Model of gated imaging in turbid media

Range-gated imaging can improve the signal to backscattering noise ratio (SBR) in turbid media. This is achieved by synchronizing a short duration, high intensity pulse with precise camera gating. It is well known that shorter pulse length and shorter camera gate duration can enhance the SBR. However, there is no analytical model of the backscattering noise (as a function of the pulse length and gate timing) that can be used to minimize backscattering noise within the camera-captured signal. We propose a formulation (a modification of Falk's lidar equation) that models the backscattering noise as a convolution with a fixed upper limit. This formulation predicts a variation of backscattering noise within the returning signal. In particular, the model predicts higher SBR toward the tail region of the target-reflected irradiance. It confirms the experimental results reported by other authors. Additionally, the model explains experimentally observed SBR improvement for shorter pulses and shorter gating intervals (if adequately positioned within the returning pulse.