  We introduce spatial deformations to an array of light sources and study how
the estimation precision of the interspacing distance, d, changes with the
sources of light used. The quantum Fisher information (QFI) is used as the
figure of merit in this work to quantify the amount of information we have on
the estimation parameter. We derive the generator of translations, G, in d due
to an arbitrary homogeneous deformation applied to the array. We show how the
variance of the generator can be used to easily consider how different
deformations and light sources can effect the estimation precision. The single
parameter estimation problem is applied to the array and we report on the
optimal state that maximises the QFI for d. Contrary to what may have been
expected, the higher average mode occupancies of the classical states performs
better in estimating d when compared with single photon emitters (SPEs). The
optimal entangled state is constructed from the eigenvectors of the generator
and found to outperform all these states. We also find the existence of
multiple optimal estimators for the measurement of d. Our results find
applications in evaluating stresses and strains, fracture prevention in
materials expressing great sensitivities to deformations, and selecting
frequency distinguished quantum sources from an array of reference sources.
