Most of the 2D studies on granular materials consider an assembly of cylindrical particles in the small deformation regime. Investigating the range of validity of the small deformation hypothesis is therefore of crucial importance in order to determine the quantitative relevance of the predictions emerging from these 2D studies. We introduce here a novel experimental setup based on high resolution imaging and image correlation, and capable of measuring the strain field inside the particles with a cutting edge accuracy. We measure the strain field inside a unique circular cylindrical elastic particle undergoing an uniaxial compression. The significant deviations arising from the comparison with the predictions of the small deformation limit predicted by the Hertz's theory, and numerical simulations, give insight to improve the modeling of 2D granular materials.