What does a linear photon-counter twin of a SPAD lidar miss about dead time?

What it found

An ideal counter twin reads flux linearly; a real detector with dead time τ reports half the flux at nτ=1 (non-paralyzable) or 36.8% (paralyzable), and the paralyzable curve peaks at 1/e, so one reading has two fluxes (0.259 or 2.543 at mτ=0.2; a twin is 12.7× too low on the high branch). First-photon timing of a Gaussian pulse is biased early by −N/(2√π)σ at small N (exact) and saturating near −2σ: −0.28σ at N=1 and −1.50σ at N=10 (−22.6 cm for σ=1 ns) while the spread shrinks to 0.62σ, so it is bias, not averaging noise. A Coates correction of the first-photon histogram restores the mean to within 0.02σ. Stylised: one pulse, no background light, afterpulsing or crosstalk.

A figure from its own output

Paper, code and results

• README and method
• White paper
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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.