Projected thickness reconstruction from a single defocused transmission electron microscope image of an amorphous object

Abstract

Single defocused transmission electron microscope phase contrast images are used to reconstruct the projected thickness map of a single-material object. The algorithm is non-iterative and stable, and we extend it to account for the presence of spherical aberration in the objective optics. The technique can reconstruct the projected thickness map of general single-material objects in the strong phase/weak amplitude regime. It is sensitive to any excursions in the projected thickness from the average, and ideal for examining voids and free volume accumulation in amorphous/glassy materials at the nanometer scale. The resolution of the technique depends on the choice of defocus and the thickness of the specimen. In a certain regime, we demonstrate that variations in the transverse projected thickness with a lateral diameter of ∼ 0.25 nm may be detected. We use our algorithm to quantitatively reconstruct the projected thickness of latex sphere test specimens from single defocused electron micrographs. We demonstrate that the reconstruction has a large tolerance for error in the input parameters. Simulations confirm that the technique is quantitative, and demonstrate that the origin of low-frequency artifacts is an instability due to noise. We show that the autocorrelation of the projected thickness map may be used to measure the size of open structures in the object using both simulation and latex sphere data.