In certain applications, it is very desirable to maintain the temperature or the temperature profile of an optical mirror device on a given and in particular on a constant level.  Examples for such applications are in particular EUV (Extreme Ultra Violet) illumination and projection optics operating with illumination light wavelengths, in particular in the range between 10 nm and 30 nm.  These optics generally have to operate in ultra high vacuum environment since the EUV photons are absorbed by atmospheric gases.  Reflective and diffractive elements are generally the only possible optical elements to form and to guide EUV radiation since there is no transparent material available for this wavelength.  Since it is very difficult to produce reflective coatings for mirror elements having a reflectivity close to 1 as a rule a portion of light hitting a mirror surface will be absorbed by the optical coating and/or the mirror substrate underneath.  This absorbed radiant power in turn heats up the mirror substrates and, due to thermal expansion, changes the surface figure and consequently the optical properties of the mirror which is undesirable.  In particular regarding EUV wavelengths this residual absorption leads to absorbed radiant powers which are not at all negligible.  Temperature stabilization for high-quality optical mirrors faces several drawbacks since the surface figures of high quality optical mirrors are sensitive to parasitic forces and thus the mirror holding and suspension design has to be optimized for minimum parasitic forces and torques.  Minimizing stiffness for appropriate force and torque directions often goes along with reducing cross-sections available for heat conduction.  Therefore, a good holding structure in terms of minimum parasitic forces always is a bad thermal conductor raising thermal load problems on the mirror.  Since in particular in EUV illumination systems the mirrors are held under vacuum, no gases can be used for mirror cooling purposes.  Water cooling of a mirror substrate is problematic since water flowing through channels and tubes always gives rise to dynamic excitation of structural eigen-modes and therefore gives undesired vibrations.  Ultra low expansion ceramics as the materials Zerodur made by Schott or ULE made by Corning which tolerate temperature changes to a certain amount are expensive and not easy to manufacture. 
US 2004/0035570 A1 and US 2004/0051984 A1 show a mirror cooling method involving on radiation heat transfer.  These mirror cooling systems involve on a controlled cooling of a heat sink.  A rising thermal load on the mirror can be compensated by lowering the temperature of a cold surface of the heat sink.