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Jack Yellott; Mitigating visual defocus by prefiltering the object spectrum. Journal of Vision 2008;8(17):91. doi: 10.1167/8.17.91.
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© ARVO (1962-2015); The Authors (2016-present)
Spectacles correct visual defocus by altering the light coming from objects to the eye. Another approach is to alter the objects themselves by spatial filtering that pre-compensates for the anticipated spectral consequences of defocus, i.e., canceling amplitude reductions by prior amplitude boosts, and phase reversals by pre-reversals. Suppose a defocused eye's retinal image Io of object O is formed by convolving O with a point spread function P: Io = P,O. If another object O′ can be created such that O = P, O′, then a perfect retinal image of O can always be produced by replacing O with O′: Io′ = P* O′ = O. If O′ exists, its Fourier transform is related to those of O and P by Fo = Fp Fo′, so O′ can be found by inverting the ratio Fo/Fp. The stumbling block is that the O′ produced by this mathematical operation may not be a nonnegative real function—i.e., a physically realizable object. Analysis shows that O′ is realizable only if the original object's normalized amplitude spectrum |Fo(u,v) / Fo(0,0)| is , the eye's modulation transfer function |Fp(u,v)/Fp(0,0)|. This means that prefiltering cannot raise the ceiling imposed on retinal image contrast by any given amount of defocus—all it can do is to protect low-contrast objects from being, in effect, defocused twice. But partial prefiltering confined to phase alone is always possible (though generally at the cost of low retinal contrast), and for some objects (notably, printed characters) the elimination of phase-reversal errors in defocused images can greatly improve recognizability.
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