Limitations of superoscillation filters in microscopy applications

The idea of superresolving pupil filters comes from the concept of superoscillations that may occur in regions of a band-limited signal with small amplitude having oscillations faster than the fastest Fourier component of the signal. In optical microscopy, superresolution can be achieved by appropriate design of pupil functions where the angular aperture determines the ultimate focal spot smaller than the Abbe diffraction limit outside the evanescent field region. The angular aperture cannot be increased indefinitely and the huge sidelobes cannot be avoided that are present in superresolving filters. The limitations of using such kind of filters in microscopy applications are discussed through computational examples.