An improvement of Fourier synthesis optics for hard x-ray imaging is described, and the basic performance of the new optics is confirmed through numerical simulations. The original concept of the Fourier synthesis imager utilizes nonposition-sensitive hard x-ray detectors coupled to individual bigrid modulation collimators. The improved concept employs a one-dimensional position-sensitive detector (such as a CdTe strip detector) instead of the second grid layer of each bigrid modulation collimator. This improves the imaging performance in several respects over the original design. One performance improvement is a two-fold increase in the average transmission, from 1/4 to 1/2. The second merit is that both the sine and cosine components can be derived from a single grid-detector module, and hence the number of imaging modules can be halved. Furthermore, it provides information along the depth direction simultaneously. This in turn enables a three-dimensional imaging hard x-ray microscope for medical diagnostics, incorporating radioactive tracers. A conceptual design of such a microscope is presented, designed to provide a field of view of 4 mm and a spatial resolution of 400 microm.