A comment on `The interpretation of x-ray rocking curves by the Fourier transform method'

Abstract

Li et al published recently a paper presenting a method for the interpretation of x-ray rocking curves to obtain crystal lattice-strain profiles in GaAs superstructures. The method is described as a phase-retrieval technique in x-ray scattering. However, the paper contains a number of questionable theoretical statements which are discussed in this comment.

Reply to a comment on `The interpretation of x-ray rocking cures by the Fourier transform method'

“…One must flip all of the zeros into the lower half plane in order to reproduce the correct profile given by equation (1) above. This example shows clearly that flipping the zeros into the lower half plane is indeed physically meaningful, contrary to the statement of Nikuin in [1]. The author of [1] cited a few of his own papers [7][8][9][10][11] to show that we should establish a firmer understanding of the inverse problem first.…”

“…This example shows clearly that flipping the zeros into the lower half plane is indeed physically meaningful, contrary to the statement of Nikuin in [1]. The author of [1] cited a few of his own papers [7][8][9][10][11] to show that we should establish a firmer understanding of the inverse problem first. In those papers a procedure to retrieve the complex diffraction amplitude by analysing two measured intensities with two radiation energies was proposed.…”

“…In his comment [1] on our paper [2], Nikulin stated, but without mathematical derivation, that equation (2) in [2] is apparently incorrect. He argued that the electron density derivation dρ/dz is zero for a perfect crystal so that the amplitude reflection coefficient in equation ( 2) [2] is zero, too.…”

“…Without this term, one does not obtain the q −2 law from equation (2) [2]. Furthermore, the Braggdiffraction amplitude for a perfect crystal as derived from equation (2) in [2] is proportional to 1/q(H + q), not to q −3 as stated by Nikulin [1]. The reason lies in the fact that, again, dρ H /dz in equation ( 2) is a Dirac-delta function, δ(z), for a perfect, semi-infinite crystal.…”

“…The process of flipping the zeros produced by the Laplace transform into the lower half plane [2] is physically meaningful. The physics on which the author of the comment [1] based his argument is, however, questionable.…”