Optics of Progressive Lenses—Part 1

By Darryl Meister, ABOM

INTRODUCTION

This is a technical, intermediate level course intended for dispensing opticians, laboratory technicians and paraoptometric personnel. An understanding of both basic algebra and intermediate optical theory is required.

BACKGROUND

Although progressive addition lenses—or PALs—didn’t enjoy commercial success until the 1960s, the concept has been around for nearly a century. Owen Aves, cofounder of London’s Institute of Optometry, patented a progressive lens design in 1907. Because of the dual-surface nature of this lens design, it was limited to spherical prescriptions. Shortly after, Henry Gowlland patented improved progressive lens designs in 1909 and 1914, which utilized a conicoidal back surface to produce the addition power. Estelle Glancy at American Optical patented one of the earliest progressive lens designs that relied exclusively on a single progressive front surface in 1923.

However, early lens designs generally proved impractical to produce in prescription form in mass quantity with the technology available at the time. The first commercially successful progressive lens in Europe, Essel’s Varilux lens, was introduced in 1959. The Univis Omnifocal, introduced in 1965, became the first commercially successful lens in the United States. The success of these lenses was due in no small part to technical achievements in fabricating asymmetric surfaces on a large-scale production basis, often relying on clever grinding assemblies. Since the 1960s, progressive lens usage has increased rapidly as the designs continued to improve. Today, over half of all multifocals sold are progressive lenses.

Arguably, well-designed progressive lenses replicate natural vision more effectively than traditional (lined) bifocals, since they provide smooth changes in vision and a full range of focus. In fact, according to some clinical studies, progressive lenses actually have a higher rate of adaptation than traditional bifocals and are preferred to traditional bifocals 4-to-1 by wearers. We can summarize the primary benefits of progressive lenses as follows:

• No bifocal lines. The most obvious advantage to progressive lenses is the absence of any visible lines of demarcation, which are considered tell-tale signs of age.

• Intermediate utility. Progressive lenses produce a gradual change in power from the distance zone to the near zone, which affords the wearer an infinite range of focus between distance and near. This infinite range of focus provides excellent intermediate or mid-range utility, which becomes absent from traditional bifocal lenses as the add power increases.

• No image jump. Traditional bifocal lenses produce a jump in magnification and image location when crossing the segment boundary, as well as blur and scotoma—or blind area—around the segment margin. The gradual change in power of progressive lenses results in a lens design that is free from any abrupt changes in vision.

This course will focus on the optics of traditional, general-purpose progressive lens designs. However, the principles discussed here apply to virtually all classes of progressive lenses. In addition to traditional progressive lenses, there are several “specialty” classes of progressives that are worth mentioning:

• Free-form progressives. Progressive lenses delivered via free-form manufacturing are becoming increasingly common. Free-form generators can surface a progressive lens design directly onto a lens blank, which makes possible individualized customization and prescription optimization.

• Computer progressives. There are several progressive lenses available that are designed specifically for computer and office use. These lenses offer enhanced intermediate and near viewing zones, at the expense of distance utility.

• Short-corridor progressives. Smaller fashion frame styles are still very popular and often require fitting heights well below those afforded by traditional progressive lenses. Many progressive lenses are now designed with relatively short corridors in order to maximize near utility at low fitting heights.

THE PROGRESSIVE PROBLEM

Most opticians are (painfully) aware of the geometrical aspects of Executive- and Franklin-style bifocals, lenses producing both distance and reading power across the entire width of the surface. The surface of an Executive-style bifocal is essentially a section from two conjoined hemispheres of differing surface curvature. A flatter distance curve, representing the major portion for the distance prescription, meets a steeper near curve, representing the segment for the Add power. The junction between these curves results in a prominent ledge across the surface.

At the center of the lens, the two front curves of the front surface meet at only a single point, and are only contiguous (or unbroken) at that point. Away from this point, the individual curves gradually break farther and farther apart as the near curve steepens more quickly than the distance curve, resulting in the infamous edge profile typical of Executive-style bifocals. This ledge represents an increasing discontinuity as the surface breaks farther and farther apart.

However, we can reduce this ledge by inserting an intermediate curve between the distance and near curves, with a surface curvature that is slightly steeper than the distance curve. The addition of this intermediate curve converts our bifocal into an Executive-style trifocal, complete with intermediate power for mid-range vision. Although this results in two ledges, each individual ledge is smaller is smaller than the original ledge.

We can continue inserting narrow horizontal sections of spheres that represent additional intermediate curves, each progressively steeper than the last. If we do this an “N” number of times, we create an Executive-style N-focal. As with the bifocal (N = 2) and trifocal (N = 3), each subsequent spherical section of this N-focal is still only contiguous with the section above it at a single point. Moreover, a vertical meridian at the center of the lens surface is formed that contains the locus of these contiguous points. This vertical meridian is known as the umbilic of the lens surface

The addition of more and more, narrower and narrower horizontal sections continues to reduce the individual heights of the ledges separating these curves. As the number of these horizontal sections increases to infinity, the individual ledge heights approach zero. Further, once these heights reach zero, the final surface becomes perfectly smooth and continuous, with no visible junctions between the curves. We have now created a very simple progressive lens surface compromising a distance zone, a near zone, and a progressive section connecting the two.

The curvature of this very basic progressive surface increases smoothly from the distance to the near regions, providing a gradual change in power as well as midrange vision. You can verify this gradual change in surface power with a common lens clock (or lens measure). The vertical curvature will vary from its lowest (flattest) value in the distance zone to its highest (steepest) value in the near zone; the difference between the two will be equal to the add power of the surface. Moreover, the horizontal curvature of this surface is equal to its vertical curvature at any single, infinitely small point.

Unfortunately, while the horizontal curvature of this surface is equal to its vertical curvature at any point, the curvatures in oblique meridians at these points are not equal in the peripheral regions of the progressive section. In fact, each point actually behaves like a tiny cylinder lens oriented near either axis 45° or axis 135°. These oblique curvatures are only completely equal to each other along the single, vertical umbilic meridian of the lens. Away from the umbilic meridian, in the lateral regions of the lens where the ledges of our infinite N-Focal have essentially been “blended” together, the minimum and maximum surface curvatures grow farther and farther apart.

In ophthalmic optics, a surface that produces both a minimum curvature and a maximum curvature at the same point is referred to as a toric surface. The difference in surface curvatures on a toric surface results in cylinder power, which in turn produces an astigmatic focus. This situation is analogous to spectacle lenses, which employ a toric surface in order to produce cylinder power. Consequently, we can say that points in the “blending” regions of a progressive lens surface are locally toric. However, we more commonly refer to this difference in surface curvature as surface astigmatism, since the surface produces an astigmatic focus at these points.

In summary, while the curvature in the horizontal and vertical meridians at any point on the simple progressive lens surface described here depends only on the vertical location on the lens surface, the minimum and maximum curvatures of the surface at any point—which occur in oblique meridians—also depend upon the horizontal location on the surface. Further, the curvatures at any point in the progressive blending region of the lens are only equal along the vertical umbilic meridian. Away from the umbilic meridian of the lens, the curvatures in oblique meridians (near axis 45° and axis 135°) immediately start to differ, and this difference increases toward the periphery of the lens. This results in the characteristic surface astigmatism inherent in progressive lenses.

The basic progressive lens we have examined here, which employs circular cross-sections (that is, horizontal sections of spheres), suffers from a great deal of unwanted astigmatism in the lateral blending regions of the surface. The wearer will perceive the effects of this surface astigmatism as blur and distortion. Fortunately, use of more complex surfaces can reduce this surface astigmatism. For instance, replacing the circular crosssections with conic sections, including ellipses, hyperbolas and parabolas, will significantly reduce the levels of unwanted astigmatism. Indeed, one of the primary goals of progressive lens design is the minimization and sensible distribution of this unwanted surface astigmatism.

SURFACE ASTIGMATISM

In order to better understand the presence of surface astigmatism in progressive lenses and to develop a more solid intuition regarding the optics of progressive lenses, let us return to our Executive-style bifocal. How could we go about blending the two hemispheres together in order to produce a smooth, continuous surface? That is to say, how could we “fill in” the region beneath the ledge that exists between the flatter distance curve and the steeper near curve? We examined a progressive surface produced by making an “infinite” N-focal, but we will now consider a lens design that may be simpler to imagine.

For simplicity, let us visualize an Executivestyle bifocal with a plano (flat) back curve and a plano front curve in the distance region. In this case, the near region of the lens will have a front surface roughly equal to its add power, while the distance zone will be perfectly flat. We will now remove a 90° wedge from the side of this lens. The cross-section of the lens formed by this missing wedge is now similar to a plano plus-cylinder that has been cut in half. Note that the surface astigmatism of a plano cylinder is equal to the surface power of the cylinder across its meridian of curvature—or power meridian.

Now visualize a plano plus-cylinder lens equal in power to the bifocal segment (or add power). Such a plus-cylinder lens will be flat (plano) and produce no power along its axis meridian, while it will produce its maximum plus power through its power meridian. We will take this plano plus-cylinder, cut it in half along its axis (flat) meridian, and then insert it into the space left by our missing wedge. It should be a perfect fit. Essentially, we are showing that it is possible to “blend” the flatter distance portion to the steeper bifocal portion with the use of cylinder power (at an oblique axis).

Finally, trim away the excess material. The cylinder power of this plano plus-cylinder will be equal to the power of the bifocal segment, since the power curve of this cylinder is in fact an extension of the curve of the segment. Moreover, it should be apparent that this cylinder has no power along the axis meridian (that is, it’s a plano cylinder) because this meridian is an extension of the Plano distance curve. Further, this cylinder will be oriented at axis 45° (the angle the wedge makes in the distance). Of course, when we repeat this process for the other side of the lens, the cylinder will be oriented at axis 135°.

We have now created a “No-Line” Executive-style bifocal. While this isn’t a true progressive lens, since it has no progressive change in surface curvature, it demonstrates geometrically how surface astigmatism can smoothly blend two hemispheres of differing curvature—the flatter distance curve and the steeper near curve. This lens design also provides some intuition about the surface astigmatism of progressive lenses in general, since they both share the following characteristics:

1. There are two “wings” of unwanted surface astigmatism bordering the central viewing zones
2. This surface astigmatism is generally oriented at an oblique (i.e., neither horizontal nor vertical) axis
3. The magnitude of this surface astigmatism in well-designed lenses is comparable to the add power of the near zone

ANATOMY OF A PROGRESSIVE LENS

The proceeding sections will frequently reference various regions of progressive lenses, so a brief overview of the “gross anatomy” of a typical progressive lens surface is in order. General-purpose progressive lenses belong to a class of surfaces that offer four very important structural features:

1. Distance Zone: General-purpose progressive lenses have a stabilized region in the upper portion of the lens that provides the specified distance prescription.
2. Near Zone: Progressive lenses also provide a stabilized region in the lower portion of the lens that provides the specified add power for reading.
3. Progressive Corridor: These two zones are connected by a corridor of progressive power that provides intermediate or midrange vision.
4. Blending Region: The peripheral regions of the lens contain surface astigmatism, which produce blur and distortion, and offer only minimal visual utility.

Progressive addition lenses are supplied with two types of marking for layout, power verification, dispensing and identification purposes. Removable markings, which are ink markings stamped onto the lens, identify the layout, verification and dispensing points of the lens. In addition, permanent markings, which are etched upon the lens surface, provide the brand identification and add power of the lens, as well as alignment reference markings—which are 34mm apart and used to reapply the ink markings when necessary. The removable ink markings indicate the locations of the cardinal reference points of the progressive lens design:

• Distance Reference Point: The distance reference point (DRP) represents the location on the surface that provides the exact base curve, which is the optimal location for verifying the distance prescription. It is located at the center of the distance checking circle ink marking.
• Fitting Point: The fitting point (FP) represents the alignment point of the lens design, which is placed directly in front of the visual axis of the eye during primary gaze. It is located at the fitting cross ink marking.
• Prism Reference Point: The prism reference point (PRP) represents the optimal location on the surface for verifying prescribed prism or prism-thinning. It is located at the prism reference point ink marking, centered exactly between the permanent alignment reference markings.
• Near Reference Point: The near reference point (NRP) represents the location on the surface that provides the full target add power, which is the optimal location for verifying the add power of the prescription. It is located at the center of the near checking circle ink marking.