An improved differential algorithm for the critical-angle refractometer

Due to the limit of the pixel size of the charge-coupled device (CCD) or complementary metal oxide semiconductor (CMOS) sensor, the traditional differential algorithm has a limited measuring accuracy by determining the critical angle in integral pixel. In this paper, we present a practical algorithm based on the centroid value of the reflective ratio around the critical angle pixel to address the traditional differential algorithm problem of determining the critical angle under sub-pixel in a critical angle refractometer (CAR). When the change of refractive index (RI) of a liquid sample is beyond the sensitivity of the traditional differential algorithm, the RI of the liquid can be obtained by using the centroid value of reflectivity around the critical angle pixel. The centroid value is associated with the RI change of the liquid in sub-pixel. Demonstrated by both theoretical analyses and experimental results using saline solutions with RI that changes in sub-pixel tested through the reflective CAR, the algorithm is found to be computationally effective and robust to expand the measuring accuracy of the Abbe-type refractometer in sub-pixel.