Determining the average effective refractive index of biological cells from light diffraction patterns of disordered monolayers of cells

Abstract In this study, we present a technique and methodology for determining the average refractive index (RI) of biological cells. This technique involves analyzing the scattering pattern produced by a disordered monolayer of cells immersed in a suitable solution. Analyzing cell scattering patterns in a monolayer offers several practical advantages over current alternative techniques. First, we discuss the fundamentals of the proposed optical technique and its practical implementation. We show theoretically and experimentally that disorder in the monolayer is essential to this technique. We then present and validate an optical model, appropriate for a monolayer of cells, and use it to extract the average RI of biological cells from the experimental intensity profiles of the monolayer’s scattering pattern. After a thorough analysis, we determined that the RI obtained from the optical model of equivalent spherical particles corresponds to the average among cells, of their inner-spatial-average RI. We provide a detailed explanation of the restrictions on fitting the model to experimental data in order to circumvent an ill-conditioned inverse problem. Finally, we present experimental results on determining the average RI of Saccharomyces cerevisiae yeast cells. We examine the uncertainty in estimating the average RI from fitting the model to a particular experimental intensity profile and combined it with that obtained from replicating the measurements many times. In this work, we achieved a total uncertainty of ± 0.005 RIU for the average RI of S. cerevisiae yeast cells. The value obtained for the average RI of these cells coincides closely with values obtained by three other methods based on cell-by-cell measurements. To illustrate the applicability of the method we present results of measuring the RI of these cells after inducing apoptosis on them. The proposed technique and related methodology offer clear advantages over current cell-by-cell techniques in terms of inferring the average RI of round cells. This method provides directly the average RI over many cells ( ∼ 10 4 ) while requiring relatively simple instrumentation.