Correction of over-focus in digital images using centered discrete imaginary-power fractional fourier transformations with high-accuracy orthonormal eigenvectors

A method for correcting mis-focus of an image, the method comprising:

• receiving an image file at a numerical processor, the image file comprising a portion of the image in an original mis-focused condition, the mis-focused condition comprising an over-focus condition for at least a portion of the image;
• selecting a numerical value for a variable a;
• beginning a first iteration of a numerical procedure executing on the numerical processor;
• in the numerical procedure, applying a two-dimensional reflection operator composed with a two-dimensional centered discrete fractional Fourier transform operator of imaginary power i χ to the image file and applying a phase correction operator associated with the two-dimensional centered discrete fractional Fourier transform matrix of power 2−i χ to the image file, where is a real number and i is the square root of −1;
• obtaining a modified portion of the image file from the above operations;
• inspecting the modified portion of the image file and determining a change in the mis-focused condition;
• based on the determined change, adjusting numerical value of x;
• and
• beginning a next iteration of the numerical procedure on the numerical processor;
• wherein a specific value of χ is chosen providing the best correction of the mis-focused condition.