Simple Method to Calculate the Surgically Induced Refractive Change

letters to the editor Simple Method to Calculate the Surgically Induced Refractive Change To the Editor: The recent article "Calculating the Surgically Induced Refractive Change Following Ocular Surgery" 1 described a ten-step method based on the oblique crosscylinder solution to calculate the surgically induced refractive change. Although the aim of the paper was to propose a cookbook for surgeons to report their refractive results in a consistent manner, the method appeared unnecessarily complicated for most surgeons for daily clinical work. I would like to draw attention to a much simpler method, which can be described in six lines. The principle of the method, originally described by W. E. Humphrey, 2 is based on astigmatic decomposition of any cylinder into two vector components at 0 and 45 degrees, respectively. Geometrically, the angles are doubled so the two vector components can be found as

and

where sqrt = square root. The resulting axis is found from A3 = (ArcTan[SumC45/SumC0])/2

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with the conditions: 1. If Sum CO = 0, then A3 becomes 90 degrees; 2. IfSumCO < 0, then 90 degrees is added to A3; 3. If A3 > 180", then 180 degrees is subtracted from A3. The resulting sphere (S3) is found from S3 =MeanS- C3/2

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The advantage of this method is that there is no need to transpose C 1 and C2 so their cylinders have the same sign. There is also no need to arrange the cylinders so A 1 is smaller than A2, and there is no need to find angle "alpha" (difference between A2 and A I). Of course, ifSC3 is known, SC2 can be found from the formula SC2 = SC3- SCI

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Thus, the induced refraction of any surgical procedure can be found by the addition of the negative refraction (-SC 1) to the postoperative refraction (SC3) according to the above formulas. When the sphere is zero, the method gives the same results as the vector analysis of Jaffe and Clayman. 3 Thomas Olsen, M.D.

C45 = C•sin(2•a),

where C = cylinder (any sign) and a = axis. The cylinder C, resulting from the combination of any number of cylinders can then be found from the formula C1 = sqrt(SumC0 2 + SumC45 2 )

where SumC0 and SumC45 are the summated 0 and 45-degree components, respectively. Thus, for the addition of two spherocylinders SCI and SC2, we have the following calculation: SumC0 = C ioCos(2•A I) + C2•Cos(2•A2) SumC45 = CI •Sin(2•A I) + C2•Sin(2•A2)

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REFERENCES I. Holladay JT, Cravy TV, Koch DO. Calculating the sur-

gically induced refractive change following ocular surgery. J Cataract Refract Surg 1992; 18:429-443 2. Bennet AG, Rabbetts RB. Clinical Visual Optics, 2nd ed. London, Butterworth, 1991; I 06 3. Jaffe NS, Clayman HM. The pathophysiology of corneal astigmatism after cataract extraction. Am J Ophthalmol 1975; 79:615-630

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where C1 and C2 represent the cylinder component of SC 1 and SC2, and A 1and A2 represent the axis of their cylinders, respectively. The mean power (MeanS) is calculated according to MeanS= (SI + CI/2) + (S2 + C2/2)

Aarhus, Denmark

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The cylinder of the resulting spherocylinder SC3 is calculated according to

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Jack T. Holladay, M.D., Thomas V. Cravy, M.D., Douglas D. Koch, M.D., reply: As we mentioned in our article, there are several different methods for determining the result of obliquely crossed spherocylinders. It appears to us that there are the same number of formulas for Olsen's technique as with ours, except that he begins numbering with the fourth equation and we begin numbering with the first. The difference in the appearance of the equations is merely the result of trigonometric identities.

J CATARACT REFRACT SURG-VOL 19. MARCH 1993

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