Angle-resolved X-ray photoelectron spectroscopy (ARXPS) can be used non-des
tructively to find the depth-distribution of chemical species. Although the
experimental technique has been available for 25 years or more, approximat
ely 20 different methods for calculating concentration depth-profile inform
ation from measured data have been published in this time. Some of the algo
rithms were originally developed in other areas of applied science, and imp
licitly impose vestigial constraints on the depth-profile inherited from th
eir original application. In this paper we examine (1) why constraints are
important, (2) which constraints are possible, and (3) which constraints ar
e valid for different classes of XPS analysis problems. It is shown that th
ree distinct regions of prior knowledge exist, and by fixing appropriate co
nstraints for each in rum we reach definite conclusions on how to improve r
egularization methods for calculating depth-profiles from ARXPS data. (C) 1
999 National Physical Laboratory. Published by Elsevier Science B.V. All ri
ghts reserved.