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Optimizing freeform systems can encounter convergence difficulties due to the many degrees of freedom that these surfaces bring to optical systems. Moreover, the description of these freeform surfaces in a polynomial basis may impose prior knowledge on the shape of the surface. In this presentation, we will showcase a differential ray tracer with NURBS capabilities called FORMIDABLE. In contrast to available commercial optical design software, such as Zemax OpticStudio and Synopsys Code V, this library ican simulate and especially optimize Non-Uniform Rational B-Spline (NURBS) surfaces. The key advantage of NURBS lies in their ability to locally describe an optical surface, thereby minimizing preconceived notions about the surface shape, aside from the surface sampling determined by the density of the NURBS representation. The main drawback, however, is the significant increase in the degrees of freedom within the optical system, making the optimization of these surfaces a complex task with a conventional commercial optical design software. FORMIDABLE's implementation of differential ray-tracing capabilities allows faster convergence of systems described by many degrees of freedom and makes optimization with NURBS surfaces viable. The features of FORMIDABLE will first be described. Then its capabilities will be illustrated with the optimization of a classical non-reimaging Three-Mirror Anastigmat (TMA) by considering either a description of surfaces by NURBS or a description by the polynomial basis XY. Then, this optimized TMA will be compared with its equivalent optimized with Zemax OpticStudio. To enable this software comparison, we will use the same starting point and practically the same merit function. Standard metrics, such as Root Mean Square (RMS) spot size across the field of view (FOV) will be used to assess the imaging quality.
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