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In order to relate nanoparticle properties to function, fast and detailed particle characterization, is needed. The ability to characterize nanoparticle samples using optical microscopy techniques has drastically improved over the past few decades; consequently, there are now numerous microscopy methods available for detailed characterization of particles with nanometric size. However, there is currently no ``one size fits all'' solution to the problem of nanoparticle characterization. Instead, since the available techniques have different detection limits and deliver related but different quantitative information, the measurement and analysis approaches need to be selected and adapted for the sample at hand. In this tutorial, we review the optical theory of single particle scattering and how it relates to the differences and similarities in the quantitative particle information obtained from commonly used microscopy techniques, with an emphasis on nanometric (submicron) sized dielectric particles. Particular emphasis is placed on how the optical signal relates to mass, size, structure, and material properties of the detected particles and to its combination with diffusivity-based particle sizing. We also discuss emerging opportunities in the wake of new technology development, with the ambition to guide the choice of measurement strategy based on various challenges related to different types of nanoparticle samples and associated analytical demands.

Traditional single-nanoparticle sizing using optical microscopy techniques assesses size via the diffusion constant, which requires suspended particles in a medium of known viscosity. However, these assumptions are typically not fulfilled in complex natural sample environments. Here, we introduce dual-angle interferometric scattering microscopy (DAISY), enabling optical quantification of both size and polarizability of individual nanoparticles without requiring a priori information regarding the surrounding media or super-resolution imaging. DAISY achieves this by combining the information contained in concurrently measured forward and backward scattering images through twilight off-axis holography and interferometric scattering (iSCAT). Going beyond particle size and polarizability, single-particle morphology can be deduced from the fact that hydrodynamic radius relates to the outer particle radius while the scattering-based size estimate depends on the internal mass distribution of the particles. We demonstrate this by optically differentiating biomolecular fractal aggregates from spherical particles in fetal bovine serum at the single particle level.

Through digital imaging, microscopy has evolved from primarily being a means for visual observation of life at the micro- and nano-scale, to a quantitative tool with ever-increasing resolution and throughput. Artificial intelligence, deep neural networks, and machine learning are all niche terms describing computational methods that have gained a pivotal role in microscopy-based research over the past decade. This Roadmap is written collectively by prominent researchers and encompasses selected aspects of how machine learning is applied to microscopy image data, with the aim of gaining scientific knowledge by improved image quality, automated detection, segmentation, classification and tracking of objects, and efficient merging of information from multiple imaging modalities. We aim to give the reader an overview of the key developments and an understanding of possibilities and limitations of machine learning for microscopy. It will be of interest to a wide cross-disciplinary audience in the physical sciences and life sciences.

Video microscopy has a long history of providing insights and breakthroughs for a broad range of disciplines, from physics to biology. Image analysis to extract quantitative information from video microscopy data has traditionally relied on algorithmic approaches, which are often difficult to implement, time consuming, and computationally expensive. Recently, alternative data-driven approaches using deep learning have greatly improved quantitative digital microscopy, potentially offering automatized, accurate, and fast image analysis. However, the combination of deep learning and video microscopy remains underutilized primarily due to the steep learning curve involved in developing custom deep-learning solutions. To overcome this issue, we introduce a software, DeepTrack 2.0, to design, train and validate deep-learning solutions for digital microscopy. We use it to exemplify how deep learning can be employed for a broad range of applications, from particle localization, tracking and characterization to cell counting and classification. Thanks to its user-friendly graphical interface, DeepTrack 2.0 can be easily customized for user-specific applications, and, thanks to its open-source object-oriented programming, it can be easily expanded to add features and functionalities, potentially introducing deep-learning-enhanced video microscopy to a far wider audience., Comment: 25 pages; 13 figures

The characterisation of the physical properties of nanoparticles in their native environment plays a central role in a wide range of fields, from nanoparticle-enhanced drug delivery to environmental nanopollution assessment. Standard optical approaches require long trajectories of nanoparticles dispersed in a medium with known viscosity to characterise their diffusion constant and, thus, their size. However, often only short trajectories are available, while the medium viscosity is unknown, e.g., in most biomedical applications. In this work, we demonstrate a label-free method to quantify size and refractive index of individual subwavelength particles using two orders of magnitude shorter trajectories than required by standard methods, and without assumptions about the physicochemical properties of the medium. We achieve this by developing a weighted average convolutional neural network to analyse the holographic images of the particles. As a proof of principle, we distinguish and quantify size and refractive index of silica and polystyrene particles without prior knowledge of solute viscosity or refractive index. As an example of an application beyond the state of the art, we demonstrate how this technique can monitor the aggregation of polystyrene nanoparticles, revealing the time-resolved dynamics of the monomer number and fractal dimension of individual subwavelength aggregates. This technique opens new possibilities for nanoparticle characterisation with a broad range of applications from biomedicine to environmental monitoring.