We describe a camera to record coherent scattering patterns with a soft-x-ray free-electron laser (FEL). The camera consists of a laterally graded multilayer mirror, which reflects the diffraction pattern onto a CCD detector. The mirror acts as a bandpass filter for both the wavelength and the angle, which isolates the desired scattering pattern from nonsample scattering or incoherent emission from the sample. The mirror also solves the particular problem of the extreme intensity of the FEL pulses, which are focused to greater than ${10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ . The strong undiffracted pulse passes through a hole in the mirror and propagates onto a beam dump at a distance behind the instrument rather than interacting with a beam stop placed near the CCD. The camera concept is extendable for the full range of the fundamental wavelength of the free electron laser in Hamburg (FLASH) FEL (i.e., between 6 and $60\mathrm{nm}$ ) and into the water window. We have fabricated and tested various multilayer mirrors for wavelengths of 32, 16, 13.5, and $4.5\mathrm{nm}$ . At the shorter wavelengths mirror roughness must be minimized to reduce scattering from the mirror. We have recorded over 30,000 diffraction patterns at the FLASH FEL with no observable mirror damage or degradation of performance.