An examination of an iterative method for the solution of the phase problem in optics and electron optics: I. Test calculations

Abstract

An evaluation is made of an iterative method for determining the amplitude and phase from the image intensity recorded in optical systems. The method, which requires two images recorded at different lens defocus values, is tested with simulated data subject to error arising from the photographic recording of the image. In the case of error-free data, the solution for the phase distribution appears to be indeterminate to within a constant. The results for photographic noise levels of up to 20% of the maximum image intensity reflect the small effect of error on the calculated phase distribution. The calculation of phase distributions for both symmetric and asymmetric amplitude-phase distributions shows that the use of two images, taken at defocus values differing by about 100 nm in electron optics and about 1 mm in optics (depending on the numerical aperture of the objective lens), may be used to determine the complex object wave-function in both dark-field and bright-field optics.