Describing ocular aberrations with wavefront vergence maps

Abstract

A common optometric problem is to specify the eye's ocular aberrations in terms of Zernike coefficients and to reduce that specification to a prescription for the optimum sphero‐cylindrical correcting lens. The typical approach is first to reconstruct wavefront phase errors from measurements of wavefront slopes obtained by a wavefront aberrometer. This paper applies a new method to this clinical problem that does not require wavefront reconstruction. Instead, we base our analysis of axial wavefront vergence as inferred directly from wavefront slopes. The result is a wavefront vergence map that is similar to the axial power maps in corneal topography and hence has a potential to be favoured by clinicians. We use our new set of orthogonal Zernike slope polynomials to systematically analyse details of the vergence map analogous to Zernike analysis of wavefront maps. The result is a vector of slope coefficients that describe fundamental aberration components. Three different methods for reducing slope coefficients to a spherocylindrical prescription in power vector forms are compared and contrasted. When the original wavefront contains only second order aberrations, the vergence map is a function of meridian only and the power vectors from all three methods are identical. The differences in the methods begin to appear as we include higher order aberrations, in which case the wavefront vergence map is more complicated. Finally, we discuss the advantages and limitations of vergence map representation of ocular aberrations.

Key words:

• ocular aberrations
• power vectors
• wavefront vergence
• Zernike analysis

Notes

a.  As an example, we consider astigmatism W=ρ² cos-2θ. The radial derivative is ∂W/∂ρ= 2ρ cos-2θ. To recover the phase, we integrate this radial derivative ∂W/∂ρ and obtain W=ρ² cos-2θ+f(θ) for some f(θ). Because f(θ) is arbitrary, a large family of solutions is possible. If we can assume W is a polynomial in x and y, then f(θ) must be a polynomial. At the same time, f(θ) is a function of angle θ only. The only possibility is that f(θ) is a constant. Therefore, we can find a phase from the radial derivatives up to constants as long as the phase is assumed to be a polynomial. We note that the tangential derivative ∂W/∂θ= ‐2ρ² sin-2θ can safely be estimated from the phase that was reconstructed from just the radial slope.