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100 P H Y S I O L O G I C A L OPTICS: Contents

Spectacle Lenses Terminology Dioptric power and major reference point 103

Optical centre 103 Geometrical centre 103 Pre-decentration 103

Single-vision spectacle lenses Back vertex power and form 104 with spherical power Calculation of the back vertex power 104

Sagittal depth and lens thickness 105 Volume and weight 105

Single-vision spectacle lenses Notation 106 with astigmatic power Tabo graduated arc scale 107

Production methods 107 Weight 108

Single-vision spectacle lenses Notation 108 with prismatic power Prentice's formula 109

Decentration of single-vision lenses 109

Bifocal, multifocal and Bifocal and multifocal lenses 110 progressive lenses Prismatic jump 114

Progressive lenses 116

Special types of spectacle lens Cataract lenses 118 Lenticular lenses 118 Fresnel membranes 119

Lens power determination Practical value and measured value 119 Addit ion 120

Image-forming properties Aberrations 123 Astigmatic error 124 Spherical error 125 Transverse chromatism 126 Distortion 127

Light-transmission properties Sun-protection and filter lenses 127 Photochromic lenses 130 Reduction of reflections 131 Laser safety filters 132

P H Y S I O L O G I C A L OPTICS: Contents 101

The Lens/Eye System Terminology Lens fitting 134

Frame tilt 134 Principal visual direction 134 Distances between lens and eye 135

Monocular centration Optical centration point 136 Centre of rotation requirement 136 Vertical centration 13 7 Corneal vertex distance 137

Binocular centration Centration distance 139 Near visual points 140 Horizontal centration 141 Vertical centration 142 Anisometropia 143

Accommodative effort and Spherical ametropia 143 amplitude of accommodation Astigmatic ametropia 144

Anisometropia 144 Addit ion 144

Space perception Field of fixation and field of view 145 Perspective 147 Magnification 147 Aniseikonia 148

Low vision aids Visual handicap 149 Magnification 150 Visual aids for distance 150 Visual aids for near 151 Supplementary aids 152 Visual aids for precision work 153

SPECTACLE OPTICS: Spectacle lenses 103

Spectacle Lenses Terminology

Dioptric power and major The spherical, cylindrical and prismatic power for a specific ray reference point direction at any point of a spectacle lens is generally termed as

its dioptric power at this point. A spectacle lens with no dioptric power is known as an afocal or piano lens. The major reference point B of a spectacle lens is the point on the object-side surface of the lens in which the prescribed dioptric power should be found in the ray path present when the lens is used in front of the eye. The admissible tolerances are stipulated in the various standards for each country. The thickness at the major reference point is the thickness of the lens in the direction of the normal at the major reference point. Table 22 shows the symbols used for the values used in spectacle optics.

Optical centre The vertex of the object-side surface of a spectacle lens is called the optical centre O of this lens, as a light ray running along the optical axis of the lens is not refracted. The centre thickness of a spectacle lens is the thickness in the optical centre in the direction of the optical axis. In lenses with a negative back vertex power the optical centre lies at the thinnest, and in lenses with a positive back vertex power at the thickest point of the lens. Sometimes the optical centre may lie outside the edge of the lens, but it can still be determined in every case. In lenses with a spherical or astigmatic power the optical centre coincides with the major reference point.

Geometrical centre The centre of the object-side surface of an unprocessed (uncut) spectacle lens is called the geometrical centre G of this lens. It should not be confused with the geometrical centre M of the lens former.

Pre-decentration A distance between the major reference point and the geometrical centre of a spectacle lens defined by the manufacturer is

104 SPECTACLE OPTICS: Spectacle lenses

known as pre-decentration. A pre-decentred blank may be superior to a centred blank with a larger diameter if the distance between the centration points is smaller than that between the centres of the lens formers. Fig . 80 shows that a pre-decentred blank 66/76 (diameter 66 mm), whose optical centre 066/76 lies 5 mm from the geometrical centre G 6 6 / 7 6 , fulfils the same purpose as a centred blank with a diameter of 76 mm which must be decentred by 7 mm. In this case there is a saving in raw material and edging work. Pre-decentration has special practical significance for multifocal and progressive lenses.

Fig. 80 Pre-decentred spectacle lens blank (see text for details)

Single-vision spectacle lenses with a spherical power

Back vertex power Spectacle lenses with a spherical power have the same back and form vertex power in all meridian planes and are designed as spheri

cal or (especially in the higher dioptre range) aspheric lenses. Spectacle lenses are specified according to their back vertex power regardless of their form, as this ensures that the image-side vertex focal length, important for full correction, is identified. Lenses with different forms but with the same back vertex power are therefore interchangeable. Similarly, the change in the necessary back vertex power with a change in the corneal vertex distance is independent of the form of the lens. This fact is of special practical significance when the actual spectacle lens takes over from that used in the trial frame or the phoropter. A focimeter calibrated in dioptres is used for rapid determination of the back vertex power. The difference between the image-side and object-side vertex focal lengths becomes larger, the more the lens deviates from the symmetrical shape. It is for this reason that the lens must be placed with its back surface pointing downwards for measurement on the focimeter.

Calculation of the back vertex power

If the surface powers F | and F 2 , the centre thickness t and the refractive index n of a spectacle lens are known, the back vertex power is obtained from the formula

SPECTACLE OPTICS : Spectacle lenses

(77) F ' v = — 1 — + F 2 ,

F) and F 2 are defined according to formula (12) and the reduced thickness 8 should be substituted in the unit metres.

Sagittal depth and lens thickness

Fig. 81 Sagittal depths of a spherical surface (r radius of currature, 0 diameter)

The sagittal depth s of a spherical convex or concave surface (Fig. 81) can be calculated from its radius of curvature r and the diameter 0 of the unedged lens:

(78) = r - ] / r ^ 0\i 2

For spectacle crown glass with the refractive index 1.525 the sagittal depth s (in mm) can be approximated from the surface power F (in D) and the lens shape diameter 0 (in mm) from the formula

(79) 1000

0 \2 2

If the sagittal depths S] of the front surface and s 2 of the back surface are known, the following formula applies for the relationship between the centre thickness t and the edge thickness e:

(80) t + s 2 = Si + e

This means that either the edge thickness can be calculated with a known centre thickness or the centre thickness with a given edge thickness. Tables 24 to 32 give values for the centre thickness.

Volume and weight The volume V of an uncut spherical spectacle lens is obtained from the spherical segment of the front surface plus a slice of the edge thickness e minus the spherical segment of the back surface:

(81) V = - H S , 3 ( f ) - s

/0\2 1 W y ) - e - - 7 t s 2

+

3 , f f + ,


where Si and s 2 are the sagittal depths. The weight W is obtained from:

(82) W = V o ,

where q is the density which can be read off in Table 23 for the most common types of spectacle lens material. The weight of an edged lens can be approximated by determining the weight of the circular lens with the same surface area. The given formulae cannot be used for aspheric surfaces. Tables 24 to 32 provide thicknesses and weights, also for lens types deviating from the spherical form (Zeiss Hypal, Clarlet Aphal and Gradal HS spectacle lenses).

Single-vision spectacle lenses with an astigmatic power

Notation Spectacle lenses with an astigmatic power have different back vertex powers in two meridian planes (the principal planes) lying at right angles to each other. Astigmatic power is a collective term for astigmatic difference (cylinder) and cylinder axis (axis position). Spectacle lenses with an astigmatic power are usually identified by specification of the "sphere" and the "cylinder" (sph...cyl...). This sphero-cylindrical notation is possible in two ways: 1. Plus cylinder notation. Here the power is given as a "sphere"

and a "plus cylinder". This is the standard form of notation. 2. Minus cylinder notation. Here the power is given as a

"sphere" and a "minus cylinder". This form of notation is normally used in refraction.

The cylinder axis lies in the principal meridian which is selected as the "sphere". It is given as an angle in the Tabo graduated arc scale. The back vertex power of the other principal meridian is "sphere + cylinder" (the signs must be taken into account). When converting, the back vertex power "sphere 4- cylinder" of the latter principal meridian is taken as the new sphere, the cylinder remains unaltered but its sign is changed and the direction of the axis of the new cylinder is changed by 90° relative to the old one. In the focimeter the cylinder axis results from the direction of the target lines when the value "sphere + cylinder" has been set. A further way of designating spectacle lenses with an astigmatic


power is by specifying the back vertex powers for the two principal meridians.

Tabo graduated arc scale The position of cylinder axes (or principal meridians) of spectacle lenses with an astigmatic power is given in Tabo notation in accordance with D I N 58201 (Fig. 82).

Fig. 82 Tabo graduated arc scale R right lens L left lens

The zero points are located on the horizontal, on scale R for the right-hand lens nasally, and on scale L for the left-hand lens temporally. This means that the angles for R and L increase equally in the anti-clockwise direction (mathematically positive direction). The scale is divided into intervals of 5° ; the graduation is continued in the lower semicircle from 180° to 360° in such a way that any base position can be specified for lenses with a prismatic power. The millimetre grid in the centre is used for marking decentrations. The zero direction which is used to specify the cylinder axis and the base position according to the Tabo graduated arc scale and which passes through the major reference point of a spectacle lens is called the lens horizontal.

Production methods Lenses with an astigmatic power have at least one toroidal (or atoroidal) surface. If the back surface is toroidal, the lens is described as a "back surface toric", otherwise it is a "front surface toric". Lenses with two toroidal surfaces are known as bitoric. The formulae (77) to (80) also apply with the corresponding radii of curvature and surface powers for the base curve and cross curve (longitudinal and equatorial) directions.

108 SPI (TACIT OPi ics: Spectacle lenses

Weight The weight of spectacle lenses with an astigmatic power can be approximated by first determining the weight of the lens with a spherical power corresponding to the mathematically larger principal meridian and by then adding to it the value given in Table 33.

Single-vision spectacle lenses with a prismatic power

Notation If a light ray is incident upon a lens outside the optical centre, it is deviated from its original direction. This deviating power of the lens is called the prismatic power at the point of the lens concerned and is identified by the magnitude of the deviation (prismatic effect) and by the direction of deviation (base direction, base). The prismatic effect P is given in the unit cm/m, and the base position (B) by the corresponding angle on the Tabo graduated arc scale. If, for example, the prismatic power 2.5 cm/m B 230° is present at a particular point on a lens, a ray entering at this point is deflected by 2.5 cm in the direction 230° of the Tabo scale 1 m behind the lens. The prismatic power can be determined for every point of a lens by using the focimeter; this measurement is, however, only an approximation of the ray path actually present for the spectacle-wearer. Instead of using the Tabo scale, the cardinal base directions can be designated base-in (= base 0° for the right lens and base 180° for the left lens), base-out ( = base 180° for the right lens and base 0° for the left lens), base-up ( = base 90°) and base-down (= base 270°) . Spectacle lenses with a prismatic power prescribed in their major reference point are described as spectacle lenses with a prismatic power. A n example of a prismatic prescription:

R: -3 .00/+ 0.75 x 120 c 1.5 A base out & 0.5 A base up L : -2 .50/+ 1.00 x 5 c 1.5 A base out & 0.5 A base down

C D = 68

The optical centre of spectacle lenses with a prismatic power may lie outside the lens area and in this case cannot be located with the focimeter.


Prentice's formula The prismatic deviation P at any given point of a spectacle lens with a spherical power is chiefly dependent on the amount of back vertex power F ' v and the distance c of that point from the optical centre. The prismatic effect is approximated with normally sufficient accuracy using Prentice's formula:

(83) P = c • F'v .

To obtain the prismatic effect P in cm/m, the distance c must be substituted in centimetres and the back vertex power F'v in dioptres. The base direction of the prismatic power results from the sign of the back vertex power. In positive lenses the base lies towards the optical centre relative to the measured point; in negative lenses it lies in the opposite direction towards the periphery of the lens (always in the direction of the greatest thickness). A parallel ray incident upon any given point of a spherical lens is thus always deviated in the meridian plane through that point.

Decentration of If a (not excessively high) prismatic power is required at the single-vision lenses optical centration point, it can be achieved approximately by

decentration of a spectacle lens with a spherical power. The decentration c by which the optical centre of the lens must be displaced relative to the optical centration point, can be determined from formula (83). In positive lenses the decentration must be performed in the direction of the required base position, and in negative lenses in the opposite direction. Although there is no basic difference between spectacle lenses with a prismatic power and decentred spectacle lenses with a spherical power when they have an identical vertex power, their production data and their measuring data do, however, differ on exact computation. In lenses with an astigmatic power, in the same way as in lenses with a spherical power, the prismatic power can only be determined for points located on one of the two principal meridians. In points outside these meridians a light ray is no longer deviated in the meridian plane through its point of incidence. If a specific prismatic effect is required by decentration of a spectacle lens with an astigmatic power, it is no longer possible to determine the necessary direction of decentration from the desired base direction, or the amount of decentration from formula (83). The data necessary in such cases can be approxi-

110 SPECTACLE OPTICS : Spectacle lenses

mated in the workshop using the focimeter. The amount and direction of the necessary decentration are calculated with the following formulae:

(84) tan p = *j . t a n a a n d

(85) c = _ P . c o s a here v S cos p

a: angle between the cylinder axis ( 0 C = 0° to 180° Tabo) and the required direction of deviation (base position $ B

= 0° to 360° Tabo), thus a = § c - % , S: vertex power of the principal meridian "sphere" in D . S + C: vertex power of the principal meridian "sphere and

cylinder" in D (3: angle between the cylinder axis and the required direc

tion of decentration ( 3 D = 0° to 360° Tabo), thus 3 D =

O: the required prismatic effect in cm/m c: decentration in cm If c is positive, the decentration is performed in the direction of $ D ; if c is negative, it is performed in the opposite direction.

Bifocal, multifocal and progressive lenses

Bifocal and multifocal lenses Bifocal and multifocal lenses have different, visibly separate

areas characterized by their different spherical powers. A bifocal lens is composed of a main lens and additional or segment lens. A trifocal has two segment lenses which are either separated or adjacent. The area in which the power of the main lens alone is effective is called the main portion. Here the lens has the same dioptric power as an equivalent single-vision lens. The area in which the powers of the main lens and the additional lens are combined is called the additional or segment portion. The dioptric power of the segment portion must not be confused with the power of the segment lens in its own right. In the majority of bifocal and multifocal lenses the optical centre of the segment lens is decentred with respect to the optical centre of the main lens. The prismatic power at any given point of the segment portion must therefore be determined as the geometrical sum of the individual prismatic


powers of the main lens and the segment lens at this point, taking into account the base directions. The individual prismatic powers of the main lens and the segment lens should be determined in the same way as for single-vision lenses. The main portion or a segment portion can be used for distance vision (distance portion), intermediate vision (intermediate portion) or near vision (near portion). In most cases, the main portion is the distance portion. A dividing line separates the different portions. The segment top is either the point of intersection of the dividing line with the line connecting the geometrical centres of the main portion and the segment portion (in the case of a rotatable segment portion (Fig. 83a)), or it is the point of intersection of the straight line perpendicular to the lens horizontal through the geometrical centre of the segment portion with the dividing line (in the case of non-rotatable segment portions - Figs. 83b, 84 and 85). The segment lenses are either cemented, fused - in which case they have a different refractive index - or ground onto the surface of the main lens. While the main portion is generally point-focal, this is not always the case in the segment portion. If the segment portion is fused onto the main portion, it is more favourable for point-focal imagery to perform the fusion on the back surface of the lens.

Different shapes are possible for the segment portion, a distinction being made between rotatable and non-rotatable types. Circular or types located at the periphery of the main lens are rotatable (Fig. 83a). With these types the major reference point can be decentred horizontally with respect to the geometrical centre of the main lens by rotation through an angle oo. The line connecting the two geometrical centres of the main lens and the segment lens and the line perpendicular to the lens horizontal form the angle (0. If c is the required horizontal decentration

Fig. 83 Example of bifocal spectacle lenses: a) rotatable b) non-rotatable (see Table 22 for symbols) a) b)


and k the distance between the major reference point of the segment portion and the geometrical centre of the main lens, the required rotation to of the segment portion is obtained from

(86) sino) = | .

While lenses with a spherical power and a rotatable segment portion can be rotated as desired, the required rotation of lenses with an astigmatic power must be known prior to production of the astigmatic surface (position of the cylinder axis). Non-rotatable segment portions (Fig. 83b) are oriented relative to the lens horizontal and exhibit a specific horizontal decentration of the major reference point of the segment portion relative to the major reference point of the main portion. This geometrical inset e is taken to be positive in the nasal direction. Fig. 83 shows two examples of bifocal spectacle lenses, and Fig. 84 an example of a trifocal lens.

distance portion (main portion) ~

lens horizontal -

intermediate portion

near portion

Fig. 84 Example of a trifocal lens (see Table 22 for symbols)

Pre-decentred multifocal lenses are blanks with non-rotatable segment portions in which (as in pre-decentred single-vision lenses) the major reference point of the main lens is decentred with respect to the geometrical centre. F ig . 85 shows an example. The major reference point in the distance portion of a bifocal or multifocal (or progressive) spectacle lens is called the major reference point for distance, and that for near vision the major

113

Fig. 85 Example of a pre-decentred bifocal lens (see Table 22 for symbols)

distance portion

lens horizontal

near portion

(main portion)

b, d T

reference point for near. If the geometrical centre of the near portion is not the major reference point for near at the same time, the position of the major reference point for near relative to the geometrical centre of the far portion is specified by the manufacturer. The prescribed prismatic power in the major reference point for distance is called the distance prism, that in the major reference point for near the near prism. The near prism N p r should only be specified separately i f it differs from the distance prism. A specification of the near prism does not take into account the prismatic power of the main lens caused by the decentration of the major reference point for near with respect to the major reference point for distance. The toroidal surface of bifocals or multifocals with an astigmatic power is generated on the side of the lens without an additional power, with the result that the cylinder power and axis direction are practically identical in the distance and near portions. Cases with different astigmatisms for near and distance can be taken into account in solid bifocals by obliquely crossed cylinder powers in the two distance portion surfaces, and in fused segment lenses by a toroidal fusing surface. This requires a high degree of technical sophistication. In bifocal or multifocal spectacle lenses with a prismatic power the surface without an additional power is provided with a wedge. Cataract and lenticular lenses are also produced as bifocals and multifocals. If an anisometropic pair of eyes is corrected with bifocals or multifocals, a compensating prism can be ground onto the near portion of the mathematically weaker lens in accordance with


formula (105). This ensures that an undesired binocular vertical prismatic power does not occur in the near visual points of the lens pair. In the case of a fused near portion the compensating near prism is produced by the so-called slab-off technique, in which the lens is given a double surface of the same curvature on the side with the additional power. The barely noticeable line between the two parts of the double surface runs horizontally through the segment top.

Prismatic jump If different prismatic powers exist on either side of the dividing line between two portions of a bifocal or multifocal lens, the object perceived appears to jump when the fixation line of the eye crosses the dividing line. The difference between these two

Fig. 86 Prismatic jump J as a function of the distance h of the segment top from the optical centre of the segment lens (Z additional power)

is 1

£ o

- / Z = 4 D

- / / z = 3 D ^

- , Z = 2 D

- //

I I

Z=1 D

• •

0 Distance h

10 15 20 mm 25

for straight dividing lines and other no-jump designs J « O

additional portion with h < i d s

(cf. Fig. 83 b) 2

round-shaped segment portions

SPECTACLEOPTICS: Spectacle lenses 115

prismatic powers is called the prismatic or image jump J , as it is not the object but the image produced by the spectacle lens which is in fact jumping. The prismatic jump is at its most pronounced at the segment top between the main portion and the segment portion (Figs. 83 to 85). The amount of prismatic jump equals the prismatic effect Ps of the segment lens at the dividing line:

C2.S

-C2,D O A D

OAs

Fig. 87 Types of segment: a) solid with divided double surface

(no prismatic jump) b) solid with continous double sur

face (prismatic jump through wedge angle a)

c) fused (prismatic jump through wedge angle a)

6

(87) h - A .

Fig. 88 Dead angle in the field of fixation and the field of view due to prismatic jump ( H D principal ray for vision through distance portion, H N through the near portion)

Progressive lenses

According to formula (83), J is obtained in cm/m if the distance h of the point on the dividing line from the optical centre of the segment lens is substituted in cm and the additional power (addition) A in D . The prismatic jump is therefore dependent on the type of segment portion and on the amount of additional power (Fig. 86). It is independent of the main lens. In solid bifocals and multifocals it is produced by a wedge angle between the distance portion surface and the near portion surface (Fig. 87b), and in fused bifocals and multifocals by a wedge angle between the two surfaces of the segment lens at the dividing line (Fig.87c). If the optical centre of the segment lens lies on the dividing line (h = 0), there will be no prismatic jump at this point (Fig. 87 a). The image jump is taken to be positive i f its base faces downwards. In this case the object seems to jump upwards when the direction of gaze is lowered across the dividing line. With the head in its rest position and a very narrow iris aperture, the prismatic jump practically leads to a blind angle in the field of fixation and the field of view (Fig. 88), whereas with a larger aperture double images may result in this region in the field of view.

In progressive lenses there is a gradual transition from the distance portion to the near portion without any dividing line or prismatic jump. Progressive lenses are produced from one piece of material. Their power is achieved with a surface whose curvature is not the same all over as in a spherical surface. In the progression zone between the distance portion and the near portion the spherical power gradually becomes greater (mathematically) until the power of the near portion has been obtained (Fig. 89). As the viewer lowers his direction of gaze and observes objects of increasing nearness, the vertex power on the lens


a)

Fig. 90 The astigmatic aberration in progressive spectacles lenses a) older design b) Zeiss Gradal HS

is increased accordingly so that even an aphakic eye has sharp vision at all distances between distance and close range. The area on both sides of the line connecting the major reference point for distance and the major reference point for near in which clear vision is possible is known as the progression channel. Its width is dependent on the design of the progressive lens and on the size of the near addition; the greater the near addition, the narrower the progression channel. A progressive lens intended for all-round use takes into account the visual tasks confronting the spectacle-wearer in all ranges, ensuring sharpness and comfortable vision and making allowance for the interplay of the two eyes in binocular vision. Fig. 90 shows the progress which has been made in the reduction of aberrations; the astigmatic aberration in a older type of lens is compared with a new design (Zeiss Gradal HS progressive lens). Progressive lenses may contain a prism with a vertical base direction to decrease their thickness. This thickness-reducing prism must be identical in the two lenses of the lens pair. The fitting of progressive lenses should be extremely exact; they should not be fitted too low to ensure that the usable near zone is not too small, and at the same time not too high to prevent any reduction of distance vision.


Special types of spectacle lens

Cataract lenses After cataract surgery the power of the absent crystalline lens can be replaced by a spectacle lens which must normally have a high positive back vertex power. In lenses with spherical surfaces and back surface powers higher than approx. 8 D the astigmatic aberration can reach substantial proportions depending on the form of the lens. The aberrations of these lenses are optimally corrected by the use of aspherical or atoroidal surfaces whose deviation from the spherical or toroidal form is exactly calculated mathematically. To be able to produce light, thin lenses with a high positive back vertex power, a special design is possible for the peripheral area in which the optically effective zone of the lens merges continuously with the marginal area. This also eliminates the possibility of annular scotoma (Fig. 91).

Lenticular lenses To reduce the weight of high-power spectacle lenses, only the central area of the lens, the aperture, is given the desired dioptric power. The periphery or margin of these lenticular lenses serves merely as a supporting rim. The optically effective area can have any desired shape (usually circular or oval). While the field of view is sufficiently wide in lenticular lenses with a negative power, the weight reduction is only achieved in positive lenticular lenses at the expense of a markedly reduced field of view.


Fresnel membranes Fresnel membranes are transparent, flexible plastic membranes with a spherical or prismatic power. They are usually applied to the back surface of spectacle lenses. The barely 1 mm thick sheets are cut into the required shape and stick to the lens surface due to adhesion. If possible, they should be used on lenses with spherical back surfaces. The sheets have an insignificantly low weight compared with the carrier lens and can be easily and quickly replaced, but they also cause a marked reduction in acuity. Fresnel lenses with a spherical power are designed in such a way that they have concentric zones of prismatic deviation which increase from the centre towards the periphery, with the result that an overall spherical power is produced. These lens membranes are used for temporary correction of the eyes subsequent to cataract surgery and for special bifocal and multifocal spectacles. Fresnel prisms consist of small prisms of the same power arranged parallel to each other. These prism membranes can be used for temporary prismatic prescriptions (e.g. prior to surgery on the ocular muscles).

Lens power determination

Practical value and In refraction the combination of lenses in the trial frame or measured value phoropter results in a specific ray path which produces the best

possible correction of the patient's visual deficiency. The lenses in the finished spectacles are intended to provide the same effect in the same ray path. The dioptric power in the major reference point of a spectacle lens for the ray path in the using situation as experienced by the spectacle-wearer is called the practical value. As this value refers to the lens/eye system, all differences between the trial frame or phoropter and the finished spectacles (e.g. corneal vertex distances or, binocularly, the centration distances) must be taken into account when it is being obtained. In higher powers it may also be necessary to take into consideration the type and position of the trial lenses in combination (and to include this on the prescription). The dioptric power in the major reference point of a spectacle lens obtained by measurement with the focimeter is known as the measured value of the spectacle lens. In the focimeter the measuring ray is vertically incident on the spectacle lens surface


(see Fig . 94b), while in the lens/eye system the principal ray runs from a given point on the spectacle lens to the optical centre of rotation of the eye (see Fig . 94a). Only when the gaze is directed along the optical axis of a spectacle lens at an (infinitely) distant object does the ray path of the lens/eye system coincide with the ray path in the focimeter. The measured value can therefore only correspond to the practical value in the case of spectacle lenses which are used for distance vision and in which the optical centre is also the major reference point. In all other cases the practical value cannot be obtained with the focimeter. This would only be possible by using a special instrument which actually simulates the ray path present in front of the eye of the spectacle-wearer. The difference between the measured value and the practical value is called the correction value:

correction value = measured value - practical ^ value. If, allowing for the admissible tolerances, the measured value and the practical value do not correspond, the manufacturer of the spectacle lens must also specify either the measured value or the correction value in addition to the practical value.

Addit ion The addition A is the difference in power between the near portion and the distance portion of a bifocal, multifocal or progressive spectacle lens. This difference is dependent on the geometry and materials of the lens as well as on the respective ray path in the near and distance portions. There are three different definitions for the addition, depending on the ray path used as a basis for obtaining the dioptric power in the major reference point: 1. Addi t ion using the practical value (Add R ) :

Difference between the practical values in the major reference point for near and in the major reference point for distance. The symbol for A d d R is A R .

2. Addit ion using the concave measured value (Add c c ) : Difference between the concave-side measured values of the back vertex powers in the first principal meridians in the major reference point for near and the major reference point for distance. The symbol for A d d c c is A c c .

3. Addit ion using the convex measured value (Add c x ) : Difference between the convex-side measured values of the

SPECTACLE OPTICS : Spectacle lenses 121

Fig. 92 Standardized using situation as per DIN 58208: b' = 28.5 mm (distance from

centre of rotation to vertex)

du + d* = 20 mm (thickness in major reference point plus distance from principal point to vertex)

/ = - 3 8 0 m m f o r A R < 2.5D (object distance for A d d R

to 2.5 D) / 1000 mm D / A R f o r A R

> 2.5 D (object distance for A d d R over 2.5 D)

back vertex powers in the second principal meridians in the major reference point for near and in a point of the distance portion which lies diametrically opposite the major reference point for near with respect to the major reference point for distance. The symbol for A d d c x is A c x .

The addition using the practical value corresponds to the ray path in the lens/eye system and cannot be directly measured with the focimeter. It is calculated from the mean values of the back vertex powers in the principal meridians for a standarized using situation as shown in Fig. 92.

object

Two different measuring methods are used to determine the addition using a measured value. In the concave measuring procedure the spectacle lens is laid with its back surface down on the support of the focimeter; the vertex powers F ' v c c / I are then measured in the major reference point for near B N and on the major reference point for distance P»D, each in the first principal meridian (Fig. 93a). The addition using the concave measured value is then:

(89) A c c — F ' v c c / | at B N - F'vcc/! at B D .

Fig. 93 Measurement of the addition using a measured value: a) concave measurement method b) convex measurement method


In the convex measurement method the spectacle lens is laid with its front surface down on the surface of the focimeter; the vertex powers F ' v c x / n are then measured in the major reference point for near and in a point B d i a lying diametrically opposite with respect to the major reference point for distance, each measured value being obtained in the second principal meridian (Fig. 93b). The addition using the convex measuring method is then:

(90) A c x = F'vcx/n at B N — F ' v c x / n at B d i a .

To calculate the addition using the practical value from the addition obtained using a measured value, a correction value K is required as per (88):

The manufacturer of the spectacle lens must specify the definition of the addition used by him and, if necessary, the correction value. Fig . 94 shows the difference between the ray path in the lens/eye system and that in the concave measuring method for a fused bifocal. When the near portion is used in the spectacles, a divergent ray bundle is incident on the convex side of the lens, and after refraction the principal ray intersects the optical axis of the distance portion in the optical centre of rotation of the

(91)

a)

Fig. 94 Ray path through the near portion of a bifocal lens with an addition of the practical value 6 D: a) in the lens/eye system b) in the focimeter Z' optical centre of rotation of eye C), CT centres of curvature of object-side and image-side lens surface

0.0 D

measured value =t= + 6.0 D

0,

b) "+6.0"


In the convex measurement method the spectacle lens is laid with its front surface down on the surface of the focimeter; the vertex powers F ' v c x / n are then measured in the major reference point for near and in a point B d i a lying diametrically opposite with respect to the major reference point for distance, each measured value being obtained in the second principal meridian (Fig. 93b). The addition using the convex measuring method is then:

(90) Acx = F v c x / n at B N - F v c x / n at B d i a .

To calculate the addition using the practical value from the addition obtained using a measured value, a correction value K is required as per (88):

(91) A R = A c c c x — K c c c x .

The manufacturer of the spectacle lens must specify the definition of the addition used by him and, i f necessary, the correction value. Fig. 94 shows the difference between the ray path in the lens/eye system and that in the concave measuring method for a fused bifocal. When the near portion is used in the spectacles, a divergent ray bundle is incident on the convex side of the lens, and after refraction the principal ray intersects the optical axis of the distance portion in the optical centre of rotation of the


eyes (provided the centre of rotation requirement has been met). In the focimeter, however, the ray bundle on the convex side of the lens is parallel, and the principal ray lying perpendicularly on the concave side of the lens does not meet the optical axis of the distance portion until reaching the centre of curvature of the concave surface. The difference (correction value) resulting from the above is dependent on the type of bifocal or multifocal lens, the data of the main lens (back vertex power, form, thickness and material), the size of the addition and the object distance. Tables 34 to 36 show the correction values K c c for various bifocals in steps of 0.25 D (Zeiss spectacle lenses Duopal C25, Glaukar C25, Clarlet Bifokal C25). The values for the progressive lens Gradal HS are contained in Table 37. These spectacle lenses are calculated for the addition obtained using the practical value. For the measurement (the concave method), the correction value K c c should be added to practical value A R in accordance with (91). For example, a Duopal C25 lens with sph + 6.0 and the addition 2.0 should provide the value + 8.5 when measured in the major reference point for near, as the correction value according to the table is + 0.5.

Image-forming properties

Aberrations The major deviations from ideal image formation in a spectacle lens are: 1. the astigmatic error, 2. the spherical error, 3. transverse chromatism, 4. distortion. Points 1, 3 and 4 are aberrations in the sense of geometrical optics, while the spherical error results from the interplay of the field curvature with the eye. Points 1 to 3 reduce the visual acuity of the eye, with the astigmatic error exercising the greatest influence. Distortion, on the other hand, influences space perception. In spectacle lenses with spherical (and toroidal) surfaces the aberrations 1,2 and 4 can only be influenced by the form of the lens (change in bending with no change in the back vertex power), while transverse chromatism is dependent on the dispersion of the selected lens material.


Astigmatic error The astigmatic error (deviation from the spherical power) caused by the astigmatism of oblique incidence should be optimally corrected for: 1. object distances from 25 cm to infinity, 2. all possible angular fields, 3. all meridian planes and 4. the different distances between the ocular centre of rotation

and the lens vertex. These requirements differ in importance. Visual acuity reduced by aberrations is more disturbing in the working field of fixation than in the peripheral areas of the lens, while all meridian planes are of equal importance. If the astigmatic error has been so well corrected that the inevitable residual aberrations do not cause any disturbance to the spectacle-wearer, the spectacle lens is then described as point-focal. This is generally the case when the astigmatic error for common object distances is below 0.2 D in the working field of fixation.

Fig. 95 Astigmatic error as a function of the distance d of the principal ray from the optical centre of the spectacle lens (ocular-side angular field is about 2 d degrees) with different lens forms and a centred back stop at the distance b' (F(. back vertex power. FT surface power of the ocular-side surface with object distance as the parameter)

-1.6 -1.2 Astigmatic error

F V ' = + 4 0 0 F 2 5.0 D b' = 27.5 mm

Astigmatic error

/ f

\

\ / F V ' = + 4 . 0 D ' F 2 - - 3 . 0 D

b' - 2 7 . 5 mm

I

Astigmatic error Astigmatic error

Fig . 95 shows the influence of the lens form on the astigmatic error for spectacle lenses with a back vertex power of ± 4 D . It can be seen that greater bending (higher surface power F 2 of the ocular-side lens surface) is more favourable for vision at long distances, and lesser bending for shorter distances. The lens forms used are calculated for a centred back stop at a given distance (b'). The optical centre of rotation of the eye must


therefore be located at the same point i f the lens is to be correctly centred in front of the eye ("centre of rotation requirement"). The cosmetic aspect must also be taken into consideration in addition to the requirements for good image quality. The range of possible lens forms is relatively large for low-power lenses, therefore allowing greater attention to be paid to cosmetic appearance. For high-power lenses, however, and especially in the positive range, the possibilities of finding a reasonable compromise between image quality and appearance are limited.

Spherical error In all possible movements of the eye its far point moves on a sphere. The centre of this far point sphere is the optical centre of rotation of the eye. If a spectacle lens is to provide full correction for all directions of gaze, its image shell for infinitely distant objects (or the area for the circles of least confusion in astigmatic aberration) must coincide with the far point sphere. A lens which meets this requirement is called a Percival form lens. Any deviation from this is called a spherical error (or mean oblique error).

R F R F

Fig. 96 The spherical error of spectacle lenses K R far point sphere K p image shell for infinitely distant

objects K s vertex sphere (radius o = b')

fo back vertex focal length fo oblique vertex sphere focal

length

K p KR

In point-focal lenses the image shell for distant objects is not as strongly curved as the far point sphere of the eye, as shown in Fig. 96. These lenses therefore undercorrect in the peripheral zone. This spherical deviation is negligible in minus lenses and can generally be compensated in plus lenses by accommodation.


Transverse When a ray of white light passes through a spectacle lens at a chromatism point with the prismatic effect P, colour fringing results after

refraction due to the lateral chromatic aberration. The magnitude Pchrom of the chromatism is

p (92) P chrom = ~ >

where v is the Abbe number of the lens material (see Table 23).

A s the threshold of perception for this chromatism is approximately PChrom = 0.12 cm/m, a colour fringe in regular crown glass is generally not noticed until a prismatic effect of approximately P = 7 cm/m has been exceeded. While this also applies to plastics lenses made of C R 39, in high-index lenses such as those made of BaSF 64 and Hi-Crown the colour fringe is already noticeable with prismatic effects of about 5 cm/m because of the slightly greater dispersion. Formula (92) also applies to solid bifocals and multifocals and progressive addition lenses. In multifocals and bifocals with a segment lens (refractive index n s ) fused onto the main lens (refractive index n M ) the width of the colour fringe in the area of the segment portion:

(93) Pchrom = ^ + 7^ '

w h c r c

(94) \i = A " S ~ " M

A n s - A n M

is the so-called colour fringe coefficient. A n are the mean dispersions. If the segment lens is made of regular flint glass, the colour fringe coefficient is u. « 12. In most cases P s > P M at the segment top, with the result that a colour fringe can generally only be perceived with prismatic jumps (J = P s ) larger than approx. 1.5 cm/m. A suitable choice of glass types reduces this chromatic aberration to a point where it can no longer be perceived. With this purpose in mind, types of barium glass are used for the segment lenses since they exhibit a lower dispersion and therefore result in a larger colour fringe coefficient.


Distortion As distortion is a result of the spherical aberration, it is especially noticeable in large lens diameters. The pincushion-shaped distortion experienced with positive lenses and the barrel-shaped distortion with negative lenses (see Fig. 34) increases with the back vertex power and the corneal vertex distance. Distortion influences space perception in the field of view and the field of fixation. Flat lenses cause more pronounced distortion than more strongly curved lenses.

Light-transmission properties

Sun-protection and filter lenses

Light-absorbing spectacle lenses are divided according to their degree of absorption for visible light into sun protection lenses with a transmittance of less than 80% and filter lenses with a transmittance of more than 80% (low attenuation of light). In the U V range (with some lenses also in the IR range) most of these lenses absorb more strongly than clear lenses, but no limiting values have been fixed. Examples of spectral transmission are given in Figs. 97 to 99.

Fig. 97 Spectral transmission curves for Zeiss filter lenses: a Clarlet Rose uncoated b Clarlet Rose with Super ET c Uropal uncoated d Uropal with Super ET

100 %

80

S 6 0

c re

1 40 c

i 20

co 0

UV VIS IR a

—

1 • 1

: I I 1

c 1

• |

:/ ;/ :/ i

; / , • ,7

300 400 500 Wavelength X in air

600 700 800

80

% 100

900 nm 1000

20

40

60

% S

Sun-protection lenses are worn to protect the eyes against glare on the one hand, and to improve visual acuity on the other. Protection is provided against the following: 1. glare caused by visible light, leading to a reduction in visual

acuity, 2. red vision (erythropsia) caused by visible, mostly green light

and


3. inflammation of the conjunctiva (conjunctivitis, ice or snow blindness) caused by short- wave U V radiation below k = 313nm.

In modern sunglasses attenuation of the various colours of visible light has been selected in such a way that natural colour rendition is guaranteed. Although sunglasses are useful in sunshine, their use is not advisable in twilight conditions or at night. Here they may even in fact constitute a danger. It was for this reason that the Deutsche Ophthalmologische Gesellschaft (German Society of Ophthalmology) has given the following recommendations for driving: " A l l drivers are strongly advised against the use of any sun-pro-

Fig. 98 Spectral transmission curves for Zeiss spectacle lenses with filter anti-reflection coating a Punktal Filter ET b Clarlet Filter ET

100 %

80

S 60

§ 40

0 20

UV VIS IR

a 1 b —

J

/ 7

/ / !

% « 100 co


600 700 800 900 nm 1000

Fig. 99 Spectral transmission curves for Zeiss sun-protection lenses: a Clarlet brown 50% b Umbra Punktal65 300 400 500 600 700 800 900 nm 1000 c Umbral85 Wavelength X in air


tection lenses (less than 80% transmittance) when driving at night, as these may severely impair twilight vision. The use of filter lenses with a transmittance of 85 % and more is generally not dangerous except for drivers whose normal twilight vision is only just sufficient. The above recommended transmittance limits are also applicable to photochromic lenses." Filter lenses are used to avoid or reduce eyestrain and to increase visual performance by enhanced contrast. Despite the harmlessness of normal daylight and its invisible components it may nevertheless give rise to asthenopic problems in the form of eyestrain, headache or fatigue, especially in hazy weather (high colour temperature) or in artificial light (filament lamp, fluorescent lamp, visual display units). It has been proven that problems of this type can be eliminated or relieved by filter lenses, while ordinary clear lenses with the same corrective power have no effect. N o exact or completely satisfactory explanation for this well-known phenomenon has yet been found. It is attributed mainly to the absorption of longer-wave U V and blue-violet light (reduction of the scattered light or fluorescence of the crystalline lens, enhancement of image contrast). Sun-protection lenses and filter lenses are produced as single-vision lenses with spherical, astigmatic and prismatic powers and as bifocal, multifocal and progressive lenses. The following possibilities exist: 1. Solid tinted lenses, in which the light attenuation is, however,

dependent on the thickness. They are therefore mostly used as piano lenses and as fused equitint shells on clear base lenses;

2. Lenses with an absorptive layer which is vacuum-deposited onto the main lens. These lenses offer uniform attenuation over the whole surface, even in lenses with very high powers. The vacuum-deposited coatings are as hard as glass and do not increase the weight of the lenses.

For spectacle lenses made of CR 39, absorptive surface coatings are generally produced by using an immersion procedure suitable for all lens powers. Standard sun-protection lenses are produced with a light attenuation of up to 85 %. Lenses with still higher reduction of light are protective lenses for special applications. The requirements for these are stipulated in D I N 4646 and D I N 4647.


Photochromic lenses Photochromic lenses darken when exposed to short-wave radiation between about 300 nm and 450 nm. The lenses clear again when the radiation is removed. The clearing process occurs due to heat (thermal bleaching) and long-wave radiation (optical bleaching). The hue ranges from brownish-grey to bluish-grey depending on the type of glass, the temperature and the ad-sorptance attained. Fig . 100 shows spectral transmission curves for a photochromic lens.

Fig. 100 Spectral transmission curves of the photochromic borosilicate lens Um-bramatic SB (thickness 2.0 mm) a unexposed b after exposure of 15 minutes

100 %

80

£ 60

E 40

« 20

UV VIS IR a

h _

*

>

i y

/ *

/ J.

r,


600 700 800 900 nm 1000

After an exposure period of 10 to 15 minutes a state of equilibrium is reached between darkening and clearing. The light transmission then present at 555 nm (maximum of the spectral photopic sensitivity of the eye) is known as the saturation transmission; it is dependent to a large extent on temperature. If the ambient temperature is low, darkening of the lenses is more pronouced with a light attenuation of up to 85 %; a high temperature is favourable for clearing. This is illustrated by Fig. 101. Lenses with pronounced photochromic properties can still noticeably darken out of doors with a light attenuation of over 30%, even with an overcast sky, while light attenuation indoors corresponds to that of filter lenses. Photochromic lenses are produced which feature an additional constant absorption. This is achieved by absorptive layers vacuum-deposited on the back surface or by using special melts to obtain solid-tinted lenses. Even when unexposed, these lenses exhibit a light attenuation of 30 to 35%. O n exposure, they display a higher degree of absorption than standard photochromic lenses.


Photochromic lenses are produced in almost all regular dioptric powers.

Fig. 101 Influence of temperature on darkening and clearing of photochromic lenses using Umbramatic SB as an example

100 %

80

60

40

1 20 E U) c CO _ H 0

0 Time t

10

Darkenin Clearing Darkenin Clearing

4 0 ° C _ _ —

V / 10°( / 10°(

15 0

mm 10 15

Reduction of A number of different reflections may occur in spectacle lenses, reflections The various types possible are represented schematically in Fig .

102. These reflections are reduced by antireflection coatings (T-coatings).

Fig. 102 Reflections in a spectacle lens 1 reflections visible by an observer

in front 2 internal reflections 3 reflections from behind 4 reflections at the cornea

Although the reduction of reflections also involves an increase in transmission, this does not mean that the use of antireflection coatings for absorptive lenses is a contradiction in terms; their


primary task is to reduce disturbing light in the finished spectacle lenses. They may indeed be particularly beneficial for light-attenuating lenses which, although they reduce transmission, do not decrease the reflections on the back surface of the lenses. The spectral distribution of the transmitted light is virtually unaffected by the antireflection coating. As the colour of the residual reflection is also dependent on the refractive index of the glass material used, fused bifocals and multifocals inevitably exhibit small differences in colour between the main portion and the segment portion. A single-layer antireflection coating is particularly effective on lenses made of a material with a high refractive index. This means that in lenses made of BaSF 64 and Hi-Crown a similar effect is achieved to that of the Super £ T c o a t i n g .

Laser safety filters The requirements to be met by filters for laser safety eyewear are stipulated in DIN 58215 for the spectral range from 200 nm to 1000 urn on the basis of maximum permissible corneal irradiance. The permissible radiation is dependent on the wavelength and the exposure time. The eye is particularly endangered by laser radiation with wavelengths between 400 nm and 1400 nm, as the radiation in this range can be focused on the retina. Radiation between 200 nm and 400 nm can be absorbed by the cornea and the crystalline lens; in the radiation range between 1400 nm and 1000 urn the anterior ocular media and the area surrounding the eye may be damaged.

ion

-i—r

radi

al

-1—

r as

er

-r-r

_ i

Spectral transmission curve for Zeiss 200 400 600 800 1000 1200 nm 1400 laser safety filters for N d - Y A G lasers Wavelength X in air

Safety filters which protect against all types of laser radiation at the same time do not exist. Laser safety filters must be suitable for the specific wavelength and energy of the laser used. Figs. 103 and 104 provide transmission curves for laser safety filters.


Fig. 104 Spectral transmission curve for Zeiss laser safety filters for CO2 lasers

Las

er r

adia

tion

1

II

1 1

1 1

1 1

- A

Las

er r

adia

tion

1

II

1 1

1 1

1 1

Las

er r

adia

tion

1

II

1 1

1 1

1 1

-/\- Las

er r

adia

tion

1

II

1 1

1 1

1 1

Las

er r

adia

tion

1

II

1 1

1 1

1 1

0.2 0.3 0.4 1 2 Wavelength X in air

9 pm 11

Fig . 105 shows laser safety eyewear which can either be fitted with piano lenses or with correction lenses produced to prescription.

Fig. 105 Zeiss laser safety eyewear for C C b lasers

134 SPECTACLE OPTICS: The lens/eye system

The lens/eye system Terminology

Lens fitting In lens fitting a distinction is made between anatomical and optical lens fitting. Anatomical lens fitting is the sum of all activities by which the dimensions and shape of the spectacle frame are determined in such a way that a neat, comfortable fit is assured, the cosmetic wishes of the spectacle-wearer are satisfied and the requirements of optical correction have been met at the same time. Optical lens fitting is the sum of all activities by which the position of the lenses in the anatomically fitted frame is determined in such a way that the correction in the lens/eye system subsequent to the glazing of the lenses into the frame is identical to that established in refraction.

Frame tilt The common plane passing through the base of the lens groove or the retaining ridge (see F ig . 108) is the frame plane. In anatomical lens fitting the spectacle frame is given a specific direction with respect to the perpendicular, this direction being dependent on the posture of head and body. The angle between the frame plane and the perpendicular is called the frame tilt a (see F ig . 106). The frame tilt should not be confused with the angle of side. The angle of side (the inclination of the frame sides) is the angle between the frame plane and the datum line of each of the two sides and is independent of head posture. The angle of side can be changed in the lens fitting procedure to obtain the tilt of the frame required for normal head and body posture.

The point in the frame plane through which the fixation line of the eye runs in the zero visual direction is called the zero visual point O b . Its position is dependent on head posture. The distance of the right or left zero visual point from the centre of the frame bridge (see F ig . 108) is called the monocular centration distance (p R or p L , where p R + p L = p). A specific area of the lens is used most frequently for a specific visual task. The centre of this area is called the principal visual point P B . The direction of the fixation line through the principal visual point is called the principal visual direction. In distance

Principal visual direction

SPECTACLE OPTICS : The lens/eye system 135

Fig . 106 Vertical centration and frame tilt

vision the principal visual direction is generally inclined downwards by approximately 5° to 10° with respect to the zero visual direction. Different principal visual points belong to the most frequent visual tasks (distance vision, intermediate vision, near vision). In optical lens fitting the optical centration points should be matched to these principal visual points in such a way that optimum vision is obtained for the different visual tasks. The centration point and the principal visual point do not always correspond, however, as a compromise must often be made between the different requirements of optical correction.

Distances between The corneal vertex distance d is the distance between the lens and eye ocular-side lens surface (the ocular-side lens vertex F 2 , i f the

centre of rotation requirement has been met) and the front surface of the cornea, measured in the direction of gaze at right angles to the frame plane. The distance between the ocular-side lens surface and the object-side principal point P E Y E of the eye is known as the principal point - lens vertex distance d*. The distance between the image-side (ocular-side) principal point PSP of the lens and the object-side principal point of the eye is the principal point distance d of the lens/eye system. The distance between the ocular-side lens surface and the optical centre of rotation of the eye Z ' , measured in the direc-


tion of gaze through the major reference point, is called the centre of rotation - lens vertex distance s'. It is the sum of the frame-dependent corneal vertex distance and the distance of the eye's optical centre of rotation from the front surface of the cornea, the latter distance being dependent on the ametropia present in the case of axial ametropia. A l l listed distances are taken to be positive and are shown in Fig. 107.

Fig. 107 Distances in the lens/eye system (explanation in the text)

Monocular centration

Optical centration point The point on the eyesize which is intended to coincide with the major reference point of the glazed lens is the optical centration point Z B . The position of the centration point (see Fig . 108) is determined in optical lens fitting.

Centre of rotation requirement

If the point-focal image-forming qualities of a spectacle lens are to be fully utilized, the lens must be centred relative to the eye in such a way that the object-side principal ray when viewing through the major reference point is perpendicular to the convex lens surface. In lenses with a spherical or prismatic power the optical axis then passes through the optical centre of rotation of the eye. It is for this reason that this requirement is called the "centre of rotation requirement". In a point-focal lens with a back vertex power between — 4 D and + 4 D the eye's optical centre of rotation may be located up

SPECTACLE OPTICS: The lens/eve system 137

to 3 mm away from the optical axis of the lens without any marked impairment of its image-forming properties. The higher the back vertex power of the lens, the more exactly the centre of rotation requirement must be met. In bifocals, multifocals and progressive lenses more importance should be attached to attaining a maximum field of fixation and field of view than to the centre of rotation requirement. If the centre of rotation requirement is met in lenses which are not point-focal, the gaze through the optical centre of the lens is free from oblique astigmatism.

Vertical centration The height of the optical centration point in the frame is also established in optical lens fitting. The vertical centration is directly related to the tilt of the frame as a result of the centre of rotation requirement. If the frame is tilted by the angle a, the centre of rotation requirement is met i f the major reference point of the lens is located at a certain distance h below the zero visual point. For the relationship shown in Fig . 106 the approximate formula

(95) h = a x 0.5 mm/degree

applies for a frame tilt of up to 20° with a corneal vertex distance of d = 15 mm (s' = 28 mm). If the tilt is substituted in degrees, the required vertical decentration results in mm. To meet the centre of rotation requirement, the centration point must be 0.5 mm further below the zero visual point for each degree of tilt. A lens fitting instrument is a valuable aid for correct visual centration.

Corneal vertex The refraction provides the back vertex power F' v Sp of the distance spectacle lens which fully corrects at a specific corneal vertex

distance d. This, together with the shape magnification of the selected correction lens as per formula (22), results in the refractive power F S P of the lens. The appertaining principal point distance d of the lens/eye system can be determined from the corneal vertex distance, the vertex focal length of the ocular-side principal point of the lens as per formula (24) and the distance between the anterior surface of the cornea and the object-side principal point of the eye.


The far point refraction is then

(96) K FSP

1 - d • F SP

If the corneal vertex distance for the finished spectacles does not correspond to that for the trial frame (or the phoropter), the back vertex power determined in refraction must be converted (in the case of higher powers) when ordering the lens. If x is the difference between the new and old corneal vertex distances d 2

andd[:

(97) x = d 2 - d, ,

and F'VSPI is the old back vertex power, the new back vertex power is

(98) F ; S P 2 = FySPl 1 + x • F' v vSPl

The distance x is substituted in metres. It is positive i f the corneal vertex distance is increased, and negative i f it is decreased. If the corneal vertex distance is changed in lenses with an astigmatic power, the value for each individual principal meridian must be converted. The correction values for reduction of the corneal vertex distance in positive lens powers are given in Table 38, and for an increase in the corneal vertex distance in Table 39. For negative powers, the new values obtained i f the corneal distance is increased are given in Table 38, and in Table 39 if it is decreased. If the corneal vertex distance were changed while retaining the old lens vertex power (fully correcting for the old corneal vertex distance), the result for the lens/eye system would be myopia cc for an increase in distance and hypermetropia cc for a reduction in distance, irrespective of the sign of the back vertex power.

SPECTACLE OPTICS : The lens/eye system 139

Binocular centration

Centration distance

Fig. 108 Position of the optical centration points (see Table 22 for symbols)

The distance between the two optical centration points for the two lenses of a pair of spectacles is called the centration distance z. It should be identical to the prescribed centre-to-centre distance which constitutes the distance between the major reference points of the two lenses in the trial frame or the phoropter. Every prescription should specify the necessary centre-to-centre distance in addition to the lens powers (practical values). (Note: The determination of the prescribed centre-to-centre distance is part of the refraction procedure. The prescribed centre-to-centre distance does not necessarily equal the interpu-pillary distance. P D is often written when in fact the prescribed centre-to-centre distance is intended.) If, for fitting reasons, the centration distance is required to differ from the prescribed centre-to-centre distance, this difference should be taken into account in the lens order in such a way that the mounted lenses provide the prescribed powers at the specified prescribed centre-to-centre distance. The position of the two optical centration points in the frame is established with the aid of their coordinates x,y (the distances from the nasal vertical side or the lower horizontal side of the rectangle enclosing the lens shape) or their decentration values u,v (the distances from the geometrical centre M of the lens former parallel and perpendicular to the centre of the bridge of the frame). Fig. 108 shows these distances as per D I N 58208.

\^r— vertical centre line

-m-

centre of bridge of frame

SPECTACLE OPTICS: The lens/eye system

If the centration distance is required to be asymmetrical to the centre of the bridge of the frame, the distances of the major reference points of the two lenses from the centre of the bridge should also be specified separately. The index R for the right eye and the index L for the left eye are added to the coordinates or decentration of the optical centration point. The following formula applies:

(99) z F = x R + x L + b,

where b is the bridge width of the frame (see Fig. 108). Depending on what instrument is used for the glazing process, it is sufficient to specify either the the coordinates or the decentrations. These values can be converted into each other using the following equations:

1 h (100) u = x - - und v = y - -

Near visual points In vision at a certain distance at close range the fixation lines of the two eyes intersect the frame plane in the principal points for near vision (near visual points N V P ) . The distances between these points and the centre of the frame bridge (see Fig. 108) are called NVP-to-bridge distances q R and q L . The distance p N (= Q R + QL ) between the two near visual points or the near centration distance (inaccurately also called the near P D in the lens plane) is dependent on 1. the interpupillary distance p, 2. the corneal vertex distance d, 3. the object distance and 4. the binocular prismatic power of the lenses in the near visual

points. If the (in low powers small) amount of Point 4 is neglected, then

(101) p N = Pw&TT— • r + 13 mm

where I* is the positive object distance measured from the cornea; /* and d should be substituted in mm. Table 40 gives the relationship between between p N and p for the corneal vertex distance d = 15 mm. The binocular prismatic power in the near visual points of single-vision distance spectacles is dependent on the back vertex powers of the lenses and on the centration, and can be

SPECTACLE OPTICS: The lens/eye system 141

approximated using Prentice's formula (83). The convergence requirement with spectacles deviates by this binocular prismatic power from the convergence requirement without spectacles listed in Table 21 compiled using formula (75). If the distance spectacles have been centred in such a way that the distance between the optical centres of the two lenses is greater than p N , positive lenses result in a base-out binocular prismatic power in the near visual points and therefore in an increased convergence requirement for hypermetropic eyes; negative lenses result in a base-in prism and therefore a reduced convergence requirement for myopic eyes (see Fig. 146).

Horizontal Apart from the monocular centre of rotation requirement, a centration binocular requirement must also be met, i.e. to observe the

centre-to-centre distance specified in the prescription. The accuracy of the corresponding centration distance grows in importance, the higher the lens powers. Distance errors result in undesired binocular prismatic powers in the visual points. If the centration distance is too large, the eyes must produce fusional convergence in plus lenses, and fusional divergence in minus lenses. If the centration distance is too small, the opposite holds. The tolerances recommended for observance of the centration distance constitute the maximum permissible deviations from the prescribed binocular prismatic power in the major reference points. As convergence is generally easier for the eyes (from the parallel position) than divergence, the binocular prismatic tolerance in the specified centration distance of single-vision distance spectacles is

(102) A P D = 1 — base out . m

The appertaining tolerance distances are obtained by doubling the values in Table 41. As the binocular prismatic tolerance is base-out, the centration distance for positive lenses may be larger than prescribed by the respective tolerance distance at the very most, and negative lenses correspondingly smaller. The major reference points of single-vision reading spectacles must generally be centred with respect to the centre-to-centre distance prescribed for distance spectacles. If this is not the case, the centre of rotation requirement cannot be correctly met and the switch from distance to reading spectacles or a possible changeover to bifocal, multifocal or progressive lenses becomes


more difficult, as the spectacle-wearer is used to the binocular prismatic power in the near visual points in his distance spectacles which he has also been using for near vision until now. As , in accordance with the A C A gradient of formula (70), the accommodation convergence is lessened due to the addition, a deviation from the specified centration distance may only lead to a reduced convergence requirement. The binocular prismatic tolerance in the centration distance of single-vision reading spectacles is therefore

(103) A P N = 1 — base in, m

referred to the centre-to-centre distance prescribed for the distance spectacles. A s the tolerance is base-in in this case, the centration distance for positive lenses may only be smaller than prescribed by the respective tolerance distance at the very most, and negative lenses correspondingly larger. The tolerance distances are once again twice the values given in Table 41. The same horizontal fitting regulations apply for the distance portions of bifocal, multifocal and progressive lenses as for single-vision distance spectacles. To obtain a maximum field of fixation and field of view for close range in bifocal, multifocal and progressive lenses, the frame should be tilted as much as possible and the corneal vertex distance kept as low as possible. Moreover, the distance between the two major reference points for near should be made to equal the distance between the near visual points for the selected working distance to ensure that the fields of view resulting from the two near portions optimally overlap (field-of-view requirement).

Vertical centration In general, the major reference points (for distance) of the two spectacle lenses should be given the same height in the frame. If a deviation from this is required, the desired vertical difference should be established in refraction and specified in the prescription. The vertical fitting of the near portions of bifocal, multifocal or progressive lenses is dependent on the respective optical requirements resulting from the height and visual habits of the spectacle-wearer. If the position of the major reference points (for distance) of the two lenses does not correspond to the prescribed height, the eyes are then compelled to perform fusional vertical vergence. A s the eyes are particularly sensitive

SPIX TACIT OPTICS: The lens/eye system 143

in this respect, the binocular prismatic vertical tolerance for all types of spectacles is only

cm (104) A P = 0.5 — base up or base down .

m

The corresponding tolerance distances are given in Table 41 as a function of the back vertex power of the lenses.

Anisometropia In anisometropia correct centration of the lenses in every direction is especially important, as the use of the most favourable visual points of the lenses would otherwise compel the user to adopt an unnatural viewing posture. The restriction of the useful visual field caused by the different binocular prismatic effects outside the major reference points leading to fusional vergence of the two eyes is largely dependent on the anisome-tropic difference A F'v. In bifocal and multifocal spectacles with different back vertex powers in the distance portions (main lenses) a height-compensating prism can be included in the near portion of one lens to equalise the different vertical prismatic effects in the principal visual points for near. The required power of the compensating prism is identical to the vertical prismatic difference:

(105) A P = c A F ' V .

As in formula (83), A P is obtained in cm/m if c is substituted in cm and A F' v in D . Here c ist the vertical distance of the near visual points from the optical centres of the main lenses. When the refraction results are transferred to the prescription or the lens order, the compensating prism should either be included in the near prism or be clearly indicated in some other way (e. g. "compensating prism required").

Accommodative effort and amplitude of accommodation.

Spherical ametropia If an ametropic eye is corrected by a spectacle lens with a spherical power, the amplitude of accommodation cc differs from the appertaining accommodative effort, as the spectacle-wearer does not accommodate to the near object itself, but to the image projected by the lens. The difference between the


amplitude of accommodation cc and the accommodative effort necessary for this purpose is dependent on: 1. the back vertex power of the corrective lens, 2. the principal point distance of the lens/eye system (therefore

the corneal vertex distance), 3. the magnitude of the required amplitude of accommodation

cc (therefore the working distance) and 4. the shape magnification of the lens (therefore the base

curve). If myopic eyes are corrected with spectacle lenses, the amplitude of accommodation cc is greater than the accommodative effort; i f hypermetropic eyes are corrected with spectacle lenses, the amplitude of accommodation cc is smaller than the accommodative effort. A myope with spectacles does not therefore need to accommodate as much as an emmetrope at the same object distance, while a hypermetrope has to accommodate more. See Table 42 for the numerical relationships.

Astigmatic ametropia If an ametropic eye is corrected with a spectacle lens with an astigmatic power, various differences result between the amplitude of accommodation cc and the accommodative effort in the two principal meridians. In the case of high spheres and large astigmatic differences a special pair of spectacles may be necessary for near vision (with a different cylinder than in the distance spectacles) without presbyopia being present.

Anisometropia In cases of anisometropia where lenses with high back vertex powers are required, an identical accommodative effort for the two eyes leads to different amplitudes of accommodation cc. If problem-free near vision is to be guaranteed, a special pair of reading spectacles (with a different anisometropic difference than in the distance spectacles) may be necessary even if presbyopia is not present. With the onset of presbyopia, different additions for the two anisometropic eyes may be required.

Addit ion The addition A required for presbyopic eyes is determined from the maximum amplitude of accommodation cc (A A m a x c c ) and the desired working distance (amount of focusing refraction B E c c ) using the approximate formulae


Fig. 109 Maximum amplitude of accommodation cc as a function of age (parameter back vertex power Fv of the fully correcting lens)

(106)

(107)

BE.cc - 3 • A \ * c c for A A m a x > c c > 1 D

A = B H. cc A A m a x c c for A A m a x c c < 1 D

A l l values are substituted in D . Fig . 109 shows the maximum amplitude of accommodation cc as a function of age and the back vertex power of the fully correcting spectacle lens. The additions resulting from formulae (106) and (107) should only be taken as approximate values. Individual refraction for near vision is essential in every case. As the amplitude of accommodation cc of hypermetropic eyes corrected with spectacle lenses is less than their accommodative effort, the hypermetropic spectacle-wearer requires an addition at an earlier stage than an emmmetrope of the same age. A myope with spectacles, on the other hand, does not require an addition until a later stage, as his amplitude of accommodation cc is greater.

Space perception

Field of fixation The optical centre of rotation Z ' of the eye is the image formed and field of view by a spectacle lens of the (virtual) apparent centre of rotation of

the eye Z . The apparent centre of rotation is located in front of the optical centre of rotation Z ' in lenses with a negative back vertex power, and behind it in lenses with a positive back vertex power (Fig. 110). The object-side angular field is consequently larger for minus lenses and smaller for plus lenses than the ocular-side angular field. This means that the object-side field of fixation (and the field of view) of a myopic eye corrected with spectacle lenses is larger, and that of a hypermetropic eye smaller than that of an emmetropic eye with identical ocular-side angular fields. The maximum object-side angular field and therefore the size of the appertaining field of fixation is dependent on 1. the eyesize diameter, 2. the back vertex power of the lens and 3. the corneal vertex distance. Table 43 contains the diameters of fields of fixation for a distance of 5 m.


Fig. 110 Position of the apparent centre of rotation Z of the eye relative to the ^ — ' optical centre of rotation Z' in positive — and negative corrective lenses * ^

The increase in the field of fixation and the field of view for the myopic eye corrected with spectacle lenses may result in the outer area of the field of view being seen both in- and outside the spectacle lens, leading to an annular doubling of the image (see Fig . 143a). For the hypermetropic eye corrected with spectacle lenses, on the other hand, a blind area results around the sharp field of view (annular scotoma, see Fig . 143b) due to the reduction in both the field of fixation and the field of view. Objects located in this area cannot be perceived without movement of the head, which is particularly unfavourable in the case of moving objects coming from outside. Since the field of fixation and the field of view become smaller with increasing positive power of the lens, large eyesize diameters or special cataract lenses are recommended here (see Fig. 91). Example: A t a distance of 5 m and with a lenticular of 32 mm diameter, a patient who has had cataract surgery and is now


using a corrective lens of + 12.0 D would only have a field of fixation with a diameter of 4.1 m, which would increase to as much as 5.1 m with a lens diameter of 44 mm. A myope with a corrective lens of + 12.0 D , on the other hand, has a field of fixation of 8.6 m at a distance of 5 m with a lenticular of 32 mm dia.

Perspective The differences between the object-side and the ocular-side angular fields lead to a change in depth perception. This change results in deepened perspective for myopic spectacle-wearers, i.e. depth in space is overestimated. The hypermetropic spectacle-wearer obtains a flattened perspective, i.e. depth in space is underestimated. The change in perspective is increased, the greater the back vertex power of the corrective lens.

Magnification The size of the image of an object on the retina of an eye corrected with a spectacle lens is different from on the retina of an emmetropic eye of the same length. The ratio of these image sizes (the magnification) is dependent on 1. the back vertex power of the lens, 2. the corneal vertex distance and 3. the shape magnification of the lens. The power magnification P is the ratio of the far point refraction K of the eye to the vertex power Fy of the fully correcting spectacle lens:

(108) P =

The total magnification S M in the lens/eye system is the product of the power magnification P and the shape magnification S:

(109) S M = P S .

If P and S are replaced using (108) and (22), the following magnification results together with formula (96):

(110) S M = 1 = l + d K . 1 - d F S P

Therefore, for the myopic eye corrected with a spectacle lens, the magnification S M < 1, which means a reduction in the size of the retinal image; hypermetropic eyes corrected with a spectacle lens obtain a magnified retinal image, as S M > 1. If the corrective lens is shifted 1 mm in an axial direction, the size


Fig. 111 Total magnification S M in the lens/ eye system as a function of the vertex power Fy and the corneal vertex distance d

of the retinal image is changed by approximately 0.1 %, and a reduction in the corneal vertex distance leads in minus lenses to a larger, and in plus lenses to a smaller retinal image. Fig . 111 shows the total magnification for corneal vertex distances of 12 and 16 mm.

1.8

1.6

1.4

1.2 c O « 1

0.8

- d = 16 >

mm /

-

- 12 mm

-

- d = 15

~"d""=""l6 mm

0.6 -20 -15 -10

Back vertex power FJ, -5 10 15 D 20

As the shape magnification is dependent mainly on the centre thickness of the corrective lens, it should be neglected for minus lenses, but taken into account for plus lenses with a centre thickness greater than approximately 3 mm. Table 44 contains the shape magnification of spectacle lenses with a positive spherical power from 1.5 D .

Aniseikonia In corrected anisometropia a difference between the size of the retinal images in the two eyes is caused by the different magnification in the right and left lens/eye systems and may lead to optical aniseikonia. The latter can be influenced by a change in the corneal vertex distance, as the magnification according to formula (110) is dependent on the principal point distance of the lens/eye system. The extent to which the optical aniseikonia changes is determined by the amount of the change in the corneal vertex distance (which is the same size for both the right and left eyes) and by the difference between the far point refractions of the two eyes. If the shape magnification of the corrective lenses is neglected and if P i (in %) is the aniseikonia measured at the corneal vertex distance d i , x (in cm) the change in the corneal vertex distance according to formula (97) and A F' v (in D) the anisometropic

SPECTACLE OPTICS: The lens/eve system 149

difference according to (76), the approximate aniseikonia to be expected at the new corneal vertex distance d 2 (in %) is:

(111) P 2 = P | + x A F ' v .

The measured aniseikonia should be substituted with a positive sign i f the larger visual impression belongs to the eye whose corrective lens exhibits the mathematically larger vertex power F v 2 ; i f this is not the case, it should be substituted with a negative sign. The change in the aniseikonia is approximately 0.1 % per millimetre change in the corneal vertex distance and per dioptre of anisometropia. In positive aniseikonia a decrease in the corneal vertex distance (x is then negative) results in a reduction in the aniseikonia. The position in which the two lenses must be located for the correction of two anisometropic eyes in order to provide identically sized retinal images (neglecting the shape magnification) is sometimes called the magnification zero point. In axial anisometropia this point lies at the object-side focal points of the eye, and in refractive anisometropia at the object-side principal points of the eye. The (always subjective) measurement of aniseikonia does, however, take precedence over any theoretical examination of the size of the retinal images and their effects.

Low Vision Aids

Visual handicap Social welfare legislation in the Federal Republic of Germany defines a person as visually handicapped i f his or her visual acuity is 0.3 - 0.075 in the better eye using the best possible dioptric correction. The limits for extreme visual handicaps are set at a visual acuity of 0.05 - 0.03. Similar stipulations exist in other countries. Other criteria are the field of view, the ability to perceive light and colour and, above all, the reading ability. Reading, unlike the mere recognition of single optotypes, is not possible unless a minimum expanse of functioning retina is present. Visual handicaps should always be seen in the context of congenital, acquired and age-related diseases of the eye. Common causes are degeneration of the macula, extremely high myopia, optic atrophy and tapetoretinal degeneration.


Magnification

1H|PPM gagas 1 l! ., ./ , f ,, , ,[>,.,, | \J. tt f .« >t 1

|r N a h s e h p r o b e n M a h s e h p r o

Fig. 112 Zeiss near vision test charts

The required magnification of a visual aid is essentially determined by the ratio of the visual acuity or reading ability attainable without magnification to the required visual acuity. A reading ability corresponding to the acuity grade 0.4 - 0.5 is generally sufficient for reading common newspaper or letterpress print. Similar requirements exist with regard to distance vision for the reading of road signs or bus numbers, for watching television, etc. This means that magnifications of 1.5 - 6x and in the case of severe visual handicaps 8 - 20x are required to cater for the general requirements of the visually handicapped. The required magnification is obtained taking into account the refractive condition of the eye, preferably with special test charts for near vision (Fig. 112).

Visual aids for Telescopes are used for magnification of the retinal images of distance distant objects. A distinction is made between the Galilean

telescope and the Kepler telescope, depending on the optical design. The Galilean telescope features an objective with a positive and an eyepiece with a negative power. A t lower magnifications of up to approximately 2 - 2.5x the image quality is acceptable depending on the relative aperture and decreases considerably at higher magnifications. There is no sharp demarcation of the field of view due to the position of the exit pupil (virtual between the objective and the eyepiece). Eye movement is possible within certain limits. Kepler telescopes consist of an objective and an eyepiece with positive powers and a reversing prism. Depending on the state

Fig. 113 Zeiss telescopic spectacles with a Galilean and a Kepler design

151

of correction, they even provide good image quality at high magnifications. The position of the exit pupil, which is intended to correspond to the entrance pupil of the eye, is real behind the eyepiece. Kepler telescopes must be exactly centred with respect to the eye, and eye movement is only possible to a limited extent. Monocular, or less frequently binocular, telescopes are either held in the hand or mounted in spectacles, depending on their intended use (Fig. 113). The narrowing of the field of view resulting from the telescope and the change in perspective caused by the magnification influence space perception in such a way that use of the telescopes is not recommended for mobile use.

Visual aids for The simplest type of magnification is by actually moving closer near to the object. The possibilities are determined by the degree of

the visual handicap and the accommodative power present. In the simplest case the lacking accommodation is replaced by a lens with a positive power. This is possible with the aid of spectacle lenses or loupes. Spectacle lenses with high dioptric powers can be designed as single-vision or bifocal lenses (Fig. 114).

Loupes are available for hand use or for mounting in an upright position, with or without additional illumination. High-power spectacle lenses and loupes have relatively short focal lengths and unavoidably small working distances. Larger working distances are obtained with telescopic loupes. These systems consist of, for example, a telescope and a loupe mounted on the object side. Comparable systems are created if the power of the eyepiece is decreased or the distance between the objective and the eyepiece is increased.

Fig. 114 Zeiss magnifying bifocals


Image formation is performed in such a way that the object is located in the focal point of the loupe which then produces a virtual, magnified image of it at infinity. This loupe image is then viewed through the telescope located behind it with the appropriate telescope magnification (Fig. 115).

Fig. 115 Optical design and principle of a telescopic magnifier with example of possible magnifications

Mtolal = 5 X ^telescope = 1.8 X

= 2 .78 x

Fig. 116 Zeiss Telescopic Magnifying Spectacles

The total magnification is the product of the loupe magnification and the telescope magnification:

(112) Mtotal = Mi, M , Moupe m telescope-

The working distance of a telescopic loupe is dependent on how much of the total magnification is comprised of the loupe magnification and the telescope magnification. The higher the telescope magnification, the smaller the share of the loupe magnification will be. Correspondingly, the focal length of the loupe and therefore the working distance are increased. Fig. 116 shows a visually handicapped person using binocular telescopic magnifying spectacles of the type Zeiss Prism Magnifying Spectacles C .

Supplementary The change in visual conditions caused by low vision aids aids (narrowing of the field of view, reduction in working distances)

may makeit necessary to use supplementary aids. In the case of high magnifications in particular, the use of special reading tables or desks proves very beneficial. In general, care should be taken to ensure good lighting conditions. Only in the event of turbidity of the ocular media and the scatter which this causes is it necessary to reduce the lighting.


Visual aids for precision work

Fig. 117 Zeiss Prism Magnifier with fibre optic illumination

In many activities in medicine, technology, art and other fields it is only possible to achieve optimum results i f the objects in question are observed with an adequate magnification. There are many possibilities of providing this, from loupes and telescopic loupes to surgical microscopes. Telescopic loupes are available as either Galilean or Kepler systems with magnifications of 2 - 8x. When used for this purpose, they are generally binocular in the form of spectacles or they are attached to a headband, therefore permitting stereoscopic near vision with a high degree of mobility. Fibre optic illumination devices can also be attached to some of these systems (Fig. 117) to provide sufficient brightness on the object.

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