Chapter 51B
Spectacle Lens Design
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A spectacle lens only corrects a patient's refractive error at its center; that is, when the patient is looking along the optic axis. As the patient moves his or her eyes to look away from the lens center, undesirable optical effects (aberrations) are present that limit off-axis optical quality and decrease the field of clear vision. The primary purpose of the spectacle lens design process is to minimize the errors in a spectacle prescription that occur when a patient looks away from the center of a lens. This involves the proper choice of the front surface power or base curve of the lens, taking into account such variables as the vertex distance or fitting distance of the lenses, the distance of objects from the patient, and the need to maintain normal binocular vision. With the increased use of high-index, lightweight lens materials, and with the development of aspheric lens designs that can be used for essentially any lens power, lens design has become more important than ever before.
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Clinical experience demonstrates that patients have a wide range of reactions to and acceptance of refractive errors. Some patients notice the smallest error as a decrease in visual acuity or contrast, whereas others are happy with 2.00 or 3.00 diopters (D) of blur. In part, variations in visual acuity with refractive error can be attributed to depth of focus. For average pupil sizes, a 20/25 (6/7.5) high-contrast target can be out of focus at least 0.20 D in either the myopic or hyperopic direction with no noticeable effect on target resolution (Fig. 1). A 50% probability of resolution is maintained to approximately 0.33 D of blur. For higher target luminances and smaller pupil sizes, depth of focus can be expected to be even larger. This depth of focus is greatly decreased under conditions of low luminance (large pupils) and reduced object contrast.1,2

Fig. 1. Probability of resolution of a 20/25 (6/7.5) target as a function of the dioptric blur of the target. The width of the curve represents the depth of focus of the eye for a given resolution probability. Pupil size was 4.6 mm. (Modified from Schwartz JT, Ogle KN: The depth of focus of the eye. Arch Ophthalmol 61:578, 1959. © 1959 American Medical Association.)

Visual acuity variations also may be perceptual in origin. We sometimes think we “see” an object when we actually do not because we may function by recognition rather than by identification or visual acuity. For example, the letter A can often be recognized under conditions of poor visibility because it has the shape of a triangle. C, O, and Q may be more difficult to differentiate because of the similarities in shape. A street name may be recognized by its length. Thus, reading “acuity” is possible without resolution of the detail.

When navigating in familiar territory under adverse conditions, we tend to navigate by recognition of landmarks rather than by reading signs or actually seeing low-contrast detail, such as a curb or a raised traffic island. However, where surroundings are not familiar or where unexpected objects may be in our path, good visual acuity becomes essential. If we are on a strange expressway, we must be able to read the signs. If we are approaching an unlit object, we must be able to resolve it from a dark background. Detecting a large object requires good differentiation of its edges, which is a critical visual acuity task.

Once the depth of focus is exceeded, a refractive error degrades visual acuity. Each 0.25-D step of myopic refractive error (outside the depth of focus) decreases visual acuity by approximately one line on a Snellen chart,3,4 up to about 20/100 visual acuity, when chart step sizes become large. Hyperopic errors have much less effect because accommodation can compensate for the error. The effect of an astigmatic refractive error is approximately 80% of a myopic error of the same magnitude.3,4 The off-axis aberrations of a spectacle lens create power errors that have the same effects on acuity as spherical or astigmatic refractive errors.

The importance of small refractive errors and the need for precise refractive correction were emphasized by Allen,5 who measured automobile braking distance when approaching an unlit vehicle in the presence of a glare source. Available braking distance was reduced by 1 foot for each 0.01 D of myopic refractive error (100 ft/D).

Low light levels and poor contrast also decrease visual acuity, and the effects are much worse for older patients (Fig. 2). Only young patients can achieve 20/20 (6/6) visual acuity at low light levels. At the highest (best) acuity levels, the average 60-year-old subject needs 10 times more light or 2 to 3 times more contrast than the average 20-year-old to see the same objects.6–8 Even young subjects need at least 30% contrast to resolve 20/20 objects. Older subjects need at least 40% contrast to see 20/30 (6/9) targets.7

Fig. 2. Visual acuity (in minutes of arc) as a function of target contrast at different luminance levels and for subjects of different age. A luminance level of 34.3 candelas per square meter (cd/m2) represents a minimum for adequate daytime vision. Typical highway luminances at night range from 0.343 to 3.43 cd/m2. A visual acuity of 1 minute of arc is equivalent to 20/20 Snellen. (Richards OW: Vision at levels of night road illumination: XII. Change of acuity and contrast sensitivity with age. Am J Optom Arch Am Acad Optom 43:313, 1966. Modified from Davis JK: Prescribing for visibility. Probl Optom 2:131, 1990.)

Thus, proper lens design and precise refraction are particularly important when luminance and contrast are low and where resolution of objects rather than recognition is necessary. Some of the most challenging visual situations occur during night driving or in bad weather because of the prevailing low luminance and low contrast. Driving while facing a low sun and reading backlit signs or identifying roadside detail is also difficult. The writing on a chalky blackboard can be a low-contrast, low-luminance situation, as can some sports activities. Permitting a preventable refractive error or allowing off-axis lens aberrations further lowers the contrast of a patient's visual world and makes these situations even more difficult.

Maximizing contrast requires a precise refraction and proper choice of lens parameters, especially base curve. Most patients are sensitive to 0.25-D changes in lens power, and some can differentiate 0.12 (1/8)-D changes in lens power. The American National Standards Institute (ANSI) Z80.1-1995 dress ophthalmic lens standards allow an error of 0.12 D in the manufacture of most prescriptions,9 so errors of up to 0.12 D are not uncommon at the center of a lens. Even with optimum design, off-axis errors will be present. The ophthalmologist or optometrist can minimize errors by fine-tuning the refraction to the nearest 0.25 D, and, if necessary, to the nearest 0.12 D. The last judgmental step should be in the minus power direction to allow the patient to use accommodation to compensate for any residual error. A low-contrast visual acuity test target, which increases the sensitivity to refractive errors, may allow a prescription to be fine-tuned for difficult seeing situations.

Night myopia may contribute to night-driving problems. At low light levels, the accommodative state of the eye can go to a “rest position,” focusing the eye for some intermediate distance other than infinity and making the eye effectively myopic.10 However, signs and lights often provide enough of an accommodative stimulus so that night myopia is not a problem. To prescribe for suspected night myopia, it may be necessary to provide the patient with trial lenses. The patient should be a passenger in a car driven at night and should test the appropriateness of the trial lenses before a prescription is finalized.

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A patient's refractive error is corrected when the image of a distant object formed by the correcting lens falls at the patient's far point. When the patient rotates his or her eyes to use various portions of the lens, the far point also moves, tracing out a surface known as the far-point sphere. The goal of the lens design process is to cause images of off-axis objects to fall on the far-point sphere. To accomplish this goal, off-axis lens aberrations must be reduced to minimum levels.


Of the seven commonly described lens aberrations,11 four—radial or oblique astigmatism, curvature of field (power error), distortion, and transverse chromatic aberration (lateral color)—significantly degrade vision through off-center areas of a spectacle lens. These aberrations decrease the useful field of view through a lens and may be termed field-of-view errors. The magnification effects of lenses and the difference between the magnifications of the two lenses are also factors in the design.The goal of the lens design process can be restated as an attempt to maximize the useful field of view through a lens. The other three aberrations—spherical aberration, coma, and longitudinal chromatic aberration—have little effect on vision through spectacle lenses, although they can be of importance in the design of other types of lenses.

When a patient turns his or her eye to look at a point object that is not along the optic axis of a spectacle lens, the image of the point formed by the lens may no longer be a point. Instead, the point may be imaged as two lines (line foci) perpendicular to each other, with one line closer than the other to the lens (Fig. 3). This aberration of the image is radial or oblique astigmatism. The effects of radial astigmatism on image formation are similar to that of astigmatism in general. If one of the line images falls on the far-point sphere, the patient sees the image of the point as a line. If the two foci straddle the far-point sphere, no sharp image is formed. Instead, the image appears round and blurry (a blur circle). At other positions of the line images relative to the far-point sphere, the image formed is blurry and elliptical in shape. The separation of the two line foci formed by radial astigmatism is termed Sturm's interval, and the out-of-focus circular image formed between the two line foci is known as the circle of least confusion.12

Fig. 3. Radial astigmatism formed from a bundle of light rays entering a spectacle lens at an off-axis point. The bundle entering the lens is limited in size because the rays must pass through the pupil of the eye. The magnified view in the inset shows the Sturm's interval, with its two astigmatic line foci, one closer to the lens than the other, and the circle of least confusion.

If an extended (large) object is viewed off-axis through a lens that has radial astigmatism, then each point on the object is imaged as two line foci at different distances from the lens. In the example in Figure 4, the vertical arms of the cross-object are imaged as a large number of short horizontal lines at the focus closer to the lens. The horizontal arms of the cross are also imaged as a large number of short horizontal lines, but the line images overlap along the length of the arms. If this image were to be formed at the far-point sphere of a patient's eye, the patient would see the horizontal arms of the cross in sharp focus, but the vertical arms would appear blurry. At the focus farther from the lens, the situation is reversed, with the vertical cross-arm in sharp focus and the horizontal arm out of focus. At the circle of least confusion, all points on the cross are imaged as out-of-focus circles, and both arms of the cross appear equally blurry. The appearance of the image differs at different distances from the lens.

Fig. 4. When an extended object is imaged through a lens with radial astigmatism, the appearance of the image is different at different positions along Sturm's interval.

A standard terminology describes the foci created by radial astigmatism. Suppose a patient were to look laterally away from the center of a lens at a cross target. If the patient's field of view is considered to be a circle on a vertical plane, with the cross pattern at the lateral edge of this circle, then the vertical arms of the cross are tangent to this circle. The focus of the vertical arms by the lens is termed the tangential focus, and errors in their focus position relative to the far point sphere are tangential errors. Errors in focus that affect the cross arms perpendicular to the tangential detail (i.e., the horizontal cross-arms) are termed sagittal errors, and the focus of these lines is called the sagittal focus. If the patient were to look upward at a cross at the top of the field of view, the horizontal cross-arms would be tangential to the field-of-view circle, the focus of the horizontal cross-arms would be the tangential focus, and the vertical cross-arms would be imaged to form the sagittal focus. Tangential and sagittal focus errors increase as the distance from the center of a lens increases.

The two foci formed by a lens with radial astigmatism may be in front of the far-point sphere or behind the far-point sphere, or they may straddle the far-point sphere. The average dioptric value of the two focus positions specified relative to the zero value of the far-point sphere is termed power error. Power error increases as the distance from the optic axis of a lens increases, and the image surface for an extended object is curved, resulting in curvature of field (Fig. 5). Generally, power error and radial astigmatism cannot be eliminated at the same time.13 When radial astigmatism is eliminated, there will be some residual power error, and when power error is eliminated, some radial astigmatism will still be present (Fig. 6). Rather than attempt to correct power error directly, lens designers may try to minimize individual sagittal or tangential focus errors. A sagittal or tangential focus position behind the far-point sphere (negative error) probably has less effect on visual acuity than a focus position in front of the far-point sphere (positive error) because a patient can accommodate and pull the negative focus forward onto the retina. Therefore, perfect balancing of the sagittal and tangential errors, one in front of and one behind the far-point sphere, may not provide optimal off-axis image quality. Correction of a positive error with larger tolerances for negative errors may be the best strategy.

Fig. 5. When radial astigmatism is corrected, the image of a flat object is curved. The curvature of this image surface is known as curvature of field. The dioptric difference between the image position and the far-point sphere at a given off-axis location is power error.

Fig. 6. A. When radial astigmatism is corrected, the two focal lines coincide to form a point image of a point object, but the image point is not on the far-point sphere, creating a power error. B. When the tangential and sagittal foci are equidistant from the far-point sphere, there is no power error, but radial astigmatism is present. (Modified from Atchison DA: The clinical importance of spectacle lens base curves. Clin Exp Optom 69:31, 1986.)

Which aberration, radial astigmatism or power error, is more important to correct? This question has been the source of considerable discussion and argument in the optical industry for years,14 and the discussion continues. Most current lens designs compromise, attempting to minimize both aberrations without completely correcting either. This topic is discussed more fully in the section on the evolution of lens design.

Transverse chromatic aberration, or lateral color, is caused by dispersion, the variation of refractive index with wavelength that occurs for all spectacle lens materials (Fig. 7A). When a patient looks laterally to view a point object through a lens, the different wavelengths of light from the object each are refracted differently, “smearing” the image into its component colors (see Fig. 7B). If the object is not a point, but instead a large object such as a cross, the effects of dispersion are not the same. Each wavelength of light from the vertical arms of the cross is refracted differently, resulting in color fringes that surround the image of the vertical arms. However, the image of the horizontal cross-arms is relatively unaffected because the dispersion of the light into its component colors occurs along the arms of the cross and is not noticeable except at the cross-ends. Therefore, it can be argued that the effects of transverse chromatic aberration may be more important for the tangential focus than for the sagittal focus. The effect of transverse chromatic aberration is analogous to the dispersive effects visible when looking through a prism.

Fig. 7. A. Dispersion is the variation of index of refraction with wavelength. Dispersion occurs for all lens materials and is responsible for chromatic aberration. B. When white light passes through the periphery of a lens, the various wavelengths are refracted by different amounts, creating transverse chromatic aberration.

The prismatic effects of a lens vary with the lens power and with the distance from the lens optical center that a light ray passes through the lens. The relationship is termed Prentice's rule15:

P = h × D


where P is the prism obtained in prism diopters, h is the distance from the lens optical center measured in centimeters, and D is the lens power in diopters. Prismatic effects are larger for higher-power lenses and larger angles of view, so transverse chromatic aberration, which is related to the prismatic effects of a lens, will be worse for these same conditions. High-index glass and high-index plastic lens materials have more dispersion than crown glass or CR-39 plastic, and the problems of transverse chromatic aberration are more important for lenses made of these materials. Clinically, patients report color fringes around objects only when looking away from the center of these high-power, high-index lenses, but it is unusual for patients to report color fringes when their lens powers are less than approximately 5.00 D. The lens designer cannot vary the dispersion of a given material, so in a sense, nothing can be done about transverse chromatic aberration. However, proper lens design to minimize or eliminate other aberrations and proper fitting techniques in the optical dispensary can minimize the total off-axis blur and improve visual acuity.

Distortion is a lens aberration caused by the variation in magnification from the center to the edge of a lens (Fig. 8). It has little effect on resolution of an image, but it does affect the shape of the image. When an extended object is imaged by a high-minus power lens that has decreasing magnification toward the lens periphery, the images of portions of the object farther from the lens center are magnified less than those closer to the center, resulting in a “barrel” distortion of the image. A plus-power spectacle lens, which has increasing magnification to the periphery, exhibits “pincushion” distortion. The effects of distortion are most noticeable in high-plus power (aphakic) spectacle lenses. Patients who wear these lenses often report that door frames and other rectangular or square objects appear bent when viewed off axis. In addition, the combination of magnification and distortion in thick plus-power lenses results in a swimming sensation as the patient turns his or her head. This can be dramatically reduced by using the flatter aspheric designs.

Fig. 8. Distortion affects the shape of an image. A. Barrel distortion. B. Pincushion distortion.


If one takes a large handheld magnifying glass and looks at a magazine with some vertical and horizontal lines or at a piece of graph paper, the effects of lens aberrations can be observed. With the glass held squarely with the paper and perpendicular to the line of sight, the field of view has good optical quality to the edge of the lens. If the lens is tipped away at the top and the lines are viewed through the top of the lens, horizontal lines become blurred, colored and curved, whereas vertical lines are in better focus, straight, and uncolored. If the lens is tipped sideways, similar effects occur. The blur is tangential error, the color is transverse chromatic aberration, and the curve is distortion. The difference in blur between the horizontal and vertical lines is off-axis or radial astigmatism.


At its simplest level, the design process for a spectacle lens involves the calculation of the sagittal and tangential errors of each principal meridian for different sets of front and back lens curves. This calculation is done to determine which combination provides the best off-axis optical quality. As the surface curves are altered, different combinations of aberrations occur. Some errors will always be present. Even with the use of aspheric surfaces, the same problem exists.

Thus, the lens design process is one of compromise, in which an optimal choice is made from the available options. What constitutes the optimal choice has been the topic of controversy both in the professional literature and in advertising for more than 60 years. One reason that controversy still exists is that patients seldom have a chance to compare two different designs. Another reason is that instrumentation for measuring off-axis aberrations is uncommon. Finally, factual information regarding the various lens designs is scant. Much more information could be supplied by manufacturers, but “complete” information would be difficult to handle. Several hundred tables of data would be needed to describe the performance of the different types and designs of currently available lenses. However, we attempt to explain the differences between lens products, and their significance.


Figure 9 shows the idealized geometric relationship of a spectacle lens to the eye. In the figure, the optic axis of the lens is shown as an imaginary line that connects the centers of curvature of both lens surfaces and passes through the lens optical center. When designing a lens, it is assumed that the optic axis passes through the eye's center of rotation. In spectacle lens design, the center of rotation is termed the optical stop of the system because its position determines which rays reach the fovea in off-axis gaze. The stop distance, or center of rotation distance, is the distance from the back surface of the lens to the center of rotation. Traditionally, this value has been assumed to be a constant, often 27 mm,14 but there is significant variation in this distance in the population. Lens designers calculated the optimal base curve for a lens based on this value. The center of rotation distance is the sum of the vertex distance and the sighting center distance, the distance from the corneal apex to the center of rotation.

Fig. 9. Schematic drawing of a lens in a frame. OC is the optical center, and OA is the optic axis, which should pass through the center of rotation (CR) of the eye. Ray bundles are traced to the far-point sphere (FPS) for calculation of lens aberrations. Errors are referred to the reference sphere (RS). Stop distance, or center of rotation distance, is the sum of the sighting center distance (SCD) and the vertex distance (V).

Let us assume that the lens is fitted at the same vertex distance as was used in the refractive examination or that the prescription has been compensated for any difference between the two. The image of a distant object then falls at the far point. As the eye rotates to look off axis, the far point also rotates, tracing out the far-point sphere. Note that the ray bundles pass through the center of rotation of the eye. By convention, the dioptric position of the focus of light from an off-axis object is calculated relative to the reference sphere, the sphere tangent to the back surface of the lens at the optical center and centered on the center of rotation of the eye. Errors in image formation are then expressed as dioptric differences from the desired focus position on the far-point sphere.

Until recently, throughout the history of spectacle lens design, the basic input that linked the patient to the lens was the center of rotation distance. This optical stop of the lens-eye system is where all the lines of sight to the various points in the field of view cross.

Typical Fitting Geometry

Figure 10 illustrates the positioning of a frame and lens on the face. Most lenses are worn tipped slightly toward the eye through an angle of approximately 10 degrees. This is the pantoscopic angle. Also, most frames, especially plastic frames, fit the nose such that the center of the lens is a few millimeters below the pupil when the patient is looking straight ahead. Fortunately, the combination of downward tip and lowered fitting position tends to keep the center of rotation of the eye close to the optic axis of the lens (within 3 mm), and the lens vertex is automatically approximately on the reference sphere. In short, Figure 10 is Figure 9 tipped downward, with some flexibility added.

Fig. 10. A typical spectacle-fitting situation. Most glasses are worn with the bottom of the frame tilted toward the face (pantoscopic tilt). The optical center of the lens should be below the straight-ahead line of sight so that the optic axis of the lens passes through the center of rotation of the eye. (Modified from Davis JK: Prescribing for visibility. Probl Optom 2:131, 1990.)

The fit of a frame can be evaluated by drawing an imaginary line perpendicular to the eyewire at its vertical center and projecting backward into the eyeball, as shown by the line in Figure 10. The edge of a ruler placed against the frame and cheek area aids in visualization of the line. This line indicates the location of the optic axis of the lens. It should seem to pass approximately through the center of rotation. This point is behind the canthus, as shown in the figure.

Because the greatest use of lenses is for straight-ahead and downward viewing, the normal cosmetically attractive pantoscopic angle is also functionally desirable. For most prescriptions, departures from the ideal alignment shown in Figure 10 do not create serious errors. However, in fitting aphakic lenses and strong hyperopic or myopic corrections, the dispenser must take care to obtain a proper relationship between pantoscopic angle and the vertical height of the lens center so that the optic axis will pass close to the center of rotation. As a general rule, the optical center should be positioned 1 mm below the pupil center for every 2 degrees of pantoscopic tilt (3 to 5 mm below the pupil for the normal 6 to 10 degrees of pantoscopic tilt) when the patient's line of sight is parallel to the temples. This positioning is also important for high-index and aspheric lenses.

Vertical variations in eye position could be a consideration in the lens design process, but to date, this has not been the case. For illustrative purposes, the effect of vertical misalignment on selected lens designs is sometimes calculated and published.16,17 The longitudinal or axial relationships of the lens, cornea, and center of rotation are less easily adjusted and have been the principal input variables that have governed lens design decisions.

Viewing Angle

Most lens series have been designed to minimize field of view errors for angles of 30 degrees from the optic axis on each side of the optical center.14 Some have used 40 degrees for weak prescriptions. These values have been criticized as being too large because most patients do not make eye movements 30 to 40 degrees away from the optic axis. However, although most patients may not turn their eyes 30 degrees from the normal straight-ahead position, the straight-ahead position, or zero point, on a lens may not be at the optical center. Because of posture habits, it is usually above the optical center and may be to either side of the center of the lens. The combination of this noncentral starting point with minor eye excursions in all directions can bring the angle of view to a large value.

Davis18 reanalyzed the viewing-angle problem as shown in Figure 11 when designing a polycarbonate lens series. He suggested that the straight-ahead position for a typical spectacle wearer is approximately 5 mm above the distance optical center. Around this zero point, a patient can scan a fairly small field of view without head movements. Other patients could have different zero positions that surround this first zero point, creating a set of zero positions (the circle of dots surrounding the center dot in Figure 11). Davis then assumed that for each of these zero positions, the wearer would scan an elliptical field 20 degrees vertically by 30 degrees horizontally without head movement. This pattern creates a family of ellipses within which field-of-view errors should be corrected.

Fig. 11. Spectacle lens scanning ellipses centered at different zero positions for different wearers. The outer edge of this family of ellipses subtends an angle of about 28 degrees with the optic axis. (Modified from Davis JK: Prescribing for visibility. Probl Optom 2:131, 1990.)

The nasal and temporal edges of the family of ellipses are 25 to 30 degrees from the optical center. Davis chose an angle of 28 degrees for designing his lenses. Note that eye movements (scans) of only 15 degrees laterally require correction of field-of-view errors at much larger angles of view. However, a 28-degree angle of view describes a circle on a lens of only 28 mm in diameter.


Given the aforementioned information on the geometry of a spectacle lens on a patient's face, the sagittal and tangential focus error values can be calculated for any lens using exact surface-to-surface ray-tracing procedures.14,19 Table 1 shows the results of these calculations for a crown glass lens of power -3.00 D positioned at different center of rotation distances and ground with a variety of front (base) curves. The back (ocular) curve for each base curve was chosen to provide the proper lens power of -3.00 D for the center thickness of 2 mm and index of refraction of 1.523.


TABLE 1. Field-of-View Errors at 30 Degrees for 3.00 Sphere Prescription*

 CR Distance, 24 mmCR Distance, 27 mmCR Distance, 30 mmCR Distance, 33 mm
Front CurvesVertex Distance, 10 mmVertex Distance, 13 mmVertex Distance, 16 mmVertex Distance, 19 mm
+ 3.000.320.010.310.
+ 2.000.480.060.420.400.040.360.320.010.310.250.000.25

T, tangential; S, sagittal; A, astigmatic. CR, center of rotation.
*Object at ∞ (20 ft or more) distance. Vertex distances are approximate only.


Suppose that a patient is wearing this -3.00-D lens at a center of rotation distance of 27 mm, with a base curve of + 3.00 D. As the patient looks upward at an angle of view of 30 degrees with respect to the optic axis, the tangential error will be -0.23 D. The sagittal error is + 0.01 D, essentially zero. The astigmatic error, the difference of the two foci, is -0.24 D. Looking through the lens in this position (approximately 16 mm above the center of the lens), the patient will have a prescription not of -3.00 D, but of -2.99 -0.24 × 180 (or -3.23 + 0.24 × 090). For sideways viewing at the same distance off center, the axis of the cylinder shifts by 90 degrees.

The power error for this example, the average of the sagittal and tangential foci, is -0.115 D. One focus is just (0.01 D) in front of the far-point sphere, whereas the other is almost 0.25 D behind. Therefore, the patient is slightly overcorrected or overminused when looking off axis. If the patient accommodates slightly, the foci could be pulled forward to bracket the far-point sphere and eliminate the power error.

If a + 6.00-D base curve is used on the lens front surface, the astigmatism changes to -0.01 D, essentially zero, but the power error all around the lens 30 degrees (16 mm) from the center becomes + 0.115 D (approximately 1/8 D). The values in these two examples do not seem large, but in terms of the precision of refraction and fabrication of lenses, they are significant.

An additional complexity to the lens design process is that most lenses are spherocylinders. Each principal meridian has its own set of sagittal and tangential errors to be corrected. The design of spherocylinder lenses is discussed in detail subsequently.


Davis14 and Atchison20 have reviewed in detail the historic development of spectacle lens designs. Much of the information presented in this section is based on their work.

Corrected curve or best-form lenses, lenses designed specifically to eliminate off-axis aberrations, date back to Wollaston in 1804. However, modern commercial lens design began in the United States in 1911 when von Rohr, of Zeiss, patented the Punktal lens. This was a “point-focal” lens design in which the design goal was to completely correct radial astigmatism for oblique directions of view. From the data in Table 1, assuming a 27-mm center of rotation distance, von Rohr would have chosen a base curve of nearly + 6.00 D for this -3.00-D lens. A problem with von Rohr's design was that every lens power required a different base curve to maintain the point-focal correction exactly, making lens production difficult and expensive.

In 1917, Tillyer, a physicist at American Optical Company, filed for a patent on a different lens design concept that allowed tolerances on both radial astigmatism and power error. In designing his lenses, Tillyer believed that he should be guided by the ordering and stock procedures used in the lens market. He realized that when a patient receives a prescription for weak powers, at best, it is given in steps of 0.12 D. For stronger powers, the steps may be 0.25 D for both the spherical and cylindrical components. He believed that if a patient's actual prescription tolerances were not closer than 0.25 D, then correcting oblique astigmatism to a few hundredths of a diopter was unnecessary. He therefore allowed a maximum tolerance on radial astigmatism that was equal to the customary steps in prescription accuracy (0.12 D) used at that time.

Tillyer's procedures allowed some flexibility in base curve selection so that power error could also be corrected. By applying his theory, a practical single-vision lens series was designed, using selected base curves that corrected both astigmatism and power errors to within tolerances more precise than the steps between prescriptions.

Referring to Table 1 again for the -3.00-D lens at a center of rotation distance of 27 mm, a base curve of + 5.00 D meets Tillyer's criterion. Certainly it cannot be argued that 0.07 D of cylinder would do much harm. In addition, the average power error of 0.055 D (the average of the T and S errors) is only one half the value for a + 6.00-D base curve, although the + 6.00-D base curve provides a better astigmatic correction. The + 6.00-D design is acceptable, and the + 4.00-D design is almost within tolerances (0.15 D of astigmatism is slightly too much). Any base curve within this range provides adequate correction. This example illustrates the compromises involved in the lens design process.

Another way to state Tillyer's concept is that a range of lens powers can be used with the same base curve and still correct lens aberrations within tolerances. This feature is illustrated in Table 2. Here, the base curve is maintained at + 5.00 D while the spherical lens power is changed from plano to -5.00 D. The astigmatic and power errors remain below 0.12 D for powers from plano to -3.00 D, so the same base curve could be used for any spherical lens power within this range. This flexibility allows a lens manufacturer to provide the optical laboratory with semifinished blanks using a limited number of base curves. The laboratory can vary the prescription within predetermined limits for each base curve.


TABLE 2. Field-of-View Errors for Spherical Prescriptions With + 5.00 Front Curve*

  Power of Spherical Lens
CR distance, 27 mmT0.
Vertex distance, 13 mmS0.

T, tangential; S, sagittal; A, astigmatic. CR, center of rotation.
*Object at ∞ (20 ft or more) distance. Vertex distance is approximate only.


The concept of using a single base curve for a limited range of lens powers and of using a series of base curves to cover the entire prescription range is in almost universal use currently. This system reduces lens inventory and eliminates the need for a different base curve for every possible prescription. Sets of semifinished blanks, with front curves varying in steps, are stocked in local optical laboratories, and charts or computer programs show laboratory personnel which blank should be used for each prescription. Manufacturers also supply finished uncut lenses using a similar stepped base curve system. The uncut and semifinished blanks should be compatible.

In 1927, Rayton of Bausch and Lomb introduced the point-focal lens concept to the U.S. lens market, with a modification that allowed a stepped base curve system to be used. This lens series eventually became the well-known Orthogon lens series. At one time, most commercial lens series were designed after either the Orthogon or the Tillyer concept. The debate continues as to which system is better. For many prescriptions, the performances of the two series are similar. If power error is corrected with a tolerance for radial astigmatism, or if radial astigmatism is corrected with a tolerance for power error, the base curve choices could be the same. Patient response is seldom correlated with choice of lens design, probably because the patient has no opportunity to make a comparison.


A clue to the lack of correlation of patient response with lens theory is shown in Table 1. Lens performance varies with center of rotation distance or vertex distance. For this -3.00-D lens, the changes in radial astigmatism and power error that occur as vertex distance is changed (moving horizontally along the graph) are similar in magnitude to those that occur with a change of base curve. A change of 3 mm in vertex distance results in approximately the same changes that are found with a 1.00-D change in base curve. It can be argued that the size of a patient's nose has as much to do with his or her vision as does the selection of lenses of one design or another.

Table 1 shows that a Tillyer design at 27 mm (+ 5.00-D front curve) corrects astigmatism and becomes a von Rohr type at 30 mm. A von Rohr design at 27 mm (+ 6.00-D front curve) performs like a Tillyer design at 24 mm. Also, a + 5.00-D front curve at 30 mm behaves like a + 7.00-D front curve at 24 mm.


Spectacles may be worn at center-of-rotation distances as small as 24 mm and as long as 33 mm. Davis and associates took this variability into account in the design of the American Optical Tillyer Masterpiece lens series in the early 1960s.21–24 Base curves chosen were those that performed well for a large range of center of rotation distances, from 27 to 33 mm. The original Tillyer design principle was modified to give priority to tangential errors because it was believed that tangential image detail was deteriorated not only by focus errors but also by transverse chromatic aberration from the prismatic effects of off-axis viewing. From Table 1, the tangential error is nearly zero for a base curve of + 4.00 D (+ 3.75 D was the curve selected). Lens performance also was maintained for both distance and near viewing, with power error correction emphasized at distance and radial astigmatism correction emphasized for near viewing. The base curves of these lenses tended to be flatter than those of the original Tillyer lens series.

The Masterpiece lens series was modified as the Masterpiece II series in 1971 to include correction for very short center-of-rotation distances. The tolerances for radial astigmatism and sagittal and tangential errors were modified to favor the correction of plus error and astigmatism at the expense of minus-power errors. The front curve selected for a -3.00-D lens was + 4.25 D. Table 1 shows that reasonable performance is maintained at all fitting distances. Base curves for the Masterpiece II series were steeper than those of the original series.

The Masterpiece lens series had the distinction of being the first minus cylinder design lens series; that is, the toric surface was on the back. Minus-cylinder design has a number of advantages over plus-cylinder design, as is described in the next section. Once Masterpiece lenses became popular, other manufacturers gradually began to introduce minus-cylinder designs in both glass and plastic. In the current spectacle lens market, almost all lenses made are minus cylinder.


Spherocylinder, or toric, lenses present a special problem because there is only one selection of curvatures to control errors for the two principal meridians. The cylinder power could be ground on either lens surface, but for many reasons, almost all lenses made today are of minus-cylinder design. First, the correction of off-axis aberrations is superior in minus-cylinder designs. Although it is necessary to compromise the correction between the two principal meridians, the compromise is in general a better one than is possible for plus cylinders. Plus cylinders actually have a slight advantage for plus-power prescriptions. Second, minus-cylinder design results in less meridional magnification difference between the principal meridians and between lenses. Third, almost all multifocal lenses currently made are of minus-cylinder design. When presbyopia develops, a patient is less likely to have problems adapting to bifocals if he or she is already wearing minus-cylinder lenses and there are no shifts in magnification. Finally, minus cylinders are cosmetically more attractive. A large cylinder is noticeable when it is placed on the front of a lens. A minus cylinder hides the edge thickness changes that are created by the cylinder behind the frame eyewire.

The problem of lens design for a spherocylinder lens is illustrated in Figure 12. The CR-39 plastic lens is a minus cylinder design of power + 4.00 -2.00 (or + 2.00 + 2.00, if written in plus-cylinder notation). Each of the two principal meridians of the lens has its own tangential and sagittal foci for a given base curve, and these values are not the same for the two meridians. The graph shows how these errors affect the spectacle prescription at two points, one in each principal meridian, at a viewing angle of 28 degrees for a variety of base curves. For example, at point A, the spherical error in the prescription for a + 7.25-D base curve is + 0.25 D and the cylinder error is -0.45 D. A patient looking through point A would be looking through a lens of power + 4.25 -2.45, with the axis of the cylinder depending on the orientation of the lens in the frame.

Fig. 12. Inherent lens performance errors for different base curves at an average fitting distance for a CR-39 plastic lens of power + 4.00 -2.00. Both the spherical and cylindrical errors were determined at two points 28 degrees from the optic axis. Point A was in the cylinder axis meridian, and point B was in the cylinder power meridian. Blur was defined as the absolute value of the largest of the four errors, with negative spherical errors weighted by 0.5 against radial astigmatism and plus power errors. (Modified from Davis JK: Prescribing for visibility. Probl Optom 2:131, 1990.)

Because the four errors for the two principal meridians vary, determining the single best front (base) curve is complicated. To this end, lens designers often use a single number, a “blur value,” for each base curve to evaluate the quality of the design. The blur value relates off-axis lens aberrations to their effects on visual acuity, based primarily on the effects of refractive error on visual acuity, as described previously. Blur value was defined for this example as the absolute value of the greatest of the four errors at each base curve, with negative spherical power errors weighted by one half against astigmatic errors and positive spherical power errors given the same weight as astigmatic errors.6 Negative power errors were given less weight than other errors because a patient can accommodate to minimize visual effects. The blur value is least for a base curve of approximately + 9.25 D, suggesting that + 9.25 D is the optimal base curve for this lens power.

The analysis shown in Figure 12 is performed for all important lens sphere and cylinder power combinations when a lens series is created. This illustration shows the complexity of the design process. At one time, such calculations were performed by hand. The introduction of computers has both quickened the design process and allowed more complex designs, such as aspheric lenses, to be developed.


Effects of Lens Magnification

The magnification effects of spectacle lenses are as much of a concern as off-axis aberrations. A patient with a proper refraction may have excellent visual acuity with a new pair of glasses, yet report that floors are not level, that stairs are not where they should be, or that things “just do not look right.” These problems often stem from the magnification properties of a pair of spectacles. If the two lenses of a pair are different, the sizes of the images that they form may be different.

Suppose a patient receives his or her first pair of glasses of power right eye -0.50 D, left eye -1.00 D. Images of the most distant objects are 2 m (approximately 6 feet) away for the right eye and a little more than 1 m (3 feet) away for the left. Not only is everything nearer, but the images also are smaller and may appear to be of different sizes for the two eyes. The changes in apparent distance and size of objects conflict with the patient's previous experience without the glasses. Because differences in the size of the two retinal images provide the binocular interpretation of space and stereoscopic vision, things certainly will not look quite right.

Remarkably, most patients adjust to this situation rapidly. This new set of optical inputs is correlated with inputs from the other senses, and the patient begins to function with the advantage of better visual acuity. Most people readily adapt to their first glasses or to changes in the prescription. However, their ability to adapt may differ from their willingness to do so. Some patients keep their old glasses and wear them interchangeably with their new ones, although the prescriptions vary considerably. Others cannot stand a frame that is out of alignment by more than 1 mm.

Quantifying Magnification Problems

The effects of spectacle lenses on retinal image size (spectacle magnification) may be calculated from the formula25:


SpectacleÜqnMagnification = Üp311 - (tn) D1 Üp8 × (11 - hD)

where t is the lens center thickness in meters, D1 is its true (not 1.53) front curve in diopters, n is its index of refraction, h is the distance from the lens back surface to the entrance pupil of the eye (vertex distance + 3 mm) in meters, and D is the lens back vertex power in diopters. The first portion of this equation, which includes the thickness and front curve of the lens, is termed the shape factor, and the second portion is termed the power factor. The shape factor almost always provides magnification, and the power factor provides magnification for plus-power lenses and reduction for minus-power lenses.

Part of a lens designer's job is to use small steps in base curve between adjacent prescriptions to minimize the magnification differences that occur when the spectacle lens powers are different for the two eyes (an anisometropia). In a factory-finished uncut lens series, base curve steps rarely are as large as 1.50 D. Frequently, they are less than 1.00 D. In a semifinished lens series, the steps usually are larger, but in a better series, they rarely exceed 1.50 D. Semifinished series that are not as well designed have 2.00-D steps. Shape magnification differences between base curve steps can reach clinically significant levels in plus-power prescriptions greater than about + 5.00 D, as shown in Table 3. The front curves and center thicknesses used in Table 3 were chosen for each lens power from a polycarbonate semifinished lens-surfacing chart. Shape and power magnification were then calculated for each lens power, using the aforementioned formula. For a 1.50-D or less difference in power between any two lenses, shape magnification differences can reach approximately 1.5%, but most differences are about 1.0%, and some are less. For lens powers below + 3.00 D, the thickness differences between lenses are too small for shape magnification differences to be a concern. Therefore, one simple solution to shape magnification problems is to order both lenses with the same thickness. Then, even with different base curves for good field-of-view correction, the shape magnification differences between lenses of different power are attenuated.


TABLE 3. Shape and Power Magnification Values for Selected Lens Powers*

Lens Power (D)1.53 Base Curve (D)Center Thickness (mm)Shape Magnification (%)Power Magnification (%)
+ 6.00+ 10.897.15.7011.36
+ 5.75+ 10.896.05.6110.83
+ 5.50+ 9.756.64.7010.31
+ 4.50+ 9.755.84.108.28
+ 3.75+ 8.555.13.146.81
+ 3.25+ 8.554.72.885.85
+ 3.00+ 7.524.52.425.37
+ 2.00+ 6.463.61.653.52

*Base curves and center thickness were obtained from a polycarbonate semifinished lens surfacing chart. Power magnification was calculated using a vertex distance of 14 mm.


Magnification differences between the eyes usually are small, less than 5%. (The magnifications of commonly used low-vision aids are in the neighborhood of 2× to 10× , or 200% to 1000%). However, when a small image size difference is created between the eyes, the brain interprets the difference as a clue for binocular stereoscopic depth perception. Because stereoscopic vision is so sensitive, small differences in magnification can create significant problems with spatial perception. These difficulties often are manifested as problems in adapting to new glasses. The accepted threshold at which problems can occur is a difference of 0.8% to 1% between the eyes.13

Differences in magnification caused by differences in the astigmatic corrections for each eye, whether cylinder power differences or cylinder axis differences, may result in both image size differences and changes in the shapes of the two images. Oblique cylinders (cylinder axes close to 45 or 135 degrees) tend to cause the most problems, with patients reporting problems for cylinder powers of 0.75 D or less.

The spectacle magnification formula of equation 2 does not provide a method for calculating magnification differences between the eyes in anisometropia. The difficulty occurs because the spectacle magnification formula relates the retinal image size when a correcting lens is worn to the uncorrected image size. Unless the uncorrected retinal image sizes for the two eyes are the same, spectacle magnification calculations cannot provide any information about the relative image sizes of the eyes. For example, if the spectacle magnification for the right eye is calculated to be 5% and the spectacle magnification for the left eye is 2%, it cannot be said that the right eye image is 3% larger than the left because the uncorrected right and left eye image sizes may not have been equal before the spectacles were worn. Calculation of retinal image size differences between the eyes requires knowledge of such parameters as the axial length and the power of each eye,26 information that is not easily available. For exact measurement of magnification differences between the eyes, an eikonometer must be used.

One should not assume that a patient's displeasure with a new pair of glasses is a result of magnification problems. The obvious questions to be asked are, “What were the powers of the patient's old glasses?” and “Has the patient had problems adapting to other pairs of glasses in the past?” The old adage of not changing the base curves of a new pair of glasses relative to the values of the patient's old glasses makes little sense because the new power magnification differences usually are much greater than any likely change in shape magnification difference. Before attempting to solve a suspected magnification problem, the glasses should be checked thoroughly against the lens powers ordered in all respects and the base curves verified against the manufacturer's chart.


When an anisometrope cannot adapt to the difference in the magnification effects of the two lenses, then the patient has clinically significant aniseikonia. Because eikonometers are not commonly available for clinical use, the diagnosis and management of aniseikonia is usually based on clinical signs and symptoms, with magnification differences estimated from the differences in refractive error.27–30 Correction of aniseikonia requires an alteration of base curves and center thicknesses (alteration of the shape factors) from their normal values to alter the magnifications of the retinal images. Spectacle lenses designed for this purpose are termed eikonic or iseikonic lenses. These lenses are often expensive and difficult for the optical laboratory to manufacture.

Rather than provide eikonic lenses, practitioners often alleviate spectacle adaptation problems, or aniseikonia, by modifying the prescription. When cylinder corrections are at oblique axes, patients often report distortion of images (tilting of walls or floors, floors being too close or too far away). Often the problem can be minimized or eliminated by a decrease in the cylinder power or a rotation of the cylinder axes toward 180 or 90 degrees. This prescription modification can be thought of as a modification of the lens magnification, although the resulting image blur decreases sensitivity to image magnification. A partial correction of a large spherical anisometropia, such as that created by a beginning nuclear cataract in one eye, is another commonly used solution for spectacle-induced aniseikonia. These types of prescription modification require sound clinical judgment because visual acuity is being sacrificed, but they provide an acceptable solution if correction of aniseikonia will not be attempted.


A base curve chart presents the base curves that are used for a given lens power for a particular lens design. If the back surface curves and center thicknesses are also included, then the chart is more properly termed a surfacing chart because it provides all the information needed to make a finished lens. Figure 13 shows a hypothetical base curve chart for a lens series. It is hypothetical in the sense that the base curves and boundaries between them were not evaluated by computing and do not represent any existing lens series. This type of chart is used as a guide for laboratories in selecting semifinished blanks for use in grinding a given prescription. A similar set of charts could be used in the optical dispensary if base curve selection depends on frame fitting distance.

Fig. 13. A hypothetical base curve chart.

In the ophthalmic industry, the base curve chart is a statement of the lens design. Because it delineates the structure of each lens in a series, the base curve chart is, in a sense, a blueprint and a guide to indicate the base curves that the designer intended for various prescriptions. The dispenser knows which base curves to expect when he or she orders a prescription by trade name. When the prescription is received, the base curve choice can be verified against the chart.

The spherical components of prescriptions are indicated by the horizontal rows for sphere powers from + 8.00 D to -10.00 D. The cylinder components are indicated by the various columns, labeled from 0.00 to -6.00 D across the top of the page. Each “box” at the intersection of a row and a column represents a possible spherocylinder prescription. Knowing the prescription and the 1.53 base curve, the optical laboratory can easily determine the concave curve. Some charts contain a column of thicknesses down the left side. Others use a separate table. This chart contains a number of clues to the care that went into the design. The following points are important to consider in the analysis of this hypothetical design:

  1. There is a plurality of base curves. There are a sufficient number to provide reasonably good performance, although more base curves would provide even better optical quality. Manufacturers should augment their charts with information on design criteria and tolerances.
  2. Base curves are staggered across the page for various cylinder values. It is obvious that the design for a sphere alone and for the same sphere with a -6.00 D cylinder may sometimes lead to different base curve choices, but some lens series call for no change, with the horizontal boundaries straight. However, the zigzag boundaries are too few. A good series has 8 to 10 zigzags for each base curve in the minus area. Aspheric designs may have fewer or possibly no zigzags in some areas of the chart. Manufacturers should supply information about the design performance.
  3. There is a + 1.50-D base curve step in the high-plus area. This step is too large for such thick lenses. The thickness for a + 7.00-D lens would be approximately 6 mm, resulting in an approximately 0.6% difference in shape magnification between a + 6.75-D lens that will have a + 9.50-D base curve and a + 7.00-D lens with a + 11.00-D base curve. Magnification differences, and to some extent, field-of-view errors sometimes are sacrificed in the high-plus area to minimize inventories of these seldom-used lens blanks.

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Aspheric lenses are one of the most recent results of improvements in the technology of spectacle lens manufacture. A variety of aspheric designs are available, both single vision and multifocal, in many different lens materials.

An aspheric surface, simply stated, is one in which the cross-sectional shape of the surface is not circular. The cross-sectional shape could be that of a conic section, such as an ellipse, hyperbola, or parabola, or the surface could have a shape that is best described by some polynomial mathematical function. Aspheric single-vision lenses have an aspheric front surface, whereas the back surface is spherical or toric. The front surface of an aspheric single-vision lens is also commonly described as being rotationally symmetric because its cross-sectional shape is the same in all meridians. This is in contrast to the nonrotationally symmetric aspheric front surface of a progressive addition lens, a commonly used multifocal lens. The front surface of a progressive addition lens is a highly complex surface that may vary in cross-sectional shape from the top to the bottom of the lens and also from meridian to meridian. The toric back surface of a spherocylinder spectacle lens is not considered to be an aspheric surface. Although the cross-sectional shape of the surface changes from meridian to meridian, the cross-sectional shape at each of the principal meridians is circular.

Aspheric lens designs first became popular for high-plus power “aphakic” spectacle lenses in the 1950s after the introduction of CR-39 plastic lenses.14,21 CR-39 has a tremendous weight advantage over glass at high powers, and the aspheric surfaces needed to correct off-axis aberrations for these high-power lenses could be molded from CR-39 relatively inexpensively. With the development of intraocular lenses (IOLs), research in aphakic lens design has come to a standstill, and the use of these lenses is decreasing rapidly.

More recently, lens designers have developed aspheric lens series for lower-power or moderate-power lenses. The driving forces behind the increased use of these lenses are concerns about lens weight, thickness, and cosmetic appearance, the same forces driving the increased use of high-index plastic lens materials. Many moderate power aspheric designs are available in high-index plastic lens materials, and the combination provides further decreases in weight and thickness. Moderate-power aspheric lenses were first introduced for hyperopic prescriptions, although currently almost any lens power is available in an aspheric design. Some of the more well-known aspheric designs are listed in Table 4.


TABLE 4. Representative Aspheric Spectacle Lens Designs

Product NameManufacturer*Lens Material
ASLSola1.54 index plastic
  1.586 index polycarbonate plastic
AspireX-Cel1.60 index glass
CosmolitRodenstockCR-39 plastic, 1.60 plastic
Hyperindex 160Optima1.60 index plastic
Hyperindex 166Optima1.66 index plastic
Kodak Vision 3156Signet Armorlite1.56 index plastic
Polythin ARPentax1.586 index polycarbonate plastic
ProfileGentex1.586 index polycarbonate plastic
Super 16MXSeiko1.60 index plastic
Ultrathin 1.6Pentax1.66 index plastic

*Sola Optical USA, Inc, Petaluma, CA; X-Cel Optical Co, Sauk Rapids, MN; Rodenstock USA, Inc, Danbury, Ct; Optima, Inc, Stratford, CT; Signet Armorlite, Inc, San Marcos, CA; Pentax Vision, Inc, Hopkins, MN; Gentex Optics, Inc, Dudley, MA; Seiko Optical Products, Inc, Mahwah, NJ.


The primary difference between aspheric and nonaspheric lens designs is that the front surfaces of aspheric designs are flatter. Front surface curves of nonaspheric lens series must be relatively steep to provide good off-axis vision. Steep curves make for a bulky-looking, thick lens and increase magnification. This magnification causes “image swim” when a patient first receives new glasses and also makes the patient's eyes look unnaturally large. For a given prescription, using a more shallow (flatter) spherical base curve allows the use of thinner lenses and decrease magnification, but the decrease in curvature also reduces the patient's clear field of view by increasing off-axis aberrations.

The solution to this problem is to use an aspheric front curve (base curve) on the lens. This aspheric front curve is much flatter (lower power) than the spherical front curve required for a nonaspheric lens of the same power (Fig. 14). For example, a polycarbonate lens of power + 4.00 D, which normally would have a spherical base curve of + 8.50 D, can be made in aspheric form with a front curve of + 4.50 D. A spherical design polycarbonate lens of power -6.00 D that has a spherical base curve of + 3.25 D can be made in aspheric form with a base curve of + 0.50 D. The base curves chosen for aspheric lens designs vary from manufacturer to manufacturer. Some designs have steeper base curves than others, but all have base curves that are flatter than those used for spherical designs. The aspheric polycarbonate lens series shown in Figure 14 is one of the flattest available.

Fig. 14. Base curve as a function of lens power for a spherical and an aspheric polycarbonate lens series. The base curve is much flatter for the aspheric lens series at all powers.

Figure 15 shows the effect that an aspheric design has on both the cross-sectional shape and the thickness of a lens. The aspheric polycarbonate plus-power lens of Figure 15A has a thinner center and a flatter cross-sectional shape than the nonaspheric CR-39 plastic lens of the same power. At the same time, the combination of the flat base curve and decreased thickness decreases the magnification of the patient's eyes and decreases the magnification of the patient's visual world as he or she looks through the lens. The aspheric minus-power polycarbonate lens of Figure 15B has a thinner edge than the spherical design CR-39 plastic lens of the same power. The aspheric lens design also has a flatter cross-sectional profile and a different magnification than the spherical design, but these are not major concerns in minus powers. Aspheric designs provide more benefits for plus-power lenses than for minus powers, and some dispensers prefer to use aspheric lenses for plus-power lenses and high-index plastics for minus-power lenses. However, the combination of a high-index material and an aspheric design results in the thinnest, lightest lenses.

Fig. 15. Cross-sections showing the decreased thickness and flatter profile of a polycarbonate aspheric lens compared with a typical nonaspheric CR-39 plastic lens of the same power. The lens diameter was 64 mm (32 mm from optical center to edge). A. Lens of power + 4.00 D. B. Lens of power -4.00 D.

The type or shape of the aspheric front curve chosen by the lens designer is one that corrects off-axis lens aberrations. The aspheric design chosen varies from manufacturer to manufacturer. Generally, the thinnest lenses are those with the flattest front curves. More front curves with smaller steps between curves are usually required for the range of powers for aspheric lenses than for a spherical lens series. A common misconception is that aspheric lenses have better off-axis image quality than spherical lenses. This is not true. A well-designed aspheric lens series and a well-designed spherical lens series may perform equally well. Manufacturers should supply off-axis performance data.

Aspheric lenses require careful fitting in the optical dispensary. Plus-power lenses look best, providing the least magnification to the eyes, if they are fit as close to the eyes as possible. Optimal off-axis performance is best if the optic axis of the lens passes through the center of rotation of the eye. This is more important for aspheric lenses than for spherical lenses.17 The optical center of the lenses should be positioned horizontally using split interpupillary distances (PDs) as measured by a pupillometer. Vertically, the lens optical center should be 3 to 5 mm below the center of the pupil. Some manufacturers also supply base curve selection tables that allow the base curve to be chosen based on the fitting distance of the frame.

Occasionally, a patient who has previously worn spherical designs needs a few days to adapt to aspheric lenses. When problems occur, the fitting should be evaluated carefully. In addition, reflections from aspheric lens surfaces differ from those of spherical surfaces because of the shallower curves. Some manufacturers recommend the use of antireflective coatings for aspheric lenses.

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The newest spectacle lens design available in the current market is the atoric lens. An atoric lens has a spherical or aspheric front surface, but the lens back surface, which provides the correction for astigmatism, is a type of aspheric surface that is atoric, not toric. The atoric back surface has two principal meridians, as does a standard toric surface, but each principal meridian of an atoric surface has a noncircular cross-sectional shape. Atoric lenses are flatter, thinner, and lighter than spherical lenses of the same material and power, but the primary reason to use an atoric lens design is to improve off-axis image quality for spherocylinder lenses. The off-axis image quality of an atoric lens can be better than that of a well-designed spherical or aspheric lens.

As previously mentioned, the spectacle lens designer runs into a problem when trying to correct the off-axis optics of a spherocylinder lens. Only one base curve is available to correct field-of-view errors, yet there are two meridians of different power, and each meridian has its own sagittal and tangential errors. The lens designer must compromise, choosing a base curve that minimizes a blur value, a weighted average of the errors for each meridian. The use of an atoric back surface allows the designer to eliminate this particular compromise. Working with each principal meridian on the back surface separately, the designer chooses an aspheric meridional shape that provides the optimal correction for off-axis errors. The optimal aspheric shape for each principal meridian usually is different, so the finished atoric lens has a back surface that is a complex combination of two different aspheric curves.

Atoric designs are of most benefit for large astigmatism corrections where the compromises of a nonatoric design would result in larger field-of-view errors. However, atoric surface curves are difficult to fabricate. The technology required is relatively new, and most optical laboratories in the United States do not have the capability to grind atoric back surfaces. Only lens manufacturers have the necessary equipment. Uncut single-vision atoric lenses supplied by the lens manufacturer can be edged by optical laboratories. Unusual lens powers and multifocals, lenses that are normally surfaced by the optical laboratory from semifinished blanks, must be custom-made as atorics by the lens manufacturer.

At least four atoric spectacle lens designs are presently available, the Sola ViZio single-vision lens, the Optima Hyperindex 166 single-vision lens, the Rodenstock Multigressiv 2 progressive addition lens, and the Zeiss Gradal Top progressive addition lens. Atoric lenses should become more commonly used as manufacturers and laboratories improve lens-processing technologies and as manufacturing costs decrease. The benefits of aspheric and atoric designs make it likely that most lenses manufactured will eventually have at least one aspheric or atoric surface.

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The high-plus power spectacle lenses worn primarily by aphakic individuals have been relegated to a minor position in the optical industry by the proven success of IOLs. No new aphakic lens designs have appeared for many years, and available designs address problems of off-axis image quality, weight, and magnification. A plurality of base curves is a must for an aspheric aphakic lens series.

The off-axis aberrations of lenses with powers greater than approximately + 7.00 D cannot be corrected with spherical surfaces, so all aphakic lens series must have aspheric front surfaces. Spherical or toric back surfaces provide the proper refractive correction. The base curve usually is defined as the curvature or power at the center of the front surface. Most aphakic lens designs use a relatively flat base curve that results in a shallow back curve. For example, a typical + 12.00-D lens might have a base curve of + 15.00 D and a back surface power of approximately -3.00 D. Some designs result in nearly flat back surfaces.

A well-designed aphakic lens series has more base curve steps than a conventional lens series because the lens aberrations change quickly as lens power is changed. Steps between base curves should never exceed 1.00 D. Steps of 0.50 D would be better, especially for lenses with concave curves flatter than -3.00 D. This requirement is only important for aphakic lenses. Weaker powers are not as sensitive to base curve change, and steps of 1.00 D are acceptable if fitting distance is carefully matched to the curve choice.

The flat base curve of an aspheric aphakic lens design decreases lens weight, thickness, magnification, and thickness, just as it does for lower power aspheric lenses. The choice of the proper aspheric front surface shape then corrects off-axis aberrations. A further decrease in magnification occurs if the lenses are fit by the dispenser as close to the face as possible. The use of a small, round frame keeps lens weight and thickness to a minimum.

Almost all aphakic lenses are made of CR-39 plastic because of weight considerations. The use of high-index plastic materials would provide further weight and thickness decreases, but these materials are not used because large amounts of transverse chromatic aberration would be present.

The distance optical center of an aphakic lens should be positioned at the pole (center of rotation) of the aspheric front surface for best off-axis image quality. The off-axis image quality also is best if the optic axis of the lens passes through the center of rotation of the eye. However, because the pole of the aspheric surface and the bifocal segment are in fixed locations on the front surface of the aphakic lens blank, it usually is not possible to meet both these requirements at once by moving the lens optical center vertically relative to the position of the segment. Instead, the optical laboratory positions the optical center properly on the lens, and the dispenser should adjust the pantoscopic tilt of the frame to match that required by the optical center position. Aphakic spectacles require careful fitting in the optical dispensary if the patient is to have the best possible vision.

Aphakic lenses are available in three general forms. The lenticular aphakic lens (Fig. 16) has the appearance of a fried egg. The central bowl, which is the optically useful portion of the lens, is usually 40 mm in diameter and has an aspheric front surface. The peripheral carrier serves no optical purpose but decreases lens thickness by decreasing the size of the bowl.

Fig. 16. Frontal and cross-sectional views of a lenticular aphakic lens.

Full-field aphakic lenses have an aspheric front surface but appear similar to a conventional nonlenticular lens. Some of these lenses rapidly flatten toward the periphery, with the curvature actually becoming negative, giving the lens the appearance of a “blended lenticular.”20 Full-field lenses tend to be thicker than lenticular designs, but they are better cosmetically and are more commonly used.

Aphakic lenses may have either a round or a D-shaped bifocal segment. The round segment sometimes is preferred because the base-down prismatic effect in the top of the segment neutralizes some of the base-up prism from the distance portion of the lens, providing better optics through the bifocal than for a D segment. Also, in the laboratory layout process, a round segment lens blank can be rotated about the pole of the aspheric surface to obtain the segment decentration necessary to match the patient's near interpupillary distance (PD.) Both segment types provide adequate near vision.

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Extremely high-minus power prescriptions (greater than approximately -10.00 D) have thick edges that are unattractive and difficult to mount in some frames. This problem can be reduced by providing the patient with as small a frame as is feasible. High-index plastics may also help. Although off-axis transverse chromatic aberration is present, most patients tolerate the aberrations because their lenses are so much thinner and lighter. High-minus power lenses are often biconcave because it is difficult for the optical laboratory to grind all the power onto one lens surface. Light tints and antireflective coatings attenuate the multiple ring reflections (myopic rings) near the lens edges.

High-minus power lenses are occasionally made in lenticular form (Fig. 17). In essence, the thick edge is removed at the lens back surface, creating a peripheral carrier that has no optical function and a central bowl about 40 mm in diameter that provides the refractive correction. When the lens front surface is flat and the carrier also has a flat back surface, the lens is often termed a myodisk. The junction of the carrier and bowl of a minus lenticular lens can be blended to decrease its visibility and to eliminate the sharp edge. The process used is commonly termed myothinning (see Fig. 17). All high-minus power lens designs must be used with care because of their poor cosmetic appearance.

Fig. 17. Frontal and cross-sectional views of a minus lenticular spectacle lens and a myothinned minus lenticular lens.

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