Impact of primary spherical aberration, spatial frequency and Stiles Crawford apodization on wavefront determined refractive error: a computational study

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We tested the hypothesis that pupil apodization is the basis for central pupil bias of spherical refractions in eyes with spherical aberration.


We employed Fourier computational optics in which we vary spherical aberration levels, pupil size, and pupil apodization (Stiles Crawford Effect) within the pupil function, from which point spread functions and optical transfer functions were computed. Through-focus analysis determined the refractive correction that optimized retinal image quality.


For a large pupil (7 mm), as spherical aberration levels increase, refractions that optimize the visual Strehl ratio mirror refractions that maximize high spatial frequency modulation in the image and both focus a near paraxial region of the pupil. These refractions are not affected by Stiles Crawford Effect apodization. Refractions that optimize low spatial frequency modulation come close to minimizing wavefront RMS, and vary with level of spherical aberration and Stiles Crawford Effect. In the presence of significant levels of spherical aberration (e.g. Symbol = 0.4 μm, 7 mm pupil), low spatial frequency refractions can induce −0.7 D myopic shift compared to high SF refraction, and refractions that maximize image contrast of a three cycle per degree square-wave grating can cause −0.75 D myopic drift relative to refractions that maximize image sharpness.


Because of small depth of focus associated with high spatial frequency stimuli, the large change in dioptric power across the pupil caused by spherical aberration limits the effective aperture contributing to the image of high spatial frequencies. Thus, when imaging high spatial frequencies, spherical aberration effectively induces an annular aperture defining that portion of the pupil contributing to a well-focused image. As spherical focus is manipulated during the refraction procedure, the dimensions of the annular aperture change. Image quality is maximized when the inner radius of the induced annulus falls to zero, thus defining a circular near paraxial region of the pupil that determines refraction outcome.

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