Abstract: A method of predicting thermally induced aberrations of a projection system for projecting a radiation beam, the method comprising: calculating an irradiance profile for at least one optical element of the projection system from a power and illumination source pupil of the radiation beam, estimating a temperature distribution as a function of time in the at least one optical element of the projection system using the calculated irradiance profile for the at least one optical element of the projection system; calculating the thermally induced aberrations of the projection system based on the estimated temperature distribution and a thermal expansion parameter map associated with the at least one optical element of the projection system, wherein the thermal expansion parameter map is a spatial map indicating spatial variations of thermal expansion parameters in the at least one optical element of the projection system or a uniform map.

Abstract: The invention provides a method for thermo-mechanical control of a heat sensitive element (Ml) subject to a heat load, comprising: -providing a non-linear thermo-mechanical model of the heat sensitive element describing a dynamical relationship between characteristics of the heat load and deformation of the heat sensitive element; -calculating a control signal on the basis of an optimization calculation of the non-linear model, -providing an actuation signal to a heater (HE), wherein the actuation signal is at least partially based on the control signal, -heating the heat sensitive element by the heater on the basis of the actuation signal.