Purpose: To quantify the effect of levelling the corneal surface around the optical axis on the calculated values of corneal asphericity when conic and biconic models are used to fit the anterior corneal surface. Methods: This cross-sectional study starts with a mathematical simulation proving the concept of the effect that the eye’s tilt has on the corneal asphericity calculation. Spherical, conic and biconic models are considered and compared. Further, corneal asphericity is analysed in the eyes of 177 healthy participants aged 35.4 ± 15.2. The optical axis was determined using an optimization procedure via the Levenberg–Marquardt nonlinear least-squares algorithm, before fitting the corneal surface to spherical, conic and biconic models. The influence of pupil size (aperture radii of 1.5, 3.0, 4.0 and 5.0 mm) on corneal radius and asphericity was also analysed. Results: In computer simulations, eye tilt caused an increase in the apical radii of the surface with the increase of the tilt angle in both positive and negative directions and aperture radii in all models. Fitting the cornea to spherical models did not show a significant difference between the raw-measured corneal surfaces and the levelled surfaces for right and left eyes. When the conic models were fitted to the cornea, changes in the radii of the cornea among the raw-measured corneal surfaces’ data and levelled data were not significant; however, significant differences were recorded in the asphericity of the anterior surfaces at radii of aperture 1.5 mm (p < 0.01). With the biconic model, the posterior surfaces recorded significant asphericity differences at aperture radii of 1.5 mm, 3 mm, 4 mm and 5 mm (p = 0.01, p < 0.01, p < 0.01 & p < 0.01, respectively) in the nasal temporal direction of right eyes and left eyes (p < 0.01, p < 0.01, p < 0.01 & p < 0.01, respectively). In the superior–inferior direction, significant changes were only noticed at aperture radii of 1.5 mm for both right and left eyes (p = 0.05, p < 0.01). Conclusions: Estimation of human corneal asphericity from topography or tomography data using conic and biconic models of corneas are affected by eyes’ natural tilt. In contrast, the apical radii of the cornea are less affected. Using corneal asphericity in certain applications such as fitting contact lenses, corneal implant design, planning for refractive surgery and mathematical modelling when a geometrical centre of the eye is needed should be implemented with caution.

Purpose: To investigate the effectiveness of flipping left corneas topography and analysethem quantitively along with fellow right corneas based on the assumption that they are mirror images of each other. Methods: The study involved scanning both eyes of 177 healthy participants (aged 35.3 ± 15.8) and 75 keratoconic participants (aged 33.9 ± 17.8). Clinical tomography data were collected for both eyes using the Pentacam HR and processed by a fully automated custom-built MATLAB code. For every case, the right eye was used as a datum fixed surface while the left cornea was flipped around in the superior–inferior direction. In this position, the root-mean-squared difference (RMS) between the flipped left cornea and the right cornea was initially determined for both the anterior and posterior corneal surfaces. Next, the iterative closest point transformation algorithm was applied on the three-dimensional flipped cornea to allow the flipped left corneal anterior surface to translate and rotate, minimising the difference between it and the right corneal anterior surface. Then, the RMS differences were recalculated and compared. Results: A comparison of the dioptric powers showed a significant difference between the RMS of both the flipped left eyes and the right eyes in the healthy and the KC groups (p < 0.001). The RMS of the surfaces of the flipped left corneas and the right corneas was 0.6 ± 0.4 D among the healthy group and 4.1 ± 2.3 among the KC group. After transforming the flipped left corneas, the RMS was recorded as 0.5 ± 0.3 D and 2.4 ± 2 D among the healthy and KC groups, respectively. Conclusions: Although fellow eyes are highly related in their clinical parameters, they should be treated with care when one eye topography is flipped and processed with the other eye topography in an optic-related research analysis where translation might be needed. In KC, an asymmetric disease, it was observed that a portion of the asymmetry was due to a corneal apex shift interfering with the image acquisition. Therefore, transforming the flipped left eyes by rotation and translation results in a fairer comparison between the fellow KC corneas.