Imaging past the Nyquist Edge using a Novel Stationary Optical Spectrometer

As a rising freshman, I participated in the Optics Science Olympiad event. The experimental portion of the event particularly interested me. Given several optical devices, I was tasked with designing and executing an experiment that demonstrated a concept such as dispersion or refraction. This experience sparked my interest in optics. I volunteered as an assistant coach for the event in high school, where I gained a deeper understanding of the field through teaching others. This experience made me want to further pursue the field, so I reached out to Professor Y. Fainman, the head of the UC San Diego nanophotonics lab. I was fortunate to be accepted as a volunteer intern starting the summer after my freshman year. I began by just assisting my mentor with data collection, but I gradually grew my understanding until I could contribute to a project on my own. By the end of my sophomore year, I was ready to begin working on the analysis of spectrometers. I applied my mathematics training to analyze how light interference could work with novel geometries derived from Albert Abraham Michelson’s classic experiment, and this led to my research paper. I’ve always loved working with new tools and concepts, and once I understood the relevant background, I was able to make my own contribution … Oftentimes, light that we see is comprised of many different wavelengths. A device called a spectrometer is needed to determine exactly which wavelengths make up the light emitted or absorbed from an everyday light source. Knowing this information has important practical benefits, from determining the identity of specific chemical compounds to analyzing the motion of stars and planets to detecting the presence of harmful gases, and many others. Spectrometers have been widely studied, but every spectrometer has its own strengths and weaknesses. One of the best ways to build a spectrometer is to use an interferometer, a device that analyzes interference patterns to extract information about the light source. Here, I present analysis and a demonstration of stationary interferometry with no moving parts and a camera limited by a finite resolution. I experimentally and analytically show that interference patterns that require much higher resolutions to appropriately display can be distinguished by a combination of their aliased spatial frequency and their contrast. The motivation is to enable higher spatial frequencies to be clearly distinguishable, and hence improve the flexibility and wavenumber resolution (constant finite difference between measurable wavenumbers) of the resulting spectrometer. By moving past numerous Nyquist edges, the wavenumber resolution rapidly improves, allowing for low-cost, stationary, and accurate spectrometers to be constructed. When combined with compact, state-of-the-art semiconductor lasers, the simplicity of the setup and the ability of the system and mathematical algorithm to function with low-resolution cameras (2.3 megapixels) opens the possibility for such compact spectrometers to be eventually implemented on smartphones…

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