Acta Ophthalmologica S U P P L E M E N T U M 1 5 1

The Kerala Decentration Meter A new method and devise for fitting the optical of spectacle lenses in the visual axis

Thomas K. Joseph Harrison Medical Centre, Chicago, Illinois, U.S.A.

C. P. Kartha University of Michigan-Flint, School of Management, Flint, Michigan, U.S.A.

scriptor C O P E N H A G E N 1 9 8 2

0 1982 by Scriptor Publisher ApS

Printed in Denmark by Bogtrykkeriet Forum Copenhagen

ISBN 87-87473-55-0

A C T A O P H T H A L M O L O G I C A V O L . 6 0 1 9 8 2 S U P P L E M E N T U M 1 5 1

Centring of spectacle lenses is a much neglected field of ophthalmology. The prismatic effect caused by wrong centring results in a phoria on the eye muscles which in turn causes persistent eyestrain. The theory of visual axis, optical axis and angle alpha is discussed. Using new methods the visual axis and optical axis of 35 subjects were measured. The results were computed for facial asymmetry, parallax error, angle alpha and also decentration for near vision. The results show that decentration is required on account of each of these factors. Considerable correction is needed in the vertical direction, a fact much neglected nowadays; and vertical decentration results in vertical phoria which is more symptomatic than horizontal phorias. Angle Alpha was com- puted for each of these patients. A new devise called ‘The Kerala Decentration Meter’ using the pinhole method for measuring the degree of decentration from the datum centre of the frame, and capable of correcting all the factors described above, is shown with diagrams.

The need for centring the otical center of the lens irl the visual axis

It is extremely important that when glasses are fitted the optical centre should correspong to the visual axis of the patient’s eyes, for it is only when this condition is satisfied that rays of light will travel to his eyes without suffering deviation (Duke-Elder 1965). A lens is a combination of prisms, and when light passes through any part of the lens other than its optical centre the effect is that of a prism with its base directed towards the thickest part of the lens. The optical centre is the centre of the optical system formed by the lens and all rays pass through it undeviated.

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Fig. 1. A Decentred Lens: The Optical centre (0) is placed eccentrically. The curvature of the lens is the same, but the lens behaves as if a prism bac is sandwiched between the lens curvatures. A

ray passing through the geometrical center (C) will be deflected by the prism.

The Geometric centre of the lens is the point in the middle of the lens and is just a relation of the placement of the lens in the frame. Fig. 1 shows a lens in which the optical centre does not correspond to the geometric centre of the lens. It is graphically demonstrated in the diagram that the optical effect of this lens is the same as if a prism has been interpolated into the substance of the lens. The curvatures on either side of the lens remain the same, but the lens behaves as if a prism has been sandwiched between the 2 spherical surfaces.

The strength of the prism introduced by the decentration varies with the dioptric power of the lens and the distance by which it has been decentered. The amount of decentration in millimeters equals lON/D when N i s the number of prism dioptres and D the strength of the lens. There is one prism dioptre effect for every 10 mm of decentration, for a one dioptre lens. And when a -10 D sphere is worn an error of only one mm in each eye will entail a total error of convergence of one prism dioptre (Duke-Elder 1965).

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Syrnptornatology of wrong centring

The symptomatology of wrong centring is not described in the literature, but we can postulate the symptoms. When a prism is introduced in a spectacle by wrong centring the net result is that of a phoria on the eye muscles. Decentring a convex lens inwards or a concave lens outwards has the optical effect of a prism base in, and the net result is that of an esophoria on the eye. When a convex lens is decentered upwards or a concave lens is decentered downwards, it acts as a prism with its base upwards. The results is that of a hyperphoria. As we know, a hyperphoria or hypophoria is much more difficult for the eye to tolerate and is more symptomatic than an equal amount of horizontal phoria. This is so because the eyes can converge and diverge with ease, but they connot ride up or down upon each other.

The symptoms of decentring is therefore the same as that of phoria. The most obvious symptom is a diplopia, but the eye muscles correct minor errors caused by the prisms and in so doing fatigue themselves. The symptomatology of eyestrain follows with its accompaniment of pain in the eyeballs and headache. When a patient experiences symptoms of eyestrain soon after wearing a new pair of glasses one must think of wrong centring of lenses. It has often been noted that a patient takes some time in order to get accustomed to a new pair of glasses. As we noted before the symptoms of wrong centring will be more marked in wearers of the higher dioptric power lenses because even a small error will result in a strong prismatic effect.

As the wearer of a -10 D lens, I (the senior author) go through a period of eyestrain each time I wear a new pair of spectacles. If by some mischance I misplaced or damaged my spectacles and had to wear an older pair of glasses I still get all the symptoms of eyestrain. I do not get any diplopia unless I am fatigued or drowsy. Upon wearing the older glasses I get what may be called a dysopsia (cf micropsia, macropsia), i.e., unusal angulation of the shapes and slopes of the floor and walls. Within 20 sec after wearing the older glasses I experience pain in the eyeballs, and the headache chrystallises within 15 min and lasts for several h. However, if I wear an older pair of glasses the first thing in the morning after a good night’s sleep, the the symptoms are much less. The strength of all my spectacles are the same, and I feel convinced that these symptoms are the result of wrong centring. The dioptric power of my glasses increased steadily during my school years but has remained unchanged since the age of 18 when my growth period was over. The only effort at centring, whenever the glasses were made in India or USA was to measure the interpupillar distaice with a millimeter rule. Elaborate experiments are needed to determine what percentage of the glass wearing population is suffering from headaches owing to wrong centring of lenses. However, such experiments can only be performed when instruments to measure the position of the visual axis in the spectacle plane are available.

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The variables influencing the centring of lenses

1) Facial asymmetry

No face is perfectly symmetrical. Facial symmetry of 35 subjects has been measured and described elsewhere in this article. Sasieni (1975) has observed that a difference of 1-3 mm can be observed in the relative height of the eyes in some 20% of cases. Fry & Ellenbrock (1941) have also observed vertical asymmetry of the eyes. Duke-Elder (1965) has suggested that in the event of facial asymmetry it usually looks better to decenter the lenses so that the optical centres are cut by the visual axis. In today’s optical industry the vertical position of the visual axis is totally neglected.

2) Mass production of frames

Nowadays spectacle frames are mass produced. Very often a patient may select a frame, the datum centre of which do not correspond to the visual axes of his eyes. This problem can only be solved by decentring the optical centres of the lenses to the visual axes.

3) Oddframes

Some of the fashionable frames made today are so odd shaped and unevenly large that their datum centres are invariably away from the visual axis in most patients and dencentration is needed for proper centring.

4) Angle alpha

The visual axis cuts the comers slightly to the nasal side of the cornea so that when the eye looks directly forward at an object the optical axis is directed somewhat out. The angle between the optical axis and the visual axis is called the angle alpha (see below). It may be pointed out that all the methods and gadgets available today can only measure the optical axis at best and not the visual axis .

5) Decentring to correct heterophoria

Sometimes the patient may have a heterophoria, and we may be able to correct this by decentring his lens to the desired position. In fact, this is the only indication for decentering recommended in some textbooks. Elaborate tables have been prepared as the the degree of prismatic power produced by the effect of decentring (Stimson 197 1). In these cases the optical centre has to be decentred away from the visual axis by the desired distance.

6) Near vision

The need for decentring for near vision is well recognized. Duke-Elder (1965) has recommended that the centre for near vision must be decentred 2.5 mm below the horizontal and 2.5 mm inner to the midline.

Frame measurements

Various systems were used in different countries for measuring the spectacle frame. We will consider some of these.

In the British Standard 3 199 (Sasieni 1975), the datum line of a lens is defined as the line midway between and parallel to the horizongtal and vertical tangents to the lens shape at ists highest and lowest points (Fig. 2). The datum centre is the midpoint of that part of the datum line which is bound by the lens shape. The datum length of a lens (or rim of frame) is its horizontal dimension measured through its datum centre. The vertical dimension of the lens or rim is also measured through this point and is known as the middatum depth. All measurements of a lens are taken to the outside or peak of the bevel if any and measurement of a rim to the bottom of the grove. DBL is the distance between the lenses measured at the datum line (Fig. 2) (Sasieni 1975).

In USA and Germany they use the Boxed lens size, which is the length and depth of the rectangle containing the lens and the DBL, the distance between the rectangles. Boxed GCD (geometric centre distance) is the distance between the geometric centres of the rectangles and may be different from the datum centre distance (Sasieni 19’75).

-1

I I I

C a A d - 4 Fig. 2.

Measurements of the Frame (British Standard 3199). The dotted line represents the peak of the bevel or the bottom of the groves - DD: Datum line. M: Datum Centre of the right lens. M-Datum Centre of the left lens. a: Datum length of the lens. c: Datum centre distance (DCD), d: distance between the lenses (DBL), e: distance between the rims (DBR), m:

minimum between the lenses (MBL) Note c = a+d.

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In 1964, a technical committee consisting of the representatives of the Common market countries - Groupment de Opticiens du March6 Commun (GOMAC) published a standard which was based upon a combination of the features of the datum system, the boxing system and others. They used 5 terms included in the British Standard 3 199, described above, but defined them in different terms.

Current methods of measuring the face

A number of methods and gadgets are available for measuring the interpupillar distance (PD). However, today, the only measurement taken by most opticians, in USA and India is only the horizontal distance between the 2 pupils. Brooks (1979) recommends sighting the pupillary border of the patient’s right eye with the observer’s left eye on the zero of a millimeter rule and then sighting the position in millimeters of the patient’s left nasal pupillary margin using the observer’s right eye, the other eye being closed.

Duke-Elder (1965) recommends the use of the centring glasses, in which a crosswire is etched, in sighting the reflection of a light at infinity at which the patient is looking. There are a number of gadgets available in the market that measures the Pupillary distance. The sliding PD Gauge (Sasieni 1975) has a plano lens with horizontal and vertical line etched on it, and the distance between the two is engraved in millimeters in a bar on the top. The Reflex PD Gauge (Sasieni 1975) works on the principle measuring the distance between the corneal images of a light. The Sasieni Reflex P Gauge and the Topcon PD Meter (Sasieni 1975) uses the split image (of the pupil) coincidence system based upon the principle of a simple range finder. The Essel Pupillometer (Sasieni 1975) measures the right and left half PD. The Baush and Lomb PD Gauge (Saieni 1975) also measures the half PD. The Essel Corneal Reflection Pupillometer measures the fixition axis, and in 3 scales indicate the right and left half PD and the total PD for distance. The Zeiss Jena PD gauge (Sasieni 1975) measures the distance between the centre of each pupil and measures half PDs. None of these instruments, however, measure the verticle position of the pupil on relation to each other as well as with the frame, nor do they allow for the angle alpha.

The optical axis, visual axis and angle alpha theoretical considerations

In a system with multiple refracting surfaces the optical axis is that line that passes through the centres of curvatures of all the optical surfaces. The nodal point of

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such a system can be computed using the Gaussian equation. In the human eye, there are 3 such surfaces, the anterior corneal surface, and the anterior and posterior lens surfaces. Strictly speaking, none of the refracting surfaces of the eye are symmetrical about the principal axis (Duke-Elder 1970). The cornea does not have a true optical centre and the lens is slightly tilted. Therefore, the eye does not have a true optical axis. This fact can best be illustrated by the fact that the Purkinge images of an object at which the eye looks at directly can never be accurately superimposed on one another as they would be if there were a true optical axis (Duke-Elder 1970). It has been postulated that the astigmatism produced by the tilt of the lens may tend to cancel out that of the cornea (Duke-Elder 1970).

Bearing in mind these reservations, we can therefore accept the concept of an optical axis; it is that theoretical axis upon which lie the optical centres of the refractive surfaces and is the common axis of all of them. It passes through the nodal point of the eye (Duke-Elder 1970).

The visual axis

When an object is fwated, the eye is moved in such a way that the image falls upon the fovea, the furation point and the fovea being thus conjugate foci. The Visual Axis is most simply defined as the line passing through the fixation point and the fovea; and like the optic axis it passes through the nodal point of the eye (Duke-Elder 1970).

Angle alpha

The optical axis rarely passes through the fovea, the fovea is below and temporal to the optical axis. There is an angle between the optic a x i s and the visual axis where the 2 cross at the nodal point of the eye. This angle is called angle alpha (Fig. 3).

Na Fig. 3.

The Angle A l p h - T: Temporal side, Na: Nasal Side, M: Ma&, N: Nodal point of the eye. FNM: Visual Axis, connecting the point of furation (F) to the Macula (M), ONB: Optical Axis.

The 2 cut at the nodal point (N), the angle ONF is the angle alpha (exaggerated).

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Some other axes of the eye have been described. One of these is the Pupillary axis or the Central Pupillary Line. This line is perpendicular to the corneal surface and passes through the midpoint of the entrance pupil, i.e., the limage of the real pupil as seen by the dioptric system in front of the iris (Duke-Elder 1970). This axis may be located by looking along a beam of light such as the ophthalmoscope and locating the corneal reflex that coincides with the centre of the pupil; this axis would pass through the light bulb and its corneal image.

The angle kappa

Defined as the angle between the central pupillary line and the principal line of vision (Duke-Elder 1970). It is somewhat smaller than the angle alpha, when as is usually the case there is a slight nasal decentration of the pupil. In some subjects, the angle kappa will vary with the size of the pupil if there is a tendency for the eccentricity of the pupil to alter with change in diameter (Drew 1970).

Estimation of angle alpha

In the commonest optical situation, the optical axis strikes the retina about 1.25 mm above and to the nasal side of the fovea. Correspondingly, the visual a x i s passes through the cornea above and nasal to its centre. If in Fig. 3 MB is 1.25 mm and if we eccept NM = 15 as in Donder's reduced eye, sin a = 1.25115 = 0.083, whence a

big. 5. Fig. 4.

The position of the hrkinge images when a subject looks directly into the telescope of Tscherning's phakometer. In the middle the image of the cornea, on the right those of the

anterior surface of the lens, on the left those of the posterior surface of the lens.

Fig. 5. The Purkinge images aligned when the subject looks at an angle corresponding to the angle alpha towards the nasal side. The optical axis of the eye now coincides with the axis of the

telescope.

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= 5", (Duke-Elder 1970). In this situation, angle alpha amounts to nearly 5 degrees and is said to be positive. The angle alpha is small lor leven negative in myopes and larger in Hypermetropes (Duke-Elder 1970).

The demonstration of angle alpha can be made by the Ophthalmophakometre of Tcherning. The subject first looks down the axis of the telescope; and this axis now coincides with the visual axis. The Purkinge images are now nonaligned (Fig. 4). Then the eye is moved so that the various Purkinge images of the light sources directly above and below it appear aligned. Strictly speaking this is not possible, but the closest approximation will give the position of the optic axis and the degree of rotation of the eye will indicate the size of the angle alpha (Fig. 5) (Duke-Elder 1970).

From the review of literature, no actual measurement of the visual axis or angle alpha could be found. In our experiments we have measured the actual value of the angle alpha.

Experimental measurement of visual axis, the optical axis and angle alpha

Measurement of visual axis

We used a pinhole to measure the visual axis. The subject is seated on a chair and looks at a target through a pinhole in each eye. He then sees 2 circular fields of vision. The 2 pinholes are slided gently over the empty spectacle frame by his own hands until he fuses the 2 circles into one with the target in the centre, of the circle. At this time the subject is furating his eyes on the target and its image falls on his fovea. In a cross section of the system (Fig. 6) there are two isoceles triangles with a common axis. The base of one cone is the circular area of the field of vision seen by the subject and the base of the other cone is its circular image upon the retina. At the centre of the first circle is the pointsource of light furated by the subject and at the centre of the second circle is the fovea. The 2 cones have a common axis which is a strainght line loining the object of furation with the fovea and passing through the one mm pinhole. Therefore, the pinhole is in the visual axis, of the eyes.

Why a one mm pinhole was used

Using concentric circles of different colours and of known visual angle as a target on a wall 185 cm away from the patient's eyes it was found that with the pinhole in the spectacle plane, the sue of the field of vision with undhted pupil in the dark room viewed through pinholes of different sizes varied in visual angles from .12.5 degrees to 17.5 degrees, in different persons. The size of the visual angle is the same with pinholes of 0.5 mm, 1 mm and 1.5 mm. With the narrower pinholes the

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Fig. 6. The principle of the pinhole method of locating in the visual axis. The patient is looking through the pinhole and has positioned it so that the circular field he sees through both eyes has fused into one with the centre of the target in the centre. There are 2 cones (isoceless triangles) with a common axis. At the centre of one circular base is the target (T) and at the centre of the other circular base is the macula (M) since the patient has his eyes futated on the target. The line TPM is a straight line joining the macula (M) with the object of fmation (T).

Since the Pinhole (P) is located on this line the pinhole is in the visual axis.

margins are sharper, but the brightness is less. When pinholes of 2 mm and 2.5 mm were used the size of the visual angles increased slightly, but the margins were very blurred. When the pupils were dilated the size of the visual angle increased by 2.5 degrees to 5 degrees, using the same pinhole. This proves that the circular shape of the pupil cuts off the peripheral rays and is responsible for the size and circular shape of the image. A one mm pinhole was indeed found to be the optimum sue. We had one patient with a pear shaped congenital coloboma. When she was asked to describe the shape of the image seen, she said it was elongated: when 4 shapes were drawn on a paper and presented to her, one of them circular, one ellipse, one oval and one pear shaped, she immediately pointed to the pear shape, further proving that the pupil is the factor responsible for the size and shape of the visual angle viewed through a pinhole.

Description of the pinhole devise used in the experiments (Fig. 8)

The instrument used for the experiments was a glass plate 6 mm x 6 mm. The corners were rounded off and the nasal corner was more rounded off in order to accommodate the nose. A paper of the same dimension was mounted on to the glass plate, the back side of the paper being black in order to improve the contrast, and the pinhole being only in the paper, the glass being transparent. at the upper outer corner, the paper was graduated in mm indicating the horizontal and vemcal position of the pinhole.

The frame used for all the experiments was a standard shell frame of datum length 46 mm and DBL 20 mm, the datum centre distance (cf PD) being 66 mm. A horizontal white line was made on the upper rim of the shell frame and also a vertical line perpendicular to it was made on the outer rim, as landmarks for

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n - C W - A

Fig. 7. The rays of light emanating from target (light bulb), 0 is reflected from 2 different positions on the cornea because the observer has to dodge to either the medial side or lateral to the light source. The average of the crosswire A (CW-A) and crosswire B (CW-B) is a line perpendicular to the most convex part of the cornea and therefore represents the Optical

Axis.

measurements. When the pinhole devise was mounted on the frame with the horizontal and vertical lines on the frame apposed to the zero mark on the vertical and horizontal scales, respectively, the pinhole was in the datum centre of the frame. Any decentration of the pinhole in any direction could be read off in mm by noting the readings which were apposed to the landmark lines on the r i m s of the frame.

The target

The target used for all the experiments was a screen with a bare 25 watt bulb in the centre and radial lines emanating from it, the horizontal and vertical lines being bolder. The screen was placed at a distance of 3 m.

The subjects

The subjects were all 35 healthy medical students, 31 of them being emmetropic and 4 of them having minor errors of refraction. No corrective lenses were worn during the experiments, using only the experimental empty shell frame.

The seat

The seat was a high stool and the height of the eye was equal to the height of the target. The experimentor was standing at eye-level to the subjects and the readings were taken at comfortable flexed hand length.

Measurement of the optical axis

The optical axis was measured by a modification of the method described in Duke-Elder’s Practice of Refraction (Duke-Elder 1965). The subject is seated in a stool with his eyes fmated on a light source at infinity. The image of the light is seen

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Fig. 8. The pinhole devise used in the experiments. The pinhole is on a paper glued to the glass plate. There are graduations on the paper indicating the verical and horizontal position of the pinhole with respect to the frame which can be seen on its upper outer comer. Note the

horizontal and vertical landmark lines on the frame.

in the front of the cornea and is located using a cross wires etched on a centring glass, the image on the right eye being located with the observer’s left eye and vice versa. As we proceeded with this experiment considerable parallax error was experienced and in order to correct this 2 sets of measurements were taken for each eye the right eye being sighted with the observer’s right eye as well as with the left eye and the same with the subject’s left eye. Duke-Elder, however, recommended this method for measuring the visual axis. Fig. 7 demonstrates how 2 sets of measurements with equal parallax error for the same eye cancels out by averaging, thus giving us the position of the most convex part of the cornea. The most convex part of the cornea is assumed to be the point at which the optical axis cuts the cornea when the eye is furated at infinity. Indians have black eyes and it is not easy to measure the centre of the pupil, however accurate it may be. Our results of analysis of the angle alpha from these measurements further proves that we are measuring the optical axis by th is method.

Fig. 9. The crosswires used in the experiments. The crosswire is etched on the glass and the graduations are on the paper fixed to its upper outer comer. The position of the crosswires

can be read off on the landmark lines on the frame.

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Devise used for measuring the optical axis (Fig. 9)

For this glass plates of the same dimensions which were used for the pinhole devise were used. On these glass plates perpendicular horizontal and vertical lines were etched. On the upper outer part of the plate was mounted a paper with graduations in millimeter. When the zero marks were apposed to the landmark horizontal and vertical lines on the frame, then the centre of the crosswire was in the datum centre of the frame. Any decentration of the centre of the crosswire from the datum centre could be read off in millimeters.

Crosswire A and B experiments

TWO sets of crosswire experiments were done because of the considerable parallax error that became evident (see below). In crosswire A measurement the observer stood in front of the patient and moved his head from a lateral to medial position and let the light reflex (F’urkinge image No. 1) on the cornea just pop into view, the light source until then covered by his own head, and then the observer slided the crosswires across the frame to appose the centre of the crosswires to the reflection of the light on the cornea. The readings on the landmark lines on the frame were noted. The cross-wire B experiments were also done in a similar manner, the difference being that the observer’s head was moved from a medial to a lateral position until the reflection of the light on the cornea just popped into view. While sighting the crosswires over the light reflection, the observer’s opposite eye was closed by squinting.

Near vision experiments

Centring for near vision was tested using the pinholes. The subject was shown a card with a target and holding the target at the reading position which each person is accustomed to, he was asked to view it &rough the pinholes and slide them until the 2 circles fused into one with the target in the centre. Then the decentration of the pinholes were read off on the landmark lines on the spectacle frame.

Sequence of experiments

One set of measurements consist of 4 readings. RH (Right horizontal), RV (right vertical), LH (left horizontal) and LV (left vertical). For each subject 10 sets of readings were taken for the pinhole method, 10 each for the crosswire A and crosswire B readings and 10 for the near vision method. The 4 methods were taken in series alternating each method in successive experiments. The human error was thereby equally distributed for each method. All these measurements were taken in rapid sequence and read out to an assistant who recorded the results.

In analysing the results the mean of 10 readings were used. The average of crosswire A and crosswire B readings were used in all graphs and computations except in analysing the parallax error.

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The data is analyzed and the results are plotted in graphs. The spectacle shape in the graphs is only for size comparison, the datum Centre is the zero point and the dots are computed values.

Corn pu ted resu I ts

Parallax error

The means of crosswire A readings for each subject was substracted from the means of crosswire B readings and this gives the parallax error. The results are plotted in graph in Fig. 10 and in Table 1. The parallax error was 0- 1 mm in one eye, 1-2 mm in 8 eyes, 2-3 mm in 19 eyes, 3-4 mm in 7 eyes and over 4 mm in 5 eyes. The difference in Verticle measurement was much less, being less than 1 mm in 48 eyes, 1-2 mm in 12 eyes, 2-3 mm in 5 eyes, 3-4 mm in 3 eyes and over 4 mm in 2 eyes. The average parallax error was 3.5 mm horizontal and less than 1 mm vertical.

Facial asymmetry

For computing facial aysmmetry the means of crosswire (A and B) for lthe left side was subtracted from that of the right side. The results are graphed in Fig. 11. The averages are close to zero and the results are arranged in random. Horizontal facial asymmetry of over 2 mm was found in 9 subjects, and that of over 4 mm was found

w i

Fig. 10. The Parallax error between crosswire A and crosswire B experiments is demonstrated in this graph. The means of crosswire A readings are subtracted from the corresponding means of crosswire B experiments, and the results are plotted in the graph. The average parallax error

(marked by x’s) was 3.5 mm horizontal and less than 1 mm vertical.

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0-1

mm

RH

R

V

LH

LV

RH

: Rig

ht H

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onta

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ight

Ver

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RH

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RV

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%zz? Fig. I I.

Facial asymmetry. For computing facial asymmetry the means of crosswire (A and B) for the left side was subtracted from that of the right side. The results are graphed here. The averages (marked by x’s) are close to zero and the results are randomly arranged all around it.

in 2 subjects. Vertical facial asymmetry of over 2 mm was found in 6 subjects and that of over 3 mm was found in 2. These results indicate that facial asymmetry is a considerable factor to be reckoned within the centring of spectacles.

Near vision

The amount of decentration for near vision was found by subtracting cor- responding values of the pinhole method for distant vision from the average values for the near vision. The results are graphed in Fig. 12 and shown in Table 1. Convergence of less than one mm was found in 2 eyes, 1-2 mm in 27 eyes, 2-3 mm in 8 eyes, 3-4 mm in 10 eyes and over 4 mm in 4 eyes. The visual axis was depressed by less than 2 mm in 6 eyes, 2-4 mm in 18 eyes and over 4 mm in 45 eyes. The mean convergence was 1.9 mm and the mean depression was 7.1 mm.

Measurement of angle alpha

For computing angle alpha we need 2 measurements; the distance of the visual axis from the optical axis in the spectacle plane and the distance of the spectacle plane from the nodal point of the eye. The first of these values can be obtained by subtracting the mean crosswire readings (representing the optical axis) from the mean pinhole readings (representing the visual axis). These values are plotted in Fig. 13.

6 I C mm:

Fig. 12. The amount of decentration for near vision. This was computed by subtracting the means for the distant vision from the corresponding values for the near vision both being the pinhole method. The mean convergence was 1.7 mm and the mean depression was 7.1 mm (marked

by x’s).

14 *In.

Fig. 13. Angle alpha graphically demonstrated. The means of the crosswire reading represent the position of the optical ax is in the spectacle plane; and similarly the means of the pinhole method represents the position of lthe visual axis in the same plane. The difference between the 2 gives the value of angle alpha on the spectacle plane and it is plotted on graph. It is observed that the visual axis cuts the spectacle plane nasally and inferiorly in all the subjects.

The average position is marked by x’s.

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The visual ax is cut the spectacle plane less than 1 mm medial to the optical axis in 24 eyes, 1-2 mm medial in 24 eyes, 2-3 mm medial in 10 eyes, 3-4 mm medial in 7 eyes and over 4 mm medial in 5 eyes. And it was less than 1 mm below the optical axis in 1 1 eyes, 1-2 mm below in 2 1 eyes, 2-3 mm below in 15 eyes, 3-4 mm below in 9 eyes and over 4 mm below in 9 eyes. The mean position of the visual axis was found to be 2.9 mm inferior to and 1.5 mm medial to the optical axis.

The visual ax is was found to cut the spectacle plane below and medial to the optical axis in all the cases. The horizontal direction and value of visual angle we obtained is as described in the literature. However, the vertical magnitude is different from what was expected. Duke-Elder has described the visual axis to cut the cornea above and nasal to the optic axis. Bennet 8c Francis (1962) have stated that the visual ax is is 4-5 degrees medial to and 1% above the optical axis. It is not known whether these are computed values or actually measured values. One factor which may have caused some error in our estimation of angle alpha is the fact that in the pinhole method there was possibly an upward tilt of the head when the subject has both hands raised to the shoulder level while adjusting the pinhole devise over the spectacle frame. It is understandable that when a person raises both his hands the head is also slightly tilted upward by natural coordination of movements.

Computation of angle alpha From the above values alpha can be computed if we also have the distance of the Spectacle plane from the nodal point of the eye. The distance of the nodal point of the eye from the anterior pole of the eye is 7.08 mm. The vertex distance (anterior pole of the eye to the spectacle plane) is a more variable factor, but the average vertex distance was found to be 13 mm. The sum of the two, 20 mm was used to compute angle alpha on all the subjects. The mathematics involved in the computation is detailed in Table 2.

Angle alpha is located diagonally with a horizontal component and a vertical component. Using the horizontal coordinates (of the difference between visual axis and the optical ax is at the spectacle plane) the horizontal component of angle alpha was computed. This is named alpha 1 in Table 2. Similarly using the vertical coordinate we computed the vertical component of angle alpha and it is repre- sented as alpha in Table 2. We also computed the diagonal angle alpha or the real angle alpha using both the horizontal and vertical coordinates in the equation described in Table 1 and this is called alpha 3 in Table 2. These 3 values of angle alpha for 35 subjects is detailed in Table 3.

The average horizontal magnitude of angle alpha is 4.92 degress nasally, and this compares very well with the values described in textbooks (Fig. 8). The averagae vertical component of angle alpha was 7.40 degrees, the visual axis being inferior to the optical axis. This is not like the description in textbooks. One factor of error that

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Table 2. Computed Value of Angle Alpha.

Right eye

Alpha 1 Alpha2 Alpha3 Patient

Left eye

Alpha1 Alpha2 Alpha3

1 2 3 4 5

6 7 8 9

10

11 12 13 14 15

16 17 18 19 20

21 22 23 24 25

26 27 28 29 30

31 32 33 34 35

Averages:

3.43 0.00 4.43 0.86 2.29

0.86 10.34 14.84 0.86 8.39

6.28 2.58 2.58 5.85 5.00

5.14 4.43 1.43 4.86 8.39

1.58 1.29 2.58 4.43 0.00

4.72 0.86 5.57 7.13 8.81

1.29 4.72 1.29 3.86 5.28

4.18

3.72 5.99 3.29

11.72 2.29

4.00 9.79 0.57

10.20 10.62

5.14 7.69

12.82 7.97

13.77

3.43 11.59 12.27 12.00 12.54

7.69 4.00 6.56 5.43 5.71

4.00 4.86 3.15

10.34 18.78

1.58 7.97 9.09 7.13 0.72

7.38

5.06 5.99 5.51

11.75 3.24

4.09 14.10 14.85 10.24 13.42

8.09 8.10

13.06 9.84

14.58

6.17 12.36 12.35 12.89 14.95

7.84 4.2 1 7.04 6.99 5.71

6.18 4.93 6.39

12.47 20.49

2.03 9.23 9.18 8.09 5.33

9.05

3.15 9.93 0.57

11.75 2.15

7.97 7.41 2.86 6.98 5.57

11.86 14.04 3.29 2.86 9.65

7.55 1.58 1.29 2.29 0.57

9.37 4.43 4.29

13.09 1.15

7.13 5.14 1.15 4.43 3.01

5.43 5.28 7.13 5.28

13.09

5.78

0.86 12.13 8.81

10.20 12.00

6.70 10.76 0.86 5.43 6.84

7.41 7.55

13.50 9.37

16.44

3.58 9.93 4.00

12.41 15.51

7.97 5.57 4.72 5.99 5.14

0.00 6.28 2.72 9.51

12.54

1.43 4.72

11.72 3.15 3.72

7.41

2.86 14.04 8.53

14.04 11.31

8.53 11.31 2.86 8.53 8.53

11.31 14.04 11.31 8.53

16.70

5.71 8.53 2.86

11.31 14.04

11.31 5.7 1 5.71

14.04 2.86

5.71 5.71 2.86 8.53

11.31

2.86 5.71

11.31 5.71

11.31

8.57

Averages of both sides = Alpha 1 : 4.98, Alpha 2: 7.40, Alpha 3: 8.78. Alpha 1: Horizontal Value of Angle Alpha. Alpha 2: Vertical Value of Angle Alpha.

Alpha 3 : Real or diagonal value of Angle Alpha.

Table 3.

0: optical axis, determined by crosswire method is represented by the point (XI - Y1) on the spectacle plane. XI = average of 20 observations, right horizontal Yl = average of 20 observations, right vertical

V: Visual axis determined by pinhole method is represented by the point (X, - Yz) on the spectacle plane. Xz = average of 10 observations. Right horizontal. Yz = average of 10 observations. Right vertical.

Imagine triangle ABC, point B representing 0: optical axis and point C representing. V: visual axis, both at the spectacle plane, point A being the Nodal Point of the eye. In triangle ABC, AB is the optical axis and AC is the visual axis, the angle between the two angle ABC being angle alpha.

(3 Now, in triangle ABC, angle ABC = angle alpha = tan-' x

AC is the distance from the nodal point of the eye to the spectacle plane, i.e., 20 mm as

BC is the distance between visual axis and the optical axis. described in the text.

The angle alpha has three dimensions. A horizontal component known hereafter as Alpha 1, a vertical component known hereafter as Alpha 2, and a diagonal or real component known hereafter as Alpha 3.

Calculating angle alpha

( x120x2 ) Alpha 1 = tan-'

F-= Alpha 3, the real angle alpha = tan-'

may have creeped into our experiments, namely the upward tilt of the head by natural coordination when both hands are raised to the eyelevel to adjust the pinholes, was already described. However, it may be pointed out that in all 35 subjects the visual axis was inferior to the optical axis. The combined or diagonal value of angle alpha was found to be 9.05 degrees for the right eye and 8.57 degrees for the left eye, the average of the 2 being 8.8 1 degrees.

Amount of decentration

The amount of decentration owing to all these factors is shown in Fig. 14. The average of 10 pinhole reading is plotted. This is the point at which the visual axis cut

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\ \ 1.i I /

u 10 mms

Fig. 14. The mean values of pinhole readings. This represents the amount of decentration required on all the subjects if they all had worm the same frame. The factors necessitating this amount of decentration is angle alpha facial asymmetry and oddity of the frame for the face, and disparity between the size of the bridge of the frame and the saddle of the nose. All these

factors are automatically corrected by this one measurement.

the spectacle plane in relation to the frame. If all the subjects had chosen the same frame horizontal decentration of less than one mm was needed in 7 subjects, 1-2 mm in 16 subjects, 2-3 mm in 6 subjects, 3-4 mm in 3 subjects and over 4 mm in 3 subjects. Similarly vertical decentration of less than one mm was needed in 7 subjects, 1-2 mm in 13 subjects, 2-3 mm in 5 subjects, 3-4 mm in 6 subjects and over 4 mm in 4 subjects. This graph clearly shows that decentration is needed in most patients wearing glasses and that vertical decentration is as important as horizontal decentration.

Description of the Kerala Decentration Meter

The Kerala Decentration Meter, named after my home state in India, is an instrument to measure the degree of decentration of the optical centre of the lens from the datum centre of the spectacle frame, while fitting the lens. This instrument uses the pinhole method described in the previous section and locates the point at which the visual axis cuts the spectacle plane. Factors such as the amount of facial asymmetry, the magnitude of the angle alpha and the correction for the unwieldly frame design are not separately measured by this instrument, but it is designed to provide due correction for all these factors automatically in one set of measurements. Above all, this instrument gives the accurate position of lthe visual axis in the vertical dimension as well as horizontal, and as we noted in section

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I, a vertical error is more symptomatic than a horizontal error because the eyes can converge and diverge, but they cannot ride up or down upon each other. Besides since the readings are taken after the patient has worn the frame of his choice, it also gives due vertical correction for the height of the bridge of the nose being affected by too narrow or too wide a saddle of the nose. The measurements are taken on the actual position of the spectacle frame over the face. The use of this instrument will be most beneficial in high myopes, in whom even an error of one mm counts and the errors caused by facial asymmetry and angle alpha is considerably more than one mm as we have seen already.

The Kerala Decentration Meter (Joseph 1970) was patended in the Govt. of India Patent Office during 1970, but because of some professional mishaps, I was not able to make use of the patent. This invention is hereby released to the scientific world for free use in its present form or with modifications.

This instrument may be used by the Ophthalmologist, the Optometrist or the Optician after the patient has decided which frame he is going to wear. The decentration meter is then clipped on to the frame and the degrees of decentration needed is computed, in millimeters. Today most developed countries uses grinding machines that can be pre-calibrated for the required amount of decentration in both the vertical and horizontal coordinates, and the lens is automatically ground in such a manner.

The instrument consists of 3 parts; the graduated plate holding the pinhole, the clipping bars to fur the instrument to the spectacle frame and the rack and pinion arrangements to move the pinhole vertically as wellas horizontally. The discs holding the pinhole consist of 2 parts (Fig. 15). Its total dimension is 5 cm x 5 cm. The corners are rounded off, the inferomedial part being more rounded off to accomodate the nose. The upper ?4 of the plate is transparent on which parallel horizontal and vertical lines are engraved every 1 mm, the lines being bolder every 5 mm. When th is plate is kept over a spectacle frame, the position of the pinhole can be read off at the line which is opposite the highest point of the upper rim and that line opposite the autermost point of the outer rim.

The pinhole is contained in the inferonasal $4 of the plate in an emodiment projected forward by 5 mm in a plane parallel to that of the other part. This embodiment is to reduce the size of the visual angle seen and to further enhance the accuracy of the instrument. The inferomedial $4 of the plate holding the pinhole is opaque, the back surface being black to improve the contrast. The optimum size of the pinhole is 1 mm diameter.

Fig. 16 shows the bars to be clipped on to the spectacle frame. The rear bar is curvilinear, and this and the front bar are resiliently pressed to each other holding the spectacle frame between by spring action, and tightened by one screw in the middle. Fig. 17 shows how the bars are clipped on to the frame on its superior rim.

The front bar of the clipping system has a framing member, 26, which is provided with a stationary nut, 27, in which a horizontal screw, 24, meshes. The

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Fig. 15. The discs holding the pinhole. The upper 34 is transparent with parallel vertical and horizontal lines engraved on it every mm, the lines being bolder every 5 mm. The pinhole is contained in the opaque inferonasal $4 part of lthe plate on an embodiment projected

forward by 5 mm in the same plane.

Fig. 16. The anterior (17) and posterior (18) clipping bars which are resiliently pressed against each other in a view from the top. One screw (20) tightens the bars against the superior bar of the

frame.

27

Fig. 17. The anterior and posterior bars are attached to the superior rim of the frame.

other end of the screw is attached to another framing member, 28, which is also provided with a screw and nut to move the pinhole vertically.

Thus, by rotating the screwheads 25 and 30 the pinhole can be freely moved vertically and horizontally in the spectacle plane (Fig. 18).

Once the frame is chosen by the patient, the decentration meter is attached to the upper bar of the frame with the clipping system. By manipulating the nuts 30 and 25 the patient can position the pinholes in such a way that the the circles he sees through the 2 pinholes fuse into one with the pinholes in the centre. The target must be at eye-level. It would be wise to use a head and chin rest because the patient will have a tendency to lift his chin by natural coordination of movements when both his hands are raised to shoulder level in order to manupulate the screws. The head and chin rest will also minimise the errors caused by bad positioning of the head.

Fig. 18. The framing members 27 and 27 upon which the horizontal screw 24 and the vertical screw 29 are attached. By rotating the screw heads 25 and 30, the patient can move the pinhole

horizontally and vertically across the spectacle plane.

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That horizontal line which just passes along the uppermost part of the upper rim gives the vertical position of the visual axis. Similarly, that vertical line on the plate that just touches the outermost part of the inner border of the outer rim gives the horizontal potition of the visual axis.

Now, in most frames, either the boxed lens size or the datum length and the distance between the lens is written. If they are not written they can easily be measured using an Empire Datum Rule (Sasieni 1975). If the boxed lens size is 42 X

32, then the datum centre is 21 mm medial to the outer rims and 16 mm below the uppermost part of the upper rim. In this case suppose we get the readings on the Kerala Decentration Meter as 19 mm horizontal and 15 mm vertical, then the optical centre of the lens has to be decentred 2 mm out (21- 19) and 1 mm above (16- 15) the datum centre. In the optical laboratory, the optician can make the necessary arrangements on his grinding machine to cut the lens accordingly, so that when fitted on the frame the lens is properly decentred. The face measurements and frame measurements are combined in one instrument here and one set of measurement measures both.

Acknowledgments

All the research for this paper was self-funded. The experiments were sone in the Research Cell of the Trivandrum Medical College, Kerala, India. My most sincere thanks is to the 35 medical students of the class of 1970 who were volunteers for these experiments. Dr. Sebastian Lukose was the research assistant. I thank Dr. M. Thangavely, Principal, and Dr. M. Ramachandran of the Research Cell, Trivandrum Medical College for providing space for the experiments. The statistical analysis of the data was completed by Dr. C. P. Kartha at the University of Michigan-Flint, Michigan.

Acknowledgments of Figures

Figs. I and 3. Redrawn after Duke-Elder: Practice of Refraction, 1965. The C. V. Mosby Co., St. Louis, page 3 1 1, Fig. 167, and page 54, Fig. 48.

Fig. 2. Kind permission by Sasieni LS and The British Standard Institute, (B.S.: 3199).

Figs. 4 and5. Tscherning, Optique Physiologique, Paris, 1898.

Figs. 6, 15, 16, 17, 18. These figures are copied from the author’s patent, The Decentration Meter, Patent No. 120848 (1970). Government of India Patent Office, Calcutta.

References

Bennett A G & Francis J L (1962): In: Dawson H (ed). The Eye. IV: 114. The Academic

Brooks S W & Borish I W (1979): System of Ophthalmic Dispensing, pp 27-39. The Press, London.

Professional Press, Inc, Chicago.

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Drew R (1970): Professional Ophthalmic Dispensing, p 215. The Professional Press, Inc,

Duke-Elder S (1965): The Practice of Refraction, pp 53-55,70,309-311. C. V. Mosby Co.,

Duke-Elder S (1970): System of Ophthalmology, V: 134-138. Ophthalmic Optics and

Fry G A & Ellenbrock V J (1941): Placement of Optical Centres in Single Vision Lenses,

Joseph T (1970): Indian Patent No. 120848, Calcutta, Government of India Patent Office. Sasieni L S (1975): The Principles and Practice of Optical Dispensing and Fitting, pp 40,41,

Stimson R (1971): Ophthalmic Dispensing, pp 490-499. Charles C. Thomas, Springfeld.

Chicago.

St. Louis.

Refraction. C. V. Mosby Co., St. Louis.

Optometnc Weekly 32: 933-936.

48-52,102- 109,158. Butterworth, London.

Author’s address: Thomas K. Joseph, M.D., 8801 S. Richmond, Evergreen Park, Illinois, 60642, USA.

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