This document describes a droplet-based microfluidic system for analyzing DNA sequences using fluorescence resonance energy transfer (FRET). DNA probes labeled with FRET dye pairs are encapsulated in microdroplets along with fluorescent labeling dyes. A picoinjection device is used to introduce DNA templates into the droplets for ligation reactions with the probes. By measuring FRET and dye fluorescence, the system can determine if probe sequences match the template. This allows high-throughput DNA sequence analysis using only small amounts of reagents.