Protoplanetary disks (PPDs) have gained substantial attention due to their crucial role in planet formation. Observing their features in the far-infrared (FIR) spectrum has been challenging due to limitations in current optics and detectors, with proposed missions requiring a spectrometer with a spectral resolving power on the order of magnitude of 100,000. A promising solution is the virtually imaged phased array (VIPA), which could surpass the commonly used Fabry-Perot etalon and diffraction grating spectrometers. However, due to their novelty, VIPAs have seen limited applications in space and lack a numerically efficient model, preventing confi- dent recommendation for FIR spectroscopy. In this project, a one-dimensional (1D) analytical VIPA model with a numerically efficient implementation using Gaussian beam formalism was developed, showing close alignment with an advanced 2D model by Hu et al. (2015) based on the angular spectrum of plane waves. The new model demonstrated potential for VIPAs to meet the spectral resolving power required for space missions and showed the possibility to be further expanded to 2D for higher accuracy, while retaining high efficiency. An experimental setup for verifying the simulation results was proposed. The interplay between various device parameters, coupled with the numerous degrees of freedom required for aligning the optical setup, presented significant experimental challenges. Additionally, investigations into the design of inductive metal mesh mir- rors, supported by simulations in COMSOL and MATLAB, uncovered several difficulties that were thoroughly explored. The analytical VIPA model based on Gaussian beam propagation shows promise as a method for optimizing a VIPA for high-resolution far-infrared spectroscopy but further research and experimental validation are necessary to fully establish its efficiency and effectiveness. The project was a collaboration between TU Delft and the Netherlands Institute for Space Research (SRON).

A significant focus of current and next-generation astronomical research is the study of exoplanets and the formation of habitable conditions in planetary systems. This requires high-performance spectrom- eters operating in the far-infrared (FIR) range, with the Fabry-Pérot etalon being the state-of-the-art solution. This thesis, a collaboration between TU Delft and the Netherlands Institute for Space Research (SRON), focused on identifying and overcoming the major performance limitations of the Fabry-Pérot. The performance metrics were spectral resolving power and transmission. The major performance lim- itation was identified to be diffraction, which is particularly relevant in the FIR range. A two-part model was developed based on Gaussian beam propagation and the Huygens-Fresnel principle. Gaus- sian beam propagation is a well-established method that takes diffraction effects into account but is limited to the paraxial approximation, which quickly breaks down in the FIR. The novel application of the Huygens-Fresnel principle to Fabry-Pérot propagation modeling accounts for diffraction effects and remains accurate with large beam divergence caused by diffraction. The Gaussian beam approach was used to validate initial results from the Huygens-Fresnel approach. The effect of diffraction on critical device dimensions, such as cavity length, beam waist, finite aperture, and mirror tilt was investigated. Additionally, an experiment design was proposed to further validate the model. This included research into the design of metal mesh mirrors and silicon-air distributed Bragg reflector mirrors using COMSOL and MATLAB simulations. The successful results of the Huygens-Fresnel model provide new insights into the constraints on critical dimensions of the Fabry-Pérot etalon due to diffraction effects. These insights can be used to propose high-performance Fabry-Pérots designs suitable for the exploration of exoplanets.

Linear Variable Filters (LVFs) are integral to future space missions aimed at measuring the spectral features of distant galaxies. Given the varying red-shifts (shift of light to longer wavelengths as an object moves away from the observer) of these galaxies, an LVF with a resolving power of approximately 10 can effectively identify, classify, and image large populations of galaxies, facilitating studies of cosmic evolution through hyperspectral imaging (HSI) techniques. HSI captures detailed spectral information across a wide range of wavelengths for each pixel in an image, enabling material identification and analysis. Since the galaxies to be studied are very faint, hyperspectral imagers need to be equipped with highly sensitive detectors, cryogenically cooled conditions, and filters with high transmission efficiency. This thesis investigates LVFs based on thin membranes, focusing on materials like silicon nitride (Si3N4) and silicon carbide (SiC). The primary objective is to model these thin and pre-stressed membranes using COMSOL Multiphysics to simulate the thermal expansion and mechanical behaviour of membranes in cryogenic environments. Experimental validation is conducted using Digital Holography Microscopy (DHM) and Laser Doppler Vibrometry (LDV) to ensure the accuracy and consistency of the simulations. The model enables the simulation of membranes with varying dimensions, improving the accuracy of behavioural predictions thereby eliminating the need for physical prototypes for analytical purposes, significantly reducing cost and time. Overall, this research bridges the gap between theoretical models and practical applications of LVFs in space. Enhancing the understanding of material behaviour under extreme conditions advances the development of reliable LVFs for spaceborne optical instruments, offering valuable insights into their durability and performance.

Despite advances in astronomy, much of the universe remains hidden behind gas and dust clouds that absorb optical radiation, making it undetectable by conventional telescopes. Far-Infrared (FIR) radiation is capable of propagating through these clouds, and offers a solution for observing these obscured interstellar regions. However, the sensitivity of existing detector systems is insufficient to detect FIR radiation effectively. This thesis focuses on the development of highly sensitive detectors based on Microwave Kinetic Inductance Detectors (MKIDs) that meet the sensitivity requirement for use in future space missions, specifically the NASA led POEMM and PRIMA missions, covering a frequency range from approximately 1.5 THz to 12 THz.

While detectors have been developed previously covering the upper band of this frequency range at 6.98 THz and 12 THz, the lower band remains uncovered. Therefore, lens-absorber coupled MKIDs designed to operate at 1.5 THz are presented, with their performance analysed using models based on the Geometrical Optics-Fourier Optics (GOFO) technique in combination with a Floquet wave approach for periodic absorbers. Additionally, the design methodology of MKIDs to operate at specific readout frequencies is discussed. Absorber coupled MKIDs are limited to lower resonance frequencies with respect to comparable antenna based MKIDs, which offer advantages for space-based missions due to reduced power consumption, but do present challenges for readout systems operating at higher frequencies. In this thesis, two lens-absorber coupled MKID designs were developed and are currently being fabricated as candidates to experimentally demonstrate highly sensitive detector arrays operating at 1.5 THz.

The imaging spectrometers in the POEMM and PRIMA missions require a dispersive element to separate different wavelengths of the incoming radiation. The dispersive element envisioned for these missions, the Virtually Imaged Phased Array (VIPA), suffers from non-idealities, causing phase aberrations in the transmitted field, and part of the power transmitting towards unwanted propagation directions, which can degrade instrument performance. This thesis presents and analyses optimisation techniques to mitigate these effects, thereby enhancing the overall efficiency and degrees of freedom for designing the full instrument.

Furthermore, absorbers, unlike antenna-based devices, are multi-mode detectors. Understanding how absorbers couple to higher-order modes is crucial for optimising their performance. This thesis introduces and validates a model based on a novel experimental technique, Energy Absorption Interferometry (EAI), to extract a modal description of detectors. In the future steps related to the POEMM mission, the findings from this initial investigation into multi-mode absorbers will be used to gain insight and explore possible improvement routes in the coupling of these detectors to complex optical systems.

In this thesis, an efficient optimization method is described for synthesizing lens antennas fabricated in low permittivity plastic materials to achieve wide scanning performances. The method is based on an antenna in reception representation. The optimized parameters are the location and orientation of the antenna feeder, lens angular region and its shape by adding Zernike polynomials to standard ellipsoidal shape. The synthesized lens antennas achieve scan losses lower than 3dB while scanning up to 60°. The presented theoretical results are validated using full wave simulations. Furthermore, an efficient analysis method based on Geometrical Optics and ray tracing is developed. This method is applied to the study of multi lens Quasi-Optical structures. The presented theoretical results are validated by multi surface Physical-Optics approach.