Correcting spurious resolution in defocused images

Optical modeling suggests that levels of retinal defocus routinely caused by presbyopia should produce phase reversals (spurious resolution−SR) for spatial frequencies in the 2 cycles/letter range known to be critical for reading. Simulations show that such reversals can have a decisive impact on character legibility, and that correcting only this feature of defocused images (by re-reversing contrast sign errors created by defocus) can make unrecognizably blurred letters completely legible. This deblurring impact of SR correction is remarkably unaffected by the magnitude of defocus, as determined by blur-circle size. Both the deblurrring itself and its robustness can be understood from the effect that SR correction has on the defocused pointspread function, which changes from a broad flat cake to a sharply pointed cone. This SR-corrected pointspread acts like a delta function, preserving image shape during convolution regardless of blur-disk size. Curiously, such pointspread functions always contain a narrow annulus of negative light-intensity values whose radius equals the diameter of the blur circle. We show that these properties of SR-correction all stem from the mathematical nature of the Fourier transform of the sign of the optical transfer function, which also accounts for the inevitable low contrast of images pre-corrected for SR.