Localization of Nonblinking Point Sources Using Higher-Order-Mode Detection and Optical Heterodyning: Developing a Strategy for Extending the Scope of Molecular, Super-resolution Imaging

Abstract

While the stochastic, "blinking" nature of fluorescent systems has enabled the super-resolution of their localization by the fitting of their point-spread functions (PSFs), this strategy cannot be exploited for similar resolution of "nonblinking" systems, such as those that might be encountered in a coherent Raman experiment. An alternative method for subdiffraction-limited imaging lies in the exploitation of optical heterodyning. For example, if a Gaussian PSF (a TEM00 mode) of a point emitter is displaced with respect to the origin of the optical system, photons in the higher-order TEM modes carry information about that displacement. Information concerning the displacement can be extracted from photons in these higher-order modes. These photons can be collected by optical heterodyning, which exploits the large gain in a detector's response to an optical signal from an emitter coupled to a local oscillator, which is prepared in the TEM of interest, e.g., TEM10. We have generalized and developed the heterodyning technique to localize point emitters via the detection of higher-order spatial modes. We have developed a theoretical approach to find a practical estimation limit of the localization parameters using a realistic model that accounts for shot noise, background noise, and Gaussian noise. To demonstrate the applicability of the method, we designed experiments in which a laser is a surrogate for one and two point emitters. Using the Fisher information and its accompanying Crameŕ-Rao lower bound, we demonstrate super-resolution localization in these cases: we show that objects can be localized to roughly 2−3 orders of magnitude of their point-spread function's size for a given optical system. Finally and most importantly, it is suggested that the results will ultimately be generalizable to multiple emitters and, most importantly, to "nonblinking" molecular systems, which will be essential for broadening the scope of super-resolution measurements beyond the limits of fluorescence-based techniques.

Information regret tradeoff relation for locating two incoherent optical point sources

“…Concretely, spatial mode demultiplexing (SPADE) has a much better performance than direct imaging for resolving two incoherent point sources [7]. Since then, many efforts have been devoted to pursuing the super-resolution of incoherent imaging, e.g., experimental implementations [8][9][10][11][12][13][14][15][16][17][18][19][20] and some theoretic generalizations [21][22][23][24][25][26][27][28][29][30] (see Ref. [31] for a recent review).…”