DECONVOLUTION OF ONE-DIMENSIONAL MICROPROBE SCANS USING THE NONLINEAR JANSSON METHOD

Using a reliable method for deconvolution of one-dimensional microprobe scans, the spatial resolution of a microprobe could be improved by a factor of two or more, or alternatively, a measurement could be completed in a shorter time by employing a larger beam spot and a higher beam current. Nonlinear methods, which constrain the data to be everywhere positive, are less sensitive to noise in the data than linear methods. The iterative over-relaxation method of Jansson is simple to program and use. We have applied it to both simulated and real data and performed a variety of tests to assess its reliability and usefulness. We have found it to be robust and fast. The response function employed can be of any shape but we have tested only Gaussian curves, with the sum of the elements normalized to unity. Light smoothing of the initial data is desirable, with the FWHM of the Gaussian increased slightly to compensate. The convergence process can be monitored by including some extra steps, which compute at the end of each iteration the standard deviation of the differences between the data and the reconvolved latest approximation. The program can then halt when the standard deviation is no longer decreasing or has started to increase (though we have not observed this).