This dissertation investigates various design metrologies on designing freeform surfaces for LED illumination applications. The major goal of this dissertation is to study designing freeform optical surfaces to redistribute the radiance (which can be simplified as intensity distribution for point source) of LED sources for various applications. Nowadays many applications, such as road lighting systems, automotive headlights, projection displays and medical illuminators, require an accurate control of the intensity distribution. Freeform optical lens is commonly used in illumination system because there are more freedoms in controlling the ray direction. Design methods for systems with rotational and translational symmetry were well discussed in the 1930's. However, designing freeform optical lenses or reflectors required to illuminate targets without such symmetries have been proved to be much more challenging. For the simplest case when the source is an ideal point source, the determination of the freeform surface in a rigorous manner usually leads to the tedious Monge-Ampère second order nonlinear partial different equation, which cannot be solved with standard numerical integration techniques. Instead of solving the differential equation, ray mapping is an easier and more efficient method in controlling one or more freeform surfaces for prescribed irradiance patterns. In this dissertation, we investigate the ray mapping metrologies in different coordinate systems to meet the integrability condition for generating smooth and continuous freeform surfaces. To improve the illumination efficiency and uniformity, we propose a composite ray mapping method for designing the total internal reflective (TIR) freeform lens for non-rotational illumination. Another method called "double pole" ray mapping method is also proposed to improve system performance. The ray mapping designs developed for the point source do not work well for extended sources, we have investigated different design methodologies including optimization method, deconvolution method and feedback modification method to design freeform optical surfaces for extended sources.

Naturally occurring biological nanoparticles (BNPs) and synthetic nanoparticles have a significant role in a wide range of biomedical applications. For instance, direct detection of BNPs, such as viruses, can provide new methods of viral diagnostics while synthetic particles can be used as labels to indirectly detect biomarkers for drug discovery. Therefore, developing advanced tools for nanoparticle detection has gained popularity in biotechnological research. One of the most exciting recent developments in BNP detection has been single particle (or digital) counting of individual particles which offers unprecedented sensitivity levels. However, standard optical techniques face a significant challenge for nanoparticle detection, due the weak optical contrast of sub-wavelength particles. Interferometric microscopy, overcomes the limitations imposed by particle size which allows for visualizing unresolved (diffraction-limited) optical signatures of sub-wavelength particles. Single-particle interferometric reflectance imaging sensor (SP-IRIS), is a widefield microscopy platform, developed by our group over the last years. SP-IRIS uses interferometric enhancement and a layered substrate to increase the optical contrast for the target particles of interest. While this microscopy technique has shown remarkable sensitivity levels for numerous applications including detection of viral particles and nucleic acids, it has remained a specialty tool due to the utilization of z-scan measurements for extracting the optical signature of particles. The z-scan measurements that consist of multiple frames acquired at different focal positions impose two major drawbacks. The first is the requirement of repeatable and high resolution scanning optics and the second is the time and computational processing power required to analyze the image stacks. In this thesis we describe a novel imaging method termed `pixel-diversity‘ IRIS (PD-IRIS), which aims to provide a more practical detection method for nanoparticles by eliminating the need for acquiring z-stacks. PD-IRIS is built upon SP-IRIS, however it introduces a paradigm shift for encoding the necessary optical signature of target particles. PD-IRIS compresses the relevant optical information within a single image frame rather than an image stack. This is achieved by using camera sensors that simultaneously record multiple spectral or polarization channels. Therefore, a single image can record distinct spectral responses of target particles with respect to different excitation wavelengths (multi-spectral PD-IRIS) or the distinct scattering characteristics with respect to polarization (polarization PD-IRIS). This dissertation presents a rigorous study for both PD-IRIS modes and demonstrates the practical applications of nanoparticle detection with proof-of-concept measurements. / 2024-01-16T00:00:00Z