Statistical design of position-encoded microsphere arrays.

We propose a microsphere array device with microspheres having controllable positions for error-free target identification. We conduct a statistical design analysis to select the optimal distance between the microspheres as well as the optimal temperature. Our design simplifies the imaging and ensures a desired statistical performance for a given sensor cost. Specifically, we compute the posterior Cramér-Rao bound on the errors in estimating the unknown target concentrations. We use this performance bound to compute the optimal design variables. We discuss both uniform and sparse concentration levels of targets, and replace the unknown imaging parameters with their maximum likelihood estimates. We illustrate our design concept using numerical examples. The proposed microarray has high sensitivity, efficient packing, and guaranteed imaging performance. It simplifies the imaging analysis significantly by identifying targets based on the known positions of the microspheres. Potential applications include molecular recognition, specificity of targeting molecules, protein-protein dimerization, high throughput screening assays for enzyme inhibitors, drug discovery, and gene sequencing.