Abstract
The trajectories of nanoscale particles through microscale environments record useful information about both the particles and the environments. Optical microscopes provide efficient access to this information through measurements of light in the far field from nanoparticles. Such measurements necessarily involve trade-offs in tracking capabilities. This article presents a measurement framework, based on information theory, that facilitates a more systematic understanding of such trade-offs to rationally design tracking systems for diverse applications. This framework includes the degrees of freedom of optical microscopes, which determine the limitations of tracking measurements in theory. In the laboratory, tracking systems are assemblies of sources and sensors, optics and stages, and nanoparticle emitters. The combined characteristics of such systems determine the limitations of tracking measurements in practice. This article reviews this tracking hardware with a focus on the essential functions of nanoparticles as optical emitters and microenvironmental probes. Within these theoretical and practical limitations, experimentalists have implemented a variety of tracking systems with different capabilities. This article reviews a selection of apparatuses and techniques for tracking multiple and single particles by tuning illumination and detection, and by using feedback and confinement to improve the measurements. Prior information is also useful in many tracking systems and measurements, which apply across a broad spectrum of science and technology. In the context of the framework and review of apparatuses and techniques, this article reviews a selection of applications, with particle diffusion serving as a prelude to tracking measurements in biological, fluid, and material systems, fabrication and assembly processes, and engineered devices. In so doing, this review identifies trends and gaps in particle tracking that might influence future research.
Highlights
The initial condition and subsequent interaction of a particle with the surrounding environment determines the spatiotemporal trajectory of the particle
The missing three-photon coincidence signal enables a spatial resolution that is two thirds of the diffraction limit of a tracking apparatus with an electron multiplying CCD (EMCCD) camera. These results indicate the possibility of improved temporal bandwidth in comparison to photoactivated localization microscopy and comparable spatial resolution by using even higher order missing coincidences
Experimentalists from diverse backgrounds might initially approach a variety of measurements without necessarily having a clear understanding of the capabilities of optical microscopes for nanoparticle tracking
Summary
The initial condition and subsequent interaction of a particle with the surrounding environment determines the spatiotemporal trajectory of the particle. This article reviews measurements made in the far field, typically using an optical microscope equipped with a digital optoelectronic sensor, of visible to near-infrared radiation emanating from nanoparticles Such measurements are highly relevant, as optical microscopes are widely accessible to experimentalists in many fields of research and development, and a large infrastructure of optoelectronic devices is readily available to sense light under many different conditions. This is because the design of tracking systems can, and increasingly does, explicitly incorporate the assumptions underlying the use of prior information in this algorithm
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