A "Blended" Executive Bifocal and the Optical Constraints of Progressive Lenses
By Darryl J. Meister, ABOM
Periodically, while giving presentations on progressive lenses, I am asked several questions that are all similar in nature and speak to the optical and physical requirements of progressive lens designs. Does a progressive lens really need to have unwanted astigmatism? Can you make a progressive lens with no corridor length? Is it possible to make something like a "blended" Executive bifocal? Why is prism-thinning used? And so on.
I am providing, below, a short discussion on my method for constructing a blended Executive-style bifocal, which I will use by analogy to illustrate some of the inherent optical and mechanical limitations of conventional progressive addition lenses. Hopefully, this will provide those interested with a solid intuition when it comes to the nature of progressive lenses.
Most opticians are (painfully) aware of the geometrical aspects of Executive- and Franklin-style bifocals. A flatter distance curve meets a steeper near curve, resulting in a prominent ledge-like junction on the surface. At the center of the lens, the two front surfaces meet (or at least nearly so) at a single point, and are only contiguous (unbroken) at that point. (In reality, Executive-style bifocals actually have a tiny "lip" at this point, but imagine the lens without one.) Away from this point, the surfaces gradually break farther and farther apart as the near curve steepens more quickly than the distance curve, resulting in the infamous edge profile of these bifocals.
So, how could we go about "blending" these two curves together in order to produce a smooth, continuous surface? How could we "fill in" the region beneath the ledge that exists between the flatter distance curve and the steeper near curve? For simplicity, let us visualize an Executive-style bifocal with a Plano (flat) back curve and a Plano front curve in the distance (or major portion). In this case, the near (or segment) 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-degree wedge from the side of this lens. One edge of the wedge will be 45 degrees above the bifocal ledge, while the other edge will be 45 degrees below it. 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. Also note that if we do this to both sides, the distance (or major) portion and the bifocal segment will both be 90-degree wedges (360 = 90 + 90 + 90 + 90).
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).
As previously noted, 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).
This cylinder has seamlessly and smoothly joined the distance curve to the near curve. We now have a "blended" Executive-style bifocal lens, with 90-degree wedges of distance and Add power. Of course, we will also want to trim away the excess lens material from the portion of the plano-cylinder that is protruding from the side of the lens blank. Once we have removed this excess material, also note the thickness profile of the lens blank.
Now, what are some of the pertinent features of this "blended" Executive-style bifocal? For one, it has a smooth surface. Secondly, it has large "wings" of unwanted cylinder power in the periphery, roughly comparable in magnitude to the Add power of the bifocal segment. This cylinder power is also obliquely oriented (i.e., at axis 45 on the right side and at axis 135 on the left). Lastly, the top of the lens blank is thicker than the bottom, so prism-thinning would balance this thickness difference. These are all also features of progressive addition lenses.
Is this lens design as good as a progressive addition lens? No. First and foremost, progressive lenses distribute the change in Add power over a larger region of the lens, which results in smoother and better-behaved cylinder power. This means less blur, distortion, and image swim for the wearer, as well as a larger "effective" field of vision in the distance. The blended Executive goes directly from no cylinder power to a very high level of constant cylinder power at a particularly disturbing axis. The unwanted cylinder power in the "blending" regions of progressive lenses is also more carefully controlled than the periphery of our simple blended Executive.
Progressive lenses also offer good intermediate utility. The blended Executive has no intermediate (it has no corridor), and instead produces an abrupt change in vision between the distance and bifocal regions. Progressive lenses also have surfaces that produce smooth changes in power and magnification (mathematically speaking, the surfaces have continuous second derivatives). The blended Executive has a smooth surface, but produces abrupt changes in power and magnification between its "wedges."
With the right mathematical considerations, we could refine our blended Executive surface in order to smooth the transitions in power, add some intermediate functionality, achieve the right balance between the "wedges," reduce the levels of unwanted cylinder distortion, and improve its overall optical performance. Of course, we would then have a progressive addition lens.