  The best known manifestation of the Fermi-Dirac statistics is the Pauli
exclusion principle: no two identical fermions can occupy the same one-particle
state. This principle enforces high order correlations in systems of many
identical fermions and is responsible for a particular geometric arrangement of
trapped particles even when all mutual interactions are absent [1]. These
geometric structures, called Pauli crystals, are predicted for a system of $N$
identical atoms trapped in a harmonic potential. They emerge as the most
frequent configurations in a collection of single-shot pictures of the system.
Here we study how fragile Pauli crystals are when realistic experimental
limitations are taken into account. The influence of the number of single-shots
pictures available to analysis, thermal fluctuations and finite efficiency of
detection are considered. The role of these sources of noise on the possibility
of experimental observation of Pauli crystals is shown and conditions necessary
for the detection of the geometrical arrangements of particles are identified.
