Optical microscopy is an essential tool for exploring the structures and activities of cells and tissues. To break the limit of resolution caused by diffraction, researchers have made continuous advances and innovations to improve the resolution of optical microscopy since the 1990s. These contributions, however, still make sub-10[Formula: see text]nm imaging an obstacle. Here, we name a series of technologies as modulated illumination localization microscopy (MILM), which makes ultra-high-resolution imaging practical. Besides, we review the recent progress since 2017 when MINFLUX was proposed and became the inspiration and foundation for the follow-up development of MILM. This review divides MILM into two types: point-scanning and wide-field. The schematics, principles and future research directions of MILM are discussed elaborately.

Three-dimensional structured illumination microscopy (3D-SIM) plays an essential role in biological volumetric imaging with the capabilities of improving lateral and axial resolution. However, the traditional linear 3D algorithm is sensitive to noise and generates artifacts, while the low temporal resolution hinders live-cell imaging. In this paper, we propose a novel 3D-SIM algorithm based on total variation (TV) and fast iterative shrinkage threshold algorithm (FISTA), termed TV-FISTA-SIM. Compared to conventional algorithms, TV-FISTA-SIM achieves higher reconstruction fidelity with the least artifacts, even when the signal-to-noise ratio (SNR) is as low as 5 dB, and a faster reconstruction rate. Through simulation, we have verified that TV-FISTA-SIM can effectively reduce the amount of required data with less deterioration. Moreover, we demonstrate TV-FISTA-SIM for high-quality multi-color 3D super-resolution imaging, which can be potentially applied to live-cell imaging applications.

Three-dimensional structured illumination microscopy (3D-SIM) is an essential tool for volumetric fluorescence imaging, which improves both axial and lateral resolution by down-modulating high-frequency information of the sample into the passband of optical transfer function (OTF). And when combining with the 4Pi structure, the performance of 3D-SIM can be further improved. The reconstruction results of generally used linear 3D algorithm, however, are lack of high-fidelity and proneess to generate artifacts. In this paper, we proposed a novel iterative algorithm based on gradient descent combined with a nonlinear optimizer, which can be applied to all 3D-SIM setups (including I5S setup). We verified through simulation that the proposed solution, termed as nonlinear gradient descent structured illumination microscopy (NGD-SIM), achieves more fidelity results which can reach the limitation of theoretical resolution improvement of SIM. Moreover, it can be firmly validated on simulation that this algorithm can effectively reduce the amount of raw data in the case of sinusoidal-pattern illumination, i.e., the algorithm doesn’t need five-step phase shifting; data with any number of phases can theoretically be reconstructed. Our method also provides the possibility to extend the application of sinusoidal-pattern illumination to any kind of interference fringe, which is generated by diversified types of illumination mode.

In recent years, modulated illumination localization microscopy (MILM) methods have been proposed to provide around two-fold improvement in lateral localization precision over conventional single molecule localization microscopy methods with the same photon budget. However, MILM with laterally modulated illumination was so far reported in twodimensional imaging modalities. To fully exploit its three-dimensional (3D) imaging potential, we propose a 3D Single-Molecule Modulated Illumination Localization Estimator (3D-SMILE) that uses the raw data measured from MILM, which has enabled a high localization precision that reaches the theoretical Cramér-Rao lower bound (CRLB) in all three dimensions. 3D-SMILE is based an optimal joint fitting algorithm implemented on a graphics processing unit (GPU) for acceleration. We have shown in simulations that the average lateral localization precision of 3D-SMILE has been improved by more than 3.5 folds over 3D-SMLM over an imaging depth range of around 1.2 μm.

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