In the process of IOL power calculation, the corneal power is presented in a single figure: the keratometry (K) value, which is generally computed from the measurement of the central corneal mean anterior radius of curvature. Nonetheless, in cases with irregular anterior corneal surface, a solitary figure is not sufficient to accurately present the optics of the cornea and, hence, to precisely calculate the correct IOL power. 
Since the earliest IOL power calculation formulas by Fyodorov and Gernet to the most modern by Holladay and Olsen, the corneal power was represented only by the Keratometry value, presenting the paraxial power of the cornea, computed by an approximate refractive index of the cornea to assume the non measured posterior corneal surface refractive power. The Keratometry value hypothesizes a spherical corneal shape and speculates a fixed proportion between the anteroposterior corneal curvature. This assumption yields accurate values in normal regular corneas with minimal variations in anteroposterior corneal curvature, which was proven by ray-tracing studies. 
Nonetheless, scarred corneas with irregular surface exhibit abnormal anteroposterior corneal curvature relation, violating the hypotheses allowing intraocular lens power calculation relying on Keratometry. Furthermore, the accuracy of measurements is frequently hindered in such irregular corneas, usually encountered after corneal refractive procedures, corneal ectasia, scarred corneas, or xerophthalmia. 
The application of keratometry in the measurement of the refractive power of the cornea relies on two assumptions, the first is that the four measured paracentral points represent the corneal central region, the second is that the corneal centre is comparable to a spherical shape and that the anterior corneal radius is 1.2 mm flatter than the posterior radius of curvature. [2-4] Although this proves true in regular corneas, it is not applicable in scarred and irregular corneas. [2-5]
Computerized videokeratography (CVK) measures > 5000 points over the corneal surface; therefore providing superior accuracy than manual keratometry in scarred corneas with irregular astigmatism. [3, 15] However, topographic corneal power measurement multiplies the anterior corneal curvature by a refractive index, assuming a fixed anteroposterior corneal curvature ratio, to calculate corneal power. [16, 17] In cases with marked change in the anterior and posterior corneal surfaces relationship, the default refractive index applied by most topography systems is inaccurate. [16, 17]
The Tomey Topographic Modeling System couples Scheimpflug and Placido disk technologies to determine corneal power and curvature. Anteroposterior corneal suface reconstruction can be achieved from the video-captured slit images, allowing calculation of the total anteroposterior corneal power.
In scarred corneas, these maps would provide superior accuracy than maps analyzing the anterior surface alone. 
The cornea in cases of herpetic keratitis shows scarring involving the anterior stroma, causing central flattening of the anterior corneal surface with little effect on the posterior curvature. These changes resemble alterations by refractive laser procedures and hence, CVK that relies solely on anterior corneal surface analysis would be inaccurate. 
In Irwin et al study, computerized scanning-slit videokeratography, which analyzes the anterior and posterior surfaces of the cornea, and the contact lens overrefraction method gave good estimations of corneal power in patients with irregular corneal astigmatism, improving the accuracy of IOL calculation in patients with corneal pathology and irregular astigmatism. 
The contact lens overrefraction method is reliable in estimating corneal power in patients with irregular corneal astigmatism, however, in cases in which the visual acuity is 20/70 or worse, contact lens overrefraction may not be accurate. 
Lately, OKULIX IOL power computation software became available relying on numerical ray tracing, assessing optical rays confined to the pupillary zone from cornea to fovea, unlike conventional lens power calculation formulas, compelling with paraxial rays solely, relying on Gaussian optical principles. The principles of ray tracing have existed since the 17th century, but only recently have they been applied to calculations for optical devices in ophthalmology. Although many surgeons rely on the use of third-generation IOL power calculation formulas such as the Haigis-L, Hoffer Q, Holladay 2, Olsen, and SRK/T, ray tracing is a modern technique, based on a different set of principles, that should be considered a potentially useful strategy. 
For a collective of 153 eyes undergoing cataract surgery and applying OKULIX software for IOL power calculation, the mean prediction error was -0.05±0.67D. The slope of the regression line (0.009D/mm) was not significantly different from zero. 
In a recent study by M. Ghoreyshi et al., the performance of OKULIX software ray-tracing IOL power calculation was not significantly different compared with SRK-T and Hoffer Q formulas. The MAE by OKULIX, SRK-T and Hoffer Q formulas, respectively, were 0.42 (±0.03), 0.36 (±0.02) and 0.37 (±0.02).  In the present study, The MAE was 0.2 D in corneal scarring cases, which did not differ significantly compared to controls (MAE 0.1 D, p 0.142). In another study by Karim M Nabil, OKULIX ray-tracing software accuracy was assessed in myopic cataract patients. In 83.33% of myopic patients, a prediction within ±1.00 D was obtained, whereas 70% showed a prediction within ±0.5 D. The MAE was 0.45±0.40 D.  In a third study, OKULIX ray tracing software yielded more accurate minus power intraocular lens calculation in extreme myopia, compared to SRK-T formula. SRK-T calculated IOL power (- 6.3 ± 2.8 D) showed statistically significant difference compared to OKULIX calculated IOL power (- 4.7 ± 2.6 D), rs 0.994 p < 0.001. 
In the present study, 3rd generation formulas which are based on anterior curvature only, had comparable results with ray tracing software, even in cases with cornel scarring. This could be explained by the fact that 75% of the studied cases involved stromal scarring, with more significant effect on the anterior, rather than posterior, corneal curvature.
One of the limitations of our study is the relatively small sample size, which could be justified by the rarity of cases of coexisting cataract and corneal scarring justified to undergo solely phacoemulsification without keratoplasty.
In summary, although corneal topography and keratometry are the most commonly applied tools to measure the refractive power of the central cornea for IOL power calculation in cataract surgery, both methods suffer limitations in cases with corneal scarring and irregular astigmatism.
In these cases, CVK that analyzes the anterior and posterior corneal surfaces provide a more accurate estimation of corneal power than CVK that analyzes the anterior surface only