# FPGA-based real-time autocorrelator and its application in dynamic light scattering

## TL;DR

This paper introduces an FPGA-based digital autocorrelator designed for real-time dynamic light scattering, utilizing a multi-τ method to efficiently process photon data with limited FPGA resources.

## Contribution

The paper presents a novel FPGA implementation of a real-time autocorrelator for DLS using a multi-τ approach that avoids full data storage, enabling efficient particle size analysis.

## Key findings

- Successfully implemented on a Xilinx FPGA chip
- Achieves autocorrelation from 10 ns to 45 min lag times
- Provides error estimates for the multi-τ method

## Abstract

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.