Abstract
The spatial resolution of conventional optical microscopy is limited by diffraction to transverse and axial resolutions of about 250 nm, but localization of point sources, such as single molecules or fluorescent beads, can be achieved with a precision of 10 nm or better in each direction. Traditional approaches to localization microscopy in two dimensions enable high precision only for a thin in-focus layer that is typically much less than the depth of a cell. This precludes, for example, super-resolution microscopy of extended three-dimensional biological structures or mapping of blood velocity throughout a useful depth of vasculature. Several techniques have been reported recently for localization microscopy in three dimensions over an extended depth range. We describe the principles of operation and typical applications of the most promising 3D localization microscopy techniques and provide a comparison of the attainable precision for each technique in terms of the Cramér-Rao lower bound for high-resolution imaging.
Highlights
Fluorescent point sources are widely used in science and engineering as tracers of velocity fields, indicators of mechanical forces, and labels of biological structures
The importance of point localization microscopy arises from its ability to enable fundamental advances in fields ranging from biomedicine to physics and engineering
The techniques discussed in this article have enabled precise point localization in all three dimensions and in an extended axial region, with a localization precision comparable to that which can be achieved in 2D
Summary
Fluorescent point sources are widely used in science and engineering as tracers of velocity fields, indicators of mechanical forces, and labels of biological structures. A number of techniques have emerged in recent years which optically encode the axial position of a particle in the recorded image and enable localization through an axial range that exceeds the conventional DOF. These techniques, together with their necessary procedures for digitally postprocessing images to recover the positions of particles, encompass the field of 3D localization microscopy Results from this field have extended super-resolution microscopy for 3D imaging through thick samples and have enabled investigation of the dynamics of biological processes such as blood-flow mapping and 3D single-molecule tracking within a cell. Provided that a suitable model of the image-formation process exists, all techniques can be compared using an information-based description of the measurement of the emitter position In this way, a theoretical limit of the localization precision can be derived as the Cramér-Rao lower bound (CRLB) of the estimate of the particle position.. A key benefit of MUM is that it can be used to image extended objects, whereas the emphasis for PSF-engineering has been on localization of PSFs that are the images of pointlike objects. There is the opportunity to use MUM/MFM in combination with engineered PSFs for even better localization precision, as has been done using an astigmatic PSF47–49 and an Airy-beam-based PSF.
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