July 2018
Volume 59, Issue 9
Open Access
ARVO Annual Meeting Abstract  |   July 2018
A New Polynomial Decomposition Method for Ocular Wavefront Analysis.
Author Affiliations & Notes
  • Damien Gatinel
    Ophthalmology, Rothschild Foundation, Paris, France
    CEROC, Paris, France
  • Jacques Malet
    Institute of Statistics, Pierre et Marie Curie University, Paris, France
  • Laurent Dumas
    Applied Mathematics, University of Versailles St Quentin (UVSQ), Versailles, France
  • Footnotes
    Commercial Relationships   Damien Gatinel, None; Jacques Malet, None; Laurent Dumas, None
  • Footnotes
    Support  None
Investigative Ophthalmology & Visual Science July 2018, Vol.59, 2975. doi:
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      Damien Gatinel, Jacques Malet, Laurent Dumas; A New Polynomial Decomposition Method for Ocular Wavefront Analysis.. Invest. Ophthalmol. Vis. Sci. 2018;59(9):2975.

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      © ARVO (1962-2015); The Authors (2016-present)

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Purpose : Zernike circle polynomials are in widespread use for wavefront error (WFE) analysis because of their orthogonality over a circular pupil and their representation of balanced classical aberrations. Because of artefacts due to the presence of order 1 and order 2 terms in higher order (HO) modes such as coma Z(3,1), spherical aberration Z(4,0), and secondary astigmatism Z(4,2), the coefficients of second degree modes do no predict with a good accuracy the wavefront error that can be corrected with spectacles. We propose new functions as alternatives of Zernike polynomials to represent the WFE of human eyes.

Methods : A new decomposition basis, called D2V3 is built using Gram Schmidt method, with the constraint that the analytical expression of the HO modes (n≥3) does not contain radial terms of order 1 or 2. The use of orthonormal polynomials G(n,m) of lowest radial degree n (valuation) greater or equal to 3 allows to quantify the high order aberration wavefront component (V3). The new sub-basis for the HO aberration component (V3) is no longer orthogonal to the low order aberration component sub-basis (D2).

Results : Ocular WFE can be decomposed into the sum of G(n,m) polynomials of low degree (n lesser or equal to 2) and of high degree (n greater or equal to 3). In situation where there is an increase in the HO aberrations (keratoconus, complicated refractive surgery, multifocal ablations), the 2nd degree modes of the D2V3 basis should better correlate with the clinical refraction as they comprise all the terms of radial order equal to 2. Terms of radial order equal to 1 (tilt) almost vanish in the D2V3 decomposition. Due to differences in their respective normalization constant, clinically relevant modes such as coma G(3,±1), spherical aberration G(4,0) and secondary astigmatism G(4±2) are weighted by more prominent coefficients in the D2V3 than the Zernike basis. This may facilitate the clinical interpretation and comparison of the aberrations within the HO WFE component.

Conclusions : Because it provides better separation of the lower vs HO aberration components, the new D2V3 aberration basis may quantify more accurately the aberrations that contribute to the refractive error correctable with glasses, and provide clinicians with coefficients magnitudes which better underline the impact of the most clinically significant aberration modes.

This is an abstract that was submitted for the 2018 ARVO Annual Meeting, held in Honolulu, Hawaii, April 29 - May 3, 2018.


Pyramidal representation of the G(n,m) modes constitutive of the D2V3 aberration basis.

Pyramidal representation of the G(n,m) modes constitutive of the D2V3 aberration basis.


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