A deconvolution method for obtaining nonoscillating depth distributions
Abstract
Many problems in solid state physics can be formulated as follows: find a solution ƒ(t) of an equation y(x) = K(x, t)∗ƒ(t); ∫ _{b}^{a}K(x, t)ƒ(t) dt , where a ≤ t ≤ b, c ≤ x ≤ d. y( x) is given and the kernel K( x, t) is nonnegative. Without restrictions on a set of admissible functions ƒ(t) the problem has no stable solution. Instead of this equation a functional of the type ‖ y(x)  K(x,t)∗ ƒ(t)‖ ^{2} + α·∫ ^{a}_{b}ƒ″(t) ^{2}/(1 + ƒ'(t) ^{2}) dt is considered. The minimum of the functional gives the required solution.
 Publication:

Nuclear Instruments and Methods in Physics Research B
 Pub Date:
 October 1992
 DOI:
 10.1016/0168583X(92)95293Z
 Bibcode:
 1992NIMPB..72..139Z