In modern ASML machines optical components play an important role in the lithography process. EUV light is transported from the source to wafer by reflective optics. These mirrors are subjected to large thermal loading, as a large portion of the reflected light is absorbed in the mirror structure. The portion of the absorbed light is strongly dependent on the intensity and wavelength of the considered light, introducing varying amounts of thermally induced strains on the mirror structure and thereby limiting the optical performance. Current mirror designs typically use solid mirror structures for more predictable deformations. These structures are coupled to spiral cooling channels to extract the absorbed heat to achieve more uniform temperature distributions. However, as ASML strives towards ever smaller resolutions, advances have to be found on the mirror design methodology to further reduce the thermally induced strains.
In this research, topology optimization is used as a possible method of producing designs which can minimise the thermally induced surface deformations of a mirror typically encountered when exposed to thermal loading. Due to the "multi-physics" nature of this problem, the optimization problem has to encompass thermo-mechanics, thermo-fluidics and the conjugate heat transfer at the interface of these two domains. The topology optimization formulation presented in this research, minimises surface deformations by altering the topology of the mirror structure together with the cooling channel layout producing an integrated solution.

An active fluid heat exchanger can be controlled effectively using Peltier elements to condition the temperature of the fluid flowing through the heat exchanger. The thermal resistance of the heat exchanger can be reduced to increase the speed of controlling the fluid's temperature. Topology optimization is used in this study to find the geometry of a heat exchanger with reduced thermal resistance.
The design of a heat exchanger using topology optimization requires the coupling of the fluid flow equations and the energy equation in a finite element model with a continuous design variable. The existing optimization models perform well when the goal of the optimization problem is to minimize viscous dissipation. A weighted sum multi-objective function is however necessary to optimize the thermal performance of a design, and the correct choice of weights to meet design specifications is difficult to arrive at.
The drawback in the existing model is that the conductivity distribution is defined as a function of the design variable of the optimization problem. This results in infeasible designs when the goal of the optimization problem is to minimize only thermal resistance, and this is demonstrated with several numerical examples along with a motivation for a new formulation.
A new formulation for conductivity distribution is proposed in this thesis. The new formulation defines the conductivity distribution in terms of the velocity field in the design domain. The new formulation is capable of significantly reducing the thermal resistance of the heat exchanger, and this is demonstrated with a numerical example. Finally, a 3d design case is implemented, the results of the optimization routine are post-processed and the performance of the baseline design from ASML is compared with the topology optimized design.

The stringent and conflicting requirements of optomechanical instruments and the ever-increasing need for higher resolution and quality imagery demands a tightly integrated design approach. The aim of this study is to drive the thermomechanical design of multiple components of an optomechanical instruments by the system’s optical performance. This work addresses the combination of structural-thermal-optical performance analysis and multicomponent topology optimization while taking into account both component and system level constraints. A 2D two-mirror example demonstrates that the proposed approach is able to improve the system’s spot size error by 95% compared to uncoupled system optimization to below the system's diffraction limit.