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Cataract Surgery | Jul/Aug 2014

The Safest Way to Determine Corneal Astigmatism

Physical measurements of the anterior and posterior corneal surfaces may be most effective.

Determining a patient’s corneal astigmatism prior to toric IOL implantation requires the highest level of accuracy. This procedure comprises several steps of measurements and of calculations. Theoretically, these measurements may be performed before surgery or intraoperatively. However, outcome analysis has shown that intraoperative methods, particularly intraoperative aberrometry, were unable to deliver the same amount of prediction accuracy achieved with preoperative measurements.1 That is to say, the optical properties of the postoperative eye can be more accurately characterized by the preoperative eye than by the intraoperative eye.

This article focuses on preoperative measurement of total corneal astigmatism, beginning with the astigmatism of the anterior corneal surface, which can be calculated using keratometry or topography.


Keratometry. This preoperative measurement is a twopoint approximation of a corneal vertex radius, based on the distance between two measuring points. Three measurements in different meridians are needed to define the amount and axis of cylinder. An advantage of keratometry is that it also works with a suboptimal tear film because the points are, in fact, extended light bundles. Disadvantages include that it does not take into account corneal asphericity and is restricted to measuring only a small part of the corneal surface.

Topography. Measuring the whole optical corneal surface results in a map of local corneal radii. Topography measurements can be based on Placido-ring distances, Scheimpflug imaging, or optical coherence tomography (OCT) imaging. To determine astigmatism, best-fit vertex radii and their axes can be extracted by a numerical fit procedure involving the whole optical zone.2 An advantage of topography is that it also addresses asphericity. A disadvantage of Placido-based measurements is that they are sensitive to tear film irregularities.


The posterior surface of the cornea also contributes to corneal optics, less significantly than the anterior surface but not negligibly. To simplify measurements and calculations, the anterior and posterior surfaces were combined decades ago into one surface at the location of the anterior surface.3

For this purpose, a combined corneal refractive index can be defined:

n = nc + (nh – nc ) Ra + d(nc – 1)(nc – nc) Rp nc Rp

where nh and nc = the refractive indices of aqueous humor (eg, 1.336) and cornea (eg, 1.376), respectively; Ra and Rp = anterior and posterior corneal curvature radius, respectively; and d = corneal thickness.

Different numerical values (eg, 1.375 and 1.327) and various names for nˆ are used, causing confusion among ophthalmologists. The impact of d on nˆ is nearly negligible, but the assumption of the ratio of anterior to posterior corneal curvature radius (Ra/Rp) is not.


Instead of relying on the aforementioned assumptions, I prefer to use physical measurements. With this approach, anterior and posterior corneal surfaces are measured, and the astigmatisms of both surfaces are combined into one total corneal astigmatism. The measurements can be performed by Placido-based topography for the anterior surface and/or Scheimpflug imaging for spatially resolved pachymetry or by OCT imaging of the whole cornea. The datasets measured by such devices can be transferred to the Okulix ray-tracing software (Tedics), which directly calculates the desired IOL power.

An example of determining total corneal astigmatism is shown in Figure 1. The anterior vertex radii and axes are extracted from the map of anterior local corneal radii (left). A map of local posterior radii is then generated from spatially resolved pachymetry, and again vertex radii and axes are extracted from this (right). Approximation of the cornea as a thick lens using Gaussian optics allows the definition of the total corneal astigmatism of 1.86 D at 113.7° (thick red line), the axis of which is different from that of the anterior astigmatism (105°, brown line) in this example. Thus, the thick red line is the IOL implantation axis.

In a recent investigation,4 we found a relatively small accuracy benefit of using the described tomographic approach (ie, including posterior cornea) compared with the measurement of only the anterior cornea: There was a median of 0.27 D absolute vector difference in 395 eyes. This difference seems almost negligible at first glance. However, the maximum difference was 1.50 D. Therefore, I recommend using this approach to exclude potentially unhappy patients, such as those with overlooked subclinical keratoconus, even though they are uncommon.

An additional accuracy benefit can be achieved when the averages of keratometric and topographic radii— instead of only the topographic data—are used for the anterior cornea5 This approach must not be used in eyes after corneal surgery. Such eyes should be measured only by the tomographic method described above.

Paul-Rolf Preussner, MD, PhD, practices at the University Eye Hospital, in Mainz, Germany. Professor Preussner states that he has royalty agreements with Tedics, Tomey, and Oculus Optikgeräte. He may be reached at e-mail: pr.preussner@uni-mainz.de.

  1. Preussner PR. Intraoperative aberrometry: an unneccessary tool. Cataract & Refractive Surgery Today Europe. March 2013;17-19.
  2. Preussner PR, Wahl J, Weitzel. Topography based IOL power selection. J Cataract Refract Surg. 2005;31:525-533.
  3. Olsen T. On the calculation of power from curvature of the cornea. Br J Ophthalmol. 1986;70:152-154.
  4. Preussner PR, Hoffmann P, Wahl J. Impact of posterior corneal surface on toric IOL calculation. Submitted for publication.
  5. Hoffmann PC, Wahl J, Hütz WW, Preussner PR. A raytracing approach to calculate toric intraocular lenses. J Refract Surg. 2013;29:402-408.