Validation of Mahajan's formula for scaling ocular higher-order aberrations by pupil size

Zernike polynomials for describing ocular higher order aberrations are affected by pupil aperture. The current study aimed to validate Mahajan's formula for scaling Zernike polynomials by pupil size.

Higher order aberrations for 3 intraocular lens models (AcrySof IQ IOL SN60WF, Technis ZA9003, Adapt Advanced Optics) were measured using the Zywave aberrometer and a purpose-built physical model eye. Zernike coefficients were mathematically scaled from a 5 mm to a 3 mm pupil diameter (5:3 mm), from a 5 mm to a 2 mm pupil diameter (5:2 mm), and from a 3 mm to a 2 mm pupil diameter (3:2 mm). Agreement between the scaled coefficients and the measured coefficients at the same pupil aperture was assessed using the Bland-Altman method in R statistical software.

No statistically significant mean difference (MD) occurred between the scaled and measured Zernike coefficients for 21 of 23 analyses after Holm-Bonferroni correction (P > 0.05). Mean differences between the scaled and measured Zernike coefficients were clinically insignificant for all aberrations up to the fourth order, and within 0.10 μm. Oblique secondary astigmatism (Z^-2₄) was significantly different in the 5:3 mm comparison (MD = -0.04 μm, P < 0.01). Horizontal coma (Z¹₃) was significantly different in the 3:2 mm comparison (MD = -0.07 μm, P = 0.03). There were borderline statistical differences in both vertical (Z^-1₃) and horizontal coma (Z¹₃) in the 5:3 mm comparison (MD = 0.02 μm, -0.09 μm, P = 0.05, 0.05, respectively).

A formula for the scaling of higher order aberrations by pupil size is validated as accurate. Pupil scaling enables accurate comparison of individual higher order aberrations in clinical research for situations involving different pupil sizes.