  Incommensurate charge density waves (CDW) have the extraordinary ability to
display non-Ohmic behavior when submitted to an external field. The mechanism
leading to this non trivial dynamics is still not well understood, although
recent experimental studies tend to prove that it is due to solitonic
transport. Solitons could come from the relaxation of the strained CDW within
an elastic-to-plastic transition. However, the nucleation process and the
transport of these charged topological objects have never been observed at the
local scale until now. In this letter, we use in-situ scanning x-ray
micro-diffraction with micrometer resolution of a NbSe$_3$ sample designed to
have sliding and non-sliding areas. Direct imaging of the charge density wave
deformation is obtained using an analytical approach based on the phase
gradient to disentangle the transverse from the longitudinal components over a
large surface of a hundred microns size. We show that the CDW dissociates
itself from the host lattice in the sliding regime and displays a large
transverse deformation, ten times larger than the longitudinal one and strongly
dependent on the amplitude and the direction of the applied currents. This
deformation continuously extends across the macroscopic sample dimensions, over
a distance 10 000 times greater than the CDW wavelength despite the presence of
strong defects while remaining strongly pinned by the lateral surfaces. This 2D
quantitative study highlights the prominent role of shear effect that should
play a significant role in the nucleation of solitons.
