= Diffuse photon time-of-flight experiment
A <diffuse photon time-of-flight experiment> measures the distribution of delays experienced by light traversing a scattering sample. A short-pulse source illuminates the sample; a reference timing signal starts the clock, and a fast <photodetector> records returning or transmitted <photons>. <Time-correlated single-photon counting> accumulates their delays over repeated pulses into a <histogram>.<Time-Correlated Single Photon Counting (technical note v. 2.1) by Michael Wahl>[Principle of TCSPC; scattering-medium impulse-response measurement, pp.1–3]{ref}
A useful laboratory comparison keeps the source-detector geometry fixed while changing sample thickness or scattering strength. The apparatus needs a defined optical path, a sample holder and the same detection/timing chain for a reference <instrument response function>. Longer, repeatedly scattered paths broaden the arrival distribution; <absorption> changes which paths survive to be detected.
Let $r(t)$ denote the sample's optical <impulse response> in the chosen geometry and $h(t)$ the normalized <instrument response function>. A simple model for the expected count-rate trace is
$$
y(t)=A(h\ast r)(t)+b(t),
$$
where $\ast$ denotes <convolution>, $A$ sets the signal scale and $b(t)$ represents background counts. Fitting a transport model after including $h$ separates sample broadening from instrumental timing spread. A model for an infinite medium cannot simply be substituted for a finite slab's boundary-dependent detector response.
<M. S. Patterson>, <Britton Chance> and <B. C. Wilson> developed analytic slab responses and compared them with preliminary measurements and <Monte Carlo simulations> in 1989.<Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties by M. S. Patterson and others>[Abstract: picosecond pulses, homogeneous-slab model and comparisons]{ref} The shape of the delay distribution provides information beyond total transmitted intensity.
The counting electronics also matter: if only the first arrival in each pulse period is recorded, multiple arrivals bias the sample toward earlier times. This <photon pile-up> must be represented or suppressed by the acquisition conditions, rather than mistaken for faster propagation.<Time-Correlated Single Photon Counting (TCSPC) by PicoQuant>[How Does TCSPC Work?: first-photon pile-up and reconstruction of the delay histogram]{ref}
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