Label-free quantitative imaging of two-dimensional concentration gradients using Fabry-P\'erot interferometry

Concentration gradients at the microscale play a central role in many physical, chemical, and biological systems, yet their quantitative visualization remains challenging due to the limited optical contrast associated with changes in concentration. Here, we present RIO (the Refractive Index Observer), a label-free interferometric tool for quantitative imaging of refractive index, and thus concentration fields in microfluidic systems. Implemented using a Fabry-P\'{e}rot microfluidic chip mounted on a standard optical microscope, RIO achieves a per-pixel refractive index precision on the order of $1\times 10^{-5}$ refractive index units (RIU) using a standard CMOS camera, enabling high sensitivity two-dimensional chemical imaging. We Characterize the refractive index resolution and spatiotemporal performance of the instrument and demonstrate its capabilities by measuring concentration gradients of dissolved NaCl in a co-laminar flow. RIO provides an accessible, label-free platform for quantitative studies of microscale concentration fields in systems where molecular labeling is undesirable or impractical, and enables investigations of a broad range of out-of-equilibrium phenomena, from polymerization and enzymatic reactions to cell signaling and electrochemical processes.