We present the first results of high-spatial resolution x-ray imaging studies with an upgraded version of the scanning photoemission multiple application x-ray imaging undulator microscope. The microscope is a multilayer coated Schwarzschild objective that focuses undulator radiation onto the sample. The recent upgrade improved the spatial resolution by a factor six reaching a full width at half maximum value of 0.5-mu-m. Highly polished mirrors reduced the diffuse background by almost two orders of magnitude and drastically improved the contrast. The improved microscope was used to perform a series of tests on microgrids and reverse Fresnel zone plates. The microscope capability to detect chemical and topological contrast was verified by using patterned metal overlayers on Si and GaAs substrates. Further improvements to increase the flux and the spatial resolution are underway; this includes the installation of a new undulator beamline.