[Paper Review] SRA vs histograms in the noise analysis of SPAD

N. S. Perminov, M. A. Smirnov+3 more|arXiv (Cornell University)|Dec 7, 2017

Advanced Optical Sensing Technologies7 references3 citations

TL;DR

This paper proposes the Sequence of Ranged Amplitudes (SRA) as a superior alternative to histograms for noise analysis in single-photon avalanche diodes (SPADs). SRA provides a noninvasive, information-lossless characterization of dark count intervals, enabling faster and more accurate statistical analysis with significantly smaller sample sizes—demonstrated by a 4.7-fold reduction in error deviation at 1,000-point samples compared to histograms.

ABSTRACT

A comparative analysis of the method of histograms and the sequence of the ranged am-plitudes (SRA) for statistical parametrization of the operation regime of a single-photon avalanche photodetector is carried out. It is shown that the SRA method contains all the information, which can be obtained using the method of histograms, and also allows to give a quick robust description of the dark counts of the device for a short noise sample of $\sim10^3$ points, what open the way for the introduction of SRA approach into software of a high-sensitivity photodetectors.

Motivation & Objective

• To compare the statistical efficiency of histograms and SRA in characterizing SPAD dark noise.
• To evaluate the robustness and speed of SRA versus histograms using short noise samples.
• To demonstrate that SRA preserves all information in histograms while enabling faster analysis.
• To validate SRA’s superiority in fitting Poisson processes typical of SPAD dark counts.
• To promote SRA as a practical, noninvasive method for real-time noise characterization in high-sensitivity photodetectors.

Proposed method

• SRA constructs a ranked sequence of time intervals between consecutive dark counts in descending order.
• The SRA is related to the empirical cumulative distribution function via $ F(s_n, N) \approx (N+1-n(s_n))/N $, enabling nonparametric statistical analysis.
• Histograms are generated from the same SRA data using optimal binning rules (Mann-Wald and Sturges’ criteria) for comparison.
• The coefficient of determination $ R^2 $ and normalized deviation $ \varepsilon(N) $ are used to quantitatively compare histogram and SRA performance.
• Experimental data from an ID210 SPAD (15% efficiency, 24 μs dead time) with $ 10^5 $ points was subsampled into 100 sets of varying size $ N = 20j $, $ j=1 $ to $ 50 $.
• Theoretical fitting of the exponential distribution $ \rho(x) = \lambda e^{-\lambda x} $ is applied to both SRA and histogram outputs to assess goodness-of-fit.

Experimental results

Research questions

• RQ1 Can SRA provide a more accurate and faster statistical characterization of SPAD dark noise than traditional histograms?
• RQ2 Does SRA preserve all information contained in histograms, without data loss?
• RQ3 How does the performance of SRA compare to histograms in terms of error deviation and fitting accuracy for small sample sizes?
• RQ4 What is the impact of binning choice on histogram reliability, and can SRA eliminate this dependency?
• RQ5 Can SRA be effectively used for real-time, noninvasive noise analysis in high-sensitivity photodetection systems?

Key findings

• At a sample size of $ N = 10^3 $, the normalized deviation $ \varepsilon $ for SRA was $ 0.0078 $, compared to $ 0.0369 $ for histograms—indicating a 4.7-fold improvement in stability.
• The coefficient of determination $ R^2 $ for SRA fitting was $ 0.9957 $, compared to $ 0.9875 $ for the best histogram fit, showing SRA reduces fitting error by approximately 3 times.
• SRA is noninvasive and lossless, meaning it contains all information present in the original histogram, while histograms are inherently invasive due to binning.
• Histogram performance is highly sensitive to bin count $ N_h(N) $, with significant differences in shape and fit quality between Sturges’ and Mann-Wald criteria, whereas SRA is independent of such arbitrary choices.
• The SRA method enables robust noise characterization with as few as $ 10^3 $ data points, making it suitable for real-time and embedded applications in high-sensitivity photodetectors.
• SRA’s speed and accuracy make it ideal for integration into software of high-precision photodetection systems, especially in quantum communications and optical quantum computing.