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Today's Practice | May 2012

Basic Error Sources in IOL Calculation AfterRefractiveSurgery

An overview of how to avoid or correct these errors.

An ever-increasing number of patients are undergoing refractive surgery. Consequently, more patients presenting for cataract surgery turn out to have a history of laser vision correction. The determination of the proper IOL power has been, and still is, a challenge for the surgeon, although the origins of the problems for IOL calculation in these eyes have been identified and are well understood today. In the literature, a plethora of methods and recommendations for how to proceed in these cases is published, with new manuscripts devoted to these problems appearing nearly every month. An article in the April 2007 issue of CRST Europe, “IOL Power Calculations After LASIK and PRK,” reviews 20 of these formulas.

Below I give a brief description of the basic error sources in IOL calculation after refractive surgery and how these errors can be avoided or corrected. In a separate article on page 34, the Haigis-L formula for eyes after previous laser surgery is introduced (along with an overview of several other formulas). The Haigis-L formula offers one way to overcome the intrinsic errors described here.


Treating a previously myopic patient after laser surgery as if he or she were a normal patient can create up to 3.00 D of postoperative hyperopic refractive error—a considerable amount. Basically, three independent error sources are responsible for the refractive surprise: the radius measurement error, the keratometer index error, and the IOL formula error.

Radius measurement error. This specific independent error is due to the fact that keratometry and/or topography measure not centrally but a little to the periphery, where the corneal radius of curvature may be steeper than it is in the center. Obviously, the error depends on the instrument used to measure the radius and the dimensions of the ablation zone. With the increased optical zones of modern lasers, the radius measurement error is not a significant issue any longer, contributing only a few tenths of a diopter.

Keratometer index error. For the correct calculation of corneal power, both the anterior and posterior corneal radii must be known. Classical keratometry and/ or topography, however, derive the refractive power of the cornea from a measurement of the anterior radius alone, by assuming a fixed ratio between anterior and posterior corneal radii. Yet it is this ratio, expressed in the keratometer index, that is deliberately altered by refractive laser surgery for myopia. A measurement with the standard keratometer index, consequently, leads to a wrong corneal power and causes a hyperopic refractive error because the measured keratometry (K) value will be too strong. Typically, this keratometer index error is approximately 1.10 to 1.30 D for a previous -10.00 D myope.1

IOL formula error. The biggest contribution to the overall refractive error comes from the IOL formula error. Several IOL algorithms use the corneal power as a predictor for the effective lens position (ELP). For normal eyes, this is a reasonable approach, because flatter corneal radii are usually linked to smaller ELPs than steeper radii. Yet an eye after refractive surgery for myopia has a new anterior radius of curvature, one that is not intrinsic to the eye’s original internal geometry. The resulting calculated ELP is much smaller than the actual lens position, thus again causing a hyperopic error—for example, typically up to 2.40 D for a formerly -10.00 D myope.


To avoid problems in IOL calculation after refractive surgery, allowance must be made for the above errors. The radius measurement error may be neglected or solved together with the keratometer index error. To handle the latter, a proper expression for the actual effective corneal power has to be given. Classically, this can be achieved with the refractive history method,2,3 provided all necessary data are available in good quality.

Alternatively, correction curves giving the dependence between the actual effective corneal power and the nominal error-loaded K reading can be used. In recent years, several new optical instruments for the anterior segment have appeared that allow direct measurement of both anterior and posterior corneal radii. These measurements are also suited to overcome the keratometer index error.

To address the IOL formula error, either a formula should be selected that does not use Ks as ELP predictors, such as the Haigis4 or the Shammas5 formulas, or the classic double-K correction of Aramberri6 must be applied. More methods to overcome the problems described here can be found in the literature; the Hoffer/Savini LASIK IOL Power Tool, for example, has all currently published methods programmed into an Excel file that can be downloaded for free online.7 Other online sources, such as free online calculators, can also be used.8(To read about the advantages of an online calculator, read the article by Dennis H. Goldsberry, MD, PE, FACS, on page 50.)


In our treatment of errors, we have so far mainly dealt with laser vision correction for myopia. However, a laser correction for hyperopia is significantly different from a myopic correction, as no corneal material is removed in the central region. Accordingly, IOL calculation problems for these eyes are smaller than for myopic eyes and are mainly due to the IOL formula error. Another reason for smaller errors in previously hyperopic eyes lies in the smaller refractive range that can be treated by laser vision correction in this population.

Another group that cannot readily be compared with previous myopic laser surgery patients are those who have undergone radial keratotomy (RK). It is generally assumed that the curvature ratio in these eyes is not significantly changed by the incisional procedure, and, consequently, no significant keratometer index error is present. Nevertheless, the IOL formula error is still in effect in RK eyes.

In all scenarios where only the IOL formula error is present, the regular Haigis formula or another classic IOL formula with the double-K correction of Aramberri6 applied are good choices. To stay on the safe side, a target refraction of -0.25 to -0.50 D is recommended in these cases.

Wolfgang Haigis, MS, PhD, is a Professor in the Department of Ophthalmology, University of Wuerzburg, Germany. Professor Haigis states that he is a consultant to Carl Zeiss Meditec. He may be reached at tel: +49 931 201 20640; fax: +49 931 201 20454; e-mail: w.haigis@augenklinik.uni-wuerzburg.de.

  1. Haigis W. Intraocular lens calculation after refractive surgery. European Ophthalmic Review. 2012;6(1):21-24.
  2. Holladay JT. IOL calculations following RK. Refract Corneal Surg. 1989;5(3):203.
  3. Hoffer KJ. Intraocular lens power calculation for eyes after refractive keratotomy. J Refract Surg. 1995;11:490-493.
  4. Haigis W. IOL calculation after refractive surgery for myopia: the Haigis-L formula. J Cataract Refract Surg. 2008;34(10):1658-1663.
  5. Shammas HJ, Shammas MC. No-history method of intraocular lens power calculation for cataract surgery after myopic laser in situ keratomileusis. J Cataract Refract Surg. 2007;33:31-36.
  6. Aramberri J. Intraocular lens power calculation after corneal refractive surgery: Double K method. J Cataract Refract Surg. 2003;29(11):2063-2068.
  7. The Hoffer/Savini LASIK IOL Power Tool. www.eyelab.com. Accessed April 16, 2012. 8. Post-LASIK IOL Calculator. www.ascrs.org. Accessed April 16, 2012.