ON WAVEFRONT ABERRATIONS IN ASYMMETRIC AND MULTIPLE APERTURE OPTICAL SYSTEMS

The present work deals with monochromatic wavefront aberrations in optical systems without symmetries. The treatment begins with a class of systems characterized by misaligned spherical surfaces whose behavior is analyzed using the wavefront aberration expansion proposed in the framework of the Nodal Aberration Theory (NAT). It is derived the full field behavior of the Zernike polynomials in the Fringe indexing scheme for this class of systems. Then, the attention is focused on a more general class of asymmetric systems where the misaligned surfaces can be individually double-plane symmetric. In this case, considering aberrations up to the 4th order, it is shown that the field dependence of Zernike terms is described by general second-degree polynomials. The presence of double-plane symmetric optical surfaces induces additional perturbations to the magnitude of the field variation of primary aberrations for this class of systems. In particular, one observes that coma aberration acquires an elliptical conic shape in the field domain, while the full field variation of primary astigmatism magnitude is described by a class of surfaces that we define as â generalized Cassini surfacesË® because these are more general than the standard Cassini surfaces describing the binodal behavior of astigmatism in the class of optical systems analyzed with NAT wavefront aberration expansion. These considerations are preliminary to the discussion of the second part of this thesis whose scope is to analyze monochromatic wavefront aberrations in a further class of systems, namely optical systems characterized by multiple apertures. In this sense, it is first introduced a general description of the wavefront aberration function in the framework of Hamiltonian Optics. This consists of a full power series expansion in the ray coordinates that provides the most general representation of optical systems without symmetries. These introductory remarks are necessary to carry out the analysis of optical systems with many apertures. Such a class of systems is well represented by light field (or plenoptic) cameras. Their general structure consists of a main objective followed by an ensemble of apertures whose function is to divide the field of view into many partitions. Each aperture defines an optical channel. The partial overlap between adjacent field of view partitions serves to extract depth information from the scene in a similar manner to stereo cameras. The wavefront aberration analysis of this class of systems is primarily based on the definition of an ensemble of base-rays playing the role of reference axis for the various channels. The wavefront error for each optical channel is described with a general power series in the ray coordinates expanded about the inherent base-ray. Finally, different approaches are expounded to calculate and visualize the evolution of the aberration behavior of the various channels of this class of optical systems.