Light scattered by multilayer coated extreme ultraviolet (EUV) optics is a cause of concern in EUV lithography due to its contribution to flare. Because of the extremely small wavelength of light, even subnanometer roughness on mirror surfaces can cause significant scattering. Flare is usually assumed to be an incoherent additive background, which reduces intensity modulation in the image. However, this is not universally true since flare can add coherently under certain conditions depending on the illumination coherence and mirror roughness properties. Coherent addition of flare can lead to speckle-like fluctuations in the image causing undesirable artifacts in a lithography system such as linewidth variation and line edge roughness. We experimentally observed this phenomenon in the recorded images of a pinhole using a Schwarzchild objective based EUV microscope. These images reveal a high contrast speckle pattern in the scattered halo around the specularly reflected beam. The overall distribution of scattered light is directly related to the power spectral density of roughness on the mirror surfaces. In order to better understand the potential influence of this in a lithography system, we simulated imaging of various object patterns by "rough optics." Simulation results indicate that the speckle effect is not likely to cause appreciable image degradation if current design goals for EUV lithography systems which call for sub-0.5 nm roughness on mirror surfaces are met.