Coursework: Aberrations of optical systems. Aberration of optical systems, types of aberrations

Ministry of Education

RUSSIAN FEDERATION

TYUMEN STATE UNIVERSITY

Course work

"Aberrations of optical systems"

Completed: student of the 2nd

course gr. 473

…………….

Checked:

Tyumen 2009

Introduction

1. Chromatic aberration

2. Wave and beam aberrations; aberration functions

3. Primary aberrations (Seidel aberrations)

3.1 Spherical

3.3 Astigmatism and field curvature

3.4 Distortion

Bibliography

Introduction

Aberrations of optical systems (from lat. Aberratio - evasion), distortions, image errors formulated by optical systems. Aberrations in optical systems are manifested in the fact that optical images are not quite clear, do not accurately correspond to objects, or turn out to be colored. Most common the following types aberrations of optical systems: spherical- lack of an image, in which the light rays emitted by one point of the object that passed near the optical axis of the system, and the rays that passed through parts of the system remote from the axis, are not collected at one point: coma- aberration that occurs when light rays pass obliquely through an optical system. If, during the passage of the optical system, a spherical light wave is deformed so that the beams of rays emanating from one point of the object do not intersect at one point, but are located in two mutually perpendicular segments at a certain distance from each other, then such beams are called astigmatic, and this beam itself aberration - astigmatism. an aberration called distortion, leads to a violation of the geometric similarity between the object and its image. The aberrations of optical systems also include the curvature of the image field.

Optical systems can simultaneously have several types of aberrations. Their elimination is carried out in accordance with the purpose of the system; often it is a difficult task. The aberrations of optical systems listed above are called geometric. There is also chromatic aberration associated with the dependence of the refractive index of optical media on the wavelength of light.

1. Chromatic aberration

If a beam of non-monochromatic light falls on a refractive surface, then it is split into several beams, each of which has a certain wavelength. Therefore, when crossing the optical system, rays of light with different wavelengths will propagate after the first refraction in not exactly the same ways. As a result, the image will be blurry, in which case the system is said to have chromatic aberration.

Rice. 1. Longitudinal and transverse chromatic aberrations.

We confine ourselves to considering points and rays located near the axis, i.e., we assume that for each wavelength the mapping obeys the laws of paraxial optics. In this case, one speaks of first-order chromatic aberration, or primary aberration. Let be and - point display R at different wavelengths (Fig. 1); then the projections in directions parallel and perpendicular to the axis, determine the longitudinal and transverse chromatic aberrations, respectively.

Consider change focal length of a thin lens depending on the change in the refractive index
. Value (n - 1)f for such a lens does not depend on the wavelength. Hence

(1)

Value

(2)

Fig.2. Typical dispersion curves for different types of glass

I - heavy flint; II - heavy barium crown; III - light flint; IV - heavy crown; V - borosilicate crown.

where , and are the refractive indices corresponding to the Fraunhofer lines F, D and C ( 4861 , 5893 and 6563 ), serves as a rough measure of glass dispersion and is called relative dispersion. It can be seen from (1) that this value is approximately equal to the distance between the red and blue images divided by the focal length of the lens. On fig. 2 shows the change in refractive index values ​​with wavelength for several types of glass commonly used in optical systems. Relevant values lie in the range from 1/60 to 1/30.

Rice. 3. Achromatic doublet

To obtain a good quality image, it is necessary that both monochromatic and chromatic aberrations be small. Usually some compromise solution is chosen, since in the general case it is impossible to eliminate all types of aberrations at the same time. It is often sufficient to get rid of chromatic aberration for two chosen wavelengths. The choice of these wavelengths depends, of course, on the purpose of this or that optical system; for example, photographic lenses, unlike instruments used for visual observations, usually "achromatize" for colors close to the blue end of the spectrum, since an ordinary photographic plate is more sensitive to the blue region of the spectrum than the human eye. Of course, achromatization for two wavelengths does not completely eliminate the color error. The remaining chromatic aberration is called the secondary spectrum.

Let us now consider the conditions under which two thin lenses form a combination free from focal length chromatism. The reciprocal of the focal length of a combination of two thin lenses placed at a distance l from each other, is

(3)

As we see
, when

If achromatization is performed for linesC and F, then using (1) and (2) we obtain

Where and are the relative dispersions of both lenses.

One method to reduce chromatic aberration is to use two contacting thin lenses (Fig. 3), one of which is made of crown and the other of flint. In this case, becausel = 0, we get from (5)

(6)

or using (3 ),

,
(7)

relations (7) for given types of glass and a given focal length uniquely define , and. But , and depend on three radii of curvature, therefore, the value of one of them can be chosen arbitrarily. This additional degree of freedom sometimes makes it possible to minimize spherical aberration.

Another way to create an achromatic system is to use two race lenses made of the same glass () and located at a distance from each other equal to half the sum of their focal lengths, i.e.

The achromaticity of such a combination of lenses follows directly from (5).

In a device consisting of several parts, it is generally impossible to simultaneously eliminate position chromatism and magnification chromatism if this is not done for each of its parts. Let us prove the last statement for the case of two centered thin lenses separated by a distance l.

The display of a thin lens is a central projection from its center; therefore (Fig. 4),

Fig.4. Achromatization of a system of two thin lenses

Insofar as
, we find to increase

(10)

If the wavelength changes, then the value remains the same, the value will also be the same, if we assume the absence of chromatism of the situation. Therefore, the condition for the absence of chromatism of the increase in the system can be written as

Aberration of the optical system- error or error in the image in the optical system, caused by the deviation of the beam from the direction in which it would have to go in an ideal optical system. Aberration is characterized different kind violations of homocentricity in the structure of beams of rays emerging from the optical system.

The value of aberration can be obtained both by comparing the coordinates of the rays by direct calculation using exact geometric-optical formulas, and approximately - using the formulas of the theory of aberrations.

In this case, it is possible to characterize the aberration both by the criteria of ray optics and on the basis of the concepts of wave optics. In the first case, the deviation from homocentricity is expressed through the idea of ​​geometric aberrations and ray scattering figures in point images. In the second case, the deformation of a spherical light wave passed through the optical system is estimated, introducing the concept of wave aberrations. Both methods of description are interconnected, describe the same state and differ only in the form of description.

As a rule, if the lens has large aberrations, then it is easier to characterize them by the values ​​of geometric aberrations, and if they are small, then based on the concepts of wave optics.

Aberrations can be divided into monochromatic, that is, inherent in monochrome beams of rays, and.

monochromatic aberrations

In real systems, certain types of monochromatic aberrations almost never occur. In fact, a combination of all aberrations is observed, and the study of a complex aberrational scattering figure by the extraction method certain types aberrations (of any order) - nothing more than an artificial technique that facilitates the analysis of the phenomenon.

Monochromatic aberrations of higher orders

As a rule, the picture of the distribution of rays in scattering figures is noticeably complicated by the fact that aberrations of higher orders are superimposed on the combination of all third-order aberrations. This distribution noticeably changes with the position of the object point and the system hole. For example, fifth-order spherical aberration, in contrast to third-order spherical aberration, is absent at a point on the optical axis, but it grows in proportion to the square of the distance from it.

The influence of higher-order aberrations increases as the relative aperture of the lens grows, and so quickly that, in practice, the optical properties of high-aperture lenses are determined precisely by higher orders of aberrations.

The values ​​of higher order aberrations are taken into account on the basis of an accurate calculation of the path of rays through the optical system (tracing). Typically, using specialized programs for optical modeling (Code V, OSLO, ZEMAX, etc.)

Chromatic aberration

Chromatic aberrations due to the dispersion of optical media from which the optical system is formed, that is, the dependence of the refractive index of the optical materials from which the elements of the optical system are made on the length of the transmitted light wave.

They can manifest themselves in extraneous coloring of the image, and in the appearance of color contours in the image of the object, which were absent in the object.

These aberrations include position chromatic aberration (chromatism), sometimes called "longitudinal chromatism", and

Aberration of the optical system is the distortion of images that occurs at the output of the optical system. The name comes from lat. aberratio - evasion, removal. Distortions consist in the fact that optical images do not fully correspond to the subject. This manifests itself in the blurring of the image and is called monochromatic geometric aberration or coloration of the image - chromatic aberration of the optical system. Most often, both types of aberration appear together.
In the paraxial (paraxial) region, the optical system works almost perfectly, a point is displayed as a dot, and a straight line is displayed as a straight line, etc. However, as the point moves away from the optical axis, the rays from it intersect in the image plane at more than one point. Thus, a circle of dispersion arises, i.e. aberrations occur.
The amount of aberration can be determined by calculation using geometric and optical formulas by comparing the coordinates of the rays, as well as approximately using the formulas of the theory of aberrations.
There is a description of the phenomenon of aberration both in the ray theory (deviation from identity is described through geometric aberrations and ray scattering figures) and in the representations of wave optics (the deformation of a spherical light wave is estimated along the way through the optical system). Typically, geometric aberrations are used to characterize a lens with large aberrations, otherwise wave optics representations are used.

In 1856, the German scientist Seidel, as a result of the analysis of light rays, established five lens aberrations that appear when monochrome light (i.e. light of one wave) passes through the lens. These aberrations, described below, are called the five Seidel aberrations. Monochromatic geometric aberrations of optical systems are the result of their imperfection and appear in monochromatic light. Unlike an ideal optical system, in which all rays from any point of an object in the meridional plane after passing through the system are concentrated at one point, in a real optical system, these rays intersect the image plane in different points. The coordinates of these points depend on the direction of the beam, the coordinates of the point of intersection with the plane of the entrance pupil, and structural elements optical system (surface radii, thickness of optical elements, refractive indices of lenses, etc.).

It manifests itself in the mismatch of foci for light rays passing at different distances from the optical axis, as a result of which the homocentricity of beams of rays from a point source is violated, although the symmetry of these beams is preserved. This is the only kind of geometric aberration that occurs even when the starting point is located on the main optical axis of the system. With spherical aberration, a cylindrical beam of rays, after being refracted by a lens, takes the form not of a cone, but of a funnel-shaped figure. The point image has a disk shape with non-uniform illumination. The reason is the fact that the refractive surfaces of the lenses intersect with the rays of the wide beam at different angles, due to which the distant rays are refracted more and form their vanishing points at some distance from the focal plane.

The Coma aberration violates the homocentricity of wide light beams that enter the system at an angle to the optical axis. There is no coma on the axis of centered optical systems. Each section of the annular zone of the optical system, remote from the axis by a distance R, gives a ring of the image of a point, the radius of which increases with increasing R. Due to the mismatch of the centers of the rings, they overlap, which leads to the fact that the image of the point formed by the optical system takes the form an asymmetric scattering spot with maximum illumination near the top of the scattering figure, resembling a comet. In complex optical systems, coma is corrected along with spherical aberration by lens selection. Systems without coma and spherical aberration are called aplanats.

If the lens is corrected for spherical aberration and coma, i.e. an object point located on the optical axis is correctly reproduced as an image point, but at the same time, an object point that does not lie on the axis is reproduced in the image not as a point, but as an ellipse or line, then this type of aberration is called astigmatism. The reason for the occurrence is the different curvature of the optical surface in different section planes, and the angles of refraction of the beam rays depend on the angles of their incidence. When passing through the optical system, the rays intersect at different distances from the refracting surface. As a result, in different sections the focus of the light beam is at different points.
There is such a position on the image surface when all the rays of the beam in the meridional (or sagittal) plane perpendicular to it will intersect on this surface. The astigmatic beam depicts a point in the form of two astigmatic focal lines on focal surfaces shaped as surfaces of revolution and touching each other at the point of the axis of the system. If for some point of the field the positions of these surfaces do not coincide, there is astigmatism or an astigmatic difference between the meridional and sagittal foci. Astigmatism is called positive if the meridional foci are closer to the refractive surface than the sagittal ones, otherwise it is negative.

It manifests itself in the fact that the image of a flat (perpendicular to the optical axis) object is located on a surface that is concave or convex with respect to the lens, which makes the sharpness uneven over the image field. When the center of the image is in sharp focus, the edges will lie out of focus (not sharp) and vice versa. The curvature of the image field, as a rule, reaches large values for simple lenses (up to 4 lenses). It is corrected by the selection of the curvature of the surfaces and the thickness of the lenses, as well as the distances between them. For a qualitative correction, taking into account other types of aberrations, it is necessary to have at least two negative lenses in the composition. By stopping down, the negative effect of field curvature on image quality is reduced.

Distortion (curvature) is a change in the linear increase in the field of view, which leads to a violation of the geometric similarity between the object and its image. This type of aberration does not depend on the coordinates of the intersection of the beam and the plane of the entrance pupil, but depends on the distance from the source to the optical axis. An optical system without distortion is called orthoscopic. In lenses with a symmetrical design, it appears slightly. To eliminate distortion, the selection of lenses and other elements is used in the development of an optical system. In digital photography, distortion can be corrected with computer processing.

The emission of most light sources is characterized by a complex spectral composition, which leads to the occurrence of chromatic aberrations, which, unlike geometric ones, can also occur in the paraxial region. Dispersion (scattering) of light - the dependence of the refractive index of an optical element on the wavelength of light, is the cause of two types of chromatic aberrations: focus position chromatism and magnification chromatism. In the first case, which is also called longitudinal chromatism, there is a displacement of the image plane for different lengths waves, in the second - the transverse magnification changes. Chromatic aberrations are manifested in the coloring of the image, in the appearance of color contours in it, which are absent from the source. Chromatic aberrations also include chromatic differences of geometric aberrations, in particular, the chromatic difference of spherical aberrations (spherochromatism) for beams of different wavelengths and the chromatic difference of aberrations of inclined beams.

The cause of diffraction aberration is the wave nature of light. It occurs as a result of the diffraction of light by the diaphragm and the lens barrel. Prevents an increase in the resolution of the photo lens. Due to diffractive aberration, the minimum angular distance between dots allowed by the lens is limited. High-quality lenses are subject to it to the same extent as simple ones. It cannot be completely eliminated in principle, but it can be reduced by increasing the aperture of the optical system.

It is impossible to completely eliminate aberrations in optical systems. It is important to keep them to a minimum. allowed values, which are due technical requirements and the cost of manufacturing the system.

aberrations

The idea of ​​the eye as perfect optical device we acquire from school when studying the section of physics "Optics". When studying the relevant sciences in higher or secondary specialized educational institutions such an idea of ​​the eye is fixed, acquiring additional information. Therefore, the statement of S.N. Fedorov that the eye is an imperfect device and the task of an ophthalmologist in improving it was perceived by many doctors with skepticism for a long time.

And what is laser correction, if not the improvement of the mistakes of nature? Mistakes of nature here can be called myopia, farsightedness and astigmatism. And not only. Optical scientists have known this for a long time. They knew that when designing even the simplest telescope, it is necessary not only to focus the optical system at one point (to exclude myopia, hyperopia and astigmatism of the telescope), but also to ensure the quality of the resulting image. The lenses from which a spyglass is made must be of good glass, almost perfect shape and with a well-finished surface. Otherwise, the image will be fuzzy, distorted and blurry. It was then that the study of aberrations began - the smallest roughness and uneven refraction. And with the advent of devices for detecting and measuring eye aberrations, a new dimension entered ophthalmology - aberrometry.

aberrations can be different order . The simplest and most well-known aberrations are actually the same myopia, farsightedness and astigmatism. They are called defocus or aberrations of the second, lower order. Higher-order aberrations are the same roughness and uneven refraction, which have already been mentioned above.

Higher order aberrations are also divided into several orders. It is generally accepted that the quality of vision is affected by aberrations mainly up to the seventh order. For the convenience of perception, there is a set of Zernike polynomials that displays the types of monochromatic aberrations as a three-dimensional model of refractive unevenness. A set of these polynomials can more or less accurately display any uneven refraction of the eye.

Where do aberrations come from?

Everyone has them. An individual refraction map of the eye consists of them. Modern devices detect higher-order aberrations that somehow affect the quality of vision in 15% of people. But individual characteristics everyone has breaks.

The suppliers of aberrations are the cornea and the lens.

Aberrations can be caused by:

Congenital anomaly (very small and slightly affecting vision unevenness, lenticonus);

Corneal injury (corneal scar tightens the surrounding tissue, depriving the cornea of ​​sphericity);

Surgery (radial keratotomy, removal of the lens through a corneal incision, laser correction, thermokeratoplasty and other corneal surgeries);

Corneal diseases (consequences of keratitis, cataract, keratoconus, keratoglobus).

The reason for the attention of ophthalmologists to aberrations is ophthalmic surgery. Ignoring aberrations and not taking into account their impact on the quality of vision, ophthalmology has existed for a long time. Prior to this, aberrations were studied and fought against. negative influence only manufacturers of spyglasses, telescopes and microscopes.

Operations on the cornea or lens(meaning a corneal incision) higher order aberrations increase by several orders of magnitude, which can sometimes lead to a decrease in postoperative visual acuity. Therefore, the widespread introduction of artificial lens implantation, keratotomy, and laser correction into ophthalmological practice has contributed to the development of diagnostic equipment: keratotopographs have appeared that analyze the refractive map of the cornea, and now aberrometers that analyze the entire wavefront from the anterior surface of the cornea to the retina.

Aberrations due to LASIK

By correcting defocus (nearsightedness, farsightedness), the refractive surgeon adds high-order aberrations to the patient.

The formation of a corneal flap by a microkeratome leads to an increase in aberrations of a higher order.

Complications during LASIK lead to higher order aberrations.

The healing process leads to the growth of higher order aberrations.

Fight against aberrations induced by LASIK

It was not possible to remove microroughness and irregularities using an excimer laser with a slit beam delivery. A device with the possibility of point ablation was invented and put into production, that is, the diameter laser beam in some models less than a millimeter. With the use of Zernike polynomials were put into practice computer programs, allowing you to automatically convert the individual refraction map obtained from the aberrometer in a laser installation into an algorithm that controls the beam, eliminating not only residual defocus, but also higher-order aberrations. The Zernike polynomials become a set of tools, each of which is designed to remove a specific component in the aberration complex. Like a carpenter, a planer is designed for leveling, a chisel for deepening, a saw for splitting, an ax for splitting. It's not that simple, of course. As with an ax you can find not one, but ten ways to use it, so the polynomial is designed to remove a spatially quite complex shapes. But the basic principle is clear.

The cornea during such personalized laser ablation should approximate in its shape to the level of an optically ideal sphere.

supervision

After personalized laser correction, some patients achieved visual acuity greater than 1.0. Patients saw not only ten lines, but also eleven, and twelve, and even more. This phenomenon has been called "supervision".

In scientific circles, a discussion flared up almost about the violation of human rights. How correct is it to give a person too good vision, because he will see flaws on the faces of loved ones, will begin to distinguish every pixel on the computer screen and TV, suffer from an excess of visual information. Quite scientific approach. Maybe this debate will be relevant in a few years.

However, in parallel with this dispute, commercial proposals also appeared.. Advertisements for excimer clinics promised supervision to everyone. But supervision is not predictable! Some of the patients will succeed, while dozens of others will not. After all, the ability to supervision is determined by the size of the photodetectors of the eye, those same cones on the retina. The smaller the cone and the greater its density in the macula, the smaller the object a person can see. In addition, the influence of each type of higher-order aberrations on vision has not yet been sufficiently studied. So offer super vision in the form of super LASIK (see above) is incorrect. We can only talk about personalized laser correction.

Effect of aberrations on vision

At the time of " cold war» between the USSR and the USA, scientific and military-industrial espionage has become one of the most important areas of work for the special services of the two countries. When the new Soviet MiG fighter demonstrated in local wars clear advantage their specifications over enemy aircraft, US intelligence did everything to get hold of the secret developments of Artem Mikoyan's design bureau. In the end, they managed to get almost a whole MiG.

One of the advantages of the MiG over American counterparts was its maneuverability and speed, due to the extremely low air resistance during flight at that time. The air did not seem to resist the body of the aircraft at all, smoothly flowing around its contour.

To achieve this effect, American aircraft designers tried to make the surface of their aircraft ideally smooth, even and streamlined. Imagine their surprise when they saw the uneven, rough surface of the MiG with protruding heads of "rivets and bolts." The secret of the streamlining of the Russian aircraft turned out to be simple and ingenious. All these roughnesses during the flight created a kind of air cushion to minimize air resistance.

Perhaps this is a myth or legend of aircraft designers, but such an analogy perfectly illustrates the attitude of ophthalmologists towards aberrations of a higher order. The fact is that the views of ophthalmologists on the question of the effect of aberrations on vision over the past ten years have undergone a certain evolution, similar to the evolution of American designers to the characteristics of the surface of an aircraft.

As mentioned above, ophthalmologists turned to the problem of aberrations close attention mainly due to deterioration in the quality of vision after corneorefractive surgery. Patients saw right amount lines, but complained of a decrease in dark adaptation, distortion and blurring of the boundaries of visible objects. There were also those who, with almost zero refraction (that is, the absence of myopia and hyperopia), visual acuity did not reach 1-2 lines to the level that they gave in glasses before correction. It is not surprising that the attitude towards aberrations was purely negative, as to an acquired or congenital pathology. It is this attitude that has driven the race for perfect corneal sphericity and supervision.

Now the opinion of ophthalmologists is changing. The first sign was the legendary ophthalmic surgeon Pallikaris (a refractive surgeon of world renown and one of the founders of laser correction).

In 2001, in Cannes, he suggested that each person, except for the parameters of the eye, fixed using modern appliances, there is also a "dynamic visual factor". What further research in this area will lead to, time will tell. One thing is certain: aberrations can both reduce and increase visual acuity.

Perhaps further study of the "dynamic visual factor" will be based on the following hypothesis.

Carrying out LASIK leads to an increase in aberrations of a higher order. Perhaps narrowing down these aberrations to seven orders of magnitude from a research perspective is not entirely correct. What matters here is the difference in optical density in the area of ​​the interface (sub-flap space), and the roughness of the resulting surface of the corneal bed, and healing processes (remodulation of the shape of the cornea, traction of damaged fibrils, unevenness of the epithelial layer, etc.). All this, coupled with other aberrations, leads to blurring of focus on the retina, the appearance of several images. The brain, using the accommodation mechanism, selects the most clear and satisfying image from all the presented images in a given period of time (the principle of multifocality). It is the individual characteristics of the adaptation of the brain to the variability of the resulting image that will be the “dynamic visual factor” on which it depends - this set of aberrations will improve vision in this person or reduce its quality. And this is already connected with the balance of consciousness and subconsciousness, psychomotor features, intelligence, psychological status.

From the jungle of assumptions to specific questions.

What are aberrations?

Chromatic, astigmatism of oblique beams, coma, etc. All together they form an image of the surrounding world on the retina, the perception of which is strictly individual for each person. Each of us really sees the world only in our own way. Only complete blindness can be the same for everyone.

Here are some types of higher order aberrations.

1. Spherical aberration. Light passing through the periphery of a biconvex lens is refracted more strongly than in the center. The main "supplier" of spherical aberration in the eye is the lens, and secondarily, the cornea. The wider the pupil, that is, the most of the lens takes part in the visual act, the more noticeable is the spherical aberration.

In refractive surgery most often induces spherical aberration:

Artificial lens;

Laser thermokeratoplasty.

2. Aberrations of tilt angles of optical beams. Asphericity of refractive surfaces. It is a mismatch between the centers of images of luminous points located outside the axis of the optical system. They are divided into aberrations of large tilt angles (astigmatism of oblique beams) and small tilt angles (coma).

The coma has nothing to do with the known diagnosis of resuscitators. Its aberrometric pattern is similar to a circle located in the optical center of the cornea and divided by a line into two even halves. One of the halves has a high optical power, and the other has a low one. With such an aberration, a person sees a luminous dot as a comma. When describing objects, people with such an aberration use the words "tail", "shadow", "additional contour", "doubling". The direction of these optical effects (the aberration meridian) can be different. The cause of coma may be congenital or acquired imbalance of the optical system of the eye. The optical axis (on which the focus of the lens is located) of the cornea does not coincide with the axis of the lens and the entire optical system is not focused in the center of the retina, in the macula. Coma can also be one of the components of uneven refraction in keratoconus. During LASIK, coma may appear as a result of decentering of the laser ablation zone or peculiarities of corneal healing during laser correction of farsightedness.

3. Distortion- violation of the geometric similarity between the object and its image - distortion. Points of the object at different distances from the optical axis are depicted with different magnifications.

Laser correction is not a monopolist in the correction of aberrations. Artificial lenses and contact lenses have already been developed to compensate for some types of higher-order aberrations.

An excursion into the ophthalmic classification of aberrations

Aberrations are divided into three main groups:

Diffractive;

Chromatic;

Monochromatic.

Diffractive aberrations appear when a beam of light passes near an opaque object. The light wave deviates from its direction, passing near a clear boundary between a transparent medium (air) and an opaque medium. In the eye, such an opaque medium is the iris. That part of the light beam that passes not in the center of the pupil, but at its edge, is deflected, which leads to light scattering along the periphery.

Chromatic aberration arise as a result of the following optical phenomenon. Sunlight, as already mentioned, consists of light waves with very diverse wavelengths. Visible light ranges from short wavelength violet to long wavelength red. Remember the counting rhyme for memorizing the spectrum of visible light - the colors of the rainbow? "Every hunter wants to know where the pheasant sits."

Red, orange, yellow, green, blue, blue, purple.

Each of these types of rays has its own refractive index. Each color is refracted in the cornea and lens in its own way. Roughly speaking, the image of the blue and green parts of the object is focused near the emetron by the retina, and the red parts are focused behind it. As a result, the image of a colored object on the retina is more blurry than a black and white one. It is on the effect associated with chromatic aberration that 3D video is based.

monochromatic aberrations, in fact, they are the main subject of study of refractive surgeons. It is monochromatic aberrations that are subdivided into aberrations of higher and lower orders. Monochromatic aberrations of the lowest order: myopia, hyperopia and astigmatism. Higher-order monochromatic aberrations: spherical aberration, coma, oblique beam astigmatism, field curvature, distortion, irregular aberrations.

To describe the complex of monochromatic aberrations of a higher order, polynomials of the mathematical formalism of Zernike (Zernike) are used. It is good if they are close to zero, and the standard deviation of the wavefront RMS (root mean square) is less than the wavelength or equal to 0.038 μm (Marechal criterion). However, these are the subtleties of refractive surgery.

Standard Table of Zernike Polynomials is a kind of set of three-dimensional illustrations of aberrations up to the seventh order: defocus, astigmatism, oblique beam astigmatism, coma, spherical aberration, trefoil, quatrefoil and so on, up to octrefoil (trefoil, tetrafoil, pentafoil, hexafoil...). "Shamrocks" are from three to eight uniform sectors of the circle with increased optical power. Their occurrence may be associated with the main centripetal directions of stroma fibrils, a kind of corneal stiffening ribs.

The aberration picture of the eye is very dynamic. Monochromatic aberrations mask chromatic aberrations. When the pupil is dilated in a darker room, spherical aberrations increase, but diffraction aberrations decrease, and vice versa. With an age-related decrease in the ability to accommodate, aberrations of a higher order, which were previously a stimulus and increased the accuracy of accommodation, begin to reduce the quality of vision.

Therefore, it is currently difficult to determine the significance of the positive and negative effects of each type of aberration on the vision of each person.

The role of aberrometry (with keratotopography function) in preoperative examination

Everything has already been said about this. According to the aberrometry data, an individual wavefront map is compiled, according to the parameters of which a personalized laser correction is carried out. In most patients, the level of higher-order aberrations is, to put it mildly, very small. And there is no need to use personalized laser ablation. Enough data autorefractokeratometry. But that doesn't mean you shouldn't pursue personalization. After all, if you have aberrations, then they can be detected only with aberrometry. And when corrected, you're more likely to get better visual acuity than you've ever had with glasses or even contact lenses.

Rice. 17. Eye wavefront analyzer (aberrometer with keratotopography function). The essence of keratotopography is as follows. Luminous concentric circles (Placido disc) (b) are projected onto the anterior surface of the cornea and their reflection is photographed by the apparatus (a). By the difference between the parameters of the projected and reflected circles, the device calculates the curvature of the cornea in 10,000 points and forms a "map" of refraction.

Personalized laser ablation is also used for pre-correction, for correction after other surgeries, and for thin corneas.

As for diagnostics as such, that is, the search for pathology, the main thing here is not to miss keratoconus.

More about keratoconus

It is quite easy for a refractive surgeon to identify keratoconus with the appropriate equipment. But that's not the problem. The problem is responsibility. Just like the complexity of the work of a sapper, not only in the knowledge of the intricacies of the craft. The difficulty is that the sapper is mistaken only once. You can't go wrong with keratoconus. Never. And for this you need to constantly keep in mind its indirect signs:

Myopic astigmatism is more often with oblique axes;

The optical power of the cornea is more than 46 diopters;

Thin cornea;

Surprisingly good vision without glasses and surprisingly poor with glasses when there is marked astigmatism;

Progression of astigmatism;

Local protrusion of the cornea, more often in the lower sector.

This is a protrusion and it is impossible to miss when keratotopography (or aberrometry). The protrusion is accompanied by an increase in optical power. The generally accepted standard for color indication colors in the image of the wavefront in blue color areas with a lower optical power (diopter), and in red - with a larger one. Classical keratoconus looks like a patch of red color in the lower right or lower left sector of the cornea.

By the way, ordinary high degree astigmatism looks like a red butterfly. Sometimes the wings of this butterfly lose their symmetry. One wing becomes huge, shifts downward, and the other decreases. Like sand in hourglass, the optical power flows from the top to the bottom. This may already be a manifestation of keratoconus. Doing laser correction in this case is impossible.

Who tolerates aberrations acquired after LASIK worse?

Young people with a labile psyche and a wide pupil. Each of us has a different pupil size in the light. On average, three millimeters, but some from birth have a couple of millimeters more. And the larger the pupil, the more area cornea and lens, which takes part in the act of vision. And the more small roughnesses distort the image. As a rule, the brain does not pay attention to such trifles. Just as it excludes floating opacities in the vitreous body from visual information (the majority of myopic people have them), and a person pays attention to them only sometimes, looking at blindingly white snow or, say, at a bright computer screen. But in subtle, creative, nervous natures, perception is often sharpened, and this may contribute to the fact that they constantly pay attention to such stimuli. It's not a quibble, it's a feature. nervous system, such as an individual pain threshold.

In such cases, you can try to develop in the brain an addiction to aberrations, or rather, divert its attention from this problem by instilling drops that narrow the pupil (pilocarpine) for a month. If this tactic fails, you will have to make an additional correction in order to reduce higher-order aberrations.

Where in everyday practice can an ophthalmologist encounter higher-order aberrations?

In keratoconus, visual acuity with full spectacle correction often falls short of 1.0. When checking vision through a diaphragm of three millimeters or less, visual acuity improves significantly (see above). In both cases, the cause of what is happening is in aberrations.

After cataract removal with implantation of an artificial lens, the patient often, even with full spectacle correction, does not see 1.0. Not in all cases, this is due to diseases of the retina, amblyopia or secondary cataract.

The artificial lens is smaller in diameter than the natural one. Sometimes the artificial lens can stand unevenly. During the operation with a corneal incision, the spherical shape of the cornea changes. All these reasons cause aberrations of a higher order. In extreme cases, they can be reduced by personalized laser correction (more on biooptics in the next chapter).

It makes sense to carry out aberrometry even with the so-called night blindness, manifested by a deterioration in visual acuity at dusk, but not accompanied by signs of serious retinal diseases (tapetoretinal abiotrophy, etc.).

There are many examples. If aberrations are suspected, the patient can be referred for examination at a refractive surgery center.

Article from the book:

As has already been shown, the path of rays in a real optical system and the structure of beams differ significantly from that which takes place in ideal system. As a result, real optical systems give an image that only more or less approaches the ideal. In this regard, an evaluation criterion is needed, by which one can judge the degree of approximation of a real system to an ideal one and which is evaluated by the image quality.

Recall the three Maxwell conditions for a geometrically perfect system:

1) all the rays that came out of the point of the object O (x, y) and passed through this system, must converge at the image point I(x", y");

2) each element of the plane normal to the optical axis and containing the point O(x, y) must be depicted by an element of the plane normal to the optical axis and containing the point I(x, y");

3) the height of the image h "should be proportional to the height of the object h, and the coefficient of proportionality must be constant regardless of the location of the point O (x, y) in the plane of the object.

Deviations from the first condition are called aberrations or (generally) image distortion. Deviations of the second type, respectively field and image curvature and deviations the third kind called distortion.

So, aberrations - these are image errors, due to the deviations of the rays from the directions in which they would have to go in an ideal optical system.

Geometric and wave aberrations are deviations from Maxwell's first condition. Geometric aberrations describe the displacements (relative to geometrically ideal positions) of the points of intersection of the rays with the image surface. Wave aberrations characterize OPD for each beam relative to the same parameter for the main beam.

Geometric aberrations are divided into classes depending on their order: 1st order, 3rd order, 5th order, etc.

Different types of aberrations do not equally affect image quality. Within the framework of Linfoot's criteria for evaluating image quality, aberrations that have circular or orthogonal symmetry affect the "structural content" of the image, but not its "likelihood". Asymmetric aberrations, even within the tolerance in terms of the criterion of structural content, strongly affect the credibility of the image. Such an understanding of the influencing factors, based on the ultimate goals of using this system, is very important, since in the process of calculating the lens, mutual

compensation for certain types of aberrations. Differences in influence different types can be shown already on the example of aberrations of the 1st and 3rd orders.

Aberrations of optical systems are divided into monochromatic and chromatic:

- monochromatic aberrations called the image errors that occur for rays of a certain wavelength. These include: spherical, coma, astigmatism and image curvature, distortion.

- Chromatic aberration - when passing through the refractive surfaces of radiation of complex spectral composition, it is decomposed into component spectral parts due to light dispersion. In this case, the image is the sum a large number monochromatic images that do not match in position or size. The image becomes colored.

Transverse aberrations (∆x / ∆y /) - this is the deviation of the coordinates of point A / intersection of the real beam with the image plane from the coordinates of point A 0 / ideal image in the direction perpendicular to the optical axis (Figure 30).

Figure 29. Transverse aberrations

wave aberration is the deviation of the real wavefront from the ideal, measured along the beam in the number of wavelengths.