In the field of astronomical X-ray telescopes, different types of optics based on grazing incidence mirrors can be used. This contribution describes the special design of a lobster-eye optics in Schmidt's arrangement, which uses dual reflection to increase the collecting area. The individual mirrors of this wide-field telescope are made of at silicon wafers coated with reflecting iridium layers. This iridium coatings have some advantages compared to more common gold layers as is shown in corresponding simulations. The iridium coating process for the X-ray mirrors was developed within a cooperation of the Aschaffenburg University of Applied Sciences and the Czech Technical University in Prague. Different mirror parameters essential for a proper function of the X-ray optics, like the surface microroughness and the problematic of a good adhesion quality of the coatings were studied. After integration of the individual mirrors into the final lobster-eye optics and the corresponding space qualification testing it is planned to fly the telescope in a recently proposed NASA rocket experiment.