The significance of the phase synthesis

Abstract

This paper gives an account of the results of the tests that have been carried out to assess the relative importance of the phase angles and structure amplitudes in a Fourier synthesis. For this, the phase factors, e^ia, have been combined in different ways with structure amplitudes such as when the latter are (a) replaced by the r.m.s. of the structure amplitudes (i.e., by √Σf_i²), (b) randomly chosen from the set of correct structure amplitudes, (c) made us much anti-correlated (about the mean) with the correct ones as possible and (d) taken to be those of an entirely different structure. The above syntheses which are only modifications of the phase synthesis, e^ia, have been tested on both the centrosymmetric and non-centrosymmetric projections of a known structure. They strongly establish the greater importance of the phase angles in a Fourier synthesis.