fig1 shows a geometry of cavities 14 which are formed in this exemplary embodiment from two channels 22 and 24 which do not communicate with one another the channel 22 has an inlet 21 a and two outlets 52 a and 52 b and the channel 24 has an inlet 51 b and two outlets 52 c and 52 d fig1 shows a geometry of an individual continuous cavity 14 which extends over the substrate 12 in a meandering manner from the inlet 51 to the outlet 52 fig1 shows a cavity 14 which has a circular channel 22 radially on the outside a circular channel 24 at the center and a multiplicity of radial channels 26 28 etc which connect the channels 22 and 24 together from the inlet 51 the fluid first of all passes into the radially inner channel 24 and via the spoke like radial channels 26 28 etc into the outer channel 14 and from there into the outlet 52 fig1 shows a perspective view of the substrate 12 with the channels according to fig1 fig1 shows a further configuration of the method for producing the reflective optical element 10 in fig1 in which during the fine machining of the surface 46 of the overcoating 16 according to fig7 an optically effective structure 54 is worked into the surface 46 of the.