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Structured illumination microscopy (SIM) is part of the super-resolution methods developed at the beginning of this century. To produce a super-resolution image SIM requires three things: 1) illumination of the sample with a periodic pattern, 2) acquisition of multiple images per plane under different pattern’s phases and orientations and 3) the processing of these images has to be carried with a reconstruction algorithm. The result of the reconstruction is an image with a resolution gain that is proportional to the frequency of the pattern (po). The typical SIM set-up uses an epi-fluorescence configuration, thus the interference angle of the beams that create the pattern is restricted by the angular aperture of the objective. Under this restriction the maximum value of po is given by the cut-off frequency of the objective lens and sets at 2 the maximum resolution gain of SIM under linear illumination.
In the first part of this thesis we present the implementation and characterization of the 2D-SIM set-up designed by Dr. Bo-Jui Chang (B-J. Chang et al., PNAS 2017), this design exploits the concept introduced by light-sheet microscopy, i.e. separation of illumination and detection paths to obtain resolution gains larger than the usual two-fold (Chapter 3). The set-up is named coherent structured illumination light-sheet based fluorescence microscopy (csiLSFM) and it consists of a triangular array of three objectives, such that two are used for illumination and one for detection. With the independent illumination arms is possible to interfere two coherent light-sheets at angles beyond the angular aperture of the detection lens, attaining the maximum interference angle of 180° when the light-sheets counter-propagate. This condition delivers a pattern with a po 1.4 times larger than the cut-off frequency (ωo), hence our set-up provides generic resolution gains of 2.4.
The extraction of the high spatial frequencies that produce the resolution gain in the csiLSFM is a challenge due to a low pattern modulation. The low modulation inherently arises because the frequency associated to the pattern period lies beyond the cut-off frequency of the detection lens. To overcome this challenge we developed a filtering strategy that facilitates the withdrawal of information from a SIM data set, simultaneously the proposed filtering process optimizes the reconstruction algorithm by reducing the periodic artifacts that are recurrent in SIM images. In this same chapter we also performed an spectral analysis of the artifacts and determined that they originate from irregularities in the power spectrum that occur due to the partial or total lack of certain spatial frequencies (fig.4.2 and 4.3), our reconstruction reduces this information drops and diminishes the artifact occurrence. The relevance of our reconstruction pipeline is that it delivers a standardized process to enhance the SIM image in a current context in which the commonly used reconstruction algorithms employ empirical tuning to improve it (fig.4.13). Moreover, the pipeline is applicable to the csiLSFM data and also to images acquired with any other 2D-/3D-SIM set-up (fig.4.10 and 4.11).
The processing of various image data sets acquired with the csiLSFM exposed us to the question of how low the modulation of the illumination pattern can be before no super-resolution frequencies can be extracted. Answering this question is important to guarantee that the SIM data contains enough spatial frequencies to provide significant resolution gains. Thus in chapter 5 we developed a quantitative metric to indirectly determine the pattern modulation from the SIM data and find its critical value to use it as evaluation criterion. We called this metric the quality factor (Q-factor) and it represents the normalized strength (amplitude) of the extracted frequencies respect to the Gaussian noise contained in the images. Through simulations we estimated that Q=0.11 is a critical value and a SIM data set requires this as minimum value is to deliver a significant resolution gain. Q works then as an assessment tool for classifying SIM data as optimal or sub-optimal, i.e. Q≥0.11 or Q<0.11. We demonstrated such application with data acquired in various SIM commercial set-ups to prove its feasibility in the field (fig.5.6-5.11)
As mentioned at the beginning of this abstract SIM requires a specialized set-up and a processing algorithm to produce super-resolution images. This thesis contributes to these two areas in the following aspects: first, in its linear version a structured illumination microscope is highly associated to a 2-fold resolution gain. Here we demonstrated the possibility of extending this gain to 2.4 using our custom set-up the csiLSFM. Second, a reconstructed SIM image is prone to artifacts due to the mathematical process it undergoes, here we analyzed the artifact sources and identified them with drops of spatial information in the reconstructed spectrum, based on these conclusions we designed a processing pipeline to facilitate the extraction of spatial frequencies and directly reduce artifacts. A third and final outcome of this thesis is the development and practical implementation of a quantitative index to evaluate the quality of SIM data in terms of its relevant information content (Q-factor). Accordingly, the overall contributions of this work were done in the areas of SIM set-up, SIM reconstruction procedure and SIM data evaluation.