Freeform optics for space instruments

The thesis addresses the growing demand for compact and high-performance optical systems in modern space exploration, particularly for miniaturized platforms such as CubeSats. Traditional rotationally symmetric optics often fail to deliver wide fields of view or high spectral resolution without increasing system size and complexity. To overcome these limitations, the work explores the use of freeform optical surfaces, which lack translational or rotational symmetry and enable more compact architectures with enhanced performance. After reviewing space optical systems and key principles (first-order parameters, diffraction limit, signal-to-noise ratio, exposure time), the thesis presents mathematical models for freeform surfaces, including orthogonal polynomials (Zernike, Chebyshev), splines, radial basis functions, and NURBS. It also introduces Nodal Aberration Theory (NAT) to analyze and control aberrations in non-symmetric systems. Practical applications demonstrate the benefits of freeform optics. In an Offner spectrometer, freeform surfaces increase the field of view and spectral resolution while maintaining compactness and low weight. The thesis also presents the design of a 2U hyperspectral CubeSat camera, integrating telescope and spectrometer with freeform surfaces, validated through tolerance analysis. The research shows that freeform optics are a transformative technology for next-generation space instruments, enabling reduced volume and mass without sacrificing optical quality, thus supporting both high-performance and miniaturized platforms.