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Updated: May 11, 2026

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
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Published on: February 23, 2018

Zernike vs. Bessel circular functions in visual optics.

Juan P Trevino1, Jesus E Gómez-Correa, D Robert Iskander

  • 1Departamento de Optica, Instituto Nacional de Astrofísica, Optica y Electrónica, Puebla, México. trevinojp@inaoep.mx

Ophthalmic & Physiological Optics : the Journal of the British College of Ophthalmic Opticians (Optometrists)
|May 15, 2013
PubMed
Summary

Bessel Circular Functions offer improved modeling for ophthalmic surfaces compared to Zernike Circle Polynomials, especially for complex corneal shapes and variations. These functions provide a better alternative for analyzing specific features in eye surface topography.

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Area of Science:

  • Ophthalmic optics
  • Biomedical engineering
  • Computational modeling

Background:

  • Zernike Circle Polynomials are standard for representing circular ophthalmic surfaces.
  • Limitations exist in accurately modeling complex or rapidly changing surfaces with Zernike polynomials.

Purpose of the Study:

  • To introduce Bessel Circular Functions as a novel alternative to Zernike Circle Polynomials.
  • To evaluate the efficacy of Bessel Circular Functions for representing ophthalmic surfaces.

Main Methods:

  • Orthogonal Bessel Circular Functions were assessed for their fitting capabilities.
  • Comparison was made against Zernike Circle Polynomials using computationally generated ophthalmic surfaces.

Main Results:

  • Bessel Circular Functions demonstrated superior modeling for surfaces with abrupt variations, like the anterior eye surface at the limbus.
  • Enhanced suitability was found for analyzing post-surgical corneal surfaces and influence functions.
  • Bessel Circular Functions capture intricate details more effectively than Zernike polynomials in specific ophthalmic applications.

Conclusions:

  • Bessel Circular Functions are a viable alternative for representing wavefronts due to their boundary conditions and oscillatory properties.
  • They outperform Zernike Circle Polynomials in specific cases, including certain corneal surfaces and the anterior corneal surface.
  • The findings suggest Bessel Circular Functions are advantageous for detailed analysis of ophthalmic surfaces, particularly post-surgical corneas.