  Digital correlators play a significant role in dynamic light scattering (DLS)
technology, which characterizes particle size distribution. We present a field
programmable gate array (FPGA)-based digital correlator that can be applied to
process DLS data. To satisfy the DLS requirements in the FPGA logic with
limited resources, a multiple lag time period (multi-{\tau} ) method is
employed that does not require storing the full data set in memory. Moreover,
the device directly accepts the transistor-transistor logic (TTL) signal from
the photon counting detector by measuring the time intervals between photon
events and calculates the autocorrelation functions in real time. Furthermore,
we derive estimates for the error arising from the use of the multi-{\tau}
correlator. We implement all the necessary operations in a single Xilinx FPGA
chip with a lag time from 10 ns to 45 min, including a highly optimized photon
counter.
