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John Yellott; Precorrecting visual objects destined for defocus. Journal of Vision 2008;8(6):950. doi: 10.1167/8.6.950.
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© ARVO (1962-2015); The Authors (2016-present)
Spectacles correct visual defocus by altering the light coming from an object to the eye. Another approach is to alter the object O itself, replacing it with an object O á whose defocused image is a perfect copy of O. This is sometimes physically possible, but not always. E.g., suppose a defocused eye converts objects of the form 1 + m cos fx into images of the form 1 − .1 m cos fx (i.e., defocus reduces contrast at frequency f by the factor 0.1 and also causes a phase reversal.) To create a perfect image of the object 1 + .1 cos fx (m = .1), substitute the precorrected object 1 − 1.0 cos fx. Then the defocused image is 1 − .1(−1.0) cos fx = 1 + .1 cos fx, so precorrection works. But if m = .2, the necessary precorrected object 1 − .2/.1 cos fx cannot be physically constructed because it is not nonnegative. A general theory of precorrecting objects for defocus can be developed using the tools of Fourier optics. Its main conclusion is that spectral precorrection can greatly improve the recognizability of severely defocused images (by eliminating shape-distorting phase reversals), but post-defocus contrast is inevitably low: no precorrection operation can make the total contrast energy of a defocused image exceed the contrast energy of the defocusing pointspread function. Put another way, precorrecting for defocus can only preserve the contrast of objects that are already low-contrast to begin with—objects whose Fourier spectrum is the product of the optical transfer function of the out-of-focus eye times the spectrum of some other object. Such objects have, in effect, already been defocused once, and precorrection can only save them from being defocused twice.
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