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Using for a one-dimensional centrosymmetric structure of  m  equal point scatterers an  m -dimensional coordinate parameter space  P  m  and the ( n  – 1) independent ratios  q ( h, k ) = [ I ′( h )/ I ′( k )] 1/2  =  g ′( h )/ g ′( k ) of  n  &gt; 1 structure amplitudes observed on relative scale it is shown that the determination of the structure or possibly homometric structures is equivalent to finding the common intersection(s) of ( n  – 1) ≥  m  independent isosurfaces  Q [ h, k; q ] of dimension ( m  – 1).A fast and efficient reduction of the parameter space to the fraction(s) of   P  m   that contain(s) the solution(s) can already be achieved on the basis of the qualitative inequalities between the observations. Therefore, emphasis is put on showing that each  q ( h, k )  &lt;  1,  i.e.  g ′( h ) &lt;  g ′( k ) (or vice versa) rules out all the regions in  P  m  that contain point scatterer arrangements incompatible with  q ( h, k ). For small structures, solution strategies are discussed and an estimate is given on the number of data necessary for solving even ‘tough’ problems.

Structure determination without Fourier inversion. Part II: The use of intensity ratios and inequalities