The Extended Nijboer-Zernike Diffraction Theory and its Applications

Abstract

In present-day society, we encounter optical systems on a daily basis. Most people have a DVD player capable of playing content stored on an optical disc, Big Brother is watching us nearly everywhere using surveillance cameras and we consider it to be normal to take photographs with our mobile phone. Also, in less visible areas, such as ultrafast fiber-based data transfer, we rely on optical technology. Although these applications might be considered advanced by the general public, they mostly do not reflect the state of perfection that is currently needed by the scientific and high-tech community. When we speak of advanced optical systems in this context we refer to highly corrected optical systems or optical systems having extreme optical properties. For example, in astronomy, huge optical telescopes are used to produce images of faint astronomical objects located deep in space and also in microscopy, high quality optics are applied to visualize the smallest possible details in a sample such as a living cell. However, by far the most cutting edge optical technology is applied in the semiconductor industry. A process called optical lithography is used to transfer geometrical patterns, that are part of a chip design, into a layer of photosensitive material. Using chemical technology these patterns are developed into metallic and insulating structures and, repeating lithographic pattern transfer and chemical development several times in succession, it is possible to produce a working electronic circuit or chip at the nanometer scale. The above mentioned applications of optical technology have in common that they require extremely accurate optical components. This is because the objects that they try to visualize or image are so small and faint that even the smallest aberration effects can completely conceal the features of interest. One might think that reducing the aberrations to a low level simplifies the task of simulating these systems. Unfortunately, this is not true. In fact, at this level of perfection, various optical phenomena, that would otherwise have negligible effect in comparison to the imperfections of the optical system, become significant. Therefore, existing optical methods should be extended to properly include these effects in order to allow a sensible analysis of the performance of optical systems in this regime. In addition, also the errors introduced by approximations used in image simulation models become significant and this makes it favorable to apply those methods with the smallest number of incorporated approximations. Although there has been, in recent years, a large research effort by the optical community to extend existing optical methods to correctly describe this class of systems, the results so far have not been totally satisfactory. As an alternative, we present in this thesis a novel optical model that we believe is superior in the accurate description and simulation of image formation. The formation of an image by an aberrated optical system is accurately described by the corresponding diffraction integral. However, until recently, this integral could only be evaluated numerically to obtain the three-dimensional image structure. This changed in 2002 with the introduction of the Extended Nijboer-Zernike (ENZ) theory. This theoretical framework, extensively described in this thesis, provides a generally valid analytic solution to the diffraction integral. Based on this result we have constructed a novel imaging model that includes all relevant physical effects and applies very few approximations. The resulting ENZ imaging method proposed in this thesis is, therefore, well suited to accurately describe image formation by advanced optical imaging systems. The second important contribution presented in this thesis pertains to the quality assessment of optical systems. It is shown that it is possible to determine the quality of an optical system by evaluating the image it produces from a point object. This is possible because the analytic results provided by the ENZ theory allow us to devise an expression for the intensity image of a point object. Matching the measurement data with this expression enables complete characterization of the optical system under study without the need of additional complicated optical set-ups. Altogether, we present in this thesis a comprehensive ENZ formalism that can be used to accurately simulate image formation by a large variety of imaging systems. The most important feature of ENZ imaging is its high accuracy that follows from the semi-analytic nature of the ENZ theory and the few approximations applied in the ENZ imaging model. Additionally it is shown that the aberrations of an optical system can be obtained from intensity measurements alone, introducing an appealing alternative to interferometric methods that are commonly applied for this purpose. Finally, both applications of the ENZ theory are illustrated by a number of practical examples, clearly showing the large potential of the ENZ formalism in the field of advanced optical imaging systems.