A refined bootstrap method for estimating the Zernike polynomial model order for corneal surfaces

Area of Science:

• Ophthalmology
• Biomedical Optics
• Computational Vision

Background:

• Accurate corneal surface modeling is crucial for diagnosing and managing eye conditions.
• Previous methods using Zernike polynomials have limitations in precision.
• Zernike polynomials are widely used to represent complex optical surfaces like the cornea.

Purpose of the Study:

• To develop a more accurate bootstrap-based procedure for optimal corneal surface modeling using Zernike polynomials.
• To determine the optimal number of Zernike terms for modeling normal and distorted corneas.
• To compare Zernike term requirements between normal and pathological corneal shapes.

Main Methods:

• A refined bootstrap-based statistical procedure was implemented.
• The procedure was applied to model corneal surfaces using Zernike polynomials.
• The optimal radial order of Zernike expansion was analyzed for different corneal types.

Main Results:

• The refined bootstrap procedure demonstrated improved accuracy over previous methods.
• For normal corneas, the optimal Zernike expansion typically reached the fourth or fifth radial order.
• Distorted corneas (keratoconus, post-surgical) required models with Zernike expansions up to three radial orders higher than normal corneas.

Conclusions:

• The study provides an enhanced method for precise corneal surface reconstruction.
• Optimal Zernike polynomial order is dependent on corneal topography, distinguishing normal from pathological cases.
• Findings have implications for improved diagnostic tools and personalized ophthalmic treatments.