Calculating Angle Lambda (λ) Using Zernike Tilt Measurements in Specular Reflection Corneal Topography

Abstract

Purpose: To develop a method to calculate the angle λ of the human eye using Zernike tilt measurements in specular reflection corneal topography. Methods: The meaning of Zernike tilt in specular reflection corneal topography is demonstrated by measurements on translated artificial surfaces using the VU Topographer. The relationship derived from the translation experiments is used to determine the angle λ. Corneal surfaces are measured for a set of eight different fixation points, for which tilt angles ρ are obtained from the Zernike tilt coefficients. The angles ρ are used with respect to the fixation target angles to determine angle λ by fitting a geometrical model. This method is validated with Orbscan II's angle-κ measurements in 9 eyes. Results: The translation experiments show that the Zernike tilt coefficient is directly related to an angle ρ, which describes a tilt orientation of the cornea and can therefore be used to derive a value for angle λ. A significant correlation exists between measured values for angle λ with the VU Topographer and the angle κ with the Orbscan II (r=0.95, P<0.001). A Bland-Altman plot indicates a mean difference of -0.52 degrees between the two instruments, but this is not statistically significant as indicated by a matched-pairs Wilcoxon signed-rank test (P≤0.1748). The mean precision for measuring angle λ using the VU topographer is 0.6±0.3 degrees. Conclusion: The method described above to determine angle λ is sufficiently repeatable and performs similarly to the angle-κ measurements made with the Orbscan II.

Keywords

• angle λ
• angle κ
• Zernike tilt
• corneal topography
• VU Topographer