Statistical Stability of Clipped Photon Correlations in the Self-Scaling Limit

Abstract

High-speed photon correlators commonly use digital clipping techniques to convert the photon rate time series into a series of one-bit numbers that can be multiplied rapidly, thereby improving the product rate (number of multiplication products performed per second) and the overall throughput rate of the correlator. Letting

$$\begin{array}{*{20}{c}} {{{n}_{i}} = number\,of\,photomultiplier\,anode\,pulses\,in} \\ {time\,\operatorname{int} erval\,\left( {{{t}_{i}},{{t}_{i}} + \nabla \tau } \right),} \\ \end{array}$$

(1)

the photon rate correlation <n₁n_(i+p)> with time delay pΔτ is obtained ideally by quantizing each value of n_i with enough resolution to make errors in the products of the samples negligible. Clipping processes effectively quantize n_i with one-bit resolution. In clipping without scaling the quantization occurs with respect to a set threshold level n_th, and the clipped value of n_i is given by

$${{n}_{{il}}} = \left\{ {\begin{array}{*{20}{c}} {1,\quad if\quad {{n}_{1}} > {{n}_{{th}}}} \hfill \\ {0,\quad if\quad {{n}_{i}} < {{n}_{{th}}}} \hfill \\ \end{array} } \right.$$

(2)

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