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The eye can be compared to a technical device designed to transmit images - a photo or film camera, a transmitting device of a television system.
Anatomically, the human eyeball is an almost regular sphere with a diameter of about 25 mm. It consists of three membranes - the outer fibrous, the middle vascular and the inner (retina), which surround the nucleus of the eye. It includes aqueous humor, lens and vitreous body.
In turn, the fibrous membrane consists of an opaque part - the sclera, covering most of the eyeball, and an anterior transparent part - the cornea. The cornea rises slightly above the level of the sphere of the eyeball, since its radius of curvature is smaller (about 8 mm) than the radius of the sclera (about 12 mm).
The choroid is divided into three parts: the largest in area, the choroid itself, lines approximately 2/3 of the sclera from the inside. In front, it passes into a thicker ciliary (ciliary) body, and even further anteriorly, at the level of the transition of the sclera into the cornea, into the iris. It represents lying in intraocular fluid a round membrane with a hole in the center - the pupil. The iris has two muscles, one of which dilates and the other constricts the pupil. Inner shell The eyeball - the retina - lines the entire choroid from the posterior pole of the eye to the ciliary body in the form of a thin film. It is the membrane on which the image is formed and converted into a nerve signal.
The cells in which light is converted into a nerve impulse are called photoreceptors. They come in two types: rods, which are sensitive to weak light and excite in low light; Cones, which are sensitive to changes in illumination at high levels, have high resolution and the ability to perceive color.
The rods are distributed throughout the periphery of the retina. In its central part, which occupies the posterior pole of the eyeball, there are cones. They fill a special zone of the retina - an oval measuring approximately 3x2 mm. This zone is called yellow spot. In its center there is a section with a diameter of 0.3 mm that is particularly sensitive to changes in illumination - the central fossa.
The fovea provides the ability to distinguish small details of visible objects, i.e. visual acuity. Visual acuity is measured in decimals 0.1; 0.2...1.0; 1.1; 1.2, etc. The norm corresponding to visual acuity 1.0 is taken to be such a discriminating ability of the eye that two points are visible as separate if the angle between the rays coming from them into the eye is equal to 1".
In this case, the rays from two points fall exactly on two cones, between which there is another cone (unexcited). Visual acuity can be much higher, and this depends on the conditions under which it is examined. But the hypothesis of two non-adjacent cones has not lost its force.
If the angle between the minimally distinguishable points is 2", then visual acuity is 0.5, if 10", then 0.1, etc. In other words, visual acuity is equal to the reciprocal of the maximum discrimination angle, expressed in minutes. Visual acuity is the main function of the eye, which is taken into account when choosing glasses.
The inside of the eyeball is filled with transparent intraocular media: the segment between the cornea and the iris (anterior chamber) is filled with aqueous humor. Directly behind the iris is the elastic. a dense lenticular formation - the lens. It is suspended from the ciliary body by a dense network of fibrous strands called the ciliary ligament. Most of The eyeball, located behind the lens, is filled with a gelatinous mass - the vitreous body.
The cornea, aqueous humor, lens and vitreous body are light-refracting media. Together they form the optical system of the eye.
The most successful description of the optical system of the average normal human eye belongs to the Swedish optician Gullstrand.
F1 - front main focus; F2 - rear main focus; f1 - front focal length; f2 - back focal length; H1 and H2—anterior and posterior main planes; fvp is the anterior apical (i.e., measured from the apex of the cornea) focal length; fvz - back vertex focal length
More offered simple circuits optical system of the eye, in which there is only one refractive surface - the anterior surface of the cornea - and one medium - the averaged intraocular substance. The indicators of the reduced eye were calculated by the Soviet ophthalmologist V.K. Verbitsky. Its main characteristics: the main plane touches the apex of the cornea, the radius of curvature of the cornea is 6.82 mm, the length of the anteroposterior axis is 23.4 mm, the refractive index of the intraocular medium is 1.4, the total refractive power of the eye is 58.82 diopters.
All these characteristics apply to the middle eye. In reality they vary considerably. Thus, the refractive power of the cornea ranges from 38-46 diopters, the lens - 15-23 diopters, the total refractive power of the eye - 52-71 diopters, the length of the eye axis - 19-30 mm.
As already mentioned, the eye can be compared to a device for transmitting images, for example, a television transmitting camera - a vidicon.
Like technical optical cameras, the eye is equipped with a device for pointing the lens at an object - the oculomotor apparatus - and regulating the sharpness of images of objects located at different distances - the accommodation apparatus.
Oculomotor apparatus includes the external muscles of the eye - 6 muscles in each eye: internal, external, superior and inferior rectus, superior and inferior oblique. Thanks to their coordinated work, the eye constantly makes searching movements and, when a new object appears in the field of view that attracts attention, it makes a turn (jump) so that the image of this object falls on the central fovea.
Reduced eyes- found in forms leading a parasitic or underground lifestyle, living in caves and at great depths where light does not penetrate, and in general in similar conditions. Sometimes on a number of closely related species, for example. marine crustacean Cymonomus, one can trace the gradual reduction of the eyes depending on the depth of habitat of this species. Among the vertebrates, R. eyes are represented to us by cyclostome fish and some cave fish, which lead a semi-parasitic lifestyle. Between the cyclostomes of the lamprey larva - Ammocoetes, the eye lies under the skin and is devoid of sclerosis and cornea, so that the muscles that move the eye are attached to a poorly developed choroid. The lens, which retains the embryonic cavity inside in the adult lamprey, fills a huge part of the posterior chamber, and in front lies the semilunar body, which is considered as a local thickening of the Descemetian membrane (membrana Descemetii), lining the posterior surface of the cornea in a fully developed eye. In an adult lamprey, the skin above the eye becomes transparent and the animal begins to see. In Myxine, which often penetrates into internal organs owner, there is no longer a lens, no iris, no eye muscles, and the choroidal fissure remains throughout life, so that the eye is essentially represented by one primary vesicle. In cave forms, the main parts of the eye are formed, i.e., both the primary vesicle and the secondary one, i.e., the lens, and both of these rudiments undergo simplification to varying degrees in various forms. Among teleosts, in Amblyopsis, in which the degeneration proceeds further than in others, the lens disappears completely, the vitreous body does not develop, and likewise the primary vesicle, which has completely lost connection with the brain, is preserved only in the form of a rudimentary organ without a cavity inside and with a closed pupil. The sclerosis and some muscles are developed. Other forms may lack sclerosis and muscles, but retain other parts. In general, considerable diversity is observed in this regard (Eigenmann, 1899 and 1902). Among the amphibians leading an underground lifestyle, the legless Grymnophiona and some cave forms present varying degrees of eye reduction. The eyes of Proteus reach a great degree of simplification and see Typhlomolge (Eigenmann, 1900) to an even greater degree. Their eye lies under the skin and is a primary vesicle with a small amount connective tissue, representing the vitreous body, and with a connective tissue membrane around, representing the vascular and protein membrane. There is no iris, no lens, no eye muscles. The layers of the retina are also reduced and, by the degree of simplification, represent significant individual variations. Among reptiles, some snakes (Typhlopidae) have an underground lifestyle; among mammals, the mole's eye lies under the skin and not in the socket, is small in size, and also has some minor, albeit reduced, features in its structure. In one species (Talpa coeca) the eyelids are fused, while in another (T. europaea) such fusion occurs only occasionally. Also very small are the eyes (and in some species the eyelids are also fused) in mole rats (Spalax) from rodents. The same is observed in the Madagascan mole Chrysochloris, the cetacean Platanista, etc. Although the connection between the reduction of the eyes and the way of life is very clear, however, it would be too hasty to conclude that the latter is the direct cause of the reduction. In relation to cave animals, Hamann (1896) comes to the conclusion that their eyes disappeared not at all because they live in the dark, but only depending on this condition the eyes could disappear without harm to the species. It is even possible that in some forms the eyes disappeared even when they lived on the surface of the earth. Exactly the same reasoning can be applied to deep-sea forms. Their eyes were reduced not because they live at such a depth where light rays do not penetrate, but only depending on this condition. The reason for the reduction, as in the cave forms, probably lay within the body. Apparently, with the onset of conditions under which the eyes turn out to be redundant, they become outside the influence of selection that supports the organ at a certain level and the principle of panmixia (q.v.) comes into play, i.e., indifferent crossing and experience of forms as tending to normal or even the progressive state of the organ, and those with a tendency to regress the organ, and the result is a weakening of the organ, accompanied by strong individual fluctuations in the degree of its development.
on the topic of:
“Reduced eye. Refractive and optical power. Determining focal length"
Completed by: Kilmyamyatov Denis
Saransk 2013
Reduced eye
There are several schemes for a reduced eye.
We present data from the reduced eye according to Verbitsky, which is closest to the data from the eye according to Gulstrand. In a reduced eye there is only one refractive surface, the cornea, and the entire eye is filled with a homogeneous medium with one refractive index nr. That is why both nodal points stick together into one, coinciding with the center of curvature of the cornea. The main planes also merge into one, and one main point coincides with the apex of the cornea.
Constructing an image for a reduced eye
Constructing an image in a reduced eye
simplified by the fact that we obtain point B" by simply drawing a straight line through points B and N. For y" and we obtain formulas similar to formulas (10) and (11); but the segment l" can now be given a certain meaning. From Table 2 it is clear that the value calculated above l" = 16.6 mm is close in the reduced eye to the front focal length f, taken with the opposite sign. There is some difference (0.4 mm), but, as we will now see, it is not accidental. According to the laws of geometric optics, the paraxial image of point A should be formed on the axis of the system at a point lying at a distance f" from the second main point. In a reduced eye, the second main point coincides with the first and lies at the apex of the cornea. The distance f" must be measured from it. But f" = 23.8 mm, and the entire length of the eye is 23.4. This means that the paraxial image of point A is behind the retina, just 0.4 mm further than the retina. One might think that some mistake was made in the construction of the reduced eye The point, however, is that in our reasoning we emphasized twice that we are considering paraxial rays, that is, rays passing close to the axis of the system. Only they, passing parallel to the axis of the system, converge at the main focus. from the axis, converge closer than the focus due to spherical aberration. Therefore, the clearest image is obtained not in the focal plane, but somewhat closer - in the plane of best focusing, near which point A lies on the retina.
Thus, the difference between l and |f| lies within the limits of the error that we allow when replacing wide beam optics with a paraxial approximation. Therefore, formulas (10) and (11) can be replaced by formulas
y" = αf (12)
βy = -f/l (13)
When the object approaches the eye, i.e., when the absolute value of l decreases significantly, formulas (12) and (13) can no longer be applied. Retention of the image on the retina is possible only by increasing the optical power, or, as it is also called, the refraction of the eye F. In the real eye, this is accomplished by increasing the curvature of the surfaces of the lens. Let us denote the accommodative addition to the refraction of the eye
▲F = l/|l| (14)
Formally, ▲F = 0 only for |l| = ∞. In fact, accommodation can be neglected already for |l| ≥ 5 m, i.e. neglect the imputation of the eye refraction by 0.2 diopters. In a reduced eye, accommodation is taken into account by a formal method: according to Verbitsky, for each diopter of additional refraction, the refractive index of the ocular medium must be increased by 0.004, and the radius of curvature of the cornea must be decreased by 0.04 mm. Let, for example, l = - 25 cm, i.e. |l| = 0.25 m, and ▲F = 4 diopters. Wherein
n"r = 1.40 + 4 0.004 = 1.416;
r" = 6.8 - 4 0.04 = 6.64 mm.
Since there is only one refractive surface in the reduced eye, we can use the formula derived for this case
where the distances from the top of the cornea to the object and to its image are designated l and l"r, respectively. Since
Substituting the magnitude values for F = 4 diopters into formulas (16) and (18), we obtain f"= 22.60 mm and l"r = 24.1 mm. Let us introduce the value ▲l, the change of which characterizes the displacement of the image during accommodation: ▲l = l"r - lr, where lr is the length of the eye according to Verbitsky. With ▲F = 4 diopters ▲l = 0.7 mm, which is noticeably greater than with rest of accommodation, when ▲l = 0.4 mm, i.e., the image is shifted by 0.3 mm. Thus, the method proposed by Verbitsky for taking into account accommodation, although of considerable complexity, gives low calculation accuracy. To take into account accommodation, a simpler method can be assumed, which. provides, in addition, a significantly smaller change ▲l: when increasing accommodation by one diopter, reduce the radius of the cornea by 0.1 mm, and keep the refractive index constant and equal to 1.40, i.e. in formulas (15) - (18) consider n"r = nr = 1.40. The result of this calculation of the difference ▲l using formulas (16) and (18) is given in table. 3.
Accommodation of the reduced eye
It can be seen that ▲l changes only within 0.1 mm, and not 0.3 mm, as calculated by Verbitsky.
Aberrations of the eye
Like any optical system, the eye has inherent aberrations. We have already mentioned one of them - spherical aberration. Now we should say a little more about aberrations of the eye.
Aberrations of any system, giving an image, are called distortions that lead to the fact that the image turns out to be not quite similar to the geometric projection of an object onto a plane (or a surface of another shape) and that each point of the object is depicted not as a point, but as a spot with a rather complex distribution of brightness in it.
On the system axis there are observed spherical and chromatic aberration. The spherical aberration diagram is shown in Fig.:
Spherical aberration diagram
The farther a ray parallel to it passes from the axis, the closer to the lens it intersects the axis. The rays farthest from the axis will pass from it at a distance h = D/2, where D is the diameter of the beam entering the lens, and will converge at point Ah, lying at a distance ▲f" from point A - the focus of the paraxial rays. The segment ▲f" is called longitudinal spherical aberration, expressed in units of length.
However, usually longitudinal spherical aberration expressed in diopters and calculated using the formula
Here the length of the segments must be taken in meters. If ▲f" ≪ f", the formula can be simplified:
Refractive index nr depends on the wavelength of light. Therefore, if white light falls on a lens, the rays different colors will gather in different places: the purple ones will gather closest to the lens. In any place, instead of a white dot, you will get a spot, and, moreover, not white, but colored. Again, you can carry out a calculation similar to the calculation using formula (19) and obtain the value of chromatic aberration Axp.
For any point that does not lie on the axis of the system, other aberrations must be taken into account. The rays lying in the meridional plane are collected into a straight segment at the same distance from the lens, and the rays lying in the sagittal plane (and the plane passing through the beam axis and perpendicular to the meridional plane) are collected into a segment at a different distance from the lens, perpendicular to the first segment . In any place, the image of a point is obtained in the form of a blurry asymmetrical spot. This aberration is called astigmatism of oblique beams.
On some surface this blurring is least, and this is where the screen should be placed to get the clearest image. As a rule, such a surface is not flat, which is very inconvenient in many cases, for example for photography, where the surface of the frame should be flat. The deviation of the best focusing surface from the plane is called field curvature.
There are also aberrations that distort the shape of the entire image. The most important of them is distortion- change in magnification with distance from the optical axis of the system.
What are the aberrations of the eye?? According to Ivanov, with a 4 mm pupil, the spherical aberration of the eye is Asf = 1 diopter. Chromatic aberration has the same meaning. Is it a lot or a little? Since the refraction of the eye is about 60 diopters, relative error the refraction of the eye is less than two percent.
More precisely, aberrations are assessed by the degree of their influence on the resolving power of the eye or, as it is usually called, on visual acuity. Visual acuity V is inversely proportional to the angular resolution limit:
V= l/δ; (21)
δ is usually expressed in minutes. V is a dimensionless quantity.
Doctors usually consider V = 1 as the norm. In reality, V depends on many conditions, primarily on the background brightness l.
The diameter of the pupil also depends on various factors, even on a person’s emotions. But still, basically the diameter of the pupil dr depends on the brightness. On average, this dependence is expressed by the formula
where th is the hyperbolic tangent; dr - obtained in millimeters.
We will talk in detail about visual acuity later. Now let's just say that at brightness L = 20 cd/m2 dr = 3.7 mm and δ = 0.64". If we turn to the diffraction formula (3) and calculate δ at d = 0.37 cm, then, translating radians per minute (l" = 2.91 10-4), we get almost the same value δ = 0.63. Thus, in fact, visual acuity is limited not by aberrations, but by diffraction. This is precisely the requirement that is placed on modern, well-corrected lenses: their resolving power, at least in the center of the field of view, must be diffractive. Further correction of aberrations no longer helps to increase the resolving power.
Chromatic aberration, approximately equal to the spherical one, seems to be more dangerous: it gives not just a scattering spot, but a colored spot. However, in Everyday life we never notice colored borders around visible objects. They can only be detected in specially designed experiments. Chromatic aberration can be easily corrected by placing a lens in front of the eye with chromatic aberration of the opposite sign. Experiments with lenses of this kind have been carried out repeatedly. However, their use practically did not change either the visual acuity of the eye or the appearance of objects in the field of view. Attempts have been made to correct the spherical aberration of the eye with lenses. And in this case, no improvement in visual acuity was observed.
It should be noted that if we calculate the path of rays in a schematic eye according to Gullstrand, we obtain a spherical aberration that exceeds that observed in a real eye. This is explained by the fact that Gulstrand considered the radius of curvature of the cornea to be constant, but in reality in the peripheral zone of the cornea the radius of curvature is greater than in the central zone. Increasing the radius leads to a decrease in refractive power, i.e., to increase the focal length [see. formula (16)] and, consequently, to bringing the focus of the extreme rays closer to the focus of the paraxial rays. In recent times, lenses with aspherical surfaces have begun to be used in technology, although their precise manufacturing is fraught with great difficulties.
Thus, optical system the eyes are corrected well enough to take full advantage of all the possibilities afforded by the wave nature of light.
Refraction in the eye
The eye is the optical equivalent of a conventional photographic camera. It has a lens system, an aperture system (pupil) and a retina on which the image is captured.
The lens system of the eye is formed from four refractive media: the cornea, the aqueous chamber, the lens, and the glass body. Their refractive indices do not differ significantly. Οʜᴎ are 1.38 for the cornea, 1.33 for the aqueous chamber, 1.40 for the lens and 1.34 for vitreous(Fig. 2).
Rice. 2. The eye as a system of refractive media (numbers are refractive indices)
Light is refracted in these four refractive surfaces: 1) between the air and the anterior surface of the cornea; 2) between back surface cornea and water chamber; 3) between the water chamber and the anterior surface of the lens; 4) between the posterior surface of the lens and the vitreous body.
The strongest refraction occurs on the anterior surface of the cornea. The cornea has a small radius of curvature, and the refractive index of the cornea differs most from the refractive index of air.
The refractive power of the lens is less than that of the cornea. It accounts for about one-third of the total refractive power of the eye's lens systems. The reason for this difference is that the fluids surrounding the lens have refractive indices that are not significantly different from the refractive index of the lens. If the lens is removed from the eye, surrounded by air, it has a refractive index almost six times greater than in the eye.
The lens performs very important function. Its curvature can be changed, which provides fine focusing on objects located at different distances from the eye.
A reduced eye is a simplified model of a real eye. It schematically represents the optical system of a normal human eye. The reduced eye is represented by a single lens (one refractive medium). In a reduced eye, all the refractive surfaces of the real eye are summed up algebraically, forming a single refractive surface.
The reduced eye allows for simple calculations. The total refractive power of the media is almost 59 diopters when the lens is accommodated for vision of distant objects. The central point of the reduced eye lies 17 millimeters in front of the retina. A ray from any point on the object enters the reduced eye and passes through the central point without refraction. Just as a glass lens forms an image on a piece of paper, the lens system of the eye forms an image on the retina. This is a reduced, real, inverted image of an object. The brain forms the perception of an object in an upright position and in real size.
The structure of the eye is optically equivalent a regular camera. It has a lens system, a variable aperture system (pupil), and a retina that matches photographic film.
Own index refraction of air is 1, cornea - 1.38, aqueous humor - 1.33, lens (on average) - 1.4 and vitreous - 1.34.
Reduced eye. If we algebraically add up all the refractive surfaces of the eye and consider them as one lens, the optics of the eye can be simplified and schematically represented as a reduced eye (this is useful for simplifying calculations). It is believed that in the reduced eye there is one refractive surface, its central point is located at a distance of 17 mm in front of the retina, and the total refractive power is 59 diopters, provided that the lens accommodates gaze at a far distance.
Approximately 2/3 of 59 diopters total refractive power of the eye falls on the anterior surface of the cornea (not the lens of the eye). This is because the refractive index of the cornea is significantly different from that of air, while the refractive index of the lens is not very different from the indices for aqueous humor and vitreous humor.
General refractive power of the eye lens, when it is normally located in the eye and surrounded on all sides by liquid, is only 20 diopters, i.e. it accounts for approximately 1/3 of the total refractive power of the eye. But the significance of the lens is that, under the influence of nervous regulation, its curvature can increase significantly, providing accommodation, which is discussed later in this chapter.
Formation of an image on the retina. Just as a glass lens focuses an image on a piece of paper, the optical system of the eye focuses an image on the retina. Although the image of an object on the retina is inverted, our mind perceives the object correctly because the brain is “trained” to view the inverted image as normal.
In children refractive power of the lens eyes can increase from 20 diopters to 34 diopters, i.e. accommodation is approximately 14 diopters. This occurs as a result of a change in the shape of the lens from a moderately convex lens to a very convex lens. The mechanism of accommodation is as follows.
In a young man lens consists of a durable elastic capsule filled with a viscous protein but transparent liquid. If the capsule is not stretched, the lens has an almost spherical shape. However, there are about 70 suspensory ligaments arranged radially around the lens, which pull the edges of the lens toward the outer orbit of the eyeball. These ligaments are attached to the anterior border choroid and the retina of the eye and are constantly stretched. Tension of the ligaments leads to the fact that when normal conditions the lens remains relatively flat.
However, in place attachment of ligaments to eyeball There is a ciliary muscle containing two separate sets of smooth muscle fibers - meridional and circular. Meridian fibers run from the peripheral ends of the suspensory ligaments to the junction of the cornea and sclera. With the contraction of these muscle fibers, the peripheral sections of the lens ligaments at the site of their attachment shift in the medial direction, to the edges of the cornea, while the degree of their tension decreases and the lens is freed from their traction.
Circular fibers are located around the place of attachment of the ligaments, and when they contract, a sphincter-like action is carried out, reducing the diameter of the circle around the perimeter of which the ligaments are attached; this also leads to a release of ligament tension and release of the lens capsule.
Thus, reduction of any set smooth muscle fibers of the ciliary muscle reduce the tension of the ligaments and, consequently, the capsule of the lens, the shape of which, due to its natural elasticity, approaches spherical.
Accommodation regulated by parasympathetic nerves. The ciliary muscle is almost entirely regulated by signals from the parasympathetic nerves transmitted to the eye along the III pair cranial nerve from its nucleus in the brain stem. Stimulation of these nerves leads to contraction of both sets of ciliary muscle fibers, which relieves the tension of the ligaments, as a result of which the lens becomes thicker and its refractive power increases. This allows the eye to focus closer objects than with lower refractive power. Therefore, to continuously focus an object clearly as it approaches the eye, the number of parasympathetic impulses arriving at the ciliary muscle must gradually increase.
