Label-free quantitative imaging of two-dimensional concentration gradients using Fabry-Pérot interferometry

Abstract

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-Pérot 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.

Figures (3)

• Figure 1: (a) Operating principle of RIO. Monochromatic light, with its wavelength selected by adjusting the angle of two rotating dichroic filters, illuminates a microfluidic Fabry–Pérot chip. The spatial interference pattern is imaged through an inverted microscope onto a CMOS camera. One measurement consists of a complete wavelength scan ranging from $\sim 508$ nm to $\sim 532$ nm. (b) Illustration of wavelength-resolved image stacking. As the filters rotate, a wavelength $\lambda(\theta)$ is selected and the entire field of view is sequentially illuminated, one wavelength at a time, yielding a total of 400 images per measurement. A representative image pixel $p$ is indicated. (c) Example images of a microfluidic Fabry–Pérot chip filled with deionized water, acquired at three different wavelengths, with pixel $p$ highlighted. (d) Intensity spectra measured at pixel $p$ for an initial reference state (black diamonds) and a subsequent measurement (green circles). The spectra are smoothed with a Gaussian kernel (see SI section 3, figure S1) to identify FECO; the inset highlights the wavelength shift of the first peak. Using the initial refractive index $n_{\text{(ref)}}$, the shifted FECO wavelengths are used to determine the new refractive index $n$ at pixel $p$.
• Figure 2: Normalized refractive index shift of aqueous NaCl solutions with concentrations ranging from 1 mM to 100 mM measured with RIO at 4x, 10x, and 20x magnifications. Error bars represent the standard deviation of the refractive index measured over a 10 x 10 pixel area. Reference values from the Handbook of Chemistry and Physics 100th Edition (rumble_crc_2019) are shown as (+) signs, and a linear projection of these values is plotted as a dashed line for concentrations below 10 mM. Representative 20x magnification RIO measurements for each NaCl concentration are shown alongside the corresponding data points, with colors corresponding to the refractive index according to the color-bar on the right. A RIO image of deionized water is also shown for comparison.
• Figure 3: (a) Refractive index map of 100mM NaCl solution (top, n$_{1}$) and deionized water (bottom, n$_{0}$) streams co-flowing in a y-junction channel at $0.4$$\mu$L/min from left to right. (b) Refractive index as function of the $x$-coordinate at positions $y = 0$$\mu m$, $y = 750$$\mu m$, and $y = 1500$$\mu m$ extracted from the RIO image in a and fitted using equation \ref{['eq:diffequn']}. (c) Mixing layer width $w(y)$ obtained using the fitting equation \ref{['eq:diffequn']} and plotted against the $y$-position. The shaded region is the standard deviation of 4 consecutive measurements. Four different co-laminar flow rates were tested: $0.4$$\mu$L/min, $1.2$$\mu$L/min, $1.4$$\mu$L/min, and $1.6$$\mu$L/min. (d) The diffusivity $D_{local}$ is evaluated from every discrete "$w$" value along the $y$-axis using equation \ref{['eq:IWeqnD']}. The circle marker is the mean of 4 consecutive measurements, and the shaded region represents their standard deviation. (e) Comparison of $D_{global}$ and the mean $<D_{local}>$ at different flow rates. $D_{global}$ is evaluated by fitting the curves of $w(y)$ shown in c using equation \ref{['eq:IWeqn']}, where $<D_{local}>$ is the average of the values plotted in d representing the diffusivity extracted using the 1D information at individual $y$-locations along the channel.