Frank Allen, M.A., Ph.D., LL.D, F.R.S.C.
Professor Emeritus in Physics
University of Manitoba, Winnipeg, Canada
"Sturmius, says Paley, held that the examination of the eye was a cure for atheism'. Yet Helmholtz, who knew incomparably more about the eye than half a dozen Sturms, describes it as an instrument that a scientific optician would be ashamed to make; and Helinholtz was no atheist."
This quotation from Professor Ward's Gifford Lectures1 is a reference to the celebrated popular lecture2 of Helmholtz on vision. In view of the commanding influence on visual science which he has exerted for over ninety years since the beginning of the publication of his Handbuch der Physiologischen Optik (1856-66), his views on the characteristics of the eye as an optical instrument carry great weight. The importance of this subject from several standpoints has led the writer to assemble the latest measurements on the defects of the eye, as well as all the statements of scientific men of unquestioned authority in this field of enquiry that he could find.
First of all, the words of Holmholtz himself are given so that there may be no doubt as to what he did say.
"Now it is not too much to say that if an optician wanted to sell me an instrument which had all these defects, I should think myself quite justified in blaming his carelessness in the strongest terms, and giving him back his instrument. Of course, I shall not do this with my eyes, and shall be only too glad to keep them as long as I can--defects and all. Still, the fact that, however bad they may be, I can get no others, does not at all diminish their defects, so long as I can maintain the narrow but indisputable position of a critic on purely optical grounds .... All these imperfections would be exceedingly troublesome in an artificial camera and in the photographic picture it produced. But they are not so in the eye--so little, indeed, that it was difficult to discover some of these .... The chief reason (for not observing the defects) is that we are continually moving the eye, and also that the imperfections almost always affect those parts of the field to which we are not at the moment directing our attontion ....For the eye has every possible defect that can be found in an optical instrument, and even some which arc peculiar to itself but they are all so counteracted, that the inexactness of the image which results from their presence very little exceeds, under ordinary circumstances of illumination, the limits which are set to the delicacy of sensation by the dimensions of the retinal cones .... The adaptation of the eye to its function is, therefore, most complete, and is seen in the very limits which are set to its defects .... Tho defects which result from the inexactness of vision and the smaller number of cones in the greater part of the retina are compensated by the rapidity with which we can turn the eye to one point after another of the field of vision, and it is this rapidity of movement which really constitutes the chief advantage of th eye over other optical instruments."
The defects of the eye, which are set forth so prominently in this discussion, should be reviewed in the light of the most recent knowledge of visual optics which has been assembled both by Duke-Elder3 in his exhaustive treatise on ophthalmology, and also by Hartridge4 in his recent investigation of the visual perception of fine detail. For no optical instrument has been examined so minutely, critically and accurately as the eye, by men of the highest genius such as Helmholtz, Gullstrand and Tscherning.
In the optical system of an instrument, such as the microscope or a telescope, the surfaces of the lenses should be perfectly spherical and they should be centered upon a common optical axis. The mathematical theory of such a dioptric system, as originally developed by Gauss, demands, in addition, that it should be of small aperture, not more than 100°, so that the rays of light are limited to the axial regions, of homogeneous media, and that monochromatic light should meet the refracting surfaces nearly at right angles. It is with such an ideal system that all practical optical instruments are compared.
Because of the nature of light and its mode of propagation, as well as the nature of the refracting media which form the image of an object, all optical systems are subject to many aberrations. Those defects must in some way be overcome or minimized or the image will be more or less imperfect. The method of optical correction is to use combinations of several lenses of different refractive powers and curvatures. In the microscope, an achromatic object glass, which forms.the image, is composed of as many as six lenses, and an apochromatic object glass may have ten. These lenses must be made of carefully selected glass with accurately figured surfaces, and adjusted to each other with extreme precision. The focal length is quite small. So perfect can the image be made, that magnifications of more than 1500 diameters are possible. They operate at a fixed distance from the object under observation, and the field of view is extremely small. In addition to the object glass there is the eyepiece with which the image is magnified and viewed. All the lenses are immersed in air so that the numerous surfaces have abrupt discontinuity with that medium. The telescope has fewer lenses, but the focal length is relatively large which minimizes or eliminates the most troublesome defects.
Compared with such complicated optical instruction, the human eye is rudimentary. The refracting system consists of the cornea, the aqueous humor, the lens and the vitreous humor or body. The lens, therefore, is immersed in the humors and not in air, which greatly minimizes the optical discontinuities. The indices of refraction of the two humors are practically the same (1.336), which differs but little from that of water (1.334). The lens is extraordinary in constitution since it consists of many layers or zones which vary in refractive index from 1.386 at the surfaces to 1.406 at the canter. The cornea and aqueous humor taken together, form the major refracting medium of the eye, and the lens, by its power of accomodation, operates as the fine adjusting mechanism. The cornea-aqueous combination is about 2.5 times greater in refracting power than the lens, which is due to the relatively great difference in refractive index between the air (1.00) and the cornea (1.376), as compared with (refractive index) between the humors (1.336) and the surface of the lens (1.386). The rays of light are first refracted at the cornea and aqueous humor, second by the anterior zones of the lens, then by the core, and further by the posterior zones. In. consequence of its structure, the lens has a greater refracting power if it were homogeneous with a refractive index equal to that of the core. Besides increasing the refractive power considerably, this arrangement diminishes the spherical aberration.
The fact of its decontration constitutes the main feature of the optical system of the eye. Strictly the cornea has no axis of symmetry, though the deviation is extremely small. The centering of the cornea and the two surfaces of the lens is never exact, nor are the various zones of the lens concentric with one another, and the lens itself is not concentrically placed upon the optic axis. The visual axis, which touches the fovea, makes an angle of about 5° with the optic axis upon which all refracting surfaces should ideally be centered. Vision therefore occurs obliquely through the system. "It is," remarks Duke-Elder, "as if one of the lenses of an optical instrument had slipped a little out of place and then when we looked through the instrument we tilted it very slightly. The deviations, however, are usually so small as to be functionally negligible, and they tend to some extent to minimize the aberrations of the eye."
It would seem, therefore, that the construction of the eye slightly violates all the conventions that apply to optical instruments. But the final result, nevertheless, is the formation of an improved image, as free from perceptible defects as those produced by the finest artificial systems.
The defects of dioptric systems, whether of glass or of the eye, comprise two main classes: first, aberrations originating from the composite nature of white light, termed chromatic aberration, and those arising from the structure of light and the manner of its propagation, called diffraction; second, monochromatic aberrations, or defects oeeuring with rays of light of a single wavelength; spherical aberration, the sine condition, refraction of eccentric rays, curvature and distortion of the image, and depth of focus, which is not a defect but a property of a lens.
The defects of the first group depend on the nature of light; those of the second group on the structure of the optical instrument.
The discovery of the spectrum by Newton (1664) established the composite nature of white light and the different refrangibilities of the colors. From these discoveries he erroneously concluded that an achromatic combination of lenses was impossible to devise. Apparently he gave no thought to the construction of the eye. As no chromatic aberration had ever been observed in it, Euler (1750), convinced that it was achromatic, stimulated the eminent optician Dollend (1758) to construct achromatic systems of lenses, such as telescopes, in which he was highly successful. He also discovered the chromatic aberration of the eye.
Since white light is a mixture of many different wavelengths and as a lens has the nature of a series of prisms, the real image of a disc of white light formed by a convex lens consists of a superimposed series of images of all colors of the spectrum focused at slightly different distances from the lens. The violet image, formed by the most refrangible rays, is nearest the lens, and the red image the most remote. The chromatic difference of focus is very small, being from red to violet, about 0.47 mm. (Hartridge). Since the eye accommodates itself to the brightest yellow-green rays, the difference of focus is normally about half the amount for violet in front of the retina, and half for red, as it were, behind it. The separate color images or aberration discs are also of different sizes, termed the chromatic difference in magnification, varying, according to Hartridge, for the usual entrance pupil of 4 mm. diameter for the eye, from 0.0216 mm. in diameter for orange light to 0.0588 mm. for blue, the latter being 2.7 times the former. In ordinary vision these defects are extremely small, and since the blue image completely overlaps the red, it neutralizes that color into white leaving a narrow blue border which, because of its low luminosity, is practically invisible. The whole effect of chromatic difference in magnification tends to counteract the chromatic difference of focus. In the eye the effects of chromatic aberration are small; and with a 2 mm. diameter pupil, as Duke-Elder remarks, 70 per cent of the light falls on a retinal area of 0.005 mm. diameter. The remaining light is more widely diffused and normally is therefore unnoticed, so that images are free from colored borders, as common observation shows.
Diffraction is due to the spreading of the waves of light at the edges of the wave front. The effect is the opposite of chromatic aberration since it is greatest with the longest waves, the red, and least with the shortest, the violet. It follows from the nature of light that a point of white light is always brought to a focus as a small blurred disc (Airy's disc) of light and dark bands with a bright spot in the center. No point image can therefore be formed but only a diffraction pattern, which varies in dimensions directly as the focal length of the system and the wavelength of light, and inversely as the aperture, or area of the pupil, through which the light passes. Diffraction is inherent in the nature of light and its propagation and cannot be overcome. In optical instruments, such as the microscope, its effects are not troublesome except at very high magnifications about 2000 diameters, when the image itself becomes a complicated set of diffraction patterns.
The central bright spot of the diffraction pattern of a point source receives
about 84 per cent of the incident light; the first ring 1/57th and the second
1/240th of the intensity of the central area. At a distance of only 0.02 nun.
from the center, the light is of too low an intensity to be seen. Since the
eye has a very short focal length of 22.78 mm., the diffraction effects with
a pupil 4 mm. in diameter are correspondingly small.
Comparison of the figures for chromatic aberration and diffraction shows that they have the same order of magnitude, and are much too slight to be observed in the ordinary usage of the eyes. It is to be noted that the effects of chromatic aberration increase as the pupil widens; but as this condition changes act together to leave the actual definition of the image practically unchanged with alterations of the pupil. As pupillary areas are governed by the illumination, the definition of the image is therefore the same with all intensities of light.
Those are the characteristics of the images of point sources. But "the extended source", according to Hartridgc, "differs from the point source in an important respect, namely, that its image is largely composed of white light, and that color fringes are only found near its margins. Each of the fringes for a 4 mm. pupil is about 0.01 mm. wide. Only parts near the edge are strongly colored, and that as the distance from the edge increased the yellow fringes become progressively whiter and the blue fringe progressivcy blacker, until the yellow fringe merges imperceptibly with the white interior of the image, and the blue fringe merges similarly with the black background."
The mathematical theory of optical systems of lenses demands a very small aperture so that the rays are limited to the axial regions. In optical instruments an aperture of 100 is considered to be the maximum compatible with efficiency. It is with this aperture that sueh instruments are designed to eliminate chromatic aberration and other defects. But the pupil of the eye is rarely less than 4 mm. in diameter which corresponds to an aperture at the cornea of 200. With a double size of aperture, therefore, the eye is equally free from aberrations, while optical instru raonts with such wide apertures would probably be useless.
Spherical aberration In a biconvex spherical lens the peripheral or marginal rays are refracted more than the axial, so that the former come to a focus nearer the lens than the latter. This effect is called spherical aberration. It can be eliminated by grinding the lens so that its curvature decreases from the center to the periphery. Such lenses are termed aplanatic. Spherical aberration is diminished by making the curvature of the anterior surface of the lens, where the light enters, greater than that of the posterior surface. In the eye the lens has the opposite orientation since the anterior surface has a smaller curvature than the posterior.
With a glass lens of refractive index 1.5, immersed in air, the ratio of curvatures to give maximum spherical aberration is 1;6. With the lens of the eye, assuming an equivalent refractive index of 1.43, the ratio of curvatures would be 1:4, if surrounded by air. Actually the ratio is 1:1.7. The small degree of spherical aberration which the eye exhibits therefore indicates that the theory of glass lenses doos not apply, in this regard to a lens of variable refractive index like the eye, when immersed in media of nearly the same index of refraction.The chief corrective of spherical aberration is the pupil which shuts out the peripheral rays of light and admits the axial and those near it. The brighter the light, the more noticeable would be the aberration; but with greater illumination the smallr becomes the pupil, and the more axial become the rays admitted. "Although the eye does not form an aplanatic systom", remarks DukeElder, "the effects or spherical aberration are small - much smaller than the effects of either diffraction or chromatic abcrraticn. This is do partly to the fact that the cornea is flatter in the periphery than in the canter, but more largely to the fact that the lens core is more highly refractive than the periphery. Both these circinstances cause the axial rays to be refracted more strongly than the peripheral ones, a tendency which counteracts the effect of spherical aberration .... Regarding the eye as a whole, the axial ara is usually under-corrected and shows a positive aberration, while the periphery is usually negative."
Th Sine Condition. It is clear, therefore, that, by means of the automatic adjustable aperture of the pupil, as well as by other devices peculiar to the eye itself which are not available in any optical instrument, spherical aberration in the eye is reduced to such a small amount that no perceptible blurring occurs in the visual image.
Even though a lens system is desinod to produce an image of a point free from spherical aberration, a wide pencil of light does not necessarily give a clear image of the area surrounding the point. Different zones of the lens may bring light from various parts of the object to different positions, so that the image is drawn out like the punctuation mark, the comma, the tail of which points to the optic axis. To prevent this from occurring, a certain mathematical condition must exist relative to the object in air and its image at the back of the vitreous body on the retina;namely, the product of the refractive index of air, the size of the object and the sine of the angle of divergence of the rays of light from it to the eye, must be equal to the product of the refractive index of the vitreous body, the size of the image and the sine of the angle of convergence of the rays forming it. This relationship is called the sine condition. "The eye," states Duke-Elder, "appears to obey the sine condition almost exactly, so that as far as comma is concerned the displacement of the fovea to the side of the optic axis is no disadvantage.
Refraction of Eccentric Rays Since the eye is a decentred optical system, the pupillary line and the optic axis do not coincide, but differ in position by an angle of 5°. The so-called determining ray to the foveais therefore somewhat peripheral or eccentric, and consequently suffers a little radial astigmatism. The determining rays are brought to a focus sooner than the equatorial rays which tend to interfere somewhat with visual acuity. The amount of the defect is only about oneeighteenth of the chromatic aberration, and still less of the spherical aberration; and is therefore of no significance in vision.
Curvature of the Field. It is a characteristic of a spherical lens to form a curved image on aiTbjoct. On a plane surface the whole of the image cannot be in focus at once. The curvature of the field, as it is called, is corrected by having a curved image-plane. In the eye the retina is such a curved screen. Since its radius of about 10 mm. is shorter than the posterior focal distance (22.78 mm.) of the optical system, "it satisfies very losaly the theoretical curvature for complete correction.
The image of an object formed by a lens is also subject to two kinds of distortion; one, in which straight lines crossing one another at right angles arc either curved outwards, barrel-shaped, or inwards in the opposite direction in the image. At the same time the image is respectively diminished or enlarged in size compared with its normal area. The magnification of the ends of an object is also different from that of the middle. "Peripheral distortion of the image is almost theoretically corrected in the same way as curvature of the field," that is, but suitable curvature of U.-v. retina (Duke-Elder).Depth of Focus. If several objects are at different distances from an optical system, their images will be formed at different distances also, so that if one is in facus the others will be slightly out of focus. The greatest distance of the objects from one to another, still having their images satisfactorily focused, is called the depth of focus. In other words, the greatest distance through which an object can be moved and still produce a satisfactory image without change of accommodation, is the depth of focus.
In the case of the eye, Hartridge has shown that with a pupil 3 mm. in diameter
and with the eye focused for 24 meters, objects both at infinity and 12 meters will
still be in focus at the same time. But if the eye is working at 25 cm., the normal reading distance, the depth of focus is reduced to 1.1 cm. As the pupil contracts during accommodation, the depth of focus increases. With bright light, a pupillary diameter of 2 mm. the depth becomes 3.2 cm. This property, therefore, relieves the
strain of accommodation.
Loss of Light In traversing the optical structures of the eye, light is reflected at all surfaces of sufficient discontinuity to do so. By this process a considerable quantity of light is deflected from the main dioptric path. There are six principal surfaces in the eye at which light may be reflected: the anterior and posterior surfaces of the cornea, the anterior and posterior surfaces of the lens and the surfaces between the zones of optical discontinuity within the lens. At each of them an image formed by reflected light can, by suitable means, be observed. But for four of the chief six images, the light forming them travels out of the eye and is lost. In the case of two, the light reaches the retina and tends to diminish the optical efficiency of the eye. In the case of microscope objectives there may be from 12 to 20 surfaces of such discontinuity where loss of light occurs. "The eye, however, says Duke-Elder, "sets a higher standard in this respect than most optical instruments, for the whole of the light thus lost does not equal 2 per cent." The loss of light is negligible in quantity since the refractive indices of the ocular media are so closely related, the lens being immersed in a medium of approximately the same index as itself. That of the humors of the eye is 1.336, and the refractive index of the outer layers of the lens is 1.386, so that the difference between thorn is extremely small; while in optical instruments the difference in refractive index between glass, 1.5, and air 1.0, is ten times larger.
Scattered Light There is considerable scattered light reflected from the retina by which the tis can be ophthalmologically examined. But very little of it confuses the retinal image. The shape of the fundus causes the reflected light to pass out at the pupil or to strike the insensitive anterior portion of the retina. The eye is also protected from oblique illumination by the nose arid eyebrows, and the scattered light is effectively absorbed by the retinal pigment.
Halation "Halation would appear to be of negligible amount. The term applies to the reflection of light back to the sensitive surface from other surfaces immediately above it; but the reflecting layer of the retina is so close to the rods and cones that this disturbance can be of little moment."
The defects which are recognized by ophthalmologists can all be detected by careful and expert examination. But by the vast majority of humanity they are never noticed, and they have no influence on the normal visual properties of the eye. Because they exist they can be referred to as defects, as the quotation from Helntholtz shows. But to exaggerate thorn grossly into an instrument that an optician would be ashamed to make, is to magnify them out of all proportion to the minute and unnoticed degrees in which they are to be found.
The mechanism of accommodation of the eye is the means by which accurate Thcusing of the image on the retina is automatically brought about. It is a muscular device which is optically and neurally controlled, and peculiar to the eye. It cannot beimitated in an optical instrument. The lens of the eye is quite plastic and enclosed within a transparent and highly elastic capsule which, under tension, is capable of moulding the lens into a more spherical form, but when relaxed permits the eye to resume its original shape.
In accommodation three elastic forces are involved which operate on the principle of double antagonism, that is beautifully adapted for protection of the lens from sudden and dangerous deformations. It has been fully described by Gulistrand'. The form of the lens is controlled by two antagonistic elastic forces, those of the ohoroid and the capsule; and at the same time the force of contraction of the ciliary muscle and the stronger of the two elastic forces, that of the choroid, act antagonistically. This arrangement protects the lens from the action of too strong external forces and from sudden variation of these forces. The elastic force of the capsule, that protects the change of form of the lens, is the weakest of the three, and, like all elastic forces, constantly diminishes in strength during the development of its effect, so that the movement terminates without any jerk. In the relaxation of accomodation, the greatest force producing the change of form is the elasticity of the choroid, and this force diminishes steadily during the movement, and at the same time the resistance of the lens capsule is continually increased by dilation. However, this means of protection would fail with decrease of power of the lens to change its form. Without that power every strong tendency to accommodation would result in a dangerous jerk on its structure. When it is realized that opacities, which impair or destroy vision, can occur in the transparent lens of the older person from its sudden and violent deformation, the groat importance of the protective arrangement provided by the double antagonism of the forces acting in accommodation is obvious.
Listing's Law. A conspicuous and useful characteristic of the eyes is their extraordinary mobility which enables them to be voluntarily turned in perfect coordination in any direction within the obvious limits of possibility. No rolling motion of the eyes occurs as that would at once cause disorientation of the relative positions of corresponding retinal areas with a serious disturbance of vision. But when the ayes are moved in any direction, the movement is carried out with the greatest dispatch and the least expenditure of effort (Listing's Law). Operation according to this law causes the least degree of fatigue to the extra-ocular muscles which enables them to function for many hours a day. Listing's Law is a special case of the universal law of nature, known as Least Action, according to which all operations are performed with the least expenditure of time and energy. The law of economy of nature therefore operates with the eyes.
After reviewing the most recent estimates of the visual defects of the eye, it will be interesting to quote several other opinions of competent investigation.
Gullstrand2 states: "Helmholtz's famous dictum that the monochromatic aberrations of the eye are such as would not be tolerated in any good optical instrument, is sometimes construed to mean that the eye is a very badly constructed optical affair which Helmholtz never said and certainly did not mean. But another question that this statement raises is whether these aberrations are not serviceable and what is their purpose. First of all, it should be noted, as Helmholtz pointed out, that a limit is imposed by diffraction to the physical sharpness of the image."
In accommodation there is an elevation of the total index of refraction of the lens due to its structure which denotes a change of focusing out of proportion to the change of form that is unattainable with a lens of glass and is of the highest advantage. The monochromatic aberrations," continues Gulistrand, "are the necessary evil
-In Physiological Optics. Holmholtz. Eng trans. Southall. Vol. I. p. 408.
2lbid. pp. 440,443.for obtaining this advantages and, even if the convergence of the rays is not as good as it might be, the clearness of the image in good illumination is still above the limit of the capacity of the eye as imposed by the laws of diffraction. Hence, the monochromatic aberrations are a witness for the perfection of the eye, if what is meant by the perfection of an optical instrument is good convergence of rays to the degree that is needed to obtain the greatest useful sharpness of image; any-thing in excess of this being sacrificed in order to gain some other end."
In regard to the statement of Eelmholtz, Duke-Elder- remarks- "As in all optical systems, many aberrations are met with in the eye. It is frequently said that those arc gross, and the statement is attributed to Helmholtz that the construction of the eye is such as would not be tolerated in any good optical instrument. If Helmholtz ever said this he certainly never meant it, for, as Helmholtz fully realized, the eye is constructed with extreme attention to detail in keeping the image as physiologically useful as possible, while at the same time retaining an immense range of adaptability. It is true that the peripheral field is sacrificed to some extent for the central fields but it is the latter which is of importance for the purposes of accurate function, and the functional capacity of this region is up to the limits imposed by the diffraction of light. For yellow light and a pupillary diameter of 0.6 mm. the limit of capacity would be a visual angle of 0,3 minute of angle; for a pupil of 3 rpm, it would be 0.82 minute, and only for a pupil of 4 mm. is the angle for yellow light 1.22 minutes, while for green light it is 1.05 minutes. When these figures are compared with those of the minimum visual angle (0.40 minute) it is evident that the limit of possible visual capacity as imposed by diffraction is attained by the visual acuity. It would appear, therefore, that to sacrifice adaptability in the attempt to make the central acuity greater by optical means would merely b a task of supererogation."
It has also been remarked by Southall2 "The process whereby the normal eye is enabled to focus on the retina in succession sharp images of objects at different distances is called accommodation, and it is this marvelous adaptability of the human eye together with its mobility, which perhaps more than any other quality entitles it to superiority over the most perfectly constructed artificial optical instrument."
In the introduction to his extensive investigation of the visual perception of fine detail, Hartridge3states: ilThC resolution of a grating test object by a microscope requires that instrument to possess lenses of fine porformace. These contain as a rule achromatic combinations of carefully figured lenses which have been adjusted in relative position with the utmost precision. The design of the eye appears rudimentary in comparison with such lenses, yet practical tests with grating and other test objects show that this elementary lens system, possessing apparently no chromatic correction of any kind, and certainly no flourite-like medium which could impart an apochromatic correction, behaves in. an almost flawless manner. So good, in fact, is the apparent definition of the foveal image, that if the lens system of the eye could be removed and an apochromatic lens, selected for its good performance, could be substituted, it is doubtful if the possessor of this eye would detect any improvement in his perception of fine detail. What ho would certainly notice would. be a very serious deterioration at the periphery of his visual fields. His original eye lens gave him an angle of view exceeding a right angle. His now microscopic ions gives him a field of view almost insignificant in comparison. Ho now knows for the first time what it feels like to have 'tubular vision', that is, the type of vision produced by looking down a narrow tube. But other more subtle differences would soon be noticed. His original eye lens adjusted its focus automatically, and was almost equally good for observing near and distant objects. His now microscopic lens possesses no such valuable features.
-Tcxt-Book of Ophthalmology. Vol. I, p. 756.
2blirrors, Prisms and Lenses. MacIil1an. 3rd Ed. 1936, p. 434.
3Phil. Trans. Roy. Soc. Land. B. 232, 1947, 523.It has been designed to work at one fixed distance between object and eyepiece only, and a small error in this adjustment produces either over- or under-correction for spherical aberration. The performance of the eye lens is superior to that of the microscope lens, for the purposes for which it was designed."
The investigation of ophthalmologists which have been revised amply show that the optical defects of the eyes are so minute and unobtrusive in character that they are without detrimental effect on normal vision, as the testimony of the leading recent authorities indicate. It is therefore clear that the strictures on the eye in the first part of the remarks of Helmholtz are decidedly unjustified. But when the practical perfection of visual optical imagery, accommodation, rapidity of accurate focusing, breadth of visual field and mobility of the eyes, are added the remarkable acuity of vision and color sensations with which images are prceived in detail and adorned, as well as direction of vision, binocular coordination, perception of depth and adjustof distance, all of which are automatic in action, the eyes obviously far surpass all possible optical instruments in performance.
Finally it should be remembered that the eye differs from all other optical instruments in being a living system, and is preeminently the organ of the chief intellectual sense. By itself its own minute defects are assessed. With its exquisite discriminating power it pronounces ultimate judgment on the degrees of perfection of performance attained by artificial instruments. No inferior instrument could give a valid judgment on a superior.
The Visual Apparatus As A Telescope. It is often stated that the eye resembles a camera in its construction, and in some ways the likeness is quite complete. But the eye itself comprises only half the visual apparatus, for the area striata in the cortex cannot be separated from the visual process for it is there that vision actually takes place. The striate area, however, exercises a much wider function than only to provide sensations of vision.
The area striata, or visual cortex, consists of a number of folds in the calcarine areas of both cerebral hemispheres. If spread out flat it would be oval in shape with a total surface of about 3000 sq. mm., about evenly divided between the macular and peripheral areas of the retina.' The area of the functional retina is about 905 sq. mm., of which the macula comprises only about 3 sq. eon. The optic nerve fibres, about 500,000 for each eye proceed from the retina to the lateral geniculate body, whence they continue in increased numbers, as the optic radiations, to the area striata. The macular fibres number about half the total; that is, there are as many nerve fibres reaching the striate area from the 3 sq. mm. of the macula, as there are from the remaining 900 sq. mm. of the rest of the retina. The macular fibres therefore spread out over the striate area of 1500 sq. ma., in the ration of 3:1500 or 1:500. There is clear evidence that both retinas are represented in the same striate area. Possibly the two macular images of an object differ sufficiently in the striate area so as to excite the perception of depth.
From those figures it follows that an image covering the macula is spread out over a striate area 500 times the size, or the image is magnified at least 500 times. Since there is an increasing concentration of cones, which function in form vision, from the boundary of the macular towards the central fovea, it is probable that in the striate area the part corresponding to the fovea is expanded in like proportion.
Marshall and Talbot2 state that a pattern 1 minute of arc wide at the fovea expands in the striate area 100 times linearly, or 10,000 times in area. The area striata is also stated to be from 30 to 600 times as fine grained as the retina, which
Elliot Smith. Now Light on Vision. Nature. 125, 1930, p. 820
2Biologioal Symposia. Cattell Press. 1942. VII, 117 -165.would counteract its relatively coarse mosaic structure.
The fovea, which is the retinal area of distinct vision, has an area of about 0.05 sq. mm. Its cortical expansion in the striate area will not be less than 500 times this amount, or 25 eq. mm., nor more than 10,000 times, or about 500 sq. mm. (lsq. in -- 645 sq. mm.). In other words the fovoal image is magnified in the cortex by an undetermined amount between 500 and 10,000 times, possibly about their mean value.
These facts and computations signify that the visual apparatus as a whole represents a telescope, of which the eye is the objective, the area striata the magnifying device, arid consciousness the observer. The macular image of a man's face at a diS tance of about 3 metcrsis approximately 0.75 sq. mm. in area. To detect in this minute image all the details of form and color would be little short of miraculous. But in an image enlarged several thousand times, the discrimination of fine detail and color would be easy, as experience shows to be the case.
The optical magnification of retinal images in the cortex Is obviously out of the question. But the neuro-mechanical magnification is effectively designed to take its place. In a telescope the eyepiece and the objective must always be kept rigidly in alignment. In the visual apparatus this is unnecessary since the vital connection between the two parts is neutral. Sufficient slackness in the optic nerve is allowed to permit all the delicately coordinated motions of the eyes in their orbits without interfering in the least degree with the conduction of the nerve impulses to the magnifying and perceiving area in the cortex. A flexible connection between the two parts in which optical alignment has no significance is impossible in artificial optical instruments.
To obtain a similarly enlarged image on the retina itself would moan redesigning the dioptric system of the eye in a form impracticable with living tissues. Such an eye would be much enlarged, sluggish in movement, slow and inaccurate in focusing and subject to considerable muscular fatigue as well as greatly, probably grotesquely, disproportioned to the size of the face and depth of the orbit. The increased retinal area would mostly be wasted in any case, as attention could be directed only to a very small portion at a time.
In their present form, due to their small volume (6.5 cc.) and weight (7 gr.), the eyes have a wide and easy mobility, swift and accurate accommodation, and perfect coordination, which enable rapid judgments of the form, direction and distance of objects under observation to be made. The magnifying cortex can unobtrusively and effectually supply the necessary enlargement of the images, the perception of detail and the appreciation of color. While magnifications as high as those in a microscope cannot be obtained, experience shows that they are unnecessary in the normal exercise of vision. If the retinal image were grossly defective, as sometimes erroneously asserted, the magnified image in the cortex would be useless for accurate visual purposes, and optical instruments designed for visual observation would be without value.
The magnificence of the achievement of the theoretical arid practical designers of microscopes and telescopes in overcoming the natural defects of images due to the, nature of light and lenses, and in obtaining the high magnifications which they have thereby accomplished, can scarcely be exaggerated. Infinitely greater is the glory of the Divine Designer not only in having contrived the far simpler and more efficient optical system of the eye, but also in establishing biological laws by which the minute details of ocular construction have boon transmitted with precision to countless individuals of all generations of mankind.
1. Naturalism and Agnosticism. Black. London. 3rd Ed. 1906. 2 vols, Vol. 1, p. 6.
2. Popular Scientific Lectures. Trans by Atkinson. London, 1873. The Recent Progress of the Theory of Vision, p. 219, et. seq.
3 . T:xt-Boek ofFhyth.lmology. Kimpton, London, 1932. Vol. 1. Chaps. XSTI and XtII.
4. Phil. Trans.Rou. Soc. London. Ser. B. Vol. 32 14'7. ' •"'
Distortion of Image
Diagram of the Eye
1. optic nerve, 2. Fovea, 3. Retina, 4. Vitreous body,
humor, 7. Cornea, Iris.
Diffraction pattern produced by light passing through small circular aperature. Bands like these, but insignificantly small and practically invisible, are produced on the retina by the pupil.
5. Lens, 6. Aqueous
The dispersion of the lens brings each color to a differëntfocus the most refrangible, blue, nearest the lens, the least refrangible, red, farthest, away, the other colors between them.-20
/CLIS [to CUs
Diagram to show that rays of light passng through a lens at different places have different foci. Rays travel from left ;o right.
The lens of the Eye
Three zones of the lens of the eye. (diagammatic) Innermost is the high refractive nucleus, the others being progressivily less refractive outwards. The zones are very numerous.
"In all probability the complexity of its architecture, with its layers of graduated curvatures and zones of varying refrativities, is especially designed to counteract and neutralize the effects of sr.herica'i and chromatic aberration. It also increases the converging power of the lens, which is thus enabled to cover a greater range of accommodation and, in aidition tends to minimize the formation of secondary images in tho eye."
(Duke-Elder: Text Book of Ophthalmology, Vol. I. p 126).