letters to the editor
Response to “Basics of Residual Astigmatism”
The article in the October 2012 issue titled “Basics of Residual Astigmatism,” by Clarke D. Newman, OD, FAAO, is not as basic as the title suggests and contains what I believe is a technical error.
Common GP lenses range in index of refraction from 1.41 to 1.49. Because the index of refraction (index) as a variable is limited, it is not critical in the design of a given lens. Each index permits the fabrication of an appropriate junction thickness, edge thickness, and power in all designs including bitorics.
For a given center thickness, bitoric lenses of a higher index do have relatively thicker junction thicknesses, as Dr. Newman suggests, but this is true only for plus lenses. Exactly the opposite is true with minus lenses. More importantly, the difference is small, and labs typically correct for this by altering the center thickness. Other factors are much more critical compared to index in designing a bitoric lens.
When designing a bitoric, I recommend calculating the powers needed to correct each meridian without regard to the contact lens index or “residual astigmatism” (RA).
However, it is not difficult to calculate the unwanted power, “RA,” generated by adding a toric curve to spherical base and spherical front GP. (RA may not be the best term to describe this error.)
Given that F = (n' − n) / r, then the difference in interface power is as follows:
“RA” = (Nt − Ncl) / Rsteep − (Nt − Ncl) / Rflat
(R in meters, RA in diopters)
If (−RA) is added to the steep meridian power (in air), a bitoric lens results.
Inspection of the formula also shows that a lower-index material will reduce the RA (unwanted power), but not typically 50 percent as predicted in the article.
John C. Heiby, OD, FAAO Saint Clairsville, Ohio
Dr. Newman’s Response
I thank Dr. Heiby for his interest in my article and for his letter. First, lens materials range in index from the low range (Boston XO [Bausch + Lomb] at 1.415) to the high range (Paragon HDS HI [Paragon Vision Sciences] at 1.540), with PMMA in the middle at 1.490.
So, if we take Dr. Heiby’s own formula (which is correct), or the more traditional formula that gives the percentage of induced cylinder (index of tears – index of plastic / index of air – index of plastic), you get the “rule of onehalf” that we learned in optometry school when you plug in PMMA at 1.490. In other words, the induced residual astigmatism (IRA) is 42.65 percent of the amount of the toricity on the back of the lens (∆K).
If we put the 1.415 index for Boston XO into the same formulas, we get an IRA that is 23 percent of the ∆K, which is roughly half of the amount for the lower of the two indices as I stated in my article. If we put in the 1.54 for Paragon HDS HI, we get an IRA of 60.04 percent of the ∆K. Because the IRA is less for low-index materials, that, in turn, changes the front surface compensation.
Okay, now, so what? Well, if everything about the geometry of the lens is held constant, in minus bitoric lenses the junctional thickness changes with index, and in plus lenses the center thickness does. True, you can fix some of that by altering the center thickness for a minus lens, but the labs have thickness/power standards that, for each material, must be followed to avoid flexure; the same holds true for junctional thicknesses in plus lenses.
My primary point was that the index can affect the IRA significantly, and that, in turn, can affect the lens dynamics. Using low-index materials can make for better bitoric lenses if the other material properties (Dk/t, in vivo wettability and deposit resistance, and material dimensional stability) are equally as good.
You can easily make a bitoric lens from one of the higher-index materials. That is fine, but I use the low-index materials for torics.
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