Soft X-rays are very suitable for the examination of biological samples by means of an X-ray microscope. The X-rays are generated by focusing an electron beam onto a fluid jet, thus producing a very small electron focus on the jet and hence a very small monochromatic X-ray spot. The electron spot can be obtained by means of a standard electron microscope (a SEM) or by means of a standard electron gun for a cathode ray tube (a CRT gun). The imaging optical elements in the X-ray microscope may be Fresnel zone plates.