A modification to the tangent formula of Karle and Hauptman was made by
Germain et al [37], the main difference being the inclusion of a weighting
scheme into the formula. The most likely value, 
, of the phase 
, in
this case, is given by
where 
and 
are the weights associated with 
and 
.
The corresponding weight 
which is assigned to may be calculated using
The corresponding value of 
given by Eq. 
is modified to
This weighted Tangent formula has been implemented in the computer program package MULTAN80 [81]. The program takes a multi-solution approach to solving the phase problem, i.e. having identified a `good' triplet phase relationship (the starting set) at which to start calculating phases using other triplet invariants, it generates a number of different solutions starting with different permutations of the values of phases assigned in the starting set. All solutions are then tested by means of three figures of merit (FOM's) which hopefully indicate the correct solution(s).
The program function may be summarised by a series of logical steps, the major points of which will be described in more detail afterwards.
are normalised to give 
. The strongest 
reflections are output along with 
of the weakest for use in calculation of the FOM's.
, 
and 
). All phase relationships with 
in Eq.
less than 0.6 are rejected.
and their associated are calculated
for the best solutions as determined by the FOM's.
