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Jack Yellott; Precompensating for defocus by spatial filtering. Journal of Vision 2013;13(15):T4. doi: https://doi.org/10.1167/13.15.4.
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© ARVO (1962-2015); The Authors (2016-present)
Beyond magnification, what can be done typographically to mitigate defocus for presbyopes forced to read without glasses? Ideally, topographical precompensation would correct defocus for a given object O(x,y) (e.g., a printed letter) by transforming it into another object O'(x,y) which yields O(x,y) when convolved with the pointspread function P(x,y) of the defocused eye: P*O' = O. (O, P, and O' are nonnegative real functions representing light intensity.) This can always be done for P itself, regarded as an object, by replacing it with the point object delta(x,y), since P*delta = P. In general an object O can only be completely precompensated for defocus in this way if its Fourier transform Fo contains the transform of P as a factor: Fo = FpFo', where Fo' is the transform of another object. This constraint (together with nonnegativity) implies that an object's spectral contrast |Fo(u,v)/Fo(0,0)| can only be precompensated if it does not exceed the eye's modulation transfer function (i.e., only if |Fo(u,v)/Fo(0,0)| <= |Fp(u,v)/Fp(0,0)| ). For levels of defocus routinely created by presbyopia this means only objects that are already severely blurred can be precompensated for the contrast-reduction component of defocus—ordinary printed letters need not apply! However the phase component of defocus—phase reversal (“spurious resolution”)—can always be precompensated by selectively pre-reversing portions of the object's phase spectrum. This can dramatically improve legibility by correcting retinal image shape. The talk will demonstrate how well phase precompensation for defocus works for letter-like objects, and discuss theoretical and experimental questions posed by phase-prefiltering.
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