The X pinch is a very small size radiation source in the 3-10 keV x-ray band. As such, it has been used successfully to obtain high resolution images of :5 2 mm thick biological samples ranging from small bugs (flies, beetles, etc.) to a small piece of mouse intestine. The X pinch source size as a function of the x-ray energy is important because it directly determines the spatial resolution of the imaging system. Furthermore, a small source size can provide high spatial coherence of the imaging x-rays, enabling their use for imaging low absorptionj low contrast objects with excellent spatial resolution by a method called phase-contrast imaging. In order to determine the source size, several structures have been micro-fabricated that involve gold on a membrane that is transparent to the x-rays. If these structures are imaged in point projection radiography, a finite source size will cause penumbral blurring. Therefore, the shape of the shadow image pattern depends on the source size of the x-rays, the energy band of the x-rays, the shape and material used for the structures, and the geometry of the experiment. The experimental results must be compared with wave-optics calculations for the expected image pattern as a function of all of the above parameters, but especially the source size. The several conditions for phase-contrast imaging are discussed. Examples of high-resolution images of biological objects are presented.