Light scattering enables the interrogation of nanoscale systems with minimal perturbation to their dynamics. However, this advantage of optical techniques is partially offset by requiring complex inference procedures to accurately estimate physical quantities of interest from features extracted by the optical measurement. In this thesis, I investigate optical techniques for the characterization of nanoparticle properties in solutions, the associated statistical inference problems and consider how nanosensors can be used to extend optical methods to probe nanoscale systems.

In the first part, we consider how multiwavelength light scattering combined with statistical inference can be applied to Photon Correlation Spectroscopy. By viewing the inverse problem of size distribution estimation within the Bayesian framework, a method for extracting an uncertainty quantified (UQ) estimate of the size distribution is presented. The technique is further generalized from a static inverse problem to a dynamic one, allowing sequences of temporally spaced measurements to be inverted simultaneously. Next, a novel single-particle tracking configuration is presented for simultaneous dual colour scattering inside hollow-core anti-resonant (HC-ARF) fibres at microsecond timescales. Simultaneous monitoring of multiple scattering signals allows observation of transient signatures linked to the reorientation of particles as they undergo rotational diffusion. The second part of the thesis considers transmission modulation in nanoapertures caused by local refractive index changes due to nanoparticles flowing through them. Protocols for the fabrication of nanoapertures are presented for gold films deposited on thin silicon nitride membranes. Effects of aperture parameters on optical response investigated using Finite-Difference Time-Domain (FDTD) simulations. Optical transmission measurements are performed using a constructed transmission microscope, with the nanoapertures integrated into microfluidic chip, enabling both optical interrogation and electrical flow control. These measurements allow detection of nanoparticle translocation through the nanoapertures as well as docking and ejection of larger nanoparticle aggregates, sterically prevented from translocating. Evidence of nanoaperture geometry and surface charge variation between the metal and silicon nitride layers manifests as asymmetry in the response of the optical signal to the applied potential. Finally, to extend the optical measurement modalities available in the constructed microscope, a photon counting system based on time-to-digital converter is developed using Field-Programmable Gate-Arrays (FPGA). The system has a time resolution in the 30 ps range with continuous photon readout rates of up to 3 million counts per second, providing comparable performance to commercial instrumentation at a fraction of the cost, enabling many optical measurement techniques.