The quality of the multiple solutions produced after application of the tangent formula are assessed
by three figures of merit. ABSFOM is a measure of the internal consistency
of the triplet phase relationships.
We can define 
as the expectation value of 
for a random
set of phases and is given by [37]
ABSFOM is defined as
For a poor solution with near random phases ABSFOM
while for a good solution
where 
approaches its estimated value 
, ABSFOM
.
The second FOM is defined as
and tests how far the triplets deviate from their statistically predicted behaviour. The lowest values of RESID will generally indicate the best solutions.
The third FOM is
The summations w.r.t 
are taken over the 
weak reflection which are output after
normalisation. The summation term over 
in the numerator is equivalent to the right hand side
of Sayre's equation (Eq. 
) and is taken over all the triplet phase relationships
linking the weaker structure factors to those structure factors for which phases have been evaluated. The
numerator will therefore tend to be small if the phases of 
and 
calculated by the Tangent formula are correct, thus giving a low value of PSIZERO.
A final combined FOM , CFOM is calculated using,
where the subscripts 
and 
refer to the maximum and minimum values of the FOM's of
all the solutions given by the Tangent formula and 
are weights with 
, 
and 
. CFOM has a maximum value of 3.0 and a minimum value of 0. The weights have been
determined from experience. ABSFOM is generally considered to be the least reliable of the
three FOM's and is given a lower weight.
