Optimal modeling of corneal surfaces with Zernike polynomials

Area of Science:

• Ophthalmology
• Optical Engineering
• Biomedical Optics

Background:

• Zernike polynomials are crucial for analyzing optical wavefronts and modeling corneal surfaces.
• Accurate corneal modeling requires appropriate selection of Zernike polynomial expansion order based on measured data.

Purpose of the Study:

• To compare classical model order selection techniques with a bootstrap approach for fitting Zernike polynomials to corneal data.
• To demonstrate the superiority of the bootstrap method for objective selection of the optimal number of Zernike terms.

Main Methods:

• Simulations were conducted to compare the performance of classical model order selection techniques.
• A bootstrap-based approach was developed and validated for fitting Zernike polynomials to corneal elevation data.
• The method was applied to both normal and distorted corneas to assess its efficacy.

Main Results:

• The bootstrap method significantly outperformed classical techniques in simulations for Zernike polynomial order selection.
• The bootstrap technique proved to be the most appropriate method for fitting Zernike polynomials to corneal elevation data.
• Optimal model order selection was found to be dependent on the corneal diameter.

Conclusions:

• The bootstrap method provides an objective and effective way to select the optimal number of Zernike terms for corneal surface analysis.
• This approach enhances the accuracy of corneal modeling, particularly for eyes with significant distortions.
• The findings support the use of the bootstrap technique in clinical and research settings for precise ophthalmic optical analysis.