Markov chain Monte Carlo methods in 3-D structure inversion from electron microscopy images

The ability to extract three-dimensional information from data obtained from the surface of a material is a fundamental problem in the field of non-destructive testing.

In particular two-dimensional images obtained from a scanning electron microscope (SEM) contain depth information due to the fact that an energetic electron beam produces back-scattered electrons from different depths of the sample, dependent on the beam energy. The main idea behind the work contained in the thesis is that from images obtained from electron beams of different energies over the same area of the surface of a material, three-dimensional density information about the sample can be determined.

The reconstruction technique needs to be robust because

the material density is not generally a continuous function of position as the material may contain voids or inclusions of particles of a material of different density. The reconstruction technique involved analysing the contrast of the different SEM images produced at the different energies. The images were discretised into pixels, and the interior of the material discretised into voxels whose surface area matched the pixels of the images. Mathematical techniques were then used to determine the density of the material in the voxels. The density of the material in the voxels was determined by generating random values, based on Markov Chain Monte Carlo methods, projecting them in a similar way to what a microscope would do and judging the likelihood of the random values being a true representation by comparing the projections with the image data.