In this paper we develop a three-dimensional (3D) ray tracing tool based on the ABCD ray transfer matrices. With symmetric optical components and under paraxial approximation, two sets of 2×2 ABCD matrices, each for a two-dimensional subspace, can be used to describe the 3D ray propagation completely. Compared to commercial ray-tracing software packages, our tool requires no tedious drawing, and the results for various conditions, such as different device dimensions and incident angles, can be easily obtained by simply changing the parameter values used for the calculation. We have employed this matrix-based 3D ray tracing tool to model cat's eye retroreflectors. The cat's eye performance, including the retroreflection efficiency, acceptance angle (i.e., field of view), and beam divergence and deviation, is fully studied. The application of this 3D ray tracing technique can be further extended to other optical components.
A cantilever sensor integrated with an on-tip micro spherical reflecting mirror (MSRM) exhibits a larger optical beam displacement than a conventional one, i.e. the system sensitivity/responsivity is enhanced. In this paper, it is employed as a concentration gauge that only requires 0.5 μL of solution. The MSRM-integrated cantilever is first set above a sodium chloride-water droplet carried by a glass substrate, and then the droplet is moved up gradually. Once the cantilever is touched by the droplet, it is pulled and bent down as the droplet is reshaped. The cantilever deformation amount is related to the surface tension of the solution, which increases with the mass percentage of sodium chloride. Therefore, by measuring the bending amount of the cantilever, the concentration of the NaCl-water solution can be determined. We also perform the experiments on the alcohol-water mixture, whose surface tension, conversely, reduces as the alcohol percentage increases.
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