Fractional Fourier transform properties inherent in lens systems and other light and particle-beam environments are used to correct optical misfocus utilizing numerical operations. The invention produces a focused image from a partially-focused operation computed by at least one processor and a misfocused lens or other imaging system. Image data is operated on by a two-dimensional discrete fractional Fourier transform operation and a two-dimensional discrete fractional Fourier transform phase operation to create misfocused phase-adjusted image data comprising some amount of misfocus, the misfocus resulting from the application of the two-dimensional discrete fractional Fourier transform operation. The misfocused phase-adjusted image is presented to a misfocused exogenous optical system to create a resulting image. The power parameter of the fractional Fourier transform is adjusted to maximize sharp edge content of the resulting image. The invention can be used in imaging, integrated optics, optical computing, particle beam systems, and radiation accelerator systems.