We present a fast calculation of the electromagnetic field near the focus of an objective with a high numerical aperture (NA). Instead of direct integration, the vectorial Debye diffraction integral is evaluated with the fast Fourier transform for calculating the electromagnetic field in the entire focal region. We generalize this concept with the chirp z transform for obtaining a flexible sampling grid and an additional gain in computation speed. Under the conditions for the validity of the Debye integral representation, our method yields the amplitude, phase and polarization of the focus field for an arbitrary paraxial input field on the objective. We present two case studies by calculating the focus fields of a 40 x 1.20 NA water immersion objective for different amplitude distributions of the input field, and a 100 x 1.45 NA oil immersion objective containing evanescent field contributions for both linearly and radially polarized input fields.

We designed a fluorescence correlation spectroscopy (FCS) system for measurements on surfaces. The system consists of an objective-type total internal reflection fluorescence (TIRF) microscopy setup, adapted to measure FCS. Here, the fluorescence exciting evanescent wave is generated by epi-illumination through the periphery of a high NA oil-immersion objective. The main advantages with respect to conventional FCS systems are an improvement in terms of counts per molecule (cpm) and a high signal to background ratio. This is demonstrated by investigating diffusion as well as binding and release of single molecules on a glass surface. Furthermore, the size and shape of the molecule detection efficiency (MDE) function was calculated, using a wave-vectorial approach and taking into account the influence of the dielectric interface on the emission properties of fluorophores.

Fluorescence correlation spectroscopy (FCS) has emerged as a powerful technique for measuring low concentrations of fluorescent molecules and their diffusion constants. In FCS, the experimental data is conventionally fit using standard local search techniques, for example, the Marquardt-Levenberg (ML) algorithm. A prerequisite for these categories of algorithms is the sound knowledge of the behavior of fit parameters and in most cases good initial guesses for accurate fitting, otherwise leading to fitting artifacts. For known fit models and with user experience about the behavior of fit parameters, these local search algorithms work extremely well. However, for heterogeneous systems or where automated data analysis is a prerequisite, there is a need to apply a procedure, which treats FCS data fitting as a black box and generates reliable fit parameters with accuracy for the chosen model in hand. We present a computational approach to analyze FCS data by means of a stochastic algorithm for global search called PGSL, an acronym for Probabilistic Global Search Lausanne. This algorithm does not require any initial guesses and does the fitting in terms of searching for solutions by global sampling. It is flexible as well as computationally faster at the same time for multiparameter evaluations. We present the performance study of PGSL for two-component with triplet fits. The statistical study and the goodness of fit criterion for PGSL are also presented. The robustness of PGSL on noisy experimental data for parameter estimation is also verified. We further extend the scope of PGSL by a hybrid analysis wherein the output of PGSL is fed as initial guesses to ML. Reliability studies show that PGSL and the hybrid combination of both perform better than ML for various thresholds of the mean-squared error (MSE).

No abstract