In this contribution we discuss the possibility of designing a modified transmission X-ray microscope by using fractal zone plates (Fzps) as diffractive optical elements. In the modified transmission X-ray microscope optical layout, we first introduced a fractal zone plate as the microscope objective. Indeed, a fractal zone plate cannot only be used as an image-forming component but also as a condenser element to achieve an extended depth of field. Numerical analysis reveals that fractal zone plates and conventional Fresnel zone plates have similar imaging capabilities under different coherent illumination. Using a fractal zone plate as a condenser we also simulated axial irradiance. Results confirm that fractal zone plates can improve focusing capability with an extended depth of field. Although preliminary, these simulations clearly reveal that fractal zone plates, when available, will be of great help in microscope layouts, in particular for foreseen high-resolution applications in the "water window" as strongly required in biological research.
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