The scientific community recognizes the critical role played by ptychography in nanoscale imaging. Compared with the conventional imaging, which has high requirements on the manufacturing of optical elements, ptychography, as a computational imaging technique, uses a set of measured intensities of the diffraction patterns to reconstruct the image of the object and hence no imaging system is needed. This technique is especially useful in the short wavelength, e.g. EUV, regime, where manufacturing high quality optical elements such as mirrors is extremely expensive. Most of the present ptychographic algorithms require the illumination of the object to be both spatially and temporally coherent so that the diffraction pattern can be interpreted as the intensity of the Fourier transform of the field exiting the object. However, the coherence of the sources that produce the EUV radiation often cannot be guaranteed. Therefore, it is crucial to extend the ptychography method to consider partial coherence effects. This requires the use of a flexible propagator which depends on the wavelength to deal with the temporal partial coherence and a modal representation for the spatially partially coherent field. Also, the ambiguity of the reconstructed modes of the probe will be solved by an orthogonalization approach, which could enhance the reproducibility of the results. These methods will be implemented on an existing ptychography platform based on automatic-differentiation and will be validated using both simulation data and experimental data.

In this thesis, several phase retrieval methods are discussed. Since the focus will mainly be on theory rather than experiment, the structure has been determined by the similarities and differences of the mathematics of these methods. For example, a distinction is made between non-iterative and iterative methods, and between single-shot iterative phase retrieval and multiple-shot iterative phase retrieval (ptychography). However, it must be noted that phase retrieval methods that are mathematically similar, are suitable for fundamentally different experimental setups. For example, one can consider setups for lensless imaging, of which an interesting application is metrology using Extreme Ultraviolet (EUV) radiation. In such setups, no focusing optics are used, and one typically computes an image from far-field intensity patterns. On the other hand, there are setups for aberrated imaging. In these setups, one does use focusing optics to form images, but by introducing some sort of variations or perturbations, one can generate a set of images from which a complex-valued field can be computed. For example, regular ptychography and Fourier ptychography are mathematically the same, but the former is used for lensless imaging, while the latter is used for aberrated imaging. Mathematically, the only difference between these two ptychographic approaches is that the roles of object space and Fourier space are interchanged.@en

This thesis demonstrates the feasibility of Extreme-ultraviolet (XUV) high-harmonic generation from structured silica, and was performed at the Advanced Research Centre for Nanolithography (ARCNL). The project focuses on High-harmonic generation (HHG) from condensed matter, and further explores the possibility of high-harmonic generation from micro- and nano-structured silica. HHG from solids was discovered less than a decade ago, and it is expected to be a new source for coherent ultrafast pulses, showing potential in many applications such as HHG spectroscopy, imaging and photonic devices. By generating high-harmonics in structured solids, the capability to control HHG properties by engineering the topology of the surface on solids has been demonstrated. Previous research has demonstrated the control of HHG in the visible light regime by generating from structured semiconductors. In this project, we aim to generate high-harmonics in the XUV regime, and control the properties of XUV light. Our work shows the potential of using structured dielectric materials as new XUV optics, and applications on HHG high-resolution lens-less imaging.

The importance of inverse problems is paramount in science and physics because their solution provides information about parameters that cannot be directly observed. This thesis discusses and details the application of a few inverse methods in optical imaging, metrology and inspection of lithographic targets, particularly patterned structures on top of an extreme ultraviolet (EUV) lithographic mask...@en