3D Structured Illumination Microscopy Reaching Minimal Measurement Uncertainty

The idea of structured illumination to improve the lateral resolution of an optical system has been existing for a long time and was firstly suggested by Lukosz and Marchand in1963. Nevertheless, it took nearly further40years until this method could be efficiently implemented in the field of microscopy, which is owed to the rapid development of the computational performance and the high accurate and fast linear actuators.Although different structured illumination microscopes have been presented in the last decade on the market, it still exist some important open questions. Very important is hereby the knowledge about the minimal axial uncertainty and how to achieve it. Thereby it is necessary to analyze the error budget of the main error sources to the axial uncertainty. The main error sources are hereby the systematic error determine the axial distance information, the inaccurate phase shift of the structured illumination and the photon noise. This analysis provides information about the accuracy of the phase shift for the structured illumination and which algorithm causes the smallest systematic error. The error analysis leads further to the question of an improved design of such systems, especially with respect to the optimal spatial frequency of the structured illumination and the optimal pixel pitch of the digital sensor in order to minimize the axial uncertainty.The published information about the mentioned questions above are very limited. For the minimal required position accuracy of the structured illumination no information are detectable. Similarly, the influence of the photon noise on the axial uncertainty has not been studied yet, neither the systematic error of different existing algorithms. Furthermore, the optimal spatial frequency to achieve a minimal axial uncertainty has not been analyzed in literatures yet.To analyze the axial uncertainty of structured illumination microscopy with incoherent light, a wave optical model of the microscope based on Fourier optics is realized. The model is used as tool to simulate the signal evaluation of structured illumination microscopes and to vary the spatial frequency of the structured illumination in order to analyze the influence on the axial uncertainty. Additionally, the error budget of the most important error sources can be determined individually. The wave optical model is the base to simulate a new algorithm which is robust against inaccurate phase steps. The good accordance between experimental and simulation results confirm the correctness of the wave optical model. Beside results based on numerical simulations an analytic calculation is presented which results in the optimal spatial frequency of structured illumination microscopy when a minimal axial uncertainty should be obtained.A consequence of the analytic approach is the fact that the axial uncertainty is decreasing for increased full well capacity of the digital sensor and thus recommends to increase the pixel size. But increasing the pixels has consequences on the resolution and the image quality. The question is how far the Nyquist criterion can be violated to ensure that the edges can be localized with subpixel accuracy. This investigation analyzes the systematic error and the error caused by photon noise for different algorithms. The experimental and simulation results are matching very well and confirm to increase moderately the pixel size and to violate the Nyquist criterion.In summary the main content in the thesis are as follow:(1) Determine the axial uncertainty for different error sources:Systematical error of different algorithms, phase shift error caused by inaccurate phase shift of the stripe pattern and the error caused by photon noise. These errors are analyzed by a wave optical model.(2) Determine analytically the optimal fringe pattern frequency in order to minimize the axial uncertainty by photon noise. Analytical closed form solutions are presented, which allow calculating the axial uncertainty depending on the spatial frequency of the stripe pattern, the axial sampling distance and the signal-to-noise ratio of the digital sensor.(3) As result of the error analysis the optimal sampling distance of the digital sensor has to be determined influence the measurement uncertainty. For this investigation the measurement uncertainty of localized edges under influence photon noise is analyzed for different algorithms. This analysis shows that the accuracy of edge localization can be increased by violation the Nyquist criterion.(4) A new algorithm for structured illumination microscopy systems with incoherent light is presented which is robust against inaccurate phase shifting of the structured illumination. Preliminary experimental results confirm the function of the algorithm.