The Research On Axial Super Resolution In Total Internal Reflection Fluorescence Microscopy

Benefit from the advantage of wide-field illumination,total internal reflection fluorescence microscopy(TIRFM)has been becoming a powerful tool to study live sub-cellular structures at molecule level with the low phototoxicity and high signal-to-noise ratio.Since the axial resolution of TIRFM is still in wide-field range,Multi-angle total internal reflection fluorescence microscopy(Multi-angle TIRFM)was proposed.In this technique,the images sequences were obtained at different penetration depths by changing the incident angle of the light.Then,the mathematical forward model was constructed by the images sequence acquired from multiple angles.And the 3D structure of the sample can be reconstructed using alternating direction method of multipliers(ADMM)to achieve axial super-resolution.In this study,aiming at the problem of strict selection of the parameter in ADMM algorithm,we present an improved reconstructed method,named relaxed-alternating direction method of multipliers(r-ADMM)to reconstruct 3D structure of the sample in Multi-angle TIRFM,which can achieve an axial resolution of 40 nm,and improve the convergence speed of the reconstruction,and be less dependent on selection of the parameter.Firstly,the principle of TIRFM,classification and application have been introduced based on evanescent field theories in this paper,and the theory of Multi-angle TIRFM imaging technology has been explored.The mathematical forward model between the Multi-angle images,the intensity distribution of the light field at different incident angles,and the 3D position distribution of the sample has been established.Then,the solving ways of the inverse problems about the forward model have been given,and transformed into the solution of the convex optimization problems.Secondly,several typical methods solving the convex optimization problems have been summarized,in which ADMM algorithm enjoys faster convergence and higher robustnessthrough analysis and comparison.While the parameter is sensitive to convergence in ADMM algorithm,the r-ADMM algorithm for solving optimization problems has been given.Then we analyzed the convergence of the primal and dual residuals for ADMM algorithm and r-ADMM algorithm with the same penalty parameter ? value,and compared the iterations for the two algorithms with different penalty parameter ? value.Experimental results show that the convergence speed of the iterates is improved by more than 20% in r-ADMM algorithm,and the ? value has poor effect on the iterations.Then we simulated the microtube structure and reconstructed the 3D structure using r-ADMM algorithm,the mean square error(MSE)between the reconstructed microtubules and ground truth is 21 nm,ensuring the quality of image reconstruction.Finally,the Multi-angle TIRFM setup has been built,in which the image stacks of the fixed tubulin sample in Pt-K2 cells,the fixed tubulin sample in Vero cells and the mitochondria in live U20 S cells at 20 angles starting from 62° with an interval of 0.3° can be acquired.Then,the image stacks of the fixed tubulin sample in Pt-K2 cells were reconstructed by the PPXA,ADMM and r-ADMM algorithms,respectively.The reconstruction results with reconstruction time show that r-ADMM algorithm is the optimal method for reconstruction,since it can improve the reconstruction speed while achieve a 40 nm axial resolution.The image stacks of the fixed tubulin sample in Vero cells were reconstructed by the ADMM and r-ADMM algorithms,and the images of microtubules at different depths reconstructed by r-ADMM algorithm were given.The image stacks of mitochondria in live U20 S cells was reconstructed by r-ADMM algorithm,and we took a sequence of 10 image stacks with a time interval of 2s,where the consecutive processes of active mitochondrial fusion and fission were successfully recorded,ensuring the reliability of the reconstruction algorithm.