersect with the edge of the first dark ring of the other (Fig.). Illumination distribution system, if it is known at what illumination distributions the receiver (eye, photo layer) perceives the image separately. In accordance with the condition introduced by J. W. Rayleigh (1879), images of two points can be seen separately if the center of the diffraction the spots of each of them intersect with the edge of the first dark ring of the other (Fig.). E in the image of two point light sources located so that the angular distance between the illumination maxima Df is equal to the angular value of the radius of the central diffraction spot Dq (Df = Dq - Rayleigh condition). If the points of the object are self-luminous and emit incoherent rays, the execution corresponds to what is called. the illumination between the images of resolved points will be 74% of the illumination in the center of the spot, and the angle. distance between diffraction centers spots (illumination maxima) is determined by the expression Df = 1.21l//system, if it is known at what illumination distributions the receiver (eye, photo layer) perceives the image separately. In accordance with the condition introduced by J. W. Rayleigh (1879), images of two points can be seen separately if the center of the diffraction the spots of each of them intersect with the edge of the first dark ring of the other (Fig.). D system, if it is known at what illumination distributions the receiver (eye, photo layer) perceives the image separately. In accordance with the condition introduced by J. W. Rayleigh (1879), images of two points can be seen separately if the center of the diffraction the spots of each of them intersect with the edge of the first dark ring of the other (Fig.)., where l is the wavelength of light, system, if it is known at what illumination distributions the receiver (eye, photo layer) perceives the image separately. In accordance with the condition introduced by J. W. Rayleigh (1879), images of two points can be seen separately if the center of the diffraction the spots of each of them intersect with the edge of the first dark ring of the other (Fig.). in mm) (about the R. s. of microscopes, see Art. Microscope). The given formulas are valid for points located on the axis of ideal optical lenses. devices. The presence of aberrations and manufacturing errors reduces the R.s. real optical systems R.s. real optical The system also decreases when moving from the center of the field of view to its edges. R.s. optical device R op, including a combination of optical. system and receiver (photolayer, cathode electron-optical converter etc.), associated with R. s. optical systems devices. The presence of aberrations and manufacturing errors reduces the R.s. real optical R oc
and receiver
n approximate f-loy
Regardless of their specificity and purpose, they necessarily have one common physical characteristic, which is called “resolution”. This physical property is decisive for all optical and optical devices without exception. For example, for a microscope, the most important parameter is not only the magnifying ability of its lenses, but also the resolution, on which the quality of the image of the object under study directly depends. If the design of this device is not capable of providing separate perception of the smallest details, then the resulting image will be of poor quality even with significant magnification. The resolution of optical instruments is a value that characterizes their ability to distinguish the smallest individual details of observed or measured objects. The resolution limit is the minimum distance between adjacent parts (points) of an object, at which their images are no longer perceived as separate elements of the object, merging together. The smaller this distance, the correspondingly higher the resolution of the device. The reciprocal of the resolution limit serves as a quantitative indicator of resolution. This
the most important parameter and determines the quality of the device and, accordingly, its price. Due to the diffraction property of light waves, all images of small elements of an object look like bright spots surrounded by a system of concentric interference circles. It is this phenomenon that limits the resolution of any optical instruments. According to the theory of the 19th century English physicist Rayleigh, the image of two nearby small elements of an object can still be distinguished when their diffraction maximum coincides. But even this resolution has its limit. It is determined by the distance between these the smallest details separately perceived lines per millimeter of image. This fact was established experimentally.
The resolution of instruments decreases in the presence of aberrations (deviations light beam from a given direction) and various errors manufacturing optical systems, which increases the size of diffraction spots. Thus, the smaller the diffraction spots, the higher the resolution of any optics. This is an important indicator.
The resolution of any optical device is assessed by its hardware functions, which reflect all the factors that influence the quality of the image provided by this device. Such influencing factors, of course, should first of all include aberration and diffraction - the bending of light waves around obstacles and, as a result, their deviation from the rectilinear direction. To determine the resolution of various optical instruments, special test transparent or opaque plates with a standard pattern, called worlds, are used.
