Helical point spread functions (PSFs) provide a powerful computational imaging tool for modern optical imaging and sensing applications. However, their utilization is, so far, limited to a single field of application, i.e. super-resolution microscopy, which is due to multiple shortcomings in their current system implementation. A new computational imaging approach is developed in this thesis, which enables the utilization of helical PSFs and their unique advantages for applications in the area of machine vision. In particular, the approach can be used to acquire the three-dimensional distribution of a passively illuminated, extended scene in a single shot based on a compact, monocular camera setup. A novel image processing routine is established to overcome a major challenge of computational imaging using helical PSFs, i.e. the retrieval of the PSF rotation angle in the case of an extended object distribution. The hardware implementation of computational imaging setups that rely on helical PSFs is based on a combination of a conventional optical element, such as a microscope objective or a camera lens, and an additional, dedicated pupil mask. This mask is commonly realized using either a spatial light modulator or a lithographic element that features a structured surface profile. Two new fabrication schemes with different advantages are explored in this thesis. The first scheme utilizes wafer-scale optical lithography in combination with UV-replication in order to fabricate highly cost efficient phase elements. The second method is based on femto-second laser direct writing. It enables the inscription of the phase element directly inside a transparent optical element using a single fabrication step. Therefore, it facilitates a flexible realization of highly integrated PSF engineered optical systems. Current design concepts for pupil masks that generate helical PSFs only focus on doublehelix distributions that feature two, laterally separated irradiance peaks. Furthermore, a diffraction limited performance of the computational imaging system is assumed. A new design method that enables the generation of multi-order-helix PSFs with an arbitrary number of rotating peaks is developed in this thesis. A study of the influence of first order aberrations on the rotation angle of multi-order-helix PSFs is performed in order to assess their effect on the accuracy limits with respect to three-dimensional imaging. In this context, the superior aberration robustness of high-order-helix PSFs featuring three or more rotating spots is demonstrated. Whereas, on the one hand, the effect of aberrations on helical PSFs degrade the depth retrieval accuracy of three-dimensional imaging systems, their influence can be explored in order to obtain information on the system’s wavefront aberrations on the other hand. To this end, the computational imaging approach developed for three-dimensional imaging is extended and combined with a conventional phase diversity method. The novel approach enables a numerically efficient estimation of general wavefront aberrations based on the acquisition of an extended, unknown object scene. In summary, the research performed in this thesis provides the foundation to exploit the unique advantages of computational imaging systems based on helical PSFs for applications in the area of three-dimensional imaging and wavefront sensing. @en

A practical method for determining wavefront aberrations in optical systems based on the acquisition of an extended, unknown object is presented. The approach utilizes a conventional phase diversity approach in combination with a pupil-engineered, helical point spread function (PSF) to discriminate the aberrated PSF from the object features. The analysis of the image’s power cepstrum enables an efficient retrieval of the aberration coefficients by solving a simple linear system of equations. An extensive Monte Carlo simulation is performed to demonstrate that the approach makes it possible to measure low-order Zernike modes including defocus, primary astigmatism, coma, and trefoil. The presented approach is tested experimentally by retrieving the two-dimensional aberration distribution of a test setup by imaging an extended, unknown scene.

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