This is a progress report on development of a new x‐ray imaging system, called a Fourier transform microscope, intended for use with x‐ray emitting targets in laser fusion experiments. It is being built by Naval Research Laboratory and Lawrence Livermore National Laboratory. The system works at energies from 3 to 7 keV. We describe the development of the design, which utilizes fine etched grids to extract Fourier amplitudes for the source brightness distribution at selected spatial frequencies. The finest grids in the prototype system will have rib dimensions of 2 &mgr;m. The prototype system is expected to achieve position resolution of 4 &mgr;m in 3–7 keV. Simulations of the expected imaging performance are presented.