Reconstruction of Images from Transforms by an Optical Method

Abstract

THE holographic reconstruction of the amplitude and phase maps for a bovine liver catalase crystal, by using computer analysis of the image and diffraction pattern obtained in an electron microscope, was reported recently¹. This method used a random number generator to generate an arbitrary phase distribution, and hence to produce from the electron transform a ‘first fit’ image. This was then filtered by convolution with the image obtained in the electron microscope. We have been attempting to reconstruct images from transforms by an analogue method, using a Rank Precision Industries Image Analyser 3000 to process the images rather than a digital computer. The method which we have defined uses a random spatial frequency generator to produce a ‘first fit’ image which can be further improved by filtering in reciprocal space. As only the original transform has been used in reconstruction of the image, a task in optics that hitherto has been considered impossible seems to have been achieved (compare Gerchberg¹, where the digital procedure used for reconstruction from the transform, although it used both a transform and an image, worked even when a ‘blank’ image was supplied).