Image Deblurring and Aperture Synthesis Using a Posteriori Processing by Fourier-transform Holography

Two forms of holographic spatial filtering may be used for the deconvolution of accidentally blurred images and of images deliberately ‘coded’ for aperture-synthesis purposes. The first is generally applicable and uses a Fourier-transform division filter realized by holography from the instrumental ‘spread function’ of the system. The second, even more straight-forward, is particularly suited for the special case when the autocorrelation function of the spread function is or may suitably be made to be sharply peaked. This form should permit one to realize a new class of optical systems in cases where conventional (lens and mirror) systems may not be readily realized (e.g. for x-ray and ultrasonic imaging, for space astronomy and photography, among others). Previously unpublished, new theoretical and experimental results are given. Applications to the possibilities of achieving ‘super-resolutions’ and for solving the ‘phase problem’ in x-ray crystallography are also briefly mentioned.