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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 ≤2 min 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 absorption, 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.