 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.^[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 iswhere $\ast$ 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.^[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.^[ref]