and astigmatism). There are spherical aberrations of the third, fifth and higher orders.
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Distance δs" along the optical axis between the vanishing points of the zero and extreme rays is called longitudinal spherical aberration.
Diameter δ" The scattering circle (disk) is determined by the formula
δ ′ = 2 h 1 δ s ′ a ′ (\displaystyle (\delta ")=(\frac (2h_(1)\delta s")(a"))),
- 2h 1 - diameter of the system hole;
- a"- distance from the system to the image point;
- δs"- longitudinal aberration.
For objects located at infinity
A ′ = f ′ (\displaystyle (a")=(f")),
To construct a characteristic curve of longitudinal spherical aberration, the longitudinal spherical aberration is plotted along the abscissa axis. δs", and along the ordinate axis - the heights of the rays on the entrance pupil h. To construct a similar curve for transverse aberration, the tangents of the aperture angles in image space are plotted along the x-axis, and the radii of scattering circles are plotted along the ordinate axis. δg"
By combining such simple lenses, spherical aberration can be significantly corrected.
Reduction and correction
In some cases, a small amount of third-order spherical aberration can be corrected by slightly defocusing the lens. In this case, the image plane shifts to the so-called “best installation planes”, located, as a rule, in the middle, between the intersection of the axial and extreme rays, and not coinciding with the narrowest point of intersection of all rays of the wide beam (disk of least scattering). This discrepancy is explained by the distribution of light energy in the disk of least scattering, forming illumination maxima not only in the center, but also at the edge. That is, we can say that the “disk” is a bright ring with a central point. Therefore, the resolution of the optical system in the plane coinciding with the disk of least scattering will be lower, despite the lower value of transverse spherical aberration. The suitability of this method depends on the magnitude of the spherical aberration and the nature of the illumination distribution in the scattering disk.
Spherical aberration can be corrected quite successfully using a combination of positive and negative lenses. Moreover, if the lenses do not stick together, then, in addition to the curvature of the surfaces of the components, the magnitude of the spherical aberration will also be affected by the size of the air gap (even if the surfaces limiting this air gap have the same curvature). With this correction method, chromatic aberrations are usually corrected.
Strictly speaking, spherical aberration can be completely corrected only for some pair of narrow zones, and, moreover, only for certain two conjugate points. However, in practice the correction can be quite satisfactory even for two-lens systems.
Typically, spherical aberration is eliminated for one height value h 0 corresponding to the edge of the pupil of the system. In this case, the greatest value of residual spherical aberration is expected at a height h e determined by a simple formula
h e h 0 = 0.707 (\displaystyle (\frac (h_(e))(h_(0)))=(0.707))It is usually considered for a beam of rays emerging from a point on an object located on the optical axis. However, spherical aberration also occurs for other beams of rays emerging from points of the object remote from the optical axis, but in such cases it is considered as an integral part of the aberrations of the entire inclined beam of rays. Moreover, although this aberration is called spherical, it is characteristic not only of spherical surfaces.
As a result of spherical aberration, a cylindrical beam of rays, after refraction by a lens (in image space), takes the form not of a cone, but of some funnel-shaped figure, the outer surface of which, near a bottleneck, is called a caustic surface. In this case, the image of the point has the form of a disk with a non-uniform illumination distribution, and the shape of the caustic curve allows one to judge the nature of the illumination distribution. In general, the scattering figure, in the presence of spherical aberration, is a system of concentric circles with radii proportional to the third power of the coordinates on the entrance (or exit) pupil.
Calculated values
Distance δs" along the optical axis between the vanishing points of the zero and extreme rays is called longitudinal spherical aberration.
Diameter δ" The scattering circle (disk) is determined by the formula
- 2h 1 - diameter of the system hole;
- a"- distance from the system to the image point;
- δs"- longitudinal aberration.
For objects located at infinity
By combining such simple lenses, spherical aberration can be significantly corrected.
Reduction and correction
In some cases, a small amount of third-order spherical aberration can be corrected by slightly defocusing the lens. In this case, the image plane shifts to the so-called “best installation planes”, located, as a rule, in the middle, between the intersection of the axial and extreme rays, and not coinciding with the narrowest point of intersection of all rays of the wide beam (disk of least scattering). This discrepancy is explained by the distribution of light energy in the disk of least scattering, forming illumination maxima not only in the center, but also at the edge. That is, we can say that the “disk” is a bright ring with a central point. Therefore, the resolution of the optical system in the plane coinciding with the disk of least scattering will be lower, despite the lower value of transverse spherical aberration. The suitability of this method depends on the magnitude of the spherical aberration and the nature of the illumination distribution in the scattering disk.
Strictly speaking, spherical aberration can be completely corrected only for some pair of narrow zones, and, moreover, only for certain two conjugate points. However, in practice the correction can be quite satisfactory even for two-lens systems.
Typically, spherical aberration is eliminated for one height value h 0 corresponding to the edge of the pupil of the system. In this case, the greatest value of residual spherical aberration is expected at a height h e determined by a simple formula
Residual spherical aberration leads to the fact that the image of a point never becomes a point. It will remain a disk, although of a much smaller size than in the case of uncorrected spherical aberration.
To reduce residual spherical aberration, a calculated "overcorrection" is often used at the edge of the system's pupil, giving the edge zone spherical aberration a positive value ( δs"> 0). At the same time, the rays crossing the pupil at a height h e, intersect even closer to the focal point, and the edge rays, although they converge behind the focal point, do not go beyond the boundaries of the scattering disk. Thus, the size of the scattering disk decreases and its brightness increases. That is, both the detail and contrast of the image improves. However, due to the peculiarities of the illumination distribution in the scattering disk, lenses with “overcorrected” spherical aberration often have “double” blur outside the focus area.
In some cases, significant “re-correction” is allowed. For example, early “Planars” from Carl Zeiss Jena had a positive spherical aberration value ( δs"> 0), both for the marginal and middle zones of the pupil. This solution slightly reduces contrast at full aperture, but noticeably increases resolution at small apertures.
Notes
Literature
- Begunov B. N. Geometric optics, Moscow State University Publishing House, 1966.
- Volosov D.S., Photographic optics. M., “Iskusstvo”, 1971.
- Zakaznov N.P. et al., Theory of optical systems, M., “Machine Building”, 1992.
- Landsberg G. S. Optics. M., FIZMATLIT, 2003.
- Churilovsky V.N. Theory of optical instruments, Leningrad, “Machine Building”, 1966.
- Smith, Warren J. Modern optical engineering, McGraw-Hill, 2000.
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Physical encyclopedia
One of the types of aberrations of optical systems (See Aberrations of optical systems); manifests itself in a mismatch of Focuses for light rays passing through an axis-symmetric optical system (lens (See Lens), Lens) at different distances from ... Great Soviet Encyclopedia
Image distortion in optical systems due to the fact that light rays from a point source located on the optical axis are not collected at one point with rays passing through parts of the system remote from the axis. * * * SPHERICAL… … Encyclopedic Dictionary
spherical aberration- sferinė aberacija statusas T sritis fizika atitikmenys: engl. spherical aberration vok. sphärische Aberration, f rus. spherical aberration, f pranc. aberration de spéricité, f; aberration sphérique, f … Fizikos terminų žodynas
SPHERICAL ABERRATION- See aberration, spherical... Explanatory dictionary of psychology
spherical aberration- caused by the mismatch of the foci of light rays passing at different distances from the optical axis of the system, leading to the image of a point in the form of a circle of different illumination. See also: Aberration chromatic aberration ... Encyclopedic Dictionary of Metallurgy
One of the aberrations of optical systems, caused by a mismatch of focuses for light rays passing through an axisymmetric optical lens. system (lens, objective) at different distances from the optical axis of this system. It manifests itself in the fact that the image... ... Big Encyclopedic Polytechnic Dictionary
Image distortion in optical systems, due to the fact that light rays from a point source located on the optical axes do not gather at one point with rays passing through parts of the system remote from the axis... Natural science. Encyclopedic Dictionary
1. Introduction to the theory of aberrations
When talking about lens performance, one often hears the word aberrations. “This is an excellent lens, all aberrations are practically corrected in it!” - a thesis that can very often be found in discussions or reviews. It is much less common to hear a diametrically opposite opinion, for example: “This is a wonderful lens, its residual aberrations are well expressed and form an unusually plastic and beautiful pattern”...
Why do such different opinions arise? I will try to answer this question: how good/bad is this phenomenon for lenses and for photography genres in general. But first, let's try to figure out what photographic lens aberrations are. We'll start with the theory and some definitions.
In general use the term Aberration (lat. ab- “from” + lat. errare “to wander, to be mistaken”) is a deviation from the norm, an error, some kind of disruption of the normal operation of the system.
Lens aberration- error, or image error in the optical system. It is caused by the fact that in a real environment a significant deviation of rays can occur from the direction in which they go in the calculated “ideal” optical system.
As a result, the generally accepted quality of a photographic image suffers: insufficient sharpness in the center, loss of contrast, severe blurring at the edges, distortion of geometry and space, color halos, etc.
The main aberrations characteristic of photographic lenses are as follows:
- Comatic aberration.
- Distortion.
- Astigmatism.
- Curvature of the image field.
Before we take a closer look at each of them, let's remember from the article how rays pass through a lens in an ideal optical system:
Ill. 1. Passage of rays in an ideal optical system.
As we see, all the rays are collected at one point F - the main focus. But in reality, everything is much more complicated. The essence of optical aberrations is that rays incident on a lens from one luminous point are not collected at one point. So, let's see what deviations occur in an optical system when exposed to various aberrations.
Here it should also be immediately noted that in both a simple lens and a complex lens, all the aberrations described below act together.
Action spherical aberration is that rays incident on the edges of the lens are collected closer to the lens than rays incident on the central part of the lens. As a result, the image of a point on a plane appears in the form of a blurry circle or disk.
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Ill. 2. Spherical aberration.
In photographs, the effects of spherical aberration appear as a softened image. The effect is especially noticeable at open apertures, and lenses with larger apertures are more susceptible to this aberration. If the sharpness of the contours is preserved, such a soft effect can be very useful for some types of photography, for example, portraiture.
Ill.3. A soft effect on an open aperture due to the action of spherical aberration.
In lenses built entirely from spherical lenses, it is almost impossible to completely eliminate this type of aberration. In ultra-fast lenses, the only effective way to significantly compensate for this is to use aspherical elements in the optical design.
3. Comatic aberration, or “Coma”
This is a special type of spherical aberration for side rays. Its effect lies in the fact that rays arriving at an angle to the optical axis are not collected at one point. In this case, the image of a luminous point at the edges of the frame is obtained in the form of a “flying comet”, and not in the form of a point. Coma can also cause areas of the image in the out-of-focus area to become overexposed.
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Ill. 4. Coma.
Ill. 5. Coma in a photo image
It is a direct consequence of light dispersion. Its essence is that a ray of white light, passing through a lens, is decomposed into its constituent colored rays. Short-wave rays (blue, violet) are refracted in the lens more strongly and converge closer to it than long-focus rays (orange, red).
Ill. 6. Chromatic aberration. F - focus of violet rays. K - focus of red rays.
Here, as in the case of spherical aberration, the image of a luminous point on a plane is obtained in the form of a blurred circle/disk.
In photographs, chromatic aberration appears in the form of extraneous shades and colored outlines in the subjects. The influence of aberration is especially noticeable in contrasting scenes. Currently, CA can be easily corrected in RAW converters if the shooting was carried out in RAW format.
Ill. 7. An example of the manifestation of chromatic aberration.
5. Distortion
Distortion manifests itself in the curvature and distortion of the geometry of the photograph. Those. the scale of the image changes with distance from the center of the field to the edges, as a result of which straight lines bend towards the center or towards the edges.
Distinguish barrel-shaped or negative(most typical for a wide angle) and cushion-shaped or positive distortion (more often seen at long focal lengths).
Ill. 8. Pincushion and barrel distortion
Distortion is usually much more pronounced in lenses with variable focal lengths (zooms) than in lenses with fixed focal lengths (fixes). Some spectacular lenses, such as Fish Eye, deliberately do not correct distortion and even emphasize it.
Ill. 9. Pronounced barrel distortion of the lensZenitar 16mmFish Eye.
In modern lenses, including those with variable focal lengths, distortion is quite effectively corrected by introducing an aspherical lens (or several lenses) into the optical design.
6. Astigmatism
Astigmatism(from the Greek Stigma - point) is characterized by the impossibility of obtaining images of a luminous point at the edges of the field, both in the form of a point and even in the form of a disk. In this case, a luminous point located on the main optical axis is transmitted as a point, but if a point is outside this axis, it is transmitted as a darkening, crossed lines, etc.
This phenomenon is most often observed at the edges of the image.
Ill. 10. Manifestation of astigmatism
7. Image field curvature
Image field curvature- this is an aberration, as a result of which the image of a flat object, perpendicular to the optical axis of the lens, lies on a surface concave or convex to the lens. This aberration causes uneven sharpness across the image field. When the central part of the image is sharply focused, its edges will be out of focus and will not appear sharp. If you adjust the sharpness along the edges of the image, then its central part will be blurred.
There are no ideal things... There is no ideal lens - a lens capable of constructing an image of an infinitesimal point in the form of an infinitesimal point. The reason for this is - spherical aberration.
Spherical aberration- distortion arising due to the difference in focus for rays passing at different distances from the optical axis. Unlike the previously described coma and astigmatism, this distortion is not asymmetrical and results in a uniform divergence of rays from a point light source.
Spherical aberration is inherent to varying degrees in all lenses, with a few exceptions (one I know of is the Era-12, its sharpness is largely limited by chromaticity), it is this distortion that limits the sharpness of the lens at an open aperture.
Scheme 1 (Wikipedia). The appearance of spherical aberration
Spherical aberration has many faces - sometimes it is called noble "software", sometimes - low-grade "soap", it largely shapes the bokeh of the lens. Thanks to her, Trioplan 100/2.8 is a bubble generator, and the New Petzval of the Lomographic Society has blur control... However, first things first.
How does spherical aberration appear in an image?
The most obvious manifestation is blurring of the contours of an object in the sharpness zone (“glow of contours”, “soft effect”), concealment of small details, a feeling of defocusing (“soap” - in severe cases);
An example of spherical aberration (software) in a photograph taken with an Industar-26M from FED, F/2.8
Much less obvious is the manifestation of spherical aberration in the bokeh of the lens. Depending on the sign, degree of correction, etc., spherical aberration can form various circles of confusion.
An example of a photograph taken with a Triplet 78/2.8 (F/2.8) - the circles of confusion have a bright border and a light center - the lens has a large amount of spherical aberration
An example of a photograph taken on aplanat KO-120M 120/1.8 (F/1.8) - the circle of confusion has a weakly defined border, but it is still there. Judging by the tests (published by me earlier in another article), the lens has low spherical aberration
And, as an example of a lens in which the amount of spherical aberration is incredibly small - a photograph taken on the Era-12 125/4 (F/4). The circle has no border at all, and the brightness distribution is very even. This indicates excellent lens correction (which is indeed true).
Elimination of spherical aberration
The main method is aperture. Cutting off “extra” beams allows you to improve sharpness well.
Scheme 2 (Wikipedia) - reducing spherical aberration using a diaphragm (1 Fig.) and using defocusing (2 Fig.). The defocus method is usually not suitable for photography.
Examples of photographs of the world (the center is cut out) at different apertures - 2.8, 4, 5.6 and 8, taken using an Industar-61 lens (early, FED).
F/2.8 - quite strong software is obscured
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F/4 - software has decreased, image detail has improved
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F/5.6 - software is practically absent
F/8 - no software, small details are clearly visible
In graphic editors, you can use sharpening and blur removal functions, which allows you to somewhat reduce the negative effect of spherical aberration.
Sometimes spherical aberration occurs due to a lens malfunction. Usually - violations of the spaces between lenses. Adjustment helps.
For example, there is a suspicion that something went wrong when converting Jupiter-9 to LZOS: in comparison with Jupiter-9 produced by KMZ, LZOS simply lacks sharpness due to huge spherical aberration. De facto, the lenses differ in absolutely everything except the numbers 85/2. White can fight with Canon 85/1.8 USM, and black can only fight with Triplet 78/2.8 and soft lenses.
Photo taken with black Jupiter-9 from the 80s, LZOS (F/2)
Shot on white Jupiter-9 1959, KMZ (F/2)
The photographer's attitude towards spherical aberration
Spherical aberration reduces the sharpness of the image and is sometimes unpleasant - it seems that the object is out of focus. You should not use optics with increased sphric aberration in regular shooting.
However, spherical aberration is an integral part of the lens pattern. Without it, there would be no beautiful soft portraits on Tair-11, crazy fabulous monocle landscapes, the bubble bokeh of the famous Meyer Trioplan, the “polka dots” of Industar-26M and the “voluminous” circles in the shape of a cat’s eye on the Zeiss Planar 50/1.7. You shouldn't try to get rid of spherical aberration in lenses - you should try to find a use for it. Although, of course, excess spherical aberration in most cases does not bring anything good.
Conclusions
In the article, we examined in detail the influence of spherical aberration on photography: on sharpness, bokeh, aesthetics, etc.
Aberration is a polysemantic term that is used in various fields of knowledge: astronomy, optics, biology, photography, medicine and others. What aberrations are and what types of aberrations exist will be discussed in this article.
Meaning of the term
The word "aberration" comes from the Latin language and literally translates as "deviation, distortion, removal." Thus, aberration is the phenomenon of deviation from a certain value.
In what scientific fields can the phenomenon of aberration be observed?
Aberration in astronomy
In astronomy, the concept of light aberration is used. It is understood as the visual displacement of a celestial body or object. It is caused by the speed of light propagation relative to the observed object and the observer. In other words, a moving observer sees an object in a different place from where he would observe it if he were at rest. This is due to the fact that our planet is in constant motion, so the observer’s state of rest is physically impossible.
Since the phenomenon of aberration is caused by the movement of the Earth, there are two types:
- daily aberration: the deviation is caused by the daily rotation of the Earth around its axis;
- annual aberration: caused by the planet's revolution around the Sun.
This phenomenon was discovered in 1727, and since then many scientists have paid attention to the aberration of light: Thomas Young, Airy, Einstein and others.
Optical system aberration
An optical system is a set of optical elements that convert light beams. The most important system of this kind for humans is the eye. Such systems are also used to design optical instruments - cameras, telescopes, microscopes, projectors, etc.
Optical aberrations are various distortions of images in optical systems that affect the final result.
When an object moves away from the so-called optical axis, scattering of rays occurs, the final image is unclear, unfocused, blurry, or has a different color from the original one. This is an aberration. When determining the degree of aberration, special formulas can be used to calculate it.
Lens aberration is divided into several types.
Monochromatic aberrations
In a perfect optical system, the beam from each point on the object is also concentrated at one point at the output. In practice, this result is impossible to achieve: the beam, reaching the surface, is concentrated at different points. It is this phenomenon of aberration that causes the final image to become blurry. These distortions are present in any real optical system and it is impossible to get rid of them.
Chromatic aberration
This type of aberration is caused by the phenomenon of dispersion - light scattering. Different colors of the spectrum have different propagation speeds and degrees of refraction. Thus, the focal length turns out to be different for each color. This leads to the appearance of colored outlines or differently colored areas in the image.
The phenomenon of chromatic aberration can be reduced by using special achromatic lenses in optical instruments.
Spherical aberration
An ideal beam of light in which all rays pass through only one point is called homocentric.
With the phenomenon of spherical aberration, light rays passing at different distances from the optical axis cease to be homocentric. This phenomenon occurs even when the origin point is directly on the optical axis. Despite the fact that the rays travel symmetrically, distant rays are subject to stronger refraction, and the end point acquires non-uniform illumination.
The phenomenon of spherical aberration can be reduced by using a lens with an increased surface radius.
Distortion
The phenomenon of distortion (curvature) manifests itself in the discrepancy between the shape of the original object and its image. As a result, distorted contours of the object appear in the image. can be of two types: concavity of the contours or their convexity. With the phenomenon of combined distortion, the image may have a complex distortion pattern. This type of aberration is caused by the distance between the optical axis and the source.
The phenomenon of distortion can be corrected by special selection of lenses in the optical system. Graphic editors can be used to correct photographs.
Coma
If the light beam passes at an angle relative to the optical axis, then the phenomenon of coma is observed. The image of the point in this case has the appearance of a scattered spot, reminiscent of a comet, which explains the name of this type of aberration. When photographing, coma often appears when shooting at an open aperture.
This phenomenon can be corrected, as in the case of spherical aberrations or distortion, by selecting lenses, as well as by aperture - reducing the cross-section of the light beam using diaphragms.
Astigmatism
With this type of aberration, a point not located on the optical axis can take on the appearance of an oval or line in the image. This aberration is caused by different curvatures of the optical surface.
This phenomenon is corrected by selecting a special surface curvature and lens thickness.
These are the main aberrations characteristic of optical systems.
Chromosome aberrations
This type of aberration is manifested by mutations and rearrangements in the structure of chromosomes.
A chromosome is a structure in the cell nucleus responsible for transmitting hereditary information.
Chromosome aberrations usually occur during cell division. They are intrachromosomal and interchromosomal.
Types of aberrations:
The causes of chromosomal aberrations are as follows:
- the impact of pathogenic microorganisms - bacteria and viruses that penetrate the DNA structure;
- physical factors: radiation, ultraviolet, extreme temperatures, pressure, electromagnetic radiation, etc.;
- chemical compounds of artificial origin: solvents, pesticides, heavy metal salts, nitric oxide, etc.
Chromosomal aberrations lead to serious health consequences. The diseases they cause usually bear the names of the specialists who described them: Down syndrome, Shershevsky-Turner syndrome, Edwards syndrome, Klinefelter syndrome, Wolf-Hirschhorn syndrome and others.
Most often, diseases provoked by this type of aberration affect mental activity, skeletal structure, cardiovascular, digestive and nervous systems, and the reproductive function of the body.
The likelihood of these diseases occurring cannot always be predicted. However, already at the stage of perinatal development of the child, with the help of special studies, existing pathologies can be seen.
Aberration in entomology
Entomology is a branch of zoology that studies insects.
This type of aberration appears spontaneously. Usually it is expressed in a slight change in the body structure or color of insects. Most often, aberration is observed in Lepidoptera and Coleoptera.
The reasons for its occurrence are the influence of chromosomal or physical factors on insects at the stage preceding the imago (adult).
Thus, aberration is a phenomenon of deviation, distortion. This term appears in many scientific fields. It is most often used in relation to optical systems, medicine, astronomy and zoology.
