In this study a silicon wafer was analysed by angle-resolved x-ray photoelectron spectroscopy and the data compared with a calculation based upon a simple model of the sample surface. The parameters in the mathematical model were varied in groups of three and the sum-squared difference between the calculation and the experimental results was plotted as an error surface. Most of the error surfaces were found to exhibit a well-constrained minimum, indicating an optimum set of values for the parameters in question, but important examples of co-dependency were also noted. Copyright (C) 2003 John Wiley Sons, Ltd.