Statistical design of position-encoded microsphere arrays at low target concentrations

We design microsphere arrays with predetermined positions of microspheres, for capturing targets at low concentrations. To optimize the design parameters, we compute the Ziv-Zakai bound (ZZB) on the errors in estimating the target concentrations. We numerically demonstrate our design by computing the minimal distance between the microspheres and the optimal imaging temperature, for a desired level of errors. We also validate that, at low target concentrations, the statistical design using the ZZB is more precise than that using the posterior Cramér-Rao bound. We further quantitatively evaluate the effect of the fluorescence microscope point-spread function on the design performance, which provide useful guides to the device design and implementation. The key advantages of the proposed microsphere arrays are error-free target identification, simplified data analysis, high packing density, and reduced cost.