  We deform a two-dimensional (2D) foam, created in a Langmuir monolayer, by
applying a mechanical perturbation, and simultaneously image it by Brewster
angle microscopy. We determine the foam stress tensor (through a determination
of the 2D gas-liquid line tension, 2.35 $\pm$ 0.4 pJ$\cdot$m$^{-1}$) and the
statistical strain tensor, by analyzing the images of the deformed structure.
We deduce the 2D shear modulus of the foam, $\mu= 38 \pm 3 \mathrm{nN}\cdot
\mathrm{m}^{-1}$.
  The foam effective rigidity is predicted to be $ 35 \pm 3 \mathrm {nN}\cdot
\mathrm {m}^{- 1}$, which agrees with the value $37.5 \pm 0.8 \mathrm {nN}\cdot
\mathrm {m}^{-1}$ obtained in an independent mechanical measurement.
