We study the inverse scattering from a screen with using only one incoming time–harmonic plane wave but with measurements of the scattered wave done at all directions. Especially we focus on the 2D–case i.e. (inverse) scattering from an open bounded smooth curve. Besides the inverse scattering problem we also study the inverse electrostatic problem. We then show that one Cauchy–data of any continuous and bounded function vanishing on the screen and harmonic outside it, determines the screen uniquely.