Because of the growing demand for more advanced electric devices, an exponential growth of the number of transistors are supposed to be integrated into a single chip. To manufacture devices in the scale of nanometer cost-effectively, an accurate measurement for lithography process calibrating is necessary. Ptychography is a computational imaging technique which has the potential to serve as a metrology solution for semiconductor devices. It can reconstruct complex-valued permittivity function of an object from an extensive set of measured intensities of the diffraction patterns in the far field. It should be noted that also 2D and 3D a-periodic objects can be measured with this technique. Currently, this technique has been widely used in reconstructing thin and weakly scattering (satisfying the first Born approximation) objects in a transmission geometry (detectors and sources are placed on different sides of the objects).We propose an accurate 3D ptychography multi-layer Born model, and apply it to reconstruct refractive index distributions of semi-conductors. This model slices the sample into thin layers and first Born approximations are applied to each layer sequentially. For a transmission geometry, this model considers both forward scattering effects and backward scattering effects \cite{Chen2020Multi-layerMicroscopy}, as opposed to normal beam propagation models. For reflection geometry (detectors and sources are placed on the same side of the object), this model collects reflected fields on each layer of the sample and these fields will interact with the object again later together with other upwards fields. This procedure enables detectors arranged in a reflection geometry to gather complete information about the object. We implement the model on the existing ptychography platform based on the auto-differentiation (AD) solvers and manage to reconstruct high-resolution images of 3D objects.

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.

Cameras are used in various applications and one such common application has been space. Delfi Space is the CubeSat Development program of the Delft University of Technology and a subprogram of Defi-Space is Delfi-PQ which aims to develop PocketQubes which are an order of magnitude smaller than the CubeSat standards. One of the advanced payloads that would potentially be a part of the Delfi-PQ is an imager/camera. The imager needs to be as small as possible in order to fit into the Delfi-PQ satellites. The design of the camera has remained the same throughout the years and one of the reasons that increase the thickness of the camera is the presence of lenses. A way to reduce the size of the camera would be to remove the lens out of the equation. However, this introduces additional problems and trade-offs in the camera. These lenses can be replaced by masks/coded apertures. One of the additional steps in using coded-apertures is that additional computational steps need to be performed in order to reconstruct the image. The kind of computation that needs to be performed depends on the kind of masks that would be used. In this thesis, a separable mask is chosen and computer simulations on separable masks have been performed. Two image sensors that can be used in the picosatellite were chosen for implementation and the hardware/software is designed and developed. The experimental setup for determining the field of view of a lensless camera has been developed and tested. One of the trade-offs observed through the experiments is that the acceptance angle of a lensless imager had reduced by 38 percent and 31.8 percent in the horizontal and vertical directions compared to a conventional lens-based system. Based on the experimental results, the field of view of the camera has also been determined. A singular value decomposition based method has been developed and is used to align and calibrate the camera with the mask. The final step is estimating the system matrices of the lensless system. The system matrices enable the perfect reconstruction and a complete realization of a separable mask based lensless camera. A scheme for estimating the system matrices of the lensless imager using Hadamard basis is proposed and confirmed using simulations and the strategy for experimental verification is proposed. As far as we know, this is the first study that focuses on designing and developing a lensless camera in the visible light domain for use in picosatellites.