Integrated Spectral Sensitivity as Physics-Based Figure of Merit for Spectral Transducers in Optical Sensing

The design of optical sensors aims at providing, among other things, the highest precision in the determination of the target measurand. Many sensor systems rely on a spectral transducer to map changes in the measurand into spectral shifts of a resonance peak in the reflection or transmission spectrum, which is measured by a readout device (e.g., a spectrometer). For these spectral transducers, figures of merit have been defined which are based on specific assumptions on the readout and the data analysis. In reality, however, different transducers achieve optimal performance with different types of readout. Additionally, some transducers present a more complex spectral response for which existing figures of merit do not apply. In this paper, we investigate an approach to quantifying the potential performance of a given transducer for a more general class of readout methods. Starting from the Cramér-Rao lower bound, we define a new figure of merit, the integrated spectral sensitivity, which is directly related to the physical limit of precision and applicable to a wide variety of sensing systems. We apply this analysis to two different examples of transducers. The results bring useful insights into the design of optical sensors.