A method is given for the evaluation, in transmission electron microscopy, of the amplitude and phase from the intensity distribution of an electron micrograph. The method requires a minimum of two micrographs taken under different defocus conditions. The iterative scheme requires only the relative defocus between micrographs, and the procedure is valid both in bright-field and dark-field microscopy for any specified coherence of the electron source. Assumptions on the scattering properties of the specimen, such as the weak-phase-weak-amplitude object, are not required. For a complete determination of the amplitude-phase distribution for electron transmission through the specimen, the electron micrograph must be corrected for the effect of lens aberrations and defocusing to give the electron wavefunction immediately after transmission; only in the case of a weak-phase object can this wavefunction be directly related to the projected potential distribution in the object.Inelastic electron scattering is explicitly omitted from the analysis presented.
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.
The application of approximate methods such as the weak-phase and the weak-phase/weak-amplitude approximations, to the analysis of conventional transmission electron microscope images is examined. The specimen thickness must be respectively less than 5 and 15nm for stained and unstained biological specimens for the valid application of the weak-phase approximation. These thickness limits can be extended to 10 and 25 nm respectively using the weak-phaselweak-amplitude approximation. The effect of specimen thickness and an error in determining the image defocus distance on the interpretation of the image (after correction for lens aberrations) is discussed. The effect of specimen thickness is to place severe restrictions on the interpretation of an image in terms of the specimen structure. The thickness effect becomes increasingly severe as the image resolution improves, so that for a specimen 5nm thick the image may be interpreted in terms of specimen structure to a resolution of 0.5 nm, whereas for a specimen thickness of 20 nm, the image may be only interpreted to a resolution of 1 nm. Suggestions are made for minimizing experimentally both the effects of specimen thickness and defocus error.
A study has been made of small-angle (1*10-4-8*10-3 rad) electron scattering in thin films of evaporated carbon for a series of incident electron energies (30-80 keV). The angular distribution of the electrons scattered in such films has been interpreted in terms of plural scattering of the incident electrons within the specimen film. The plural scattering calculations were based on both the free atom theory and the Bohm-Pines plasma oscillation theory. The two sets of theoretical calculations both agree with experiment to within a deviation of 20% for angles of scattering in the range 5*10-4-5*10-3 rad and for films thinner than about 1000AA.
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