Figure - available from: Applied Optics
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Temporal representation of function psin ( α , β , e ) , for 0 ≤ α < 4 π , with the sign convention for radii, with β = π / 3 and e = 0.8 , 0.9 and 0.999. When e = 1 , the function converges to a zero amplitude pulse, which is useful for modeling other physical and engineering problems. The canonical function sin ( α ) is drawn using dashed lines.
Source publication
Principal meridians of the corneal vertex of the human ocular system are not always orthogonal. To study these irregular surfaces at the vertex, which have principal meridians with an angle different from 90°, we attempt to define so-called parastigmatic surfaces; these surfaces allow us to correct several classes of irregular astigmatism, with non...
Citations
... In fact, the existing literature that evaluates corneal irregularity by Fourier series harmonic ignores the irregular astigmatism phase angle β 3 and does not associate it with a specific physical meaning. 11,14,15 While it is acknowledged that a quantitative degree of irregularity in refractive power exists in normal eyes and this knowledge has been simulated by mathematical modeling 16 , no technique is available to locate the axes of irregular astigmatism. As a result, irregular astigmatism cannot be fully corrected by existing spectacle lenses and a degree of astigmatism will remain after correction. ...
Purpose: To investigate the prevalence of non-orthogonal astigmatism among normal and keratoconic Brazilian and Chinese populations
Methods: Topography data was obtained using the Pentacam High Resolution (HR) system ® from 458 Brazilian (aged 35.6±15.8 years) and 505 Chinese eyes (aged 31.6±10.8 years) with no history of keratoconus or refractive surgery, and 314 Brazilian (aged 24.2±5.7 years) and 74 Chinese (aged 22.0±5.5 years) keratoconic eyes. Orthogonal values of optical flat and steep powers were determined by finding the angular positions of two perpendicular meridians that gave the maximum difference in power. Additionally, the angular positions of the meridians with the minimum and maximum optical powers were located while being unrestricted by the usual orthogonality assumption. Eyes were determined to have non-orthogonal astigmatism if the angle between the two meridians with maximum and minimum optical power deviated by more than 5° from 90°.
Results: Evidence of non-orthogonal astigmatism was found in 39% of the Brazilian keratoconic eyes, 26% of the Chinese keratoconic eyes, 29% of the Brazilian normal eyes and 20% of the Chinese normal eyes.
Conclusions: The large percentage of participants with non-orthogonal astigmatism in both normal and keratoconic eyes illustrates the need for the common orthogonality assumption to be reviewed when correcting for astigmatism. The prevalence of non-orthogonality should be considered by expanding the prescription system to consider the two power meridians, and their independent positions.
