Transition Metal Dichalcogenide Thin Films for Precise Optical Wavelength Estimation Using Bayesian Inference

Despite its ability to draw precise inferences from large and complex data sets, the use of data analytics in the field of condensed matter and materials sciences—where vast quantities of complex metrology data are regularly generated—has remained surprisingly limited. Specifically, such approaches could dramatically reduce the engineering complexities of devices that directly exploit the physical properties of materials. Here, we present a cyber-physical system for accurately estimating the wavelength of any monochromatic light in the range 325–1100 nm by applying Bayesian inference on the optical transmittance data from a few low-cost, easy-to-fabricate thin film “filters” of layered transition metal dichalcogenides (TMDs) such as MoS2 and WS2. Wavelengths of tested monochromatic light could be estimated with only 1% estimation error over 99% of the stated spectral range, with lowest error values reaching as low as a few ten parts per million (ppm) in a system with only 11 filters. By stepwise elimination of filters with the least contribution toward accuracy, a mean estimation accuracy of ∼99% could be obtained even in a two-filter system. Furthermore, we provide a statistical approach for selecting the best “filter” material for any intended spectral range based on the spectral variation of transmittance within the desired range of wavelengths. And finally, we demonstrate that calibrating the data-driven models for the filters from time to time overcomes the minor drifts in their transmittance values, which allows using the same filters indefinitely. This work not only enables the development of simple cyber-physical photodetectors with high accuracy color estimation but also provides a framework for developing similar cyber-physical systems with drastically reduced complexity.