# Digital Correlator Technology

The technology underlying Dynamic Light Scattering (DLS) [1], Diffusing Wave Spectroscopy (DWS) [2] or Fluorescence Correlation Spectroscopy (FCS) [3] relies on the detection and subsequent digitalization of the scattered signal [4].

In such experiments the fluctuating scattered light intensity $$I_s(t)$$ directed toward a single photon detector (e.g. a photomultiplier or an avalanche photodiode), results in the emission of electronic current pulses with a probability proportional to the scattered intensity. Within a single photon detector (SPD) a wide band amplifier then converts the output current pulses to voltage pulses.

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LSI Correlator

Subsequently a discriminator reduces detection noise by comparing voltage pulses with a reference threshold and eliminating noise components, thus producing the final output voltage pulse train where each pulse corresponds to a photon detection.

Once an electronic pulse train corresponding to the photon arrival on the SPD is produced the signal is analyzed by the digital correlator whose main task is that of implementing the best discrete approximation to the equation below which represents the raw data needed in a DLS, FCS or DWS experiment:

$$g_2(q,\tau)=\frac{\left<I_s(t)I_s(t+\tau)\right>}{\left<|I_s(t)|^2\right>},$$

with $$\tau$$ being the time lag.

In the most simple approach one will choose linear spacing of the time lag  $$\tau$$. This is referred to as a linear correlator. The more sophisticated and meaningful approach however, is based on logarithmic spacing. This is the so-called multi-tau or multiple-tau correlator

[1] B.J. Berne and R. Pecora. Dynamic light scattering. Dover Publications, Mineola, 2000.

[2] F. Scheffold. Particle sizing with diffusing wave spectroscopy. Journal of Dispersion Science and technology, 23:591{599, 2002.

[3] E. S. Elson, R. Rigler. Fluorescence Correlation Spectroscopy. Springer, 2001.

[4] Schatzel K. Dynamic Light Scattering: The Method and some Applications. Ed. Clarendon Press, Oxford University Press, 1993.