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PHYSIOLOGICAL OPTICS

58 P H Y S I O L O G I C A L O P T I C S : Contents

The Eye Structure of eye Anatomical structure 61

Optical function 63 Centres of eyeball rotation 64 Field of fixation, field of view and visual field 65

Accommodation Terminology 66 Presbyopia 67 Influence of luminance 67

Pupil Diameter 68 Interpupillary distance 68 Luminous intensity of pupil 68

Visual performance Sensitivity threshold 69 Resolving power 69 Visual acuity 70 Directional perception 71 Depth perception 72 Adaptation and dazzling 72

Colour vision Spectral sensitivity 73 Colour sensation 74 Trichromatic theory 74 Defective colour vision 76

Emmetropic eye Emmetropia 76 Schematic eye 76 Chromatic aberration 76 Focusing wavelength 76

Ametropic eye Ametropia 77 Myopia 77 Hypermetropia 78 Astigmatism 79 Aphakia 79

Monocular correction of eye Full refractive correction 80 Objective methods 80 Subjective methods 80

P H Y S I O L O G I C A L O P T I C S : Contents 59

Binocular Vision Fusion and vergence Binocular single vision 81

Vergence 81 Vergence positions 81 Fusion ranges S3

Vergence portions N4

Binocular space Directional perception 86 perception Stereovision 87

Depth of field 89 Stereoscopy 89

Stereo visual balance 90

Phoria and tropin Orthophoria 91 Heterophoria 91

Fixation disparity 92

Accommodation-vergence diagram 92

Heterotropia 94

Anisometropia and Anisometropia 94 aniseikonia Aniseikonia 95

Binocular correction Full prismatic correction 96 of eye Methods 96

Focusing balance 97

P H Y S I O L O G I C A L O P T I C S : The Eye 61

The eye Structure o f the eye

Anatomical structure

tempora l

nasal

Fig. 51 Horizontal section through a human eye (description in text)

The eyeball (bulbus oculi) is of an almost spherical shape, but it is not a precisely centred system in the sense of geometrical optics. The optical axis OA of the eye is thus by convention the normal on the corneal front surface which passes through the centre of the entrance pupil. Fig. 51 shows a horizontal meridian section with a schematic representation of the shell-like structure of the eye. The interior of the eye is filled by the vitreous humour G (corpus vitreum). In front of the vitreous is the crystalline lens L (lens cristallina) and behind it is the multilayer retina N (retina). The retina is about 0.3 mm thick and contains photosensitive cells in the form of rods (radii) and cones (coni). The area of the most acute vision is in the central part of the fovea F (fovea centralis) which has a diameter of approximately 1.5 mm (about 5°). (Note: The degrees in brackets specify the nodal point angles.) Roughly 4.5 mm (about 15°) nasally from the centre of the fovea is found the optic disc B (papilla nervi optici) which has a diameter of approximately 1.6 mm (about 6°). The point at which the optical axis touches the retina is called the posterior pole P (polus posterior). The surrounding cover is the uvea (uvea) consisting of the choroid A (chorioidea) which nourishes the eye, the ciliary body Z (corpus ciliare) which changes the shape of the lens, and the iris R (iris) which controls the amount of light entering the eye. The outer layer of the eye is a 1 mm-thick continuous fibrous tunic comprising a posterior portion, the sclera S (sclera), and a transparent anterior portion, the cornea H (cornea) which is about 0.5 mm thick at its centre; the transition zone is called the limbus. The weakest point of the sclera is the cribiform plate C (lamina cribosa) lying behind the optic disk, through which the optic nerve O (fasciculus opticus) passes. The anterior chamber V (camera oculi anterior) is located between the cornea and the iris, while the posterior chamber W (camera oculi posterior) is situated between the iris, the ciliary body and the lens. Both chambers are filled with aqueous humour (humor aqueus). Movement of the eye is achieved with six muscles which are tangentially connected with the sclera (Fig. 52). The entire eyeball has a diameter of about 24 mm and is located in the osseous orbital cavity (orbita) which is padded with fatty tissue.

62 P H Y S I O L O G I C A L O P T I C S : The Eye

The conjunctiva (conjunctiva) is the connection between the eyeball and the eyelids (palpebrae). The lacrimal apparatus with the lacrimal gland (glandula lacrimalis) on the temporal side serves mainly to clean the ocular surface.

b) right orbital cavity, profile ig medial rectus

(musculus rectus nasalis) ag lateral rectus

(musculus rectus temporalis) og superior rectus

(musculus rectus superior) ug inferior rectus

(musculus rectus inferior) os superior oblique muscle

(musculus obliquus superior) us inferior oblique muscle

(musculus obliquus inferior)


Optical function Light rays incident on the eye are most strongly refracted at the cornea and are then transmitted through the aqueous humour of the anterior chamber to the crystalline lens where they are once again refracted. After traversing the vitreous, they finally reach the photosensitive retinal elements. The cornea constitutes a convergent meniscus with a refractive index of n H = 1.376 whose positive refractive power of about F H = 43 D results from the difference between the refractive indices of the adjacent media. In front of the cornea is air with n = 1, and behind it the aqueous humour with n K = 1 336. The strongest refraction of the rays therefore occurs at the front surface of the cornea. About 5 mm behind the cornea is the bi-convex crystalline lens with a refractive index of about n L = 1.4. The vitreous humour behind the lens has the same refractive index as the aqueous humour in front of it. This results in a positive refractive power of about F L = 19 D for the crystalline lens (with static accommodation). The entire eye has a positive refractive power of about F E Y e = 59 D. The retina represents the image area, and the aperture of the iris (in front of the crystalline lens) is the aperture stop of the system. The entire ocular system includes the following on the optical axis behind the anterior corneal vertex in the order listed (Note: The numbers in brackets give for the simplified schematic eye after Gullstrand the distance of the respective point from the anterior corneal vertex in mm.): the principal points H (1.5) and H ' (1.6), the centres of entrance pupil EP (3) and exit pupil A P (3.5), the nodal points K (7.1) and K ' (7.2) and the centre of the approximately spherical eyeball (Fig. 53).


Centres of eyeball rotation When the eye performs all the movements permitted by the six extrinsic muscles, no point within the eye retains its position within the orbital cavity. The point with the least positional change in the possible ocular movements is called the mechanical centre of rotation M . In an emmetropic eye it is normally situated 13.5 mm posterior to the anterior corneal vertex. Fig. 53 shows the major points and lines of the eye, while Table 10 lists the symbols used in physiological optics. The line of vision G L is the straight line connecting a fixated object point and the conjugate image point in the centre of the fovea. The line of vision can be taken to be roughly identical to the nodal point ray. The straight line connecting the centrally imaged object point and the centre of the entrance pupil is called the fixation line FL (or line of sight) and constitutes the object-side principal ray in front of the eye. The fixation line is therefore the straight line into which front and rear sights should be brought when aiming. When an (infinitely) distant object is fixated, the line of vision and the fixation line are parallel. The direction of the fixation line when looking straight ahead into the distance is called the zero visual direction. A n inward movement of the eye is called adduction, and an outward movement abduction (Fig. 73). The direction of the fixation line changes with each viewing movement of the eye. If all fixation lines are projected into the eye, they are tangents to an approximately spherical surface whose centre is the mechanical centre of rotation of the eye. This spherical surface is usually located temporally to the mechanical centre of rotation of the eye, and the radius of the sphere is approximately 0.8 mm. The optical centre of rotation of the eye Z ' is the foot of the perpendicular running from the mechanical centre of rotation to the fixation line in the zero visual direction. It is the most important point for the correct centration of a spectacle lens. The fixation line does not normally coincide with the optical axis of the eye; the angle between the two is called the y angle. As the fixation line and the line of vision are parallel to each other in distance vision, the y angle is a measure of the distance between the centre of the fovea and the posterior pole. It is positive if the fovea is located on the temporal side of the posterior pole. Values between +8° and - 3 ° are possible (corresponding to a displacement of the fovea from the posterior pole of about 2.5 mm temporally to about 1 mm nasally). Only when y = 0 will the optical axis coincide with the fixation

Pi I Y S I O L O G I C A L O P T I C S : The Eye 65

line and the line of vision, and the posterior pole with the centre of the fovea: the optical centre of rotation of the eye is then located on the optical axis.

Field of fixation, field of Al l points which can be fixated by means of movements of the view and visual field eye while the head is kept motionless form the monocular field

of fixation. Every point in the field of fixation can be imaged at the centre of the fovea by an appropriate movement of the eye. The appertaining fixation lines intersect roughly at the optical centre of rotation of the eye. As they are identical to the object-side principal rays for the imaging of the points of the field of fixation which are fixated one after another, the optical centre of rotation constitutes the centre of perspective for the viewing eye. If a point in the field of fixation is fixated (with head and eye motionless), all object points perceived around the fixated point form the monocular field of view for this visual direction. The area corresponding to the optic disc (blind spot) is missing in this process. The centre of the entrance pupil is the centre of perspective for the motionless eye, as it is the intersection point of all object-side principal rays. The totality of all fields of view for all possible directions is called the monocular visual field. For a pair of eyes, the binocular fields are formed by superim-position of the corresponding monocular fields.


Accommodation

Terminology The ciliary muscle reduces the radius of curvature of the front surface of the crystalline lens (and also, but to a lesser degree, that of the back surface). This increases the refractive power of the lens and therefore that of the entire eye. This process permits adaptation to various object distances and is called accommodation. When the eye does not accommodate (refractive power F R of the eye), the far point M R (punctum remotum) is in sharp focus. The distance of this point from the anterior principal point of the eye is called the far point distance k; it can be negative ( M R real in front of the eye) or positive ( M R virtual behind the eye). The far point refraction is

(61) K = I (D).

With maximum accommodation (refractive power F P of the eye) the near point P p (punctum proximum) is seen in sharp focus. The distance of this point from the anterior principal point is called the near point distance b. It can be negative or positive. The near point refraction is

(62) B = I (D).

The far point and the near point limit the accommodation range. Every point within the accommodation range is a focusing point E (refractive power F E of the eye). Its distance from the anterior principal point is called the accommodation distance b E . The focusing refraction is

(63) B E = ± . (D). b E

Table 5 gives the numerical relationship of the values in (61) to (63) . The accommodative effort A F is the increase in refractive power of the eye through accommodation

(64) A F = F E - F R .

The maximum accommodative effort is


(65) A F m : l x — Fc

0 10 20 30 Age in years

Fig. 54 Average accommodative power as a function of age

^"fa'r point

l ea r j >oint-l ea r j >oint-

0 0.01 0.03 Luminance L

Cd 0.05 m 2

Fig. 55 Range of accommodation as a function of the adaptation luminance

The magnitude of A F m a x is a measure of the accommodative power of the eye. The amplitude of accommodation A A is the difference between the corresponding refractions

(66) A A = K - B E .

The maximum amplitude of accommodation (the breadth of accommodation) is

(67) A A m a x = K. — B.

cc (cum correctione) is added to the corresponding terms for the eye with a correction lens. For the eye without corrective aids, A F practically equals A A . For the eye with a contact lens, A F is approximately A A c c , but A F and A A c c are different for the eye with a spectacle lens.

If the eye assumes a refractive power which is lower than F R , this process is known as negative accommodation. Real objects at close range may induce psychic (proximal) accommodation because of the awareness of nearness (instrument myopia). If a pair of eyes is compelled to converge by optical devices with an unchanged object distance, accommodation may be induced (convergence accommodation), although the retinal images are blurred in the process. A relative divergence effected in the same way facilitates negative accommodation.

Presbyopia The accommodative power A F m a x is age-dependent. With increasing age the elasticity of the crystalline lens decreases, with the result that the range of accommodation becomes smaller. Fig. 54 shows the average accommodative power as a function of age. If A F m a x is less than 4 D, the eye is presbyopic.

Influence of luminance With decreasing luminance of the field the near point moves away from the eye (night presbyopia), and the far point moves closer to the eye (night myopia). This process which reduces the accommodation range is shown in Fig. 55 and becomes noticeable to the point of irritation in the early stages of presbyopia before reading glasses are used (especially when reading small print such as in railway timetables or telephone directories in insufficient artificial lighting).


The pupil

Diameter

i — ;otopic vis

ion

-

L_ Ph atopic visi an

i • ;

20 30 40

Age in years

50 60 70 8 0

Fig. 56 Average size of the entrance pupil of the eye as a function of age

The aperture of the iris (aperture diaphragm) is called the pupil of the eye. Its diameter is dependent on illuminance (Table 11), age (Fig. 56) and the general physical condition of the subject. Moreover, pupil size, accommodation and convergence are interrelated. The change in diameter of the pupil (pupillary reaction) ranges between 10 mm and 1 mm depending on the various influences. The cornea and aqueous humour in front of the pupil act as a magnifier and make the pupil appear 1.13 times larger (apparent pupil size or entrance pupil of the eye). The average diameter of the entrance pupil is 3 to 5 mm. For observation through optical instruments, the entrance pupil of the eye should be located at the exit pupil of the instrument. If this exit pupil is wider than the entrance pupil of the eye, the luminous flux emerging from the instrument does not enter the eye in its entirety. Myopic eyes usually have larger, and hypermetropic eyes smaller pupils than emmetropic eyes (Table 11).

Interpupillary distance The interpupillary distance (the PD, formula designation p) is the distance between the two pupil centres when a pair of eyes fixates an (infinitely) distant point, i.e. with parallel fixation lines. This (distance) PD is measured with interpupillometers and is identical to the distance between the optical centres of the rotation of the eyes. Table 12 gives a list of average PD values.

Luminous intensity Like luminance, the size of the pupil is important for the retinal of the pupil illuminance and thus the sensation of brightness. It was for this

reason that the luminous intensity of the pupil I p was introduced as a measure of the retinal illumination in daylight. It is the product of the luminance L and the surface area A p of the pupil:

(68) I P = L A P .

The luminous intensity of the pupil is obtained in the unit troland (Trol) if the luminance is entered in cd/m 2 and the surface area of the pupil in mm 2.

P H Y S I O L O G I C A L O P T I C S : The Eve 69

Visual performance

Sensitivity threshold

10"1 1 10 1 0 2 c d i o 4

m2

Luminance L

Fig. 57 Luminance threshold of the eye as a function of the adaptation luminance (a night vision, b twilight vision, c daylight vision, d dazzle limit)

Resolving power

For a corneal illuminance of about 10 9 lx the absolute sensitivity threshold for light stimuli (minimum perceptible) lies in indirect vision and is of no optometric significance. The relative sensitivity threshold (contrast sensitivity) is known as the luminance threshold and specifies the least perceivable difference in luminance. This difference is dependent on the luminance and the state of adaptation of the eye and is higher the lower the luminance (Fig. 57). The smallest visual angle at which an object (with given difference in luminance and state of adaptation) can be perceived gives the minimum visible. Periodic flickering beyond a certain fusion frequency causes the same sensation as a permanent stimulus, corresponding to the evenly distributed luminance during the flicker period. The fusion frequency is dependent on the flicker amplitude and in most cases is lower than 30 Hz. It is lower in the area of the fovea than outside it.

The resolving power of the eye or the minimum separable points (minimum separabile) characterise the ability of the eye to perceive details of an object separately. The resolving power is influenced by various factors: 1. geometrically: by the shape and orientation of the object

details, 2. physically: by the luminance and colour of the object (Table

13) and the surrounding field, and by the length of time during which the object is presented to the subject,

3. optically: by the quality of the retinal image, 4. anatomically: by the image position on the retina (Fig. 58)

100 >> %

50

0

o I in 1

T> I .y § Q. /

- nasal °J \ temporal

i i r*r—

£100

50° 0° 50° Retinal location

Fig. 58 Relative visual acuity as a function of the location on the retina (0° is the centre of the fovea)

10 20 30 40 50 60

Age in years

Fig. 59 Relative visual acuity as a function of age


5. physiologically: by the state of adaptation and the condition of the optic nerves,

6. psychologically: by the attentiveness and degree of familiarisation of the observer with the situation involved and

7. by age (Fig. 59). The resolving power is measured by means of the smallest angular separation (nodal point angle) at which the object details in question can still be separately discriminated. This critical angle of resolution measures about 40 to 60 seconds for separable points and approximately 5 to 10 seconds (vernier acuity) for lines such as those on a vernier scale.

Visual acuity

Fig. 60 The Landolt ring as standard test type

In ophthalmic optics the resolving power of the eye is determined as visual acuity by using a special standard test type known as the Landolt ring. This test type is a ring with a gap in its circumference. The width of the ring and the gap are each one fifth of its overall diameter (Fig 60). In an acuity test the location of the gap in the ring must be identified. The unit "visual acuity 1" is determined by a Landolt ring whose gap appears with an angular separation of one minute and whose overall diameter is then 5 minutes. In a standard series of test types the size of the Landolt rings is selected in such a way that a logarithmic scale of acuity values results (Table 14). The visual acuity grade is a property of the object observed and is denoted by the minimum acuity with which the characteristic object details (here: the position of the gap of the Landolt ring) are identified from a certain distance. If other test types are used, they must be referred to the Landolt ring (as the standard test type). Familiarization with specific test types finds expression in the so-called reading sensitivity or reading ability (minimum le-gibile). Here, recognition of words as a whole is checked, as, for example, in near vision tests with texts of different print sizes. If a test type is used at a different distance (actual distance) from that on which the acuity grade is based (nominal distance), the visual acuity is obtained from:

(69) acuity = actual distance nominal distance

x recognized acuity grade.

Example: If a series of test types is projected from a distance of 5 m (nominal distance), and if from a distance of 4 m (actual


distance) the smallest test types recognized are those with the acuity grade 0.8, the visual acuity is 0.64. Natural vision (visus naturalis) or the acuity s.c.(visus sin cor-rectione) is the visual acuity of an eye without the use of a corrective aid, and the corrected visual acuity or the acuity c.c. (visus cum correctione) is the visual acuity with a corrective aid. Binocular visual acuity is usually slightly better than monocular.

Directional perception The ability to recognize the different directions (from the point of view of the eye) in which the various objects in the field of view are located is called the (monocular) directional perception. Normally the object point whose image is produced in the centre of the fovea is localised as being "straight ahead in front of the eye" (central fixation). The sense of direction conveyed by the other points of the retina refer to this "straight ahead" direction of the fixation area of the retina. In the retinal point with the directional value "straight ahead" the so-called vertical and horizontal meridians of the retina intersect. If a straight object line is imaged on one of these retinal meridians, it is perceived as being vertically (or horizontally) straight ahead. Al l retinal points on the right (left) of the vertical retinal meridian therefore have the directional value "left" ("right"), and all retinal areas above (below) the horizontal retinal meridian the directional value "down" ("up"). In the (rare) case of excentric fixation the viewed object point is not imaged in the middle of the fovea.

Depth perception The ability to recognize different object distances is called depth perception (spatial perception). Here, a distinction is made between laterally disparate depth perception (stereovision), which is only possible binocularly, and laterally non-disparate depth perception which is in the main monocular. The following contribute to laterally non-disparate depth perception: 1. arrangement of the objects in the image (further up is

experienced as further to the back), 2. geometric perspective, 3. contour sharpness (unsharp is experienced as further to the

back), especially due to atmospheric influences (aerial perspective),


4. distribution of light and shadow, 5. object overlapping (overlapping perspective), 6. motion parallax, 7. convergence stimulus, 8. accommodation stimulus, 9. size of retinal image (in conjunction with the conception of

size).

Adaptation and dazzling

" 10- 2

10" 3

40 min

Fig. 61 The process of dark adaptation with time (a. inside the fovea, b. outside the fovea)

The ability of the eye to adjust to a wide range of luminance values is called adaptation. Depending on the prevailing average luminance, the rods or cones or both participate in the perception of light. The highly photosensitive rods react at adaptation luminances of below 10 cd/m2, while the less photosensitive (but colour-sensitive) cones begin to react above approximately 5 . 10 3 cd/m2. Therefore, at a luminance of less than 5 . 10 3 cd/m 2 only the rods are active: night or scotopic vision. At a luminance between approximately 5 . 10"3 and 10 cd/m 2 both rods and cones are active: twilight or mesopic vision. At a luminance of more than 10 cd/m 2 only the cones are active: daylight or photopic vision. These transitions run smoothly one into another (Table 7). Adaptation (of the cones) to higher luminance values is relatively fast: brightness adaptation. Adaptation (of the rods) to lower luminance values, however, occurs slowly: dark adaptation. The stage of dark adaptation after 3 - 5 minutes is called immediate adaptation, and after at least 30 minutes permanent adaptation. These two adaptations may be independent of each other; good immediate adaptation may be present (important for driving) with poor permanent adaptation. The adaptation over the entire retina is called total adaptation, and that in certain areas local adaptation. As local adaptation is markedly less in the fovea than at the periphery of the retina, night vision outside the fovea is better than inside it. This is shown in Fig. 61 using the process of dark adaptation over a certain period of time. So-called night blindness is a deficiency of dark adaptation. Adaptation can be measured with an adaptometer (scotopic and mesopic vision), a mesoptometer (mesopic vision) or a nyctometer (immediate adaptation in mesopic vision). Dazzling occurs if the prevailing state of adaptation of the eye is disturbed by a luminance which is higher by a certain minimum amount than the adaptation luminance.


Fig. 62 Dazzling luminance as a function of the adapted field-of-view luminance: luminance above the dazzle line causes dazzling

10 ' °

cd

10=

car head l igh ts

paraff in lamp f luorescent lamp

J,

c C 2 s

dark l l 5 E I s Si c loudy n ight

i i i i

Field-of-v iew luminance

A distinction is made between: 1. absolute dazzle: the luminance is too high, 2. relative dazzle: the difference in luminance is too great

(Fig. 62) and 3. adaptation dazzle: the changes in luminance are too rapid.

Colour vision

Spectral sensitivity

400 500 600 nm 700

Wavelength). in air

Fig. 63 Spectral luminous efficiency of the human eye: V (X) for photopic vision, V (X) for scotopic vision

Any radiation from the visible part of the electromagnetic spectrum when incident on the eye produces a certain light sensation. The relative spectral sensitivity of the eye for monochromatic radiation of the same physical power (so-called equi-energy spectrum) is shown in Fig. 63. The sensitivity curve of the cones (photopic vision) is known as the V(A,) curve; it lies approximately between 380 and 750 nm with a maximum at 555 nm. For scotopic vision of the rods the spectral sensitivity curve is shifted towards shorter wavelengths by barely 50 nm relative to the V(a.) curve (maximum at 507 nm). This displacement accounts for the Purkinje effect: objects which appear in different colours but with the same brightness in photopic vision are perceived with different brightness in mesopic and scotopic vision.


Colour sensation The colour in which an object appears is not a property of this object, but a sensory impression. The colour response triggered by a certain radiation (colour stimulus) is induced physiologically. The assignment of colour response to the frequency (or wavelength) of the radiation is given in Table 6 for the various regions of the spectrum. The transitions between the individual spectral ranges run smoothly one into the other. The hue is the means of distinguishing between a chromatic colour and an achromatic colour (white, grey, black). The saturation gives the proportion of colour in the colour response (compared with the equally bright achromatic colour). The brightness characterizes the intensity of the light response correlated with every colour response. Hue and saturation together give the chromaticity of a chromatic colour; an achromatic colour has a brightness characteristic only. Colour vision is conveyed by the cones, whereas the rods only effect an achromatic light sensation. The state of the eye in which it is adapted to the prevailing colour stimulus is called the colour adaptation. If objects are illuminated by a (not too extremely) coloured source, they appear in their natural colours again after a few minutes: physiologically induced colour constancy.

Trichromatic theory Every colour can be produced by a specific mixture of three primary colours which are independent of each other. Every colour sensation is therefore clearly characterized by three tristimulus values which are determined by colour measure-

101 1 1 1 1 1 1 1 1

Fig. 64 Curves of the tristimulus values for the 400 500 600 700 nm equi-energy spectrum Wavelength X in air


ment with three defined primary colours. The tristimulus values x, y and z of the standard chromaticity system which are preferably used are plotted in Fig. 64 against the wavelength.

In the appertaining standard chromaticity diagram of Fig. 65 every chromaticity corresponds to a point (colour point) with the coordinates x, y and z (x + y -I- z = 1). All points of the spectral colours are on the spectrum locus. This is an open curve; its ends are connected by the line of pure purples. The points of all the colours which can be produced lie within the bounds of the spectrum locus and the line of pure purples. The point of the equi-energy spectrum is the achromatic point with the coordinates x = y = z = 1/3. Points on the spectrum locus which lie on a line with the achromatic point characterize so-called compensating colours (incorrectly also called complementary colours).

Fig. 65 Standard chromaticity diagram Chromaticity coordinate x

76 P H Y S I O L O G I C A L O P T I C S : The Eve

Defective colour vision As normal colour vision is conveyed by three types of receptors, it is called trichromatic vision. If normal trichromatic vision is disturbed, a distinction is made between the following colour deficiencies: 1. colour weakness (anomalous trichromatism), 2. partial colour blindness (dichromatism), 3. total colour blindness (monochromatism). Details are given in Tables 15 and 16.

The emmetropic eye

Emmetropia An eye is defined as emmetropic if its far point lies at infinity. Far point refraction is zero: K = 0. Irrespective of the magnitude of the refractive power F R , only the correct ratio of this refractive power to the overall length of the eyeball is important, as the image-side focal point F g y e of the eye must be located on the retina. An (infinitely) distant object is imaged sharply on the retina. As the near point of an emmetropic eye is at a real finite distance in front of the eye, a real accommodation range results (Table 17).

Schematic eye Based on a careful analysis of the geometrical and optical dimensions of a number of emmetropic eyes, Gullstrand designed two model eyes, the schematic eye and the simplified schematic eye. The data of the latter is shown in Table 18, in which the cornea and crystalline lens are assumed to be infinitely thin.

Chromatic aberration The dispersion occurring in every optical medium leads to chromatic aberration of the eye. This image aberration is shown in Fig. 66, in which the eye is assumed to be emmetropic for the wavelength 680 nm. This means that it is then myopic by 1 D for approximately 490 nm. Violet illuminated advertisements appear unsharp to the emmetropic eye.

Focusing wavelength If white light serves to image an object on the retina, image positions lying one behind the other result for the individual colours due to chromatic aberration; the red image has the largest and the blue image the smallest image distance. The


wavelength whose image is given priority by the eye is called the focusing wavelength. The focusing wavelength of the eye is dependent on the object distance (accommodation). If the eye is adjusted to its far point (i.e. with static accommodation), in most eyes the rays of the wavelength 685 nm (red light) are concentrated on the retina; there is therefore no correspondence with the maximum of spectral luminous efficiency. With decreasing object distance the eye normally utilizes its chromatic aberration and adjusts to shorter focusing wavelengths (in order to minimize the necessary increase in refractive power). This relationship between object distance (accommodation) and focusing wavelength is shown in Fig. 67.

Wavelength X in air Accommodation

Fig. 66 Fig. 67 Chromatic aberration of the eye Focusing wavelength of the eye in

white light as a function of the object distance

The ametropic eye

Ametropia An eye is defined as ametropic if its far point does not lie at infinity. An (infinitely) far object point is then no longer imaged as a point on the retina. If the cornea and the crystalline lens have spherical surfaces, identical optical conditions are present in all meridian planes, and the eye is spherically ametropic. If, however, the refracted rays only converge in two meridian planes (principal meridians) perpendicular to each other, the eye is termed astigmatically ametropic.

Myopia An eye is defined as myopic if its far point is located at a real finite distance in front of it (Fig. 68a). Far point refraction is negative: K < 0. The myopic eye usually has an overall length

78

-3.0 D -2.0 -1.0 0 Far point refraction K

Fig. 69 Decrease in relative visual acuity in myopia

Hypermetropia

Fig. 70 Hypermetropic eye (with static accommodation): a) far point b) focal point

which is too long in comparison with the refractive power of the average emmetropic eye (axial myopia). Occasionally, it has a refractive power F R which is too high in relation to the overall length of the standard eye (refractive myopia). The image-side focal point Fe y e of the eye with static accommodation lies inside the eye in front of the retina, and an (infinitely) distant object is unsharply imaged in circles of confusion on the retina (O'in Fig. 68b). As the near point of a myopic eye is also

Fig. 68 Myopic eye (with static accommodation): a) far point b) focal point

real in front of the eye, the accommodation range is real (Table 17). Fig. 69 shows the relative acuity as a function of the degree of myopia. The acuity of the myopic eye would be further reduced by accommodation, as the focal point F' R would be even further in front of the retina, and this would lead to larger circles of confusion for the distant object.

An eye is termed hypermetropic if its far point is virtual behind it (Fig. 70a). Far point refraction is positive: K > 0. The overall length of the hypermetropic eye is usually too short in relation to the refractive power of the average emmetropic eye (axial hypermetropia). Occasionally the refractive power F R is too low in relation to the overall length of the average emmetropic eye (refractive hypermetropia). The focal point F e y c of the eye with static accommodation lies behind the retina, and an (infinitely) distant object is unsharply imaged in circles of confusion on the retina (O' in Fig. 70b).

The location of the near point is dependent on the maximum amplitude of accommodation of the eye. If the latter is smaller than the far point refraction ( A A m a x < K), the near point is virtual, and a virtual accommodation range also results (Table 17). For A A m a x = K the near point lies at infinity, and for


A A m a x > K the near point is real in front of the eye, with the result that part of the accommodation range is real. Appropriate accommodation increases the visual acuity of a hypermetropic eye, as the focal point F e y e then comes closer to the retina, resulting in smaller circles of confusion for the distant object. With an amplitude of accommodation of A A = K , F g y e lies on the retina, and the distant object is seen in sharp focus.

Astigmatism

different locations on the retina

Fig. 71 Designation of the astigmatism 1 compound myopic astigma

tism (astigmatismus myopicus compositus)

2 simple myopic astigmatism (astigmatismus myopicus simplex)

3 mixed astigmatism (astigmatismus mixtus)

4 simple hypermetropic astigmatism (astigmatismus hyperopi-cus simplex)

5 compound hypermetropic astigmatism (astigmatismus hyperopicus compositus)

An astigmatically ametropic eye has two different far point locations for the two principal meridians with the refractive powers F R i and F R I I . The (first) principal meridian with the higher refractive power F R I is frequently almost vertical (about 70° to 110° on the Tabo graduated arc scale). This is an astigmatism with the rule (astigmatismus rectus). If the principal meridian with the higher refractive power is almost horizontal (about 0° to 20° or 160° to 180°), an astigmatism against the rule (astigmatismus inversus) is present. In all other directions of the principal meridians, the astigmatism is called oblique astigmatism (astigmatismus obliquus). Each principal meridian itself can be emmetropic, myopic or hypermetropic, with a line resulting as the image of an (infinitely) distant object. Further designation of the astigmatism is therefore dependent on the position of the two focal lines relative to the retina. Fig. 71 shows the five possibilities. The ray path subsequent to refraction resembles Sturm's conoid. Corneal and lenticular astigmatism exist (with corneal astigmatism occurring more frequently). Both together (but not by simple addition) give the total astigmatism. The difference between the total astigmatism and the corneal astigmatism is sometimes called the residual or physiological astigmatism.

Aphakia Aphakia is the absence of the crystalline lens most frequently due to its surgical removal. An aphakic eye usually requires correction lenses for distance and close range vision. The lens removed from the eye can be replaced by a spectacle lens or a contact lens with a high positive power. In the case of contact lens correction for distance vision, a spectacle lens for near vision can be used in addition. Table 19 gives the dimensions of the schematic aphakic eye. Correction of unilateral aphakia with a spectacle lens leads to very different image sizes in the two eyes.

80 P H Y S I O L O G I C A L O P T I C S : The Eve

Monocular correction of the eye

Full refractive correction

M R . F S P , M R C C

b)

Fig. 72 Full correction: a) in myopia b) in hypermetropia

The purpose of a refraction test is normally the determination of a fully correcting spectacle lens which entirely compensates the existing ametropia of the eye. This fully correcting lens enables maximum visual acuity to be achieved, and the far point M R c c (of the lens/eye system) lies at infinity as in an emmetropic eye. The image-side focal point F ' S P of the spectacle lens and the far point M R of the eye must coincide. This condition is shown in Fig. 72. As accommodation must be at rest for distance vision, the following rule applies for correction: The best lens is the strongest plus lens or weakest minus lens with which the highest visual acuity is achieved. In the case of astigmatic ametropia of the eye, full correction must be obtained for both principal meridians and can be achieved by using lenses with an astigmatic power. The best spherical lens is the lens which (for distant objects) places the circle of least confusion onto the retina.

Objective methods With objective refraction methods the subject does not need to play an active role in vision testing. The most important aids are the retinoscope or skiascope and the refractometer. The ophthalmometer or keratometer is used to measure the radius of curvature of the cornea.

Subjective methods The most common methods are based on the determination of visual acuity and the improvement of visual acuity by the appropriate corrective lenses. The subject has to describe the change in visual acuity with the aid of test charts. Subjective methods therefore require the subject to take an active part in the refraction procedure. The most important aids apart from the test charts are the trial frame with corrective lenses or the phoropter.

P H Y S I O L O G I C A L O P T I C S : Binocular vision 81

Binocular vision Fusion and vergence

Binocular single vision Simultaneous vision means binocular vision with both eyes at the same time. When in simultaneous vision the two monocular impressions are fused to a single impression, binocular single vision has been achieved. Fusion is the sum of all processes which lead to binocular single vision as a result of the fusion stimuli of the object. These processes occur largely involuntarily (enforced fusion). A distinction is made between motor and sensory fusion. With the aid of the ocular muscles, motor fusion effects vergence in order to align the eyes as exactly as possible with the object of fixation. Sensory fusion effects binocular single vision with the aid of processes within the nervous system, even if minor disparaties are present, i.e. even if the two related monocular images of the two eyes are not exactly located on corresponding retinal points.

Vergence Vergence is a movement of the fixation lines of the two eyes in opposite directions (fixation line vergence) or of the retinal meridians of the two eyes (cyclovergence): The major types of vergence are: 1. convergence (positive horizontal vergence): inward move

ment of the fixation lines. 2. divergence (negative horizontal vergence): outward move

ment of the fixation lines. 3. positive (or negative) vertical vergence: the fixation line of

the right (or left) eye moves upwards relative to that of the other eye.

Movements of the two eyes in the same direction (e.g. viewing and peering movements) are known as versions.

Vergence positions The vergence position of a pair of eyes is determined by the angle between the fixation lines of the two eyes (fixation line vergence position) and by the angle between the vertical retinal meridians of the two eyes (cyclovergence position). The major vergence positions are: 1. convergence position K (positive horizontal vergence posi-

82 P H Y S I O L O G I C A L O P T I C S : Binocular vision

tion): inward position of the fixation lines. 2. divergence position (negative horizontal vergence position):

outward position of the fixation lines. 3. positive (or negative) vertical vergence position: the fixation

line of the right (or left) eye lies above that of the other eye. If the fixation lines of the two eyes intersect at the object point observed and if the vertical meridians of the two eyes are parallel to each other, the eyes are in the ortho position appertaining to this object distance. Binocular vision with bicentral fixation is present in the ortho position. A vergence position which requires the minimum possible effort - the (vergence) rest position - exists for each accommodative adjustment of the eyes to different distances. It is assumed that the eyes generally assume this rest position in the absence of fusional stimuli. The rest position for far point adjustment of accommodation is known as the far point rest position. Different rest positions may exist for different adaptation conditions of the eyes. The brightness rest position in (photopic vision) is of particular practical importance. The vergence position required for vision with bicentral fixation can be changed by optical devices (e.g. prisms) (Fig. 73). Adducent optical devices (e.g. base-out prisms, Fig. 73a) change the vergence position necessary for vision with bicentral fixation in the convergent direction, and abducent optical devices (base-in prisms, Fig. 73b) in the divergent direction.


Fusion ranges If the fusional ability of a pair of eyes is to be tested, a change in the vergence position is forced by optical devices (e.g. prisms); a constant accommodation stimulus and fusion stimuli are simultaneously provided by an object at an unchanged distance which places high demands on visual acuity. The convergence ability can be determined with base-out prisms, and the divergence ability with base-in prisms (Fig. 73). With an increasing change in the vergence position of the Fixation lines of the eyes as a result of a gradual increase in power of the measuring prism, the blur point is reached; this is the threshold value at which the object seen in binocular single vision starts to become blurred. This blurring occurs because the focusing refraction of the eyes has changed due to coupling between vergence and accommodation. When, with a further increase in the power of the measuring prism and unchanged accommodation stimulus, double vision starts to occur, the so-called break point (diplopia point) is reached. When the break point has been exceeded and the power of the measuring prism is gradually decreased again, binocular single vision is usually not immediately achieved at the break point again, but slightly after it. This threshold value at which - with a constant accommodation stimulus after the onset of diplopia -binocular single vision is regained is termed as the recovery point. The relative convergence range and the relative divergence range are calculated from the rest position of vergence to the corresponding blur points, and the absolute ranges to the break points. The horizontal fusion range comprises the convergence range (positive part of the horizontal fusion range) and the divergence range (negative part of the horizontal fusion range). The vertical fusion range is determined in a similar way, and all fusion ranges are given in the unit cm/m. If the measurement is performed from the far point after adjustment of accommodation, the absolute convergence range is generally wider than the relative convergence range, while the absolute divergence range is usually equal to the relative divergence range (i.e. blur point and break point coincide), as negative accommodation is barely possible by divergence stimuli alone. The fusion ranges vary considerably from subject to subject. The convergence range is normally the widest range, and the vertical fusion range the smallest. The reserve convergence and the reserve divergence are measured from the ortho position, a distinction being made


here also between the relative and the absolute reserve. The sum of reserve convergence and reserve divergence is always as large as the sum of convergence and divergence ranges (Fig. 79). The relative values therefore characterize the fusional vergence range in which the fusional object can be seen (for a short time at least) in binocular single vision and with sharp definition. The absolute values also contain the range in which binocular single vision is achieved, but where the fusional object appears un-sharp due to the coupling between vergence and accommodation.

Vergence portions Binocular single vision requires a specific work position of vergence, the ideal one being the ortho position. (In vision with fixation disparity the work position deviates from the ortho position, depending on the direction and size of the fixation disparity.) In the vergence necessary to achieve a work position a distinction is made between four different components: 1. tonic vergence, 2. accommodative horizontal vergence, 3. psychic (proximal) horizontal vergence and 4. fusional vergence. Al l vergence components are given in cm/m. The tonic vergence is the change in the vergence position between the sleeping position of the eyes and the far point rest pos i t ion .

The accommodative horizontal vergence describes the change in the rest position with respect to the far point rest position when an accommodation stimulus is received, triggering an inward movement of the eyes coupled with accommodation. The degree of coupling between accommodation and the inward movement of the eyes is described by the A C A gradient:

(70) A C A gradient = accommodative vergence accommodation

The A C A gradient is given in the unit cm (cm/m per D). It can be measured by changing the accommodation stimulus for both eyes using optical devices in the absence of fusion stimuli and with a constant object distance. A psychic horizontal vergence is caused by the subject imagining nearness or distance; in this process the proximal convergence constitutes an inward movement of the eyes triggered by


the "awareness of nearness" in the case of near real objects (apparatus convergence, instrument convergence). The magnitude of the psychic horizontal vergence is represented together with the accommodative vergence by the A C A quotient: . _. accommodative + psychic vergence (71) ACA-quotient - accommodation

The A C A quotient is given in the same unit as the gradient and is larger than it. The A C A quotient can be measured by changing the accommodation stimulus by altering the object distance in the absence of fusion stimuli. By tonic, accommodative and psychic vergence the eyes achieve the rest position of vergence appertaining to the respective object distance. If this rest position is still not a work position, a further vergence is necessary to achieve binocular single vision, this being termed fusional vergence. If the fixation lines of the two eyes are brought from the rest position into the ortho position (ideal work position) by fusional vergence, vision with bicentral fixation is achieved and therefore also binocular single vision which is ideal from the sensory viewpoint. If, however, the fusional vergence is not sufficient for this, fixation disparity occurs, ensuring normal binocular single vision; this is, however, not ideal from the sensory viewpoint.


Binocular space perception

Directional perception Binocular directional perception refers to the centre between the two eyes (to the cyclopean eye). The straight line connecting the object point fixated by the two eyes and the centre between the optical centres of eyeball rotation is called the mid-line M L of the eyes (line of gaze of the cyclopean eye). The vertical plane through this mid-line when looking straight ahead is the median plane of the pair of eyes. The retinal points of the two eyes which in binocular vision transmit identical spatial directional values irrespective of the images lying on them are designated corresponding retinal points. Retinal points of the two eyes which transmit different directional values are termed as disparate retinal points. The interaction of corresponding retinal points is called correspondence. The correspondence centres are the retinal points of the two eyes which provide the directional value "straight ahead" in binocular vision. Ideally, the correspondence centres lie in the centres of the foveae (bicentral correspondence). If the two retinae are imagined as lying one behind the other in such a way that the centres of the two foveae and the two vertical meridians coincide, the coinciding retinal points are called coincident points. In bifoveal correspondence these coincident points are quasi-corresponding retinal points. The retinal points of the two eyes on which any object point is imaged at the same time are known as identical-image retinal points. The horopter is the space through the fixation point whose points (in bicentral correspondence) are imaged on corresponding retinal points of both eyes (see Fig. 75). Object points not located on the horopter are imaged on disparate retinal points. The distance of a disparate retinal point from the retinal point corresponding to the identical-image point in the other eye is known as disparity. Lateral disparity is the horizontal component of a disparity with upright head posture; the component perpendicular to this is called vertical disparity. The appertaining retinal points are known as laterally disparate and vertically disparate retinal points. Al l object points lying on the horopter provide orthopetal fusional stimuli, i.e. fusional stimuli moving towards the ortho position. Objects not located on the horopter cause orthofugal fusional stimuli, i.e. fusional stimuli moving away from the ortho position. A distinction is made in horizontal orthofugal


fusional stimuli between esopetal (moving inwards) fusional stimuli (from objects in front of the horopter) and exopetal (moving outwards) fusional stimuli (from objects behind the horopter). Every retinal point corresponding to a retinal point of the other eye is surrounded by an area in which, in spite of disparity, monocular visual impressions are fused, provided adequate equality of the images exists. These small areas are called Panum's fusional areas and have roughly the shape of a horizontal ellipse. Depending on the measuring method used, different sizes are given for the central Panum's area in literature, varying from a few minutes of arc to about one degree (node point angle). Panum's areas increase in size towards the periphery of the retina. If the correspondence centres of the two eyes lie within the central Panum's area, normal correspondence is present. If, however, one correspondence centre lies outside the central Panum's area, this is termed as anomalous or abnormal correspondence which only occurs as the result of a heterotropia.

Stereovision

non-fixated object point I

\

fovea fovea

Fig. 74 Relationship between the stereo angle 9 and the stereoscopic parallax yp

(K: nodal point)

In normal binocular vision differences in distance between objects visible at the same time can only be perceived due to differences in lateral retinal disparity. This laterally disparate depth perception is called stereovision (stereopsis). Differences in vertical disparity do not permit space perception. The stereo angle 0 serves as a measure of the magnitude of lateral disparity. This stereo angle is the node point angle at which the stereoscopic parallax y p appears. Fig. 74 illustrates this relationship and shows that the size of the stereoscopic parallax of a point in space not located on the horopter is dependent on the distance / of the reference plane from the eyes.:

(72) 9 = &

When applied to stereoscopic image pairs, the stereoscopic parallax is measured in the image plane (see Fig. 77). With identical arrangement of real objects, the stereo angle is larger, the greater the interpupillary distance p. If the distance A/ between the fixation object and the stereo object is small compared with the distance / of the fixation object, the stereo angle is then:

(73) 3 = = P ' A /

I2

With identical real object depth, the greater stereo angle normally provides better binocular space perception. Objects lying in front of the horopter are imaged with temporal lateral disparity, and those behind it with nasal lateral disparity. The object points imaged within Panum's areas form Panum's fusional space. For object points outside Panum's fusional space, a stereoscopic evaluation of the spatial position is possible to a certain degree, although double vision is already present. These areas are shown in Fig. 75.

Stereopsis can be improved through binocular telescopes, as the stereo angle with the instrument is larger by the factor of the telescopic magnification than the stereo angle with the naked eye if the objective base is the same as the eyepiece base. An additional improvement of depth perception can be obtained if the objective base is larger than the eyepiece base.


Depth of field

10-5 10-3 10 Luminance L

Fig. 76 Threshold of stereopsis 9 g as a function of the luminance of the object space

The smallest stereo angle resulting in stereopsis is called the threshold of stereopsis 0 g and is about 10 sec of arc for photopic vision. Its reciprocal is known as the depth of field (stereo acuity). The smallest depth perceivable with this is called the depth discrimination t and is dependent on the fixation distance and the interpupillary distance. Differences in depth smaller than t result in stereo angles smaller than 0 g and cannot therefore be perceived stereoscopically. The depth discrimination becomes increasingly larger, the greater the fixation distance becomes; at distances over approximately 600 m in particular, stereoscopic discrimination is barely possible with the naked eye. Table 20 shows some theoretical figures for laterally disparate depth perception. One of the factors on which the threshold of stereopsis depends is the luminance of the object space, as is shown in Fig. 76.

Stereoscopy The production of a three-dimensional visual impression due to differences in lateral disparity by presenting separate objects to the two eyes is known as stereoscopy and is used to test stereopsis. The stereotest of the Zeiss Polatest vision-testing instrument contains two test types arranged at the same height on both sides of the binocularly fixated point O (as seen in the schematic illustration in Fig. 77), but at a slightly different height from that of the fixation point. The distance of the two test types from each other constitutes the stereoscopic parallax y P . Each of these test types is imaged in one eye only. Depth perception is induced by fusion of the test types imaged with lateral disparity in a paracentral Panum's area. If the distance / (assumed positive) of the object plane from the eyes is large enough, the distance between the nodal points of the two eyes can be assumed to be equal to the interpupillary distance p, and the object depth AI to be perceived is

(74) A / = - ^ - , p ± y P

where the plus sign applies to the temporal lateral disparity of the test type images, and the minus sign to nasal lateral disparity (Fig. 77). As formula (74) shows, a pair of eyes with a larger interpupillary distance p perceives the stereo object at a shorter distance A/ from the fixation object than a pair of eyes with a smaller interpupillary distance (due to the constant stereoscopic parallax in the test plane).


Random dot stereoscopy has now attained special importance. Here, the objects presented to the two eyes consist of random dots containing a figure with a stereoscopic parallax (e.g. a hand or a circle and rectangle, see Fig. 180). As there is no possibility of recognizing the test type monocularly or binocularly without stereopsis, a test of this type can be used to check pure laterally disparate depth perception.

Fig. 77 Relationship between object depth A/, the stereoscopic parallax yp, the distance a of the fixation point O from the eyes and the interpupillary distance p with lateral disparity of the test type: a) temporal lateral disparity, b) nasal lateral disparity (K nodal point, F fovea, stereo angles = 0 l + 9R)

Stereo visual balance In German the degree to which each of the two eyes participates in stereovision is termed "Valenz" (valence). If, in addition to the fixation object, a stereo object is also located in the median plane of the eyes (as in Fig. 77) and if it is localized binocularly in the same (horizontal) direction as the fixation point, equivalence (isovalence) of the eyes is present. If, on the other hand, one eye is dominant in stereo vision, the stereo object is perceived laterally to the fixation point: a prevalence (aniso-valence) of this eye is present. If, for example, the eye on the right is prevalent, the stereo object appears to be shifted to the left in temporal lateral disparity (Fig. 77a), and to the right in nasal lateral disparity (Fig. 77b).


If equivalence is present for both directions of disparity, then stereo visual balance is present. If deviations from this occur, a suitable test (e.g. the stereo balance test in the Polatest vision testing instrument, see Fig. 177d) can be used to provide a rough quantitative estimate of the degree of prevalence of the eye concerned.

Phoria and tropia

Orthophoria If the far point rest position of emmetropic or refractively fully corrected eyes coincides with the parallel ortho position, distance orthophoria is present. The cooperation of the eyes is ideal from the standpoint of their motor (and normally also sensory) function if the vergence rest position and the ortho position are identical in all visual directions irrespective of the distance of the binocularly fixated object. In this case orthophoria is achieved in the entire range of accommodation. A positional error of the eyes consists in a deviation from the ideal cooperation of the two eyes from the standpoint of their motor function; the rest position of vergence does not then coincide with the ortho position. A distinction is made here between heterophoria (latent positional error) and heterotropia (manifest positional error, strabismus, squinting). The term orthotropia is used to describe the specific vergence behaviour in which the two eyes always assume the ortho position; this can be either orthophoria or a heterophoria which has been fully motor-compensated.

Heterophoria Heterophoria is a positional error in which normal binocular single vision is maintained due to the fusion stimuli present in natural vision. The fusional vergence required to achieve the ortho position is equal in amount to the heterophoria. If the rest position deviates from the ortho position in an outward direction, exophoria then exists (fusional convergence requirement). If the rest position deviates from the ortho position in an inward direction, esophoria is present (fusional divergence requirement). In vertical phoria a vertical fusional vergence requirement exists. Horizontal and vertical heterophoria often appear together. Moreover, the magnitude of the heterophoria may be dependent on the visual direction and the object distance (ani-sophoria).


Cyclophoria is heterophoria in the sense of opposite rotations of the vertical meridians of the two eyes about axes which coincide approximately with the fixation lines.

Fixation disparity Fixation disparity is a phenomenon frequently found in heterophoria, whereby normal (but no longer ideal) binocular single vision is maintained when the work position of vergence does not correspond precisely with the ortho position. In fixation disparity the disparately imaged fixation point is seen in binocular single vision either due to the sensory fusional faculty in the central Panum's fusional area (fixation disparity type I, disparate fusion) or because of a reversible shift of the correspondence centre within the central Panum's area (fixation disparity type II, disparate correspondence). The central Panum's area can also be extended in the direction defined by the heterophoria (in esophoria therefore in the nasal direction, etc.). A fixation disparity is not a strabismus, and suitable testing equipment (e.g. the Zeiss Polatest) is required to distinguish between two types of fixation disparity. Every fixation disparity diminishes the quality of binocular vision, and has the consequence that stereo visual balance is no longer possible.

Accommodation-vergence The individual values of horizontal vergences and their connec-diagram tions with accommodation can be graphically illustrated in an

accommodation-vergence diagram (graphical analysis after Hofstetter). As, however, the existence of fixation disparities is neglected, diagrams of this type can only provide a rough idea of real conditions. The fixation lines of the two eyes are parallel in the ortho position when the gaze is directed into the distance. For an emmetropic eye with no positional errors this corresponds to the zero point in the accommodation-vergence diagram, in which the accommodation stimulus is plotted against the horizontal vergence position of the two eyes (Fig. 78); positive values of the horizontal vergence position mean convergence position, negative values divergence position. The ortho position for near objects is a convergence position and is dependent on the object distance and the interpupillary distance. If the interpupillary distance p is entered in cm and the inverse value E of the object distance (assumed positive) from the line connecting the two optical centres of eyeball rotation in dioptres,


(D(2) D

A V (3 |

V i i

< - 1 2 - 6 0 6 12 24 3600148 Horizontal vergence posit ion m

Fig. 78 Accommodation-vergence-dia-gram

Donders' line for an interpupillary distance of 60 mm, Phoria line for distance orthophoria and increasing near exo-phoria for decreasing object distance (e. g. 6 cm/m for E = 3 D), Phoria line for distance esopho-ria (9 cm/m), decreasing eso-phoria for decreasing object distance, orthophoria for E = 3 D and increasing exophoria for further decreasing object distance, Phoria line for distance-independent esophoria (15 cm/m)

(1)

(2)

(3)

PD

A C -*AS /

x

f i / 1 i

- 1 2 - 6 0 6 12 24 3 6 c m 4 8 Horizontal vergence position m

Fig. 79 Accommodation-vergence-diagram O Donders'line for an interpupil

lary distance of 60 mm P Phoria line for distance-inde

pendent exophoria (3 cm/m) AFmax Maximum accommodative

effort

the required convergence position results in cm/m:

(75) K = p E.

Table 21 shows a list of values using (75). These ortho positions are represented by Donder's line in the accommodation-vergence diagram (Fig. 78). The horizontal phoria measured for each accommodation stimulus (object distance) is entered from Donder's line and gives the appertaining rest position of vergence. (Vertical pho-rias cannot be included in this diagram; they should already be prismatically corrected prior to measurement of the horizontal values.) The line connecting the rest positions is known as the phoria line and is usually a straight line. If orthophoria is present in the entire accommodation range, the phoria line and Donder's line coincide. In exophoria the phoria line lies to the left of Donder's line, and in esophoria to its right. If the phoria line runs parallel to Donder's line, this is a heterophoria which is independent of the object distance; the A C A quotient is then (as in orthophoria) equal to the interpupillary distance given in cm. Fig. 78 shows three examples. The divergence and convergence ranges (with a constant accommodation stimulus!) are entered in the accommodation-vergence diagram from the corresponding rest positions (phoria line). The range in which clear binocular single vision is possible for a short time at least lies within the relative fusion ranges. With increasing accommodation stimuli, this range is limited by the maximum accommodative effort A F m a x (shaded grey in Fig. 79). The reserve divergence and convergence result from the distances between the respective ortho position (Donder's line) and the lateral limits of the fusion range. In the example used in Fig. 79 one part (3 cm/m) of the distance-independent relative convergence range (15 cm/m) is constantly required for fusional compensation of exophoria (3 cm/m); the remaining part (12 cm/m) constitutes the reserve convergence. The reserve divergence (8 cm/m) is larger by the amount of the heterophoria (3 cm/m) than the distance-independent relative divergence range (5 cm/m).


Heterotropia In heterotropia (strabismus) the fixation line of one of the two eyes deviates from the ortho position defined by the respective object distance - despite the presence of fusional stimuli - to such an extent that the image of the fixation point lies outside the central Panum's area in the deviating eye. This means that normal binocular single vision is no longer possible. The squint angle is the deviation of the fixation line vergence position of the squinting pair of eyes from the ortho position for the object distance concerned. If the deviating eye takes part in all viewing movements of the fixating eye in such a way that the squint angle always remains constant, concomitant strabismus (strabismus concomitans) is present. If the two eyes have approximately the same acuity, they normally deviate in alternation from the fixation direction, and alternating strabismus is present. If the same eye always deviates from the fixation direction, unilateral strabismus is present. Paralytic strabismus (strabismus paralyticus), in which the squint angle changes with the direction of gaze, is caused by paralysis of ocular muscles. Strabismus causes double vision unless the visual impression of the squinting eye is suppressed or if binocular single vision is achieved by abnormal retinal correspondence. A microstrabis-mus is an irreversible form of a monolateral strabismus caused by sensory factors with a squint angle smaller than 5°.

Anisometropia and aniseikonia

Anisometropia If the two eyes have different far point refractions, anisometropia exists. The difference in vertex power of the two best spherical correction lenses is called the anisometropic difference A F'v:

(76) AF ' V = F' v 2 - F ' v l ,

where F' v 2 is the mathematically larger back vertex power. A F y is therefore always positive. In axial anisometropia both eyes have the same refractive power, but different lengths; in refractive anisometropia the lengths of the two eyes are equal, but the refractive powers are different. Viewing movements of an anisometropic eye behind fully correcting spectacle lenses require different fusional vergences depending on the fixation direction, this being due to the


different binocular prismatic powers* in the respective visual points of the lenses. This heterophoria, which alters when the visual direction changes, increases as the anisometropic difference becomes larger and may lead to difficulties in vision. Special attention must be paid to anisometropia in the fitting of ophthalmic lenses.

* Note: The "binocular prismatic power" is the geometric difference between the prismatic powers in the visual points of the two lenses.

Aniseikonia If the size or shape of an object is perceived differently by the two eyes, aniseikonia exists. Aniseikonia thus means a difference in size or shape between the two monocular visual impressions. This difference is not necessarily due to different retinal images. Aniseikonia can be caused by anatomical, functional (sensory) or geometric-optical factors. In aniseikonia of anatomical (retinal) origin the visual elements of the two retinae are differently structured, with the result that the two eyes obtain different perceptions despite identical far point refractions (isometropia) and identical retinal images. Functional aniseikonia is caused by the central nervous system and can be produced by, for example, fixation disparity. Optical aniseikonia is due to different retinal images in the two eyes. Different sizes of images on the retinas of the two eyes may be caused by: 1. different overall lengths of the two eyes despite isometropia; 2. different magnifications through fully correcting spectacle

lenses in the case of anisometropia; 3. aphakia of one of the two eyes; 4. different distances of a near object from the two eyes as a

result of oblique fixation of the object.


Binocular correction of the eye

Full prismatic correction A prerequisite for testing binocular vision is a monocular test and full refractive correction of both eyes. Heterophoriae are measured by subjective methods and are compensated optically by prismatic lenses. Full prismatic correction of heterophoria covers both the motor compensation component and any fixation disparity which may be present. While full refractive correction provides emmetropia cc (the far point cc lies at infinity), full prismatic correction produces orthophoria cc (the ortho position cc is identical to the rest position of the eyes).

Methods Different principles are applied in heterophoria tests in order to eliminate fusion stimuli (to a large extent): 1. distortion method (after Maddox), 2. displacement method (after von Graefe), 3. anaglyphic method, 4. separation method. In the distortion method after Maddox the retinal image of one eye is changed (distorted) by an optical device (e.g. very strong piano cylinder lenses) in such a way that no fusion stimuli exist. In the displacement method the absolute vertical fusion range is exceeded for horizontal phoria testing (or the absolute divergence range for vertical phoria testing) with the use of prisms in such a way that fusion is rendered impossible. The displacement (the generation of vertically or horizontally displaced double images) can be performed with the aid of prisms in the case of one test object or by the polarization separation of two identical polarizing test objects. In the anaglyphic method differently coloured visual impressions are presented to the two eyes with the aid of colour filters, this causing a marked reduction in fusion stimuli. Moreover, differently shaped test types are normally used for the two eyes. In the separation method the two eyes are presented with test types which are different in shape but identical in brightness, colour, contrast and size. Image separation is performed by stops or screens (geometrical separation) or by the use of polarizing light (physical separation, e.g. in the Zeiss Pokitest instrument). Here, fusion stimuli are not fully eliminated, as the field surrounding the test types is perceived binocularly (peripheral fusion stimulus).


Focusing balance Binocular testing of vision is indispensable and just as important as monocular vision testing; only when both have been performed is a vision test complete. Here, a distinction is made between various conditions of balance which are generally achieved by the appropriate means of correction. For distance vision, the aim is accommodation balance at least. To achieve this, the two eyes must be corrected with the best spherical lens in each case. Refractive balance should, however, also be present wherever possible. This means that the best possible visual acuity must be present in both eyes (full refractive correction). In order to obtain muscle balance, a distant object must normally be imaged in the centre of the fovea of both eyes when they are in their vergence rest position for distance vision (full prismatic correction). When refraction balance and muscle balance have been achieved by full refractive and prismatic correction, focusing balance has been obtained for the two eyes.

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