A zone plate composed of Mo zones having $4\mathrm{mm}$ outermost zone diameter, $100\mathrm{nm}$ outermost zone width, and supported on a silicon nitride membrane was characterized using monochromatic synchrotron radiation in the 2 to $20\mathrm{nm}$ wavelength range. The zero and first order efficiencies were measured and compared to ab initio calculations that account for the optical properties of the materials, the width and shape of the zones, and multiple-layer thin-film effects. It is shown that the thicknesses of the Mo zones and the membrane and the ratio of the zone width to zone period can be independently determined from the measured diffraction efficiencies in the zero and first orders and that the computational code can be used to reliably design zone plates that are optimized for applications such as solar irradiance monitors in the extreme ultraviolet region.