Simultaneous measurement of refractive index and thickness with a convergent beam

A new approach to the simultaneous measurement of refractive index and thickness based on the focus shifts of a convergent beam intercepted by a test plate is proposed. By using ray optics, a defined focus shift can be derived as a function of the refractive index and thickness as well as the angular position of the test plate with respect to the optical axis. From a pair of focus shifts obtained at two different angular positions, it is shown that the desired measurands can be simultaneously determined without prior knowledge of either parameter. A simulation result for the proposed concept based on graphically solving the equations of their respective focus shifts is presented.