Expand the measurement range of a critical angle refractometer by a centroid method for transparent fluids

A simple approach to expand the measurement range of a critical angle refractometer (CAR) is demonstrated. Our method is based on measuring the centroid point of the angular reflective ratio of the CAR. According to the Snell׳s reflective law, the CAR with a divergent beam source has a limited measurement range. When the refractive index (RI) is higher than the upper limit, the reflective ratio curve is gradual changing without cutoff edge between the total internal reflection (TIR) and non-TIR. We find that the centroid point of the gradual changing curve is associated with the RI value of a liquid. Theorectical analysis and experimental results on sugar solutions with RI that varying from 1.359 to 1.3766 show that this method is effective and accurate to expand the measurement range.