Efficient sampling for three-dimensional atom probe microscopy data

The best calculation of concentration profiles, isoconcentration surfaces or Gibbsian interfacial excesses from three-dimensional atom-probe microscopy data requires a compromise between spatial positioning error and statistical sampling error. For example, sampling from larger spatial regions decreases the statistical error, but increases the error in spatial positioning. Finding the appropriate balance for a particular calculation can be tricky, especially when the three-dimensional nature of the data presents an infinite number of degrees of freedom in defining surfaces, and when the statistical error is changing from one region of a sample to another due to differences in collection efficiency or atomic density. We present some strategies for approaching these problems, focusing on efficient algorithms for generating different spatial samplings. We present a unique double-splat algorithm, in which an initial, fine-grained sampling is taken to convert the data to a regular grid, followed by a second, variable width splat, to spread the effective sampling distance to any value desired. The first sampling is time consuming for a large dataset, but needs only be performed once. The second splat is done on a regular grid, so it is efficient, and can be repeated as many times as necessary to find the correct balance of statistical and positioning error. The net effect is equivalent to a Gaussian spreading of each data point, without the necessity of calculating Gaussian coefficients for millions of data points. We show examples of isoconcentration surfaces calculated under different circumstances from the same dataset.