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The object reconstruction problem in light and electron microscopy consists of the determination of the complex amplitude from one or more images. This problem, which is usually treated for the case of weak objects, is extended to strong objects. It is shown, for the case of one spatial dimension, that the complex amplitude can be uniquely determined from the intensity distributions in two images taken at different defocus provided we know the intensity in one of the end-points of the exit pupil. It is also demonstrated how the reconstruction equations can be solved. The relation with the Gerchberg-Saxton and the similar Misell algorithm is pointed out.
Drenth et al. (1975) studied this question.