AO TECHNICAL REPORT A STUDY OF LENS CONSTRUCTION AND USE AMERICAN OPTICAL CORPORATION SOUTHBRIDGE, MASSACHUSETTS 01550

Transcription

1 AO TECHNICAL REPORT A STUDY OF LENS CONSTRUCTION AND USE AMERICAN OPTICAL CORPORATION SOUTHBRIDGE, MASSACHUSETTS

2 A STUDY OF LENS CONSTRUCTION AND USE JOHN K. DAVIS WHY A CHAPTER ON LENSES? The problem of selecting the best or even a satisfactory lens for the individual patient is a real one. There are 5 major and several smaller manufacturers of ophthalmic lenses in the United States. Although, in some instances, lenses of a given type are produced by more than one manufacturer, it is generally true that even when lenses from different manufacturers seem to be alike, there are frequently variations that can be significant for a particular patient. Each of the major manufacturers produces more than 40 different designs and types of single vision and multifocal lenses, and the types include differences in the design of single vision lenses and the distance portion of bifocals, as well as differences in type of bifocal, segment size, and shape. The variety of prescriptions necessary to meet the needs of even one ophthalmologist s group of patients is immense. A random selection of 10,000 prescriptions contains over 400 different combinations of spherical and cylindrical powers without regard to differences in cylinder axis. Each of these 400 prescriptions may require any one of 12 commonly available reading additions. Deciding which of these designs provides the best vision involves the application of optical principles and an understanding of the patient s needs. The average ophthalmologist is not expected to have a complete knowledge of spectacle lens design. He should, however, have a basic grasp of the factors that determine lens performance, especially those that may be operating in the selection of prescription lenses for a particular patient; he should also understand the optical principles that affect the fitting of finished spectacles. Discussion of these factors necessarily involves drawings and geometric optics which must be presented within a rigid context. The position of the lenses in front of the eye, however, depends on the patient s facial characteristics and the selection of the frame. In fact, the size of the patient s nose is a major factor affecting lens performance. We also know that once the lenses are fitted, frames will loosen and the lenses will not remain in their original position. 2

3 In view of the conflict between the need for rigidity and the variability of actual circumstances, the ophthalmologist should have a grasp of the areas of freedom and the available latitudes of flexibility that will not seriously affect the patient s vision adversely. Such a grasp requires an understanding of what a lens is and what it does. The optical principles that govern the passage of light through a lens will be subsequently outlined, but if at the outset we can understand what lenses do, the geometry and optics may be easier to understand. More importantly, we may learn just what happens when people use lenses. First it will be helpful to understand that in a very real sense the person wearing a lens does not see the object being regarded but its image, created by the lens just as when we look in a plain mirror, we cannot possibly touch the person in the mirror and we know we are not looking through the mirror. The mirror merely provides an optical image of ourselves. Similarly, the lens provides an image of what is out front and the lens wearer looks at that image. Certain thoughts will quickly come to mind as a result of this concept. If we tip the mirror, the image moves and is tipped. Accordingly, if we tip a lens, the image moves and is tipped. If we move the mirror away from us, the image in the mirror moves. The same thing happens with a lens. The prescription for a spectacle lens describes a lens that will create an image in a location such that the patient can see it clearly. This is the patient s far point sphere. The mirror, however, is a very simple optical instrument and its image is practically perfect. Lenses are not so simple and their images are by no means perfect. In the following pages, we will apply simple basic concepts to a study of the problems created by the variability of the needs and by the imperfections of the lenses used to meet those needs. Matching lenses to needs minimizes imperfections. Hopefully, the discussions which follow will help the reader in his further study of the published literature on lenses and in his evaluating information supplied by optical manufacturers. Review of Simple Principles, Definitions, and Language For some readers, the material in this section may seem unnecessarily simplified. We ask their indulgence while we review briefly some of the simplest optical and geometrical principles of ophthalmic lenses with a view to establishing a language and defining terms used throughout the chapter. TYPES OF LENSES First among the many ways ophthalmic lenses may be classified is by the visual defect they are designed to correct. 3

4 Plus Lenses Often call positive or convex lenses, plus lenses are used principally to correct hypermetropia. Adding positive power, they increase the vergence of the light rays forming the image, thus compensating for the lack of refractive power of the patient s eye and bringing the image onto the retina, as shown in Figure 1. Other uses are in the correction of aphakia and as reading lenses to reduce the required accommodation. They are called positive lenses because they form real images which can be focused on a screen. 4

5 Plus lenses are also positive in that when they are used in combination with other lenses or vergences of light, the net result is always a more convergent beam of light; i.e., a more powerful lens system. They are called convex because in their simplest form as shown in Figure 2 they assume a convex shape. Regardless of their overall bending, they are convex in that the convexity of the one surface is steeper than the concavity of the other. Minus Lenses Minus lenses are used to correct myopia. In myopia, the refractive system of the eye is too positive, too strong for the length of the eyeball. Minus lenses compensate by reducing the vergence of the light rays by subtracting from the positive power of the patient s refractive system. The convergence of a beam is reduced so that the image falls on the retina, as shown in Figure 3. 5

6 Such lenses are described as minus because the image they form is not real and, except in combination with plus lenses, cannot be detected with a screen or paper. Also the direction of the image is negative by conventional mathematics, as shown in Figure 4. The distance from object to lens is in the direction of light travel, but the distance from lens to image is in a negative direction with respect to light travel. An eye located to the left would see the apparent image as being located at I in Figure 4. Minus lenses are concave and always net concave by the same type of reasoning that classifies plus lenses as net convex (Fig. 5). 6

7 SPECIFICATION OF LENSES From a study of basic geometric optics, we know that lenses may be specified in terms of the radii of their surfaces, their focal lengths, or their focusing power. The distance from the lens to the image when the object is at infinity is called the focal length of the lens (F). We also know that The power of a lens is the reciprocal of its focal length. Power is usually specified in diopters (D = 1/F when F, the focal length, is given in meters) (Fig. 6). 7

8 The radius of curvature of a surface is seldom used except as a manufacturing specification. Although the use of specification in radii constitutes a definitive description of the lens, radii do not readily convey functional information. Focal length terminology is useful in instrument and photographic optics because it yields information pertinent to lens spacing, the location of the film plane, overall size of the instrument or camera, and the magnification of the image formed. Focal length designations, however, would be awkward for trial sets. The dioptric notation makes possible the simple adding of trial set lenses and is a convenient expression of the degree of ametropia. The approximate power of a spectacle lens is the algebraic sum of the dioptric value of the two surfaces. It is a convenient tool for expressing not only the prescription but also the design of the lens or combination of curves used to fill the prescription. TORIC LENSES A toric lens is one that on one surface has curvatures which are different in two major meridians. The surface is literally a section of a torus. Toric lenses are prescribed and used to correct simple astigmatism or astigmatism combined with a spherical error (Fig. 7). Astigmatism was originally corrected by cementing flat cylindrical sections onto one side of a planoconcave or planoconvex lens; thus, the word cylinder as a part of the prescription was born (Fig. 8). Early lenses were literally spheres with cylinders. The notation has persisted, even though the form of the lenses has changed. In the early construction, the cylinder created the difference between the power of the two principal meridians. The difference is still expressed as a cylinder. PRESCRIPTION FORMAT AND STRUCTURE An astigmatic correction implies that in one meridian there is a need for one dioptric power, and in a meridian at right angles to it, a different dioptric power. 8

9 For example, a patient with a need for a correction in the vertical meridian might need a correction in the horizontal meridian. This fact could be made known by writing the following prescription: 90 _ 180 _ However, since the refraction was performed either with a sphere combined with a cylinder, or alternatively with a sphere with a 1.00 cylinder, the prescription is usually written as: axis 90 or axis 180 When the lens is made, however, we must revert to the first designation to describe the structure of the lens (Fig. 9). For example, expressed in simplest terms and disregarding effects of thickness, a x could be achieved with a lens having a curve in one meridian on the front, a in the other, and a 6.00 on the concave side (Fig. 9). This lens would be described with the notation: x Such a lens is called a plus toric or plus cylinder lens because the toric surface is convex; i.e., plus. 9

10 It could also be made up with a spherical front surface and on the concave side a toric curve of 6.00 x This lens would be described with the notation: x 7.00 (Fig. 9) A lens of this construction is called a negative toric or minus cylinder lens because the toric surface is concave or minus. In general, there is a tendency for refractionists to write the prescription in terms of the refracting instrument or trial set which they use. Most refracting instruments have minus cylinders. Therefore, the majority of prescriptions are written in minus cylinder form. The cylinder 10

11 notation used by the doctor is not important if the type of cylinder and lens desired is specified. Prescriptions written with either a plus or minus cylinder notation are routinely transposed in the laboratory to the notation required for the grinding of the prescription. A plus cylinder designation of the prescription can be filled with the toric on the concave side. Indeed, when bifocals are ordered, they are almost always supplied in minus cylinder form. Figure 10 illustrates the correlation between prescriptions and lens forms. In 10A, a spherical prescription is frequently made up with a D convex curve and a 6.00 D ocular or concave curve. 11

12 In 10B, the prescription can also be written as In 10C, two different shapes or bendings with a plus cylinder form of lens are shown. In one the base, or shallower curve, is In the other it is The choice is a matter of design which will be discussed later. In 10D, the same prescription is indicated as being filled in minus cylinder form, the lower form being the more steeply curved. In 10E, one meridian has a power of +2.00; the other, In 10F, the relationship shows that the major meridians of maximum and minimum error may be corrected at any necessary axis (in this case, 45 ). This example is in minus cylinder form. In the preceding discussion, we have described the structure of toric lenses as having a front curve of so many diopters, for example, spherical front curves of D and D. In some instances, these front curves were toric surfaces and had a dioptric notation for each meridian. Similarly, we described the back surface of lenses as having either spherical or toric curves with the dioptric notations. This notation is specific. However, the specification of a particular lens is unnecessarily lengthy and awkward. The use of the notation base curve, once it is understood, simplifies the discussion of lens form and curves. The difficulty is that the phrase base curve means different things, depending on the subject under discussion. For example, when toric surfaces are discussed, the shallower curve is called the base curve of that surface whether the surface is a convex surface on the front of a lens or the concave surface on the ocular side of the lens. For example, a front surface the curvatures of which are x would be described as a base toric. The value of the other curve would be deduced from the prescription. The most common use of the term base curve is to designate the front curvature, either a spherical curve for a spherical lens, the weaker of the toric curves for a plus toric, or the spherical front of a minus cylinder lens. For example: The prescription is be supplied with the curves -2.00; ordered on a base with minus cylinders, the lens would x 6.25 Transposed to plus cylinder notation, the prescription is reads ; ordered on a base cylinder, the curves would be: x

13 Having reviewed the advantages of the dioptric notation, we can see that a given prescription lens could be produced in an infinite variety of bendings or curvatures. A D lens could be made up as: , or 0.00_ Ordinarily, a lens is made up with curves on the front between and This apparently narrow range of selection is partly owing to cosmetic considerations and partly to consideration of optical design. What are the reasons for choosing one curve rather than another? What is the need for design in the broader sense of the word? What happens when the different possible combinations of curves are used? OPTICAL THEORY AND DESIGN The ease with which the patient accepts a new prescription, his comfort and confidence, and the quality of his vision are dependent on the choice of lens design and how the spectacles are fitted. The importance of the relationship between lens curvatures and the position of the eye can be appreciated with the help of a simple experiment, illustrated in Figure 11. If a spectacle lens of 3.00 D or 4.00 D is selected and a page of typewritten material or graph paper is viewed with the lens curved toward the eye, the entire page will be imaged quite well. What is happening is that if our eye is well centered behind the lens, the center of rotation of the eye and its relation to the lens dictate that the image we view be one which lies essentially in one plane and substantially perpendicular to the line of sight. Thus, we can view the entire image comfortably. Also, since spectacle lenses are designed for an eye rotating behind them, and since we use this lens in a manner essentially as it was designed, the quality of the image, even at the corners of the page, is quite good. Now, if the lens is turned around so that it is concave toward the paper, the image will be quite good at the center of the page but distorted and blurred at the edge. This happens because the lens is not being used as it was intended and the images of the edge of the page are said to have aberrations; i.e., error exist as the eye turns to use different areas. The lens performs as if it were of a different power at different angles of view. This characteristic can be demonstrated by moving the paper slightly until a particular corner comes into sharp focus at the expense of other portions of the image. Similar imperfections of the image will occur if the lens is decentered or angle (Fig. 11). What we have said and what can be demonstrated with a simple lens and a piece of paper is that the variables which jointly determine the location of the image and its quality are the lens curvatures and their orientation relative to the eye, and more specifically, the center of rotation of the eye. 13

14 CENTER OF ROTATION Figures 12A and 12B illustrate an anlogue of an ideal spectacle lens which will help in understanding the importance of the center of rotation position. During the refraction, the trial lens is located at a particular distance in front of the cornea the vertex distance. This distance is measured from the center of the rear or ocular surface of the trial lens. As the eye turns to fixate in a different angular position, another trial lens could be placed at the same vertex distance for the new angle of view. The location of this series of trial lenses would be a spherical surface equidistant in all directions from the cornea as it turns. Thus, this spherical surface would have its center at the center of rotation of the eye. An ideal spectacle lens would provide the same corrective prescription at all points on such a spherical surface as the analogous series of trial lenses. Therefore, we call this imaginary surface the reference sphere. It is a spherical surface in space at which the performance of a spectacle lens is evaluated. In order to define this surface, it is necessary to know the vertex distance and the distance from the cornea to the center of rotation of the eye because, together, they determine its radius and location. In Figures 12A and B, it is clear that as the eye turns, in each of the directions it assumes, the pupil selects a small bundle of light rays, the center of which passes through the center of rotation of the eye. If it were possible, a diaphragm or optical aperture stop could be located at the center of rotation without altering the image on the patient s retina. 14

15 The center of rotation of the eye, therefore, is the limiting aperture or stop of the spectacle lens as it is designed to provide for the field of view of the dynamic eye. Its location is important because (1) it determines the radius of the reference sphere, and (2) as the location of the effective limiting aperture, it is one of the principal design criteria for selection of lens curvatures. CORRECTED CURVE LENSES We have been considering a trial lens or spectacle lens as correcting the focus of an eye to provide a sharp image on the retina. However, let us now consider the geometry of the correction 15

16 from another point of view. If we consider the correcting lens alone, the image it creates is not on the retina but at the patient s far point. When we consider the moving eye, turning as it does in all directions, the far point turns with it and generates a theoretical spherical surface with the center of curvature centered at the center of rotation. It is the patient s far point sphere. For a 1.00 D hyperope, this spherical surface lies 1 m. from the reference sphere back of the eye. For a myope of 1.00 D, it is located 1 m. out in front of the eye (1 m. from the reference sphere and again concentric with the center of rotation). Before we leave the concept of the trial lenses arranged around the reference circle, it is desirable to visualize the importance of the reference circle s and the far point sphere s being aligned and centered about the center of rotation. It is obvious that if the reference circle were decentered, some of the trial lenses would not be aligned properly in front of the eye. Similarly, a spectacle lens and its reference circle should be centered about the center of rotation of the eye, as shown in Figure 12C. Here we have the same reference circle, except that instead of a series of trial lenses, we have a single spectacle lens. The aperture stop is at the same place and has the same size as in Figure 12A but we have not shown the refractive system of the eye. Ideally, the surface on which the lens in 12C focuses images of different points of the field of view would have the same radius and would be located in the same place as the far point sphere. There is an important difference between the spectacle lens in Figure 12C and the trial lenses in Figures 12A and 12B. In the latter configurations, the lenses and, therefore, the entire set of optical elements were the same as the eye turned through different angles of view. In Figure 12C, however, the lens thickness is different and the concave surface is in contact with the reference circle at only one point, and the distance from the reference circle varies. As might be expected, the performance of any lens varies with different angles of view because of these differences. To make the best of the compromises resulting from this set of circumstances, the designer must assume that the lens will be well aligned in front of the patient s eye, and at the time of fitting, every effort should be made to see that it is. The optical axis of the lens or to put it more simply, the lens axis is a concept inherent in the design task and basic to good fitting practice. It is shown in Figure 12C. OPTICAL AXIS The optical axis is an imaginary line connecting the centers of curvature of the spectacle lens and is perpendicular to both surfaces of the spectacle lens. It is the axis of symmetry of the lens. The starting point of all lens calculations lies on this line. For lenses to perform optimally, the optical axis should pass through the center of rotation of the eye and the lens should be located on the reference sphere. If this is the case, the lens serves best as a substitute for the array of trial lenses already described. Just as it was of obvious importance for the trial lenses on the reference sphere to be aligned with the far point sphere through the 16

17 center of rotation of the eye as the common center, so is it necessary for the spectacle lens to be located on the reference sphere and for the optical axis to pass through the center of rotation. This is the assumption made when lenses are designed. Figure 12D illustrates the problem that develops if good centering is not achieved. The surface on which the lens has presented the best image is not coincident with the far point sphere. The entire system is misaligned and the performance of the lens is degraded. STOP DISTANCE The concept of the far point sphere and the lens image surface has been developed because of the importance of visualizing a lens, its axis, and the image it forms as a rigid entity. It is helpful in visualizing and understanding the design task and the importance of good fitting. However, in evaluating the performance of a lens and in comparing lenses of different designs, we can obtain meaningful answers which relate directly to the original prescription by asking: What is the prescription at the reference sphere and what are the errors at this surface as the eye turns? Referring errors to the reference circle relates the lens performance directly to the patient s needs. They can be evaluated in common prescription terms. The first thing to do in spectacle lens design is to decide on the center of rotation or stop distance. Whereas photographic lens designers use the stop position as a variable, spectacle lens designers cannot. The stop distance, since it is the sum of the vertex distance and the distance from the cornea to the center of rotation of the eye, obviously varies between individuals. Approximately 30 mm. is a good average, but for close fitting lenses, it may be as short as 22mm. and for myopes with large globes wearing large frames, as long as 35 mm. or more. What the designer must do is to assume a single stop distance or a range of stop distances for each prescription and select lens curvatures which perform well at the selected distance or range. Frequently one distance is used for all prescriptions. For older lenses, the stop distance was 25 to 27 mm. Some of the new lenses, such as the Tillyer Masterpiece (American Optical Corporation), are designed for a stop distance of approximately 30 mm. However, this lens in particular was balanced to fit a range of approximately 27 to 33 mm. The design task consists of trial-and-error computing of the performance of different sets of curvatures followed by selection of the best. It has not been possible to create a truly perfect image on a surface which matches the patient s far point sphere. In practice, what is done is to select a set of curvatures which in the judgment of the designer will create the best image on the far point sphere, or putting it alternatively, the least error on the reference sphere. However, for both plus and minus lenses, the common errors of most spectacles are such that the lens becomes weaker at the reference sphere as the eye turns away from the center. In a plus lens when the patient turns to use areas other than the center, there is less plus power available. For minus lenses, there is less minus power available. Also astigmatic errors are present. 17

18 CAUSE OF ERRORS To answer the question of what causes errors, it is necessary to analyze what happens when a ray of light passes obliquely through a lens. The lens can be considered as a series of prismatic elements, each element having a greater angle between its faces than the previous one as the distance outward from the center increases (Fig. 13). The figure shows a plus lens. In a minus lens, the prism element would have the sides slope toward each other, inward instead of outward as shown. The point to be stressed is that the line of sight through any point on the lens except the optical center is through a prismatic section and is deviated by the prismatic effect of the lens. This deviation is the cause of most of the problems of lens performance. In order to appreciate this point, I suggest that the reader obtain a strong trial case prism, for example, 8.00 D to D, hold it in front of his eye, and tip it. It should be held with the base vertical so that the deviation is horizontal and tipped in the horizontal meridian. It will be observed that the quality of the view through the prism changes with the angle of tip and that there is more deviation at some angles than others. The scene is curved or distorted, but for one position, there will be very little color, very little distortion, and very little blurring. The aberration of the image seen through the prism is a function of the strength of the prism (the angle between the surfaces); it also varies with the angle of incidence of the line of sight on the surface nearest the eye. This will be observed by noting the improvement in image quality for certain angles of obliquity of the prism. 18

19 In this experiment, it will be noted that lines perpendicular to the direction of tip are blurred most. This occurs because the rays of light used to image those lines are those rays which are deviated. It is the prismatic deviation that creates the blurring. LENS CURVATURES Since deviation is always in one direction, blurring is principally in one direction. This gives rise to astigmatism even with plano prisms and spherical surfaces. (Flat prisms have no astigmatism for a truly infinite object distance, but for near objects, they do, and all curved surfaces with prism are subject to astigmatic errors.) This tipping of the prism is analogous to the mathematical process used in designing a lens. Referring to Figure 14, it can be seen that lenses made of different curvatures result in a different angle of incidence of the line of sight as it strikes the rear surface. For any given prescription, center of rotation distance, and angle of view, the angle between the two surfaces will be nearly constant, regardless of the selection of curvatures. However, the angle of incidence for the line of sight will vary with different curvature selections. Some one selection will provide an optimum tipping of the particular prismatic element and, therefore, the best image through the lens for the assumed center of rotation distance and angle of view. 19

20 It can be seen that if the eye were closer to the lens, the curves would have to be made steeper in order to maintain a similar angle of approach of the line of sight to the lens surface. If the pivot point of the eye were moved farther back from the lens, as might be the case for a patient with a large nose or a large globe, shallower curves would be necessary. We can now see that the overall curvature of a lens and the position of the eye behind the lens are jointly responsible for the performance of the lens as the eye sweeps it to view the entire area of interest. Of course practical considerations, such as avoiding long eyelashes, must occasionally take precedence over optics. In such cases, the optician must deviate from the recommended base curves. For weak prescriptions, this may not create a vision problem. If the eye turns to view an object at greater angles, it will intercept areas of the lens farther out from the center. There will be more prismatic deviation by the lens and, even though optimum curvatures may be selected, prescription errors and distortions of the image will be greater simply because there is a greater deviation. The greater the deviation, the more difficult it is to provide a truly sharp image. The greater the angle of view, the more care in design is necessary. There will always be some degree of error present. These errors have the effect of and can be described as prescription errors in sphere or cylinder referred to the reference circle. 20

21 PRISMATIC DEVIATION To summarize then, except at the optical center of a lens, all areas are prismatic. Prismatic sections of lenses almost always create an astigmatic focus, both meridians of which will usually be different than the focus for the central beam through the optical center. These differences or errors may be visualized as the difference in location and shape of the image surface from that of the far point sphere. It is also convenient and more meaningful to consider these differences as errors in the patient s correction at the reference circle. It is now necessary to think in three dimensions in order to understand the full effect of these errors and the language used to discuss them. In the experiment with a prism, it was found that the angling of the prism combined with the deviation of the prism blurred the lines of detail parallel with the prism base more than detail lying in the base-apex meridian. Therefore, we can think of these prismatic elements as behaving like trial case cylinders with their axes parallel to the base of the prism and affecting the focus of detail which is aligned with their axes. We have been considering lenses illustrated only in cross-sectional drawings. However, a lens is a three-dimensional object symmetrical about its optical axis. Referring to Figure 15, we can see that as the eye intercepts one area of the lens after another, the orientation of the prismatic elements makes a complete circle around the lens. The direction of the prism base is toward the center in plus lenses (and away from the center in minus lenses). The prismatic deviation is always in radial planes radiating from the center. Therefore, the focus of the lens most affected by the deviation will be in these three radial directions vertical for upward viewing, horizontal for looking to the side, and oblique in intermediate directions. The effect is that of a trial case cylinder the axis of which, A, changes around the clock. Therefore, the axis of the astigmatic error rotates around the lens. 21

22 The meridian most affected by the prismatic effect and, therefore, by the choice of design will be horizontal for horizontal viewing and vertical for vertical viewing. That is, the prescription error can be described as an unwanted cylinder at axis 90 for horizontal viewing, at axis 180 for vertical viewing, and at 45 and 135 for intermediate points. These errors are called tangential errors because they affect the image of lines which are tangent to a circle encompassing the field of view. Also, there is usually some prescription error in the meridian 90 to the tangential. These errors are usually of lesser amounts and are less affected by base curve selection. They are called sagittal errors. The performance of a lens at any point off center can be specified in terms of a tangential, t, error and a sagittal, s, error, or as a sphere cylinder prescription error. The difficulty with the prescription terminology is that the axis of the cylinder depends on the direction of view. Consequently, the t and s notation is simpler and avoids listing the direction of view and axis designation. 22

23 Figure 16 lists the numerical value in diopters of prescription errors for a lens ground on a variety of different base curves a front curve at the left and a diopter curve at the right. BASE CURVES One can visualize a series of lenses of different base curves in a viewing situation similar to that shown in Figure 14. The tangential and sagittal errors are indicated by t and s. Data are for a 27 mm. center of rotation distance and an infinitely distant object. The astigmatism is the difference between the t and s errors and is labeled Ast. The differences between the designs of different manufacturers in the evolution of lens design has been one of differences in philosophy regarding what is best when data of this kind are scrutinized. 23

24 VON ROHR The earlier corrected curve lenses, designed by Dr. M. von Rohr in Germany in 1911, were designed to eliminate the difference in the error in the two meridians, that is, to eliminate the astigmatism due to the prismatic effect. However, this is always done at the expense of increasing the total error above what it might otherwise be. First, if we concern ourselves, as did von Rohr, only with the difference between these errors, we can see that a front curvature of slightly over 9.00 D, for example (perhaps a 9.25 or a 9.50 curve), would result in a negligible difference between these two errors. This then would have been a corrected curve lens according to von Rohr s thinking (Fig. 16, row labeled Ast.). It can be seen that this error would increase significantly but not seriously if flatter or steeper base curves were used. Von Rohr, however, believed so strongly in correcting astigmatism that custom base curves were used for every prescription, a procedure that was expensive and time consuming. TILLYER From 1917 to 1924, Dr. E. D. Tillyer, working at American Optical Company, analyzed data of this kind from a somewhat different point of view. He reasoned that precision of correction for any error for a 30 angle of view need not be greater than that used by the doctor in the office (usually D). Accordingly, any base curve between on the front and on the front would suffice as regards the correction of the astigmatic difference in the prescription error. However, he also reasoned that spherical errors are important. He realized that one could reduce the t and s errors and their average, as well as maintain astigmatic errors within reasonable limits, by using somewhat shallower base curves than the 9.50 that von Rohr would have selected. He reasoned that control of astigmatism to a greater precision than was used in the refracting room was not necessary, especially if it resulted in power errors approaching or exceeding this amount of error. By selecting a base curve of or a little steeper, the power errors could be reduced to within 0.12 diopters while maintaining the correction of astigmatism within the same limits. This was the Tillyer principle of balancing power and astigmatic errors at a tolerable and often insignificant level. Tillyer also reasoned that even with his concept of balancing errors, some latitude was available in designing a lens for a prescription such as this. Again, the exactness of the refraction should be considered. A latitude in choice of curve of nearly 1.00 D would provide corrections within the 0.12 D tolerance range. However, since at and higher prescriptions are usually stocked in 0.25 D steps and ordered accordingly, he extended his tolerance for a prescription to include 0.25 D variations at 30. Thus, any base curve from to would correct the lens at 30 to 24

25 the same accuracy as the refraction was specified. This was the essence of the Tillyer principle. All of the errors at 30 were to be kept within the accuracy of the prescription for that prescription range, and also a single base curve could be used over a range of prescriptions, thus reducing the cost and eliminating long delays. Thus, the Tillyer lens embodied two philosophies: 1. The philosophy of balancing the important spherical errors with astigmatic errors within a tolerance range based on the accuracy of the refraction. 2. The philosophy of using this tolerance to mass-produce corrected curve lenses which would perform adequately and be less costly and more readily available. 25

26 This type of thinking was adopted with variations by most major manufacturers. Some lens series had wider tolerances than others. The status of ophthalmic lens design, particularly of those lenses used for common prescriptions, remained essentially as described for many years. The two basic philosophies remained in effect and were the source of debate and discussion in the ophthalmic literature and advertising. One of these philosophies was that of correcting astigmatic errors at the expense of power errors. The other called for somewhat shallower curves in order to reduce the average of the power errors, at the same time not permitting astigmatism to exceed reasonable tolerances. However, in spite of the differences in philosophy and advertising, the actual base curves used on different designs differed very little. Figure 17 contains a listing of the base curves used by four of the leading manufacturers for their corrected curve lenses. The list is not quite complete because of the absence of fractional diopter steps. The first four columns are for the older series. The similarity is apparent. Some designs used more curves than others. It should also be kept in mind that only spherical prescriptions are listed. The last two columns are for newer designs to be discussed later. Lenses designed and marketed under both of the philosophies described were designed on the assumption of a single center of rotation distance either 25 or 27 mm. We have already seen that the center of rotation distance is a variable and that variations in this distance affect the performance of a lens. NEWER LENS SERIES Beginning in 1964, new series of ophthalmic lenses began to be available. The Univis Lens Company introduced the Bestform lens series. The American Optical Corporation introduced the Tillyer Masterpiece lens series, and later, the Shuron/Continental Company introduced the Shursite lens series. These new lens series were different from the earlier ones in several respects. The Univis Bestform lens, while designed on the older principle of weighting the astigmatic errors and apparently on a 27 mm. center of rotation distance, was produced in minus cylinder form. In other words, the toric surfaces contrary to previous practice were on the concave side of the lens. This form has advantages which will be discussed later. The American Optical Corporation Tillyer Masterpiece lens and the Shuron/Continental Company Shursite lens, which followed later, were also produced in minus cylinder form. They also differed from the Bestform and all previous designs in that the distance corrections were weighted to correct the tangential error. Additionally, these lens series took into account the variability of the center of rotation distance. As already indicated, the Tillyer Masterpiece lens was designed for a range of center of rotation distances. This range varied, depending on the prescription. The Shuron designers used an average center of rotation distance. However, this average varied with prescription on a similar basis. 26

27 We have seen from a study of the table of data for a prescription that for moderate prescriptions there is considerable latitude of design if only one type of error is to be corrected. In these new series, this latitude was exploited by selecting base curves which would not only bring the errors for distance seeing within tolerances but also reduce errors for reading distances. The desirable weighting of astigmatic errors vs. power errors for reading distances is different than for distant objects. For distance seeing, it can be assumed that accommodation is relaxed. For near objects, accommodation is in play. Astigmatic errors may cause the accommodative mechanism to hunt for the best focus and create discomfort at critical near point tasks. Minor power errors can be compensated for by moving the head. In view of these considerations, both of these lens series were designed with attention to astigmatic errors for the near point seeing tasks. The possibility of achieving this type of balance of errors is indicated in Figure 18 which gives data for two centers of rotation distances for the prescription and base curves given in Figure 16. It can be seen that a front curve between and minimizes tangential errors for distance seeing and astigmatic errors for reading distances. This is the type of choice used in 27

28 these series of lenses. There are other minor differences in concept which result in some differences in base curve choice and the resulting performance. Additional information on both of the lens series can be obtained from the respective manufacturers. For a more detailed discussion of design and fitting factors, see Reference 1. The important point is that in the newer lens series, the lens is corrected so that it performs within predetermined tolerances for more than one object distance and center of rotation distance. The center of rotation or stop distances is based on measurements that have been made on current population samples and on current frames. The Bestform minus cylinder lens is no longer available. For strong lenses, good vision even near the center of the lens depends on the proper design and good fitting. For weaker lenses, a wider area of the lens will truly fit the prescription only if good design is used. The principal difference between weak prescriptions and strong ones is in the area of the lens over which prescription errors remain within accepted limits. No prescription is so weak that errors are insignificant for all areas and needs. The remainder of these discussions will be devoted to prescriptions which present greater problems both to the designer and to the dispenser. Toric prescriptions, strong minus, and cataract prescriptions fall into this category. Much of the data will be for a smaller angle of view (20 ). We should keep in mind that a 20 angle includes an area which may well be used almost full time by the patient. Thus, small errors take on significance. Figure 19 illustrates the areas included by various angles of view. 28

29 The tables given provide the reader with a minimum grasp of the significance of the factors that affect lens performance. TORIC PRESCRIPTIONS Since most prescriptions have a cylindrical component, cylindrical and toric prescriptions cannot be ignored in a discussion of corrected curve lenses. In a toric lens, all the factors affecting the selection of proper base curves are doubled. One way of looking at the problem is to consider it as a problem of designing two different lenses at the same time. The doctor should keep in mind that the patient who requires a significant cylinder prescription will simply not be able to have lenses that perform as accurately for him as do the prescriptions of patients who require weaker cylinders and spheres. Figure 20 illustrates the problem. A face-on view of a lens and two cross-sectional views of the vertical and horizontal cross-sections V and H are shown. 29

30 If we remember that the tangential error is an error in prescription power in the meridian which contains the line of sight, the vertical cross-section indicates curves that will affect the tangential error in the vertical meridian. The horizontal cross-section indicates curves affecting the tangential error in the horizontal meridian. In the prescription described ( , axis 90), the vertical power is +3.00; the horizontal power is For a 27 mm. eye position, the front base curves which yield zero tangential error in these meridians are sphere, +8.00; sphere, This would require a toric front x (2.75 cyl.). The trouble is that the prescription cylinder is 5.00 D. Thus, the combination of curves necessary for the prescription precludes an optimum design for both major meridians. The same kind of problem exists with minus cylinder lenses. The point of this example is that with current knowledge and manufacturing methods, it is impossible to produce a strong cylinder correcting lens which maintains an accurate prescription over a very large area. Also, in studying toric lenses, we are faced with a decision not only as to the best base curve to use, but also whether to use plus or minus cylinder lenses for any given prescription. It has always been true that some lenses were supplied in plus cylinder form and some in minus cylinder form. However, until recently, minus cylinder construction was primarily limited to bifocal prescriptions and strong single vision prescriptions requiring special grinding in local laboratories. Now factory-finished minus cylinders are available from several sources. Advantages of plus cylinder lenses vs. minus cylinder lenses have been widely discussed in technical papers and in commercial literature. What are the differences and how significant are they? Minus cylinder lenses differ from plus cylinder lenses in four different characteristics that affects the patient s vision, comfort, and satisfaction. The relative importance of these characteristics depends on the prescription, the patient s previous experience, and his needs. Accordingly, for a particular patient, the order of discussion is not necessarily the order of importance. First, let us consider the question of design performance that we have been studying. We have pointed out that it is impossible to provide minimum power and astigmatic errors in both major meridians simultaneously. However, in plus prescriptions, plus cylinder lenses perform slightly better in this respect than minus cylinder lenses. There is less difference between the correction in the two major meridians. This difference between the two types of lenses is not significant for most prescriptions. In minus lenses, minus cylinder construction provides better performance and very good designs are possible even with strong cylinders in which, if the plus cylinder form is used, the errors are significant even for small fields of view. Therefore, taking both plus and minus prescriptions together, on the average minus cylinder lenses provide significantly superior accuracy for a 30

31 normal field of view. Another reasons for preferring minus cylinder lenses is that eventually all patients who wear single vision lenses will wear bifocals. Practically all bifocals are made in minus cylinder form. Therefore, the change will be easier if the previous single vision lenses were also of minus cylinder form. The third difference between the two types of lenses is cosmetic. The edge of a strong cylinder prescription lens varies in thickness around the lens. In plus cylinder form either the frame must be distorted to follow the front of this edge or an unsightly bevel will be visible. In minus cylinder lenses, the change in edge thickness is concealed in back of the frame, and the front edge which follows a spherical surface does not distort the frame. Minus cylinder lenses make possible a more attractive pair of glasses. The fourth point to consider has to do with the magnification of spectacles lenses and the importance of considering the differences in magnification between the two eyes. In order to understand spectacle magnification, let us compare a corrected eye to a telescope. Figure 21 shows a hyperopic eye corrected with a plus lens. We can think of a hyperope as a normal person on whom has been placed a minus contact lens, as illustrated in the figure. The effect of the minus contact lens must be corrected with a positive spectacle lens. The shaded lenses in the drawing comprise a Galilean telescope the type used in field glasses and some telephoto camera lenses. It is made up of a plus lens and a minus lens separated by a space. The only difference in the characteristics for a hyperope and a myope is that the plus and minus lenses would be interchanged. A hyperope looks through a telescope normally and a myope looks through a telescope reversed. For a hyperope, the image is enlarged, for a myope, it is reduced. For the sake of accuracy, it is necessary to point out that if the refractive error is entirely due to the length of the eyeball, and if the spectacle lens is placed exactly at the front focal point of the patient s eye, then from one point of view there is no change in image size. However, in practice, these conditions are seldom met. Therefore, some image size change can be expected. If the prescription is spherical and, if both eyes have approximately the same prescription, no problem is created. Except for the first feeling that things look a little different, the patients have very little trouble. Now, let us refer to the same figure and think of this as a cylindrical prescription. We have a cylindrical telescope and the image on the retina will be magnified in one direction more than the other. Again, this will be no great problem, provided that the other eye is similar or identical and the axis of the cylinder is identical. However, if either the power or axes are different, the patient may experience problems. The floors will appear to top and the familiar problems of getting used to a cylinder prescription will be increased. The problem is that sometimes patients fail to become accustomed to them at all, or, if they do, it is only after a period of considerable effort. 31

32 The farther from the cornea that a cylindrical spectacle lens is placed, the greater the problem. Magnification depends on the power of the lens and vertex distance. Therefore, the farther in front of the eye the cylinder is, the more of this cylindrical or meridional magnification will exist. This can be proved simply by taking a toric lens and holding it in the hand and moving it out from the eye. The image seen through the lens will become more and more elongated and distorted. It is logical then to conclude that the closer a toric surface is to the patient s eyes, the less probability there will be of magnification problems. On minus cylinder lenses, the toric surface is nearer to the eye by the thickness of the lens. This fact is not very important in minus prescriptions because the lenses are thin. However, in plus lenses, the lenses are thicker; therefore, the distance from the eye to the cylinder is proportionately greater. Accordingly, the difference between placing the cylinder on the back of the lens instead of on the front can well mean the reduction of magnification characteristics of the spectacles from a value just beyond that to which the patient can become accustomed to one 32

33 to which he can easily become accustomed. The thicker the lens, the more reason for using minus cylinder lenses. Table 1 compares plus and minus cylinder lenses and shows why manufacturers are increasing production of minus cylinder lenses in both glass and plastic as production methods are developed. RELATING FITTING AND DESIGN FOR STRONG LENSES The performance of these lenses is very dependent on base curve selection and fit of the lenses before the patient s eyes. While these factors are important in nearly all prescriptions, almost no latitude in their application is possible with strong lenses. Earlier, in the discussion of Figure 12, we pointed out that the optical axis of the lens should pass through the center of rotation of the eye. Only when this was the case did the reference sphere of the lens match that of the patient and the far point sphere of the lens match the far point sphere of the patient. Obviously, there is no guarantee that this will happen when a patient selects a frame. Fortunately, the departure from the ideal case ordinarily does not alter significantly the designed performance of the lenses. This is primarily true of the ordinary prescription range between and 3.00 D. 33

34 In stronger prescriptions, the vertical position of the frame and lens affects the accuracy of the prescription at the reference sphere. This is true, not only for wide fields of view, but for fulltime seeing. Accordingly then, a new variable is introduced when we consider lens performance vertical height. We have already discussed the center of rotation distance which determines the optical stop position. Since these 2 dimensions the optical stop (or center of rotation distance) and vertical height of the lens in front of the patient s eye both affect performance, it is necessary to be able to estimate what they are. One cannot easily measure the center of rotation distance. However, one can measure the largest variable that affects this distance. This is the eyewire distance, the distance from the plane of the eyewire groove to the cornea. It is the location of the bevel of the lens and is usually just forward of the center of the plastic rim of the frame. Figure 22 illustrates the meaning and measurement of the eyewire distance. In practice, this distance has a range of about 7 to 20 mm. About 90 percent of the frames, however, fit between 10 and 16 mm. from the cornea. These two distances correspond to two center of rotation 34

35 distances of roughly 27 and 33 mm., for which data were presented earlier. Throughout this chapter, eyewires of 10, 13, and 16 mm. corresponding to 27, 30, and 33 mm. center of rotations distances are called close, medium, and long fitting distances. For cataract lenses, which are usually fitted as close to the eye as possible, the close, medium, and long classifications apply to distances of 7, 10, and 13 mm. for eyewires and 24, 27, and 30 mm. for center of rotation distances. Now, let us consider variations in vertical positions. Figure 23 illustrates a typical fitting frame. The normal tilt of the lens plane causes the optical axis of the lens to pass upward into the eye. This tilt, the pantoscopic angle, creates an angle between the optical axis and the temple. When measured, the pantoscopic angle is usually taken as the departure from 90 of the angle between the lens plane and the temple. The result of this tilt is that when the patient fixates in a direction straight ahead, he uses an area of the lens above the optical center. When this direction is parallel with the temples, with the center of rotation of the eye on the optical axis, the data in Figure 23 give the amount above center for the line of sight intercept which will place the center of rotation on the optical axis. For common pantoscopic angles (approximately 10 ), this distance is 5 mm. 35

36 When the condition just described exists, the eye will pivot on the optical axis and intercept small angles above and below it for the normal frequent changes in direction of fixation. (This is a good optical relationship one for which the lenses were designed.) Figure 24 shows centered, high, and low fixation positions for viewing straight ahead (parallel with the temples). While a wide range of vertical centering will be found, positions with the eye 3 mm. too high to 3 mm. too low will include most conventional frames. Referred to the center line, these are 8 and 2 mm. above, respectively. (The new large round and square frames fit higher.) Departures from the normal range should be avoided for strong prescriptions. When we consider the role of the nose in supporting the frames, it is apparent that the longer the fitting distance, the lower the vertical position is likely to be. The two partially independent variables, eyewire distance and vertical centering, together affect lens performance. STRONG MINUS LENSES The data in Figure 25 reflect design performance in terms of the tangential, sagittal, and 36

37 astigmatic errors for a 8.00 prescription. The values are for a 20 angle of view with respect to the optical axis. The field of view would represent areas of the lens located approximately 10 mm. from the straight ahead fixation point. It is obvious that the fitting distance makes a difference in the choice of base curve. In view of the almost central area being considered, these errors are significant. They are greater than would be tolerated by most lens standards. It can be seen that a curve of approximately provides the best average performance for conditions A and B combined (Fig. 25), which are for short and long fitting distances. Condition C describes the performance for the long, low fitting situation. For close fitting frames, lenses seldom fit too low; they are more inclined to fit too high. Such a condition results in the values shown in Figure 25E. With a high frame, any base curve listed results in a significant amount of astigmatism. Thus, unusually high fitting frames should be avoided for strong prescriptions. Figure 25D lists the maximum errors of power, either tangential or sagittal, and the astigmatism that would result from the use of each base curve for any of the listed fitting situations except those in E. 37

38 Should the patient assume postures in which he used areas of the lens 15 mm. from the center, the errors listed would be approximately doubled. A good rule of thumb then is to use base curves of about +1.50, like those found on the newer minus cylinder lenses, unless the frames fit particularly close to the eye. In such instances, the steeper curves perform better, but the dispenser should be careful not to fit the frame too high. By following the same reasoning throughout the minus area from 8.00 to 20.00, front curves should be flattened so that from about to 20.00, a front curve provides the best compromise. The frame should be fitted between the ideal and low position to provide the best vision, never too high. OTHER FACTORS The factors described are pertinent only to the accuracy of the prescription as the patient uses different areas of his lenses. Frequently, however, complaints stem from other considerations. Distortion (to be discussed later) and reflections are frequent complaints which the steeper curvatures tend to reduce. Frequently, it is desirable to compromise on the refractive performance of a lens in order to reduce these complaints. When curves steeper than those recommended are used, however, it is obvious that the frames should be fitted as close as possible to the eye, not only to improve the refractive errors, but also to reduce distortion and reflections. Careful selection of base curves and fitting position are critical factors for good acuity and comfort. CATARACT LENSES Fitting factors and design choice are even more critical in cataract than in strong lens prescriptions, and success is even less assured. A simple experiment will demonstrate the importance of matching centering and angle. If a D lens placed on the Lensometer (A.O.) or Vertometer (B & L) is tipped and slid, the prescription changes very rapidly. In fact, a D lens viewed straight through the optical center with a pantoscopic angle of about 12 will have 0.50 D of astigmatism. Figure 26 shows data similar to those in Figures 16 and 18, except that the prescriptions herein shown are for D and D lenses, respectively. The tangential and sagittal errors are given and are measured in whole diopters instead of in hundredths of diopters. The values illustrate the importance of avoiding plano-convex lenses whenever possible. The body of data show why 3.00 base lenses were used as the best corrected curve lenses until the advent of aspheric lenses. It also demonstrates the need for and advantage in any lens which reduces these errors. 38

39 Although the data are for a 30 angle, the errors present at 20 and 10 (10 and 5 mm. from the straight ahead fixation point) are large enough to reduce the patient s visual acuity. It has long been known that aspheric surfaces would reduce these errors to more acceptable values. The advent of plastic lenses made it possible to produce them at a practical cost. Aspheric simply mean nonspherical. Figure 27 indicates what such a lens does. An aspheric surface on a cataract lens is one which is progressively shallower as zones are considered farther and farther out from the center. It can be seen from Figure 26 that the tangential error is the principal problem. Let us recall that we can think of the tangential error as a cylinder with its axis changing as we circle the lens: a plus cylinder, axis 90, for horizontal viewing; and a plus cylinder, axis 180, for vertical viewing. In a sense then, to make an aspheric is to grind a selection of minus cylinders circularly around the lens, zone by zone, in areas A, B, and C, so as to remove the unwanted plus cylinder effect. It is not possible to correct a surface perfectly since the same type of problem exists as in the weaker lenses. If the astigmatism is corrected, power errors will result. For cataract lenses, the errors are significant. When the astigmatism of a common cataract lens is corrected, between 0.75 D and 1.00 D of power errors may remain. As a result, the designer of an aspheric cataract lens is faced with the same decision as when using spherical surfaces, i.e., whether to correct the power errors or the astigmatism, or to strike a balance. As with ordinary lenses, one of the principal differences between the products of different manufacturers is the type of correction. 39

40 A return to the earlier tables of prescription errors for the and arranged by base curve will show that the tangential error varies widely between base curve selections and prescriptions. The designer of an aspheric lens obviously must know which prescription and which inside curve are to be used when the lens is finished in order to design the appropriate compensatory curve. This is an important consideration and an important difference between available aspherics. Some aspherics are supplied with a special aspheric surface for each 0.5 D of spherical change in prescription. Other companies supply only 2 to 4 base curves. The problem is magnified when we consider the cylinder component of toric cataract lenses. Indeed, many cataract prescriptions have cylinders approaching 2.00 D. Consequently, the aspheric surface has to be considered as working with more than one prescription even on a single lens. For example, a D lens with a 2.00 D cylinder, axis 90, has an average power of D lens. In good designs, this is done. Even in well-designed aspheric, such a prescription would still have a tangential error for upward viewing of at 30 and a 0.41 for horizontal viewing. At 20 (10 mm. from the center of the lens), it is possible to keep all the errors below 0.50 D. 40

41 With the rapid change of errors for different prescriptions and different meridians of the same prescription, we can see the need for a multiplicity of aspheric base curves in order to provide good correction. NEED FOR CAREFUL CHOICE OF OVERALL BENDING OR BASE CURVE Aspherics are supplied by different manufacturers on different concave base curves. For any one eye position and prescription almost any common concave curve will yield good results if the proper compensating aspheric front curve is used. Aspheric fronts can be matched to concave curves to provide for good correction so that for one prescription and one eye position, the designer has a freedom of choice of concave curves. However, since from a practical point of view, the best of series must provide for a small range of prescriptions, and in toric lenses there is in effect a range on any one lens, it is necessary to consider whether a particular concave base curve can provide better correction over a wider range than other curves can. Calculations and experiments have shown that concave base curves between 3.50 D and 4.00 D provide the least variation in performance over a range of prescriptions using the same aspheric front curves. Also, for the same reason for toric prescriptions, if the average value of the concave toric curve is approximately 3.75 D, the best average performance in all meridians will be obtained. For the prescription, a good concave curve would be 2.75 x NEED FOR CONSIDERING FITTING VARIATIONS Just as with ordinary prescriptions, we must also anticipate a change in the center of rotation distance (eyewire distance) and vertical centering between one patient and another. Here again, the base curve between 3.50 D and 4.00 D provides good performance throughout normal variations in these distances. If shallower curves are used, the lens may perform well for one patient but not as well for a patient with a different fitting frame or a different size of ocular globe. To sum up, aspheric cataract lenses should have a surface designed for the prescription the patient will wear. A multiplicity of aspheric front surface blanks is necessary, and concave curves averaging between 3.00 D and 4.00 D provide the highest probability of good seeing. Table 2 compares the performance of the familiar plano-convex and 3.00 base spherical lenses with a well-designed aspheric lens. The terminology regarding frame and eye positions is the same as was used in discussing Figure

42 It can be seen that the aspheric lens provides markedly better performance and, for different eyewire distances, the performance will be maintained if proper base curves are used. Table 2 also shows that fitting is important. It can be correctly inferred that for vertical centers too high or too low, the errors of all lenses exceed tolerable limits. It is occasionally recommended that the errors associated with fitting can be corrected by placing trial lenses in front of loaner spectacles. In view of the variation due to changes in frame and lens type, this is not a reliable procedure. A new refraction followed by the prescribing of welldesigned aspherics properly fitted is the only accurate way to alter aphakic prescriptions. Throughout these discussions, it has been assumed that changes in prescription owing to changes in vertex distance between the refracted distance and the fitted distance will have been taken into account by the use of tables and calculations familiar both to dispensers and to prescription laboratories and, therefore, these changes have not been included here. Different compromises of aberrations are favored by different manufacturers. Some supply pertinent information on their lenses. Some advertising is too general and noninformative. Details on the geometric configuration of the aspheric surface may be interesting, however. 42

43 Differences in mathematics are mainly a convenience of the designer or of his production department. A surface supplying the best corrections can be provided by several different mathematical expressions and methods of manufacture. In any design, it must be remembered that no single type of error can be completely corrected for more than one prescription and for one meridian of a toric. It is an oversimplification to claim a particular type of correction without discussing the flexibility of the design to different fitting situations, around the different meridians of a cylinder correction, and over a range of prescriptions. Of the many aspheric lenses available, some have little or no information regarding their design: many are supplied with too few aspheric base curves. Decisions regarding the type of aspheric lens should be solidly based if the patient is to receive what he pays for. In the selection of cataract lenses, optical considerations should be balanced with those of weight and appearance. TYPES OF CATARACT LENSES Many types of cataract lenses are available. Those shown in Figure 28 are typical unedged lenses. During the years and up to the present time, the weight, thickness, and bulk of cataract lenses have been reduced by the use of lenticular lenses. Lenticular as an adjective to describe a lens is redundant, lenticular signifying lens-like, but the redundancy will pass because what is meant by a lenticular lens is a lens within a lens, or a lens on a lens. There are many forms of lenticular lenses. Generally, however, they fall into two classifications: the one-piece lenticular lens and the fused lenticular lens. Figure 28 shows a typical one-piece lens. It would either be ground and polished or molded so that the optical portion is a circular area within the major lens. Since the thickness and bulk of a lens depend not only on its power or prescription, but on its diameter, the smaller the optical area, the thinner and less bulky the lens will be A disadvantage of such a lens is its unusual appearance unless the lenticular area extends so that it nearly fills the frames. This is the case with the newer 40 mm. diameter lenticular lenses. In a fused lenticular lens, a higher index portion of glass is fused into the major portion to provide additional refractive power, thus creating a thinner lens without having the sharp break or bulge characteristic of the one-piece lenticular. Optically, the fused lenticular high index lens is very poor. It is not recommended except for occasional social functions at which the wearer s appearance is a primary consideration. The implications of size and weight are obvious. 43

44 CONSIDERATION OF WEIGHT AND APPEARANCE A discussion of cataract lenses would be incomplete without some attention to weight and appearance. The decision regarding these factors includes consideration of glass full-field lenses, glass Lenticular lenses (34 mm. spot), plastic full-field lenses, plastic Lenticular lenses (40 mm. spot), size and shape of frame, conventional centering, and minimal effective diameter centering. We will only take up the last consideration. The implications of size and weight are obvious. Minimal Effective Diameter. There is considerable interest in minimal effective diameter (M.E.D.) lenses. This concept has been urged by Dr. Robert Welsh and others in writings and 44

45 lectures. It is simply the concept of upward decentration of the optical center of a strong lens in a frame so that the thickness at the upper corners is in balance with the thickness at the lower corners. This result is a somewhat thinner lens. Dr. Welsh and other workers also recommend small lenses for frames no larger than for a 44 eye, if possible for aphakics. The recommendation is sound. The main point to remember about upward decentration is that the pantoscopic angle should be reduced according to the values in Figure 23. If the lens is decentered upward, the pantoscopic angle should be reduced in most cases to about 5. However, the position of the eye as it views objects straight ahead parallel with the temples should be noted in view of the new location of the optical center, and the angle should be adjusted accordingly (Fig. 23). The data on pantoscopic angle vs. vertical eye position always refer to the optical center of the lens and the optical axis. If these are raised for an M.E.D. lens, the pantoscopic angle must be reduced by the values shown (Fig. 23). 45

46 We should keep in mind that if a lenticular lens with a 40 mm. spot is edged so as to conform to M.E.D. criteria, and inserted in a frame with a 44 eye, the lenticular spot blends into the frame so that from a few feet away it is visible. It can be seen then that a procedure which can be regarded as almost essential for full-field lenses still has additional advantages in weight and magnification with a lenticular lens. Figure 29 shows a body of data comparing the weight of an ordinary pair of men s spectacles to a selection of cataract lenses. We believe strongly in the aspheric lenticular lens. Lenticular lenses are advantageous in that they (1) are thinner and lighter; (2) can be used in any frame without bulky corners; (3) can be decentered to patient s P.D. (pupillary distance) in any frame without increasing weight or thickness; (4) possess more accurate vertex power. Vertex power depends on thickness and front curve. A full-field lens must vary in thickness according to the frame requirements; therefore, vertex power varies; and (5) owing to their reduced thickness, reduce magnification and distortion. Patients see better and their eyes look more natural to others. We believe that the aspheric lenticular lens, selected from a series with an adequate number of base curves with a 3.00 to 4.00 concave curve, provides the optimum combination of optics, appearance, and comfort. We have attempted to give sufficient factual data so that the reader can make objective decisions with confidence. We have also tried to point out that fitting is at least as important as choice of lens design. Details have been provided in the hope that the reader can constructively visualize the relationship of these two factors. HIGH INDEX LENSES The use of a high index glass for strong prescriptions results in shallower curves and thinner lenses than is possible with regular crown glass. The flint glass used is actually a lead glass. Low reflection coatings are recommended since the reflections are more brilliant than with crown glass. The lenses are thinner but not lighter; indeed, some are heavier than the same prescription in crown glass owing to the fact that the density of the flint glass is greater than that of crown and is sufficient to overtake the reduction in thickness. Flint lenses cannot be heat-treated to increase impact resistance. The use of high index glass is questionable from another point of view. The best base curves required for good optical performance are different from those used in corresponding prescriptions in crown glass. Since there is no published information, it is unlikely that strong prescriptions in flint glass will perform as well as a conventional lens of good design. High index flint lenses absorb ultraviolet and even x-ray radiation to a greater extent than do ordinary glass lenses. Therefore, they are sometimes prescribed for persons exposed to these radiations. However, the type of glass and the thickness of the lenses should be determined by 46

47 someone familiar with the hazards and the characteristics of the glass. Some cataract lenses are supplied in a form in which the central area is of high index. These are constructed in a manner similar to that used for bifocals. The result is a thin and attractive but heavy lens. Optically, such a lens provides a very poor field of view. The construction is counter to what is used for achromatic telescope lenses. High index lenses are also used for strong myopic prescriptions in which the optical performance is fair and the lenses are thin, heavy, and slightly yellow in appearance. DISTORTION Geometrically, distortion is caused by the fact that for wide fields of view, the lenses magnify or reduce by a different amount than they do through the center for straight ahead viewing. A frequent patient complaint is that straight lines appear curved. This is called distortion. Like power and cylinder errors, it is due to the prismatic effect and the angle of view. Unlike the power errors, changing base curves helps very little. Distortion is usually noticeable when a prescription is changed. It is directly related to prescription and angle of view. Changing the angle of view by changing the pantoscopic angle to aim the lens at the area that the patient wants to see free of distortion is the best remedy. If the patient is a draftsman or is involved with other near object tasks, a steep pantoscopic angle should be used. It will provide reduced distortion for the patient s near point needs. If, however, distortion of wall charts or the tops of control panels bothers the patient, some of the pantoscopic angle should be removed. Distortion in cataract lenses is one of the major problems encountered. The apparent curvature of straight lines is considerable even for moderate angles of view. As the patient turns his head, a particular door frame or other straight edge will be viewed through different areas of the lens having differing amounts of distortion. This causes the image to change in curvature or writhe and swim. If the head is held still and the eye moved to scan the scene, the image will remain steady. It will be curved at its edge but will not appear to swim. The lens and its image are a fixed entity. This advice is contrary to some popular concepts. However, simple experiments with strong lenses will verify its accuracy. Most aspheric lenses reduce distortion significantly. In general, those aspherics with steeper base curves reduce distortion more than those with shallower curves. However, with the best of current lenses, it is still a real problem. The doctor or optician should anticipate it and help the patient to understand it and to learn to hold his head steady for moderate scans of the field of view. 47

48 SUMMARY This concludes the discussion of design theories and errors applied to single vision lenses. Some of the errors are patently significant. Others may seem small when viewed from the point of view of a clinician. However, before we proceed to apply the basic principles to a study of bifocals, if we relate the sensitivity of the eye to a camera, we can obtain a better appreciation of the importance of these seemingly minor details. A typical fine camera in the hands of an amateur, even when finely focused, will record on the film approximately 50 light and dark cycles of detail per millimeter. The finest of films in the hands of the most professional photographers can record 100 cycles of light and dark detail in 1 millimeter. For a well-corrected eye of normal focal length, there are 100 cycles of light and dark detail per millimeter when the subject views the 20/20 line on a test chart. Enoch has shown [2] that the human retina is capable of resolving 200 cycles per millimeter. Indeed, we know that many people can read the 20/10 line or its equivalent. Thus, the eye is capable of resolution comparable to the very best camera. When we consider the care we take with our cameras and how much thought we give to auxiliary lenses or attachments, perhaps we should have more respect for the spectacle lenses we prescribe and wear. PRODUCTION OF OPHTHALMIC LENSES The method of producing lenses indicated in Figure 30 is a classic one but still widely used. The lenses start as molded pressings of glass, rough on both sides, molded to the approximate shape of the finished lens. Lenses are mounted on the iron blocks in pitch. The curve is obtained by grinding with a slurry of various grades of emery, coarse at first, then finer and finer. Finally, the surfaces are polished by the same procedure with a polishing pad mounted on the lap, and rouge or other polishing compound is used as the slurry. Newer methods, which are faster and cleaner, involve diamond generating with a ring tool or lap instead of grinding with emery. A ring tool is shown in Figure 31A. The upper drawing depicts the tool and the bowl for retaining the coolant. The lower drawing shows the geometry of the generating process. The lens L is blocked rigidly, facing the tool. To obtain a toric surface, the tool is angled through the required angle A. The angle, combined with the radius of the cutting circle, determines the curvature in a plane perpendicular to the paper. The tool rotates about its axis of symmetry, as shown in the diagram. The angled tool is then swung about the pivot point P, cutting the surface in the plane of the paper through a radius R which is the distance from the pivot point to the leading edge of the circular tool. If angle A is zero, the surface generated has the same curvature in all meridians and is, therefore, spherical. The entire assembly including the pivot point P is adjustable forward and backward to regulate the lens thickness, and the distance from the tool to the pivot point is also adjustable in order to select different values of the radius R. Thus, with the adjustment of the pivot point R and the 48

49 angle A, the base curve and the cylindrical curve can be determined with two simple settings of the instrument. The thickness is regulated by the position of the entire head. The simplicity of these adjustment facilitates the automation of the grinding process. Figure 31B shows a complete modern unit which incorporates the principles described for grinding and polishing prescription lenses in local laboratories. The unit at right in the figure consists of a projection system for location of optical center and cylinder axis and alloy blocking of the blank. The lens is then mounted at the right of the central unit within the rubber cup. The required spherical and cylindrical curves are relayed to the instrument electronically through the control button console at the left. As factories and laboratories become more automated, processes with lenses on indexing machines operating in a manner not unlike a turret lathe are coming into use. Any of these processes cuts and polishes the surface with geometrically accurate motions. Therefore, when the equipment is well maintained and well controlled, remarkably fine optical surfaces are obtained. After grinding and polishing of one side, the process is repeated for the 49

50 other, and the lenses are washed and prepared for shipment. FORM OF LENSES AS SUPPLIED BY MANUFACTURERS Single vision lenses are supplied as finished uncut lenses and semi-finished blanks. FINISHED UNCUT LENSES Finished uncut lenses are lenses that have been ground and polished to the designated prescription. Both sides of the lenses are ground and polished. Spherical lenses have two spherical surfaces; toric lenses have on toric surface and one spherical surface. The toric surface 50

51 may be either on the front (convex) surface or on the ocular (concave) surface. Uncut lenses are supplied by different manufacturers in a variety of sizes and shapes. The sizes generally range from 58 to 71 mm. in diameter. The larger sizes are supplied only in a limited range of prescriptions for use in the large modern frames. The shape of the lens varies with the manufacturer and the brand or line of the lens product. Some are round, or round with a short flat side or truncation. Others are round with truncations so that they take the shape of a rounded square. Some are octagonal. Face-on views of typical single vision and bifocal lenses are shown in Figure 32. Finished uncut lenses are used in the most frequently ordered prescriptions. The advantage is in the speed of filling the prescription and in the cost. Mass-produced lenses cost less than those finished one at a time in a local laboratory. Opticians and doctors who do their own dispensing usually have a machine on the premises for edging the lenses to fit individual frame styles. A small stock of finished uncut lenses of the most popular prescriptions is kept on hand. Thus, patients may be easily supplied with either their new prescription or the replacement of a broken lens. 51

52 A disadvantage of uncut lenses is that for plus lenses in small frames, there may be unnecessary thickness. The center thickness of a positive or convex lens must be great enough to allow a sufficient edge at its maximum diameter. For example, if a 65 mm. uncut lens is edged down to fit a small lady s or child s frame, excess thickness may be present. SEMI-FINISHED LENSES Semi-finished single vision lenses or blanks are lenses on which only the front convex surface has been factory-ground and polished. The quality of the concave surface varies with the type of lens. However, in no case is the ocular surface of a semi-finished blank suitable for use. Furthermore, the blanks are supplied thick enough and with a suitable curvature on the concave surface so that a variety of prescriptions can be filled with the same semi-finished blank. Semi-finished blanks are provided with plus toric fronts for those lens series in positive toric form and with polished spherical fronts for those lens series in minus cylinder form (Fig. 33). When minus cylinders are indicated by the brand name prescribed or by special base curves, the ocular surface ground in the local laboratory is a toric surface. This is true of practically all bifocals. The finished thickness of these custom-ground prescriptions can be adjusted according to the frame size and the requirements of the prescription, e.g., an industrial safety thickness lens, an impact resistant dress lens, or an ordinary prescription. The advantage of using semi-finished blanks lies in the fact that a relatively small selection of semi-finished blanks will enable the laboratory to fill a wide range of prescriptions. This is especially advantageous when the wide variety of prescriptions of stronger powers is considered in view of the infrequency of the demand for any one item. The variety of absorptive glass required for sunglasses and industrial protection also reduces the call for a particular prescription with a given absorptive characteristic. In the case of bifocals, local grinding is essential to provide for the required cylinder and segment position. Semi-finished blanks can be ground to the designed curves according to charts supplied by the various manufacturers, or they can be ground to solve a particular problem as ordered by the doctor or the optician. The doctor should prescribe the type of design by brand name or specify base curve, or be certain that the optician will do so. He should not leave the entire choice of base curve to the laboratory. NOMINAL VS. TRUE CURVES We have seen that the choice of base curves affects the performance of a lens as the patient turns his eyes to view different area. However, there are other factors that require a multiplicity of base curves to cover a range of prescriptions. One of the principal factors is the thickness of the lens. 52

53 Figure 34 shows a strong plus lens divided into three elements. The front and back surfaces can be considered as thin positive and negative lenses separated by a section of plate glass. The forward position of the front positive lens moves its focus forward. It has, therefore, a shorter focal length when it is referred to the ocular surface; thus, the effective power of the front curve is increased. Semi-finished blanks and the fronts of factory-finished lenses consequently are made weaker than the labeled value in order to give the correct prescription. The laboratory grinds the expected concave curve on the concave side (computed by subtracting the nominal front curve from the prescription). 53

54 This compensation of the front curvature, therefore, depends on the thickness of the lens. If the thickness of the lens is known, it can be calculated exactly. Since different prescriptions require different thicknesses, however, if the prescription of a lens is to be held to very close tolerances, a single front base curve can be used for a limited range of prescriptions only. For strong plus lenses, this range is very limited. For weaker plus lenses, the range increases as the front decreases in curvature and the thickness decreases. For minus prescriptions, the thickness is constant. It is approximately 2 mm. so as to provide adequate safety. A lens series with frequent base curve changes for plus prescriptions will yield more accurate prescriptions than a series with only a few base curve changes. Another reason why front curves are not exactly what the labels would indicate involves the use 54

55 of standard tool and standard curves. At the present time, practically all glass lenses are manufactured from a glass which has a refractive index referred to air of Years ago when ophthalmic laboratories were being established, glass indices varied but a good average refractive index value of the glasses then in use was Laboratory tools were then cut to curvatures which would yield the correct refractive power according to the label of the tool. The same curvatures and labeled values prevail today, but since the glass has changed, the resulting power of a surface is not exactly what the label would indicate. For example, a tool labeled 6.00 D will actually yield a power of 5.92 D. As a consequence, when the factory produces semi-finished blanks, the power of the front surface is compensated not only for the thickness of the lenses which are expected to be ground from the blank, but also for the fact that the tool which the laboratory will use is a standard tool with a small inherent error. Therefore, the nominal factory-finished front curves are not exactly what the labels represent but have two compensations: one for thickness of the lenses and one for the errors in the laboratory curves to be put on the second surface. These two compensations dictate that a well-designed lens series must have a multiplicity of front curves in addition to those changes in front base curve dictated by the design considerations already discussed. BIFOCAL LENSES MULTIFOCAL LENSES Bifocal and multifocal lenses are available in a wide variety of segment types and distance portion designs. The most obvious differences between types of bifocals are the size and shape of the reading portion or segment. A variety of segment styles are shown in Figure 35 and include (A) 22 mm. segment one-piece or fused bifocal, (B) straight top fused bifocal, segment sizes 22 to 45 mm. (most popular 22 to 25 mm.), (C) straight top full-field one-piece bifocal, (D) semicircular one-piece bifocal, (E) curve top fused bifocal, and (F) ribbon segment bifocal. In examining the advantages of the different types, it will be helpful to classify them by type of construction. The first main classification divides fused bifocals from one-piece bifocals. ONE-PIECE BIFOCALS A one-piece bifocal is a lens which has been ground and polished from a single piece of glass. There are three principal types of one-piece bifocals (Fig. 35 A, C, and D). Types Ad and D usually have the segment on the back surface. The reading portion gains its additional refractive power by virtue of the fact that the curvature at the reading portion is more convex (actually less concave) than it is over the rest of the lens, thus creating a slight bump on the rear surface. In plastic lenses, the segment is on the front. These one-piece lenses are available with either a small round or a large semicircular segment (Fig. 35). 55

56 A third type of one-piece bifocal is the straight top, full-field lens (Fig. 35C). It is essentially a one-piece version of the original Ben Franklin lens comprising two separate single vision lenses one for distance and one for reading. This type of lens was first introduced by American Optical Corporation under the name Executive. It is now available from several manufacturers under the names of Duo-Lens (B&L), Uniform E (Univis), Horizon (Titmus), Kurova M (Shuron- Continental), and others. Reading power is gained from an increase in the surface curvature of the front surfaced. FUSED BIFOCALS Fused bifocals derive their name from the fact that they are constructed of two or more separate pieces of glass which have been fused together, although in their final form, they are actually one-piece bifocals in that there is no way of separating the reading portion from the distance portion. A fused bifocal then is a lens containing two types of glass in which the reading addition is obtained by literally fusing into the major distance portion an additional segment of glass of a higher index of refraction, thus increasing the refracting power of that portion. Lenses A, B, E, and F in Figure 35 indicate the appearance of common fused bifocals. READING ADD In one-piece and in fused bifocals, the reading power is obtained by adding curvature or index to 56

57 the distance portion. We, thus, create a reading addition or add. The concept is basic to the study of both the structure and performance of all multifocal lenses. It is an analogue and an optical parallel to the test for the reading addition. Whether the test is made by adding a plus sphere in front of the distance prescription, or whether the distance sphere is replaced by a stronger one, what is known is the addition. The actual vergence of the light entering the eye is not known because the object is not at infinity. The early bifocals were made by selecting an additional thin lens, the concave side of which was ground to the same curve as the convex portion of the patient s spectacles and cementing it onto the major lens (Fig. 36, bottom sketch). Thus, the patient had an additional lens, or a reading add, which became a fixed part of the prescription. Later, a method was developed which accomplished the same thing, i.e., the lens was ground with two different curves on one surface, thus providing a one-piece bifocal. A cross-section of the one-piece bifocal would be the same as a cemented one. (This is shown in Figure 36, except that there is just one piece of glass instead of two cemented together. The face-on view of both these lenses is shown with the smaller segment in Figure 35A). The subsequent desire to create a bifocal which would be less conspicuous led to the development of the fusing process, which eliminated the bump and improved the appearance. In general, one-piece and fused bifocals have obvious differences in appearance and can be easily 57

58 identified. PRODUCTION OF ONE-PIECE BIFOCALS A large piece of glass is mounted on a block so that it can be turned on an axis which is perpendicular to the surface of the blank (Fig. 37). The rotation of the blank is in the horizontal plane. A ring generating (and polishing) tool is then rotated around an axis which is angled to the vertical so that the axis of the ring tool, if extended, would intersect the axis of rotation of the blank at a point P. Thus, the ring, which can oscillate to some extent, generates a spherical surface the center of curvature of which is at a point P. However, restrictions are put on the oscillation of the ring tool so that it grinds an annular area of the lens, not a complete spherical surface. Later, another ring tool is mounted so that its axis of rotation intersects the major axis at point P, thus, generating a shorter, steeper curve the center of curvature of which is at P. Its oscillation is also restricted so that the borderline between the annular and the central area is sharp and clean. The result is a surface of two different radii, both spherical one a central spherical cap and the 58

59 other an annulus, as shown in Figure 38 (a face-on view). The size of the central and annular areas can be varied. If a small segment bifocal is desired, the central area may be as small as 20 or 22 mm. When such lenses are made, the finished blank which is sent to local laboratories is cut out so that the entire central area is present on the blank (Fig. 38, right half). If a larger semicircular reading field is desired, a larger central area is used (for example, 38 mm in diameter). Such a blank when completed is cut in two, thus making 2 blanks with one operation. Each blank has a semicircular reading addition 19 mm. high (Fig. 38, left half). The process shown is also used to produce one-piece lenticular cataract lenses. Many one-piece bifocals have the segment on the concave side. However, the process is analogous to the one shown in the figure. As was previously pointed out, the cross-section of these blanks is exactly the same cross-section as if the segment had been cemented. From an optical point of view, it is convenient to think of 59

60 it as a cemented lens. Studying as we are one-piece bifocals, a brief view of the production method for the full-field, straight top, one-piece bifocal is in order (although in terms of history, the development of fused bifocals came earlier). Molded blanks are mounted with pitch or metal alloy on a cylindrical block (Fig. 39) which is actually a truncated sphere. The block and lens rotate about an axis as a cup tool generates and later polishes the reading segment. The straight line is created by the rotation of the lenses in a circle and by limitation of the upward position of the generating and polishing tool. The upper distance portion can be finished in an analogous manner by mounting the lens on a block of different radius or on a more conventional spherical block in a manner similar to the production of single vision lenses. Some manufacturers supply one-piece bifocals with cut-off segment similar in shape to the popular fused bifocals. These require a rather complicated production technique. Such lenses are available in both glass and plastic material. PRODUCTION OF FUSED BIFOCALS The oldest and simplest of fused bifocals is the Kryptok. This bifocal has a round segment, usually 22 mm. in diameter. Drawings of the production steps for these lenses are shown in Figure 40 in the column at far let. Manufacture is initiated with a crown glass major portion. It 60

61 is prepared by grinding and polishing a countersink or concave curve indented into the convex portion of a molded blank (Fig. 40, A 1 ). The depth and curvature of this concave countersink depend on the amount of reading addition desired and the amount of curvature anticipated for the convex curve of the distance portion when the blank is finished. Thus, a wide variety of curvatures is required for countersinks and segments. Sketch A 2 of Figure 40 illustrates this segment. A disc of high index glass, usually 1.61 or 1.70 flint, is ground and polished on one side to a convex curve which nearly matches the concave curve of the countersink to which it will be fused. The curve is usually made slightly steeper so that air bubbles can escape during the fusing process. The lenses are fused by laying the major portion on a ceramic support and carefully placing the segment or button in the proper location within the countersink. When assembled, the entire sandwich is heated until the glass just begins to soften. The button are supported at the edge by clips of metal or other material. This maneuver keeps the edges of the button separated from the major portion as the segment softens 61

62 so that air can escape. After fusion, the fused blank has the appearance shown in sketch A 3. The fused area of the segment is somewhat larger than the required finished segment diameter. After fusion, the entire front surface is generated to the curve required on the distance portion and to bring the segment down to the required size. The front surface is then finely ground and polished. The result is a smooth continuous surface over the entire front of the lens; a reading lens of higher index glass is imbedded in the major blank which will provide an increase in power in that section of the total lens. The general structure of the finished lens is shown in sketch A 4. The process described is for Kryptok bifocals. A similar process is used for the better quality round segment fused bifocals which are sold under a variety of names. The principal difference between these lenses is in the segment glass. The higher quality lenses use a barium rather than a flint glass, which is used in the Kryptok. Barium glass has less chromatic aberration and is a clearer whiter material. It is also less likely to scratch. In certain chemical atmospheres, both barium and flint segment glasses are more likely to tarnish and corrode than is crown glass. Therefore, for industrial milieus where corrosive vapors are present, one-piece bifocals are recommended. The most popular type of fused bifocal is the straight top or cut-off type (Fig. 40, B 1 to B 4 ). Method of manufacture is similar to that used in the Kryptok and other round segment lenses, except that additional steps are necessary in order to obtain the cut-off or truncated circle shape. First, the major portion is prepared in a manner analogous to that shown for Kryptok. The difference between the two production methods is primarily in the manufacture of the segment. A cut-off segment is created by fusing 2 truncated circles of glass at their edges. The smaller upper portion is made of crown glass of exactly the same composition as the distance portion lens. The lower portion is made of a barium glass of higher index than crown, and, therefore, it will provide the additional power needed in the reading segment. The edges of these truncated circular discs are fused (Fig. 40, B 2 ). In certain types of cut-off bifocals, the boundary between the two truncated discs is painted with an absorbing pigment or identifying pattern before fusing, thus, providing either a tinted or patterned segment line which can serve to identify or remove unwanted light scatter from the line of fusion (Fig. 41). Lenses with pigmented segment lines are called coated segment bifocals. (Segment coatings will be discussed later.) Once the disc has been assembled, as shown in Figure 40, B 3, the process is analogous to that described for Kryptok. While the drawings indicate a straight line cut-off, a curved line is often used without any significant difference in the process. Ribbon segment which are truncated top and bottom require a 3-piece disc with the crown sections above and below the barium section. Some segments have rounded corners which are obtained by inserting the high index element of the desired shape in a larger disc of crown glass which has been milled out to the exact shape of the segment, so that the disc prior to fusing actually is a crown disc with an inlay of barium of the 62

63 desired shape. The generating, fine grinding, and polishing of the cut-off bifocals must be carefully controlled because the amount of generating controls, not only the size, but also the shape of the segment. After the front surface is finished on any of the cut-off bifocals, the crown glass portions of the segment blend into the distance portion and, because they are made of exactly the same optical material as the distance portion, disappear. It is the recognition that this blending and disappearing would occur that led to the first cut-off type fused bifocals. The visibility of the borderline between two different glasses, the segment outlines, is owing to the difference in reflectivity of the two materials. In the upper portion, where the reflectivity is the same, the separation of materials is not visible; in fact, it no longer exists after fusing. FUNCTIONAL DIFFERENCES BETWEEN TYPES OF BIFOCALS The significant features of a bifocal segment which affect its performance are: 1. Size of segment, especially lateral width. (Affects size of reading field vs. distance field and cosmetic visibility of the segment.) 63

64 2. Distance from top of segment to its optical center. (Determines jump effect at top of segment and acceptance by first bifocal patients.) 3. Relation of optical center of segment to optical center of distance portion. (Determines quality of reading field in strong prescriptions.) 4. Whether segment is of one-piece or fused construction. (Closely allied to 3. One-piece bifocal generally has less chromatic aberration.) 5. Type of glass used in fused bifocals. (Barium is used in the better lenses; less chromatic aberration.) SEGMENT SIZE It is difficult to come to a decision that a small segment is desirable unless the patient has become accustomed to a segment of the particular type and size, or unless there are positive reasons why only a small area of the lens should be devoted to near point tasks. One such reason might be a desire for a pair of glasses for outdoor work or for a segment to be used for occasional convenience. In general, for most prescriptions and, especially for first-time bifocal patients, the one-piece full-field straight top bifocal is recommended. The other characteristics affect the optical performance as well as the acceptance of the bifocals. The problems created and controlled by choice of the type of segment are referred to as image jump, object displacement, and chromatic aberration. Other performance defects that are not as frequently discussed are astigmatism of the image, reflections and refractions from the cutoff lines, and distortion of the image. IMAGE JUMP Image jump occurs when the apparent position of an object is suddenly displaced as the eye moves from the distance portion into the reading portion of the lens (Fig. 42). This, the prismatic action of the segment itself at the upper edge, is independent of the distance prescription. Figure 43 shows 2 types of fused segments a round segment and a cut-off or straight top segment. In the latter segment, the top of the segment is nearer its center. There is consequently less prism effect than in the round segment. A comparison of the angle between the segment countersink curve and the front surface, as indicated by the interrupted lines, shows the difference in base-down prism which the eye will encounter as it enters the segment and, therefore, the difference in apparent jump of objects which are seen just at the segment line. In one-piece bifocals, a similar effect is present. 64

65 The amount of prism is dependent on the distance from the segment center to the top of the segment and the power of the add. An estimate of the segment center position will help determine the amount of jump. In a round bifocal, the optical center of the segment is the center of the complete circle. In the flat top or cut-off bifocals, the optical center is the center of the circular lower part. Consequently, the more of the circle that is cut off, the nearer the segment center is to the cut-off line and the less jump there will be. The greater this distance and the stronger the add, the more jump there will be. The amount of jump can be expressed in prism diopters and calculated by Prentice s rule. Prism diopters = add power x decentration in centimeters. For bifocal adds: Jump in prism diopters = add x distance (where distance is from the top of the segment to the segment center in centimeters). 65

66 Figure 44 illustrates the geometry of typical cut-off bifocals. Most such segments have their centers approximately 5 mm. below the top of the segment, thus keeping the jump effect small. In the same figure, the complete circle is shown dotted to indicate the increased distance from the center which would be encountered were a full round segment used. 66

67 Figure 45 shows the geometry of the semicircular one-piece bifocal type. The center of the segment is 19 mm. from the top of the circle. This type of bifocal yields the maximum prism base-down at the top of the segment and the maximum jump effect. The small round one-piece bifocals will have the same effect as a small round fused bifocal of the same size. 67

68 Figure 46 shows the geometry of the full-field one-piece straight top bifocal. At the top of the segment line, the distance and reading portion curves are tangent except for the slight ledge necessary for production purposes. Except for production tolerances there is no jump effect at all in this type of lens. The optical center of the segment is on the segment line. A study of the illustrations mentioned enables us to draw up rules of thumb for estimating the amount of jump in different bifocal types: Cut-off bifocals Small round segment Large semicircular one-piece segment One-piece full-field straight top 0.5 prism D per diopter of addition 1.0 prism D per diopter of addition 2.0 prism D per diopter of addition No jump 68

69 We might wonder how serious is the image jump. It is image jump that displaces stairways and curbstones and seems to make double objects in view near the borderline of a segment. It tends to be annoying until the patient learns purposefully to use either the distance portion alone or the segment alone. One can experiment with sample prisms to evaluate this effect. However, we feel that 1 prism D is not difficult to get used to. 2 prism D might be called significant but tolerable after a short adaptation period. Prisms of 4 or 5 D would definitely take some getting used to for first-time bifocal wearers, or if a new segment bifocal type were prescribed which suddenly introduced this amount of jump. RECOMMENDATIONS: For weak distance prescriptions (below ± 1.00 D), the question of image jump should be a factor in the selection of the bifocal, together with the size of the reading field. In such prescriptions, the one-piece straight top lens has the least jump and maximum field, and it would seem to be a first consideration. If smaller segments are preferred, a cut-off or straight top segment would have only a small jump effect. In these weak prescriptions, the only advantage of a round segment is cosmetic. 69

70 For stronger prescriptions, the distance prescription must be considered in selecting the type of bifocal because we are concerned with the performance of the combination of the segment and the major lens. TOTAL READING PERFORMANCE One of the problems is object displacement or, more correctly, image displacement. It describes the fact that the images of objects seen through the reading portion do not have the same apparent position as they would have if no lens were in place (Fig. 47). There is little evidence that this condition in itself causes any problem once the eyes have traversed the borderline and are looking through the segments. However, the fact that the displacement occurs indicates that a significant amount of prism is present. The amount of prism is a function of the distance prescription, the reading addition, and segment type and location. These factors are schematically illustrated in Figure 48. The relation of the optical center of the segment to the optical center of the distance portion is the determining factor. We are concerned with the total prism because the prism deteriorates the quality of the image by increasing astigmatism, distortion, and chromatic aberration. 70

71 ANALYSIS OF THE TOTAL PRISM THROUGH THE READING PORTION. The total prism is the sum of the prism in the segment together with the prism in the distance portion at that same point. Both can easily be estimated by Prentice s Rule (page 240). An area 5 to 12 mm. below the segment line should be considered when estimating prism. Qualitatively, the sketches in Figure 48 will help in understanding the need for considering the segment style in combination with the distance prescription to evaluate total reading performance. The upper row of lenses shows different types of segments schematically arranged in front of plus prescriptions. The bottom row shows the same segments combined with minus prescriptions. It can be seen that the large amount of base-down prism in the semicircular onepiece bifocal tends to reduce the base-up prism of a plus lens, but accentuates and adds to basedown prism in a minus lens. Consequently, there is a maximum amount of prism effect through the reading portion of a minus lens when a large one-piece semicircular bifocal is used. The small round segment has some base-down prism in the upper portion of the segment to partially balance base-up prism in a plus lens. In a minus lens, this tends to add to the prism but not to the extent that the large type segment does. 71

72 The cut-off fused segments have a slight amount of base-down prism. Therefore, they are perhaps slightly better for plus than for minus lenses, but the high index glass increases the chromatic aberration of plus lenses. Therefore, a one-piece round segment might be preferred for a strong plus prescription. Lastly, the one-piece straight top full-field segment has a maximum of base-up prism which makes it good for weak prescriptions because of the full-field and lack of jump. It is also preferred for all minus prescriptions, providing as it does the maximum base-up prism to be combined with the base-down of the distance portion. For example, a 2.00 D distance portion lens with a D add results in a plano lens through the reading portion with no prism effect. For strong hyperopic prescriptions, the semicircular one-piece bifocal provides the least amount of total prism through the reading portion. The smaller round segments of one-piece type which are now common in plastic lenses also provide good vision through the reading portion if larger segments are not required or desired. Figure 48 can serve as a guide in selecting bifocal types. The patient s previous experience and special needs, however, should also be considered. We can sum up the implications given by the drawings as follows: 1. For distance prescriptions under ± 1.00 D, total prism is not a factor (in most cases, under ± 2.00 D). 2. For stronger plus prescriptions, the one-piece circular or semicircular segments are recommended. 3. For strong minus prescriptions, the circular or semicircular one-piece segments are not recommended. The one-piece full-field straight top segment is recommended. It substantially removes all power from many minus lenses and provides the best vision and widest field of view. 4. The straight top fused bifocal provides intermediate performance in both plus and minus prescriptions. It is popular because it is familiar and attractive in appearance. 5. For the majority of prescriptions, the size of the segment and the amount of jump would be the determining factors. SUMMARY OF BIFOCAL PERFORMANCE There are two principal problems to be surmounted in selecting a bifocal segment. One is jump, which is caused by any base-down prism that may be present at the top of the segment. The other is the total optical performance when the segment style and the distance prescription are combined. The quality of vision through the reading portion is a function of the total prism present. 72

73 Optimum performance, therefore, may be incompatible with minimum jump. For example, in plus prescriptions, the prism through the reading area due to the distance portion is base-up. Therefore, a segment with base-down prism would help balance the base-up of the distance portion. However, base-down prism creates jump at the segment line. On the other hand, in minus lenses, to balance the distance portion, the segment must have baseup prism, and, in this case, freedom from jump is compatible with the best optical performance through the reading portion. CATARACT BIFOCAL PERFORMANCE The problems involved in the fitting of cataract bifocal segments and the optical performance of the segment are not universally appreciated. First, let us consider fitting. Because of the strong power of the distance portion of cataract lenses, when the patient converges to read, there is considerable base-out prism. This often makes binocular vision difficult if not impossible. Even in monocular vision, the natural comfortable posture of the patient should be considered in locating the segment. Although the monocular patient will not have a fusion problem, he will very likely have difficulty attaining comfortable posture, particularly in view of his work and reading needs, unless the strength of the addition and its location are correct. 73

74 In many instances, segments are not decentered enough. Figures 49 and 50 indicate the problem and the amount of decentration which would be necessary for fusion. These decentrations will not be arrived at by simply taking a near P.D. in the normal fashion because the base-out prism will not have been taken into account. The table may be used as a guide. However, the safest procedure would be to take the near P.D., using a corneal reflex method, with the patient wearing a pair of prescription lenses of about the correct average sphere power. Segment insets of as much as 4 mm. will often be indicated. It would be practical for opticians to have a typical man s frame and a typical woman s frame available in 2.00 D or 3.00 D steps of spherical power which would cover the most common needs of their patients. Some selection of P.D. s would also be necessary. Effective communication between doctor and optician is necessary to ensure that adds are not too strong. Reading adds always perform stronger than specified; therefore, the location of reading matter for binocular vision may not coincide with the location for best acuity. The data in Figures 49 and 50 should be used with caution. Even if segments are decentered sufficiently to provide a theoretical possibility of binocular vision, the resulting convergence may be uncomfortable or impossible. Monocular near vision is often the result. 74