Statistical analysis of signal measurement in time-of-flight cameras

Three-dimensional imaging systems have evolved significantly in the last two decades due to increase in demand for tasks in the field of close range photogrammetry. The fast and growing need of 3D imaging devices has given rise to range image technology, especially time-of-flight (TOF) cameras, that provide direct measurement of distance between the camera and the targeted surface. A significant advantage of TOF devices over traditional range data sensors is their capability to provide frame rate range data over a full image array. In phase shift TOF cameras, phase shift sampling of the received signal is used to measure amplitude, phase and the offset (intensity) of the received signal. As a result, the quality of the measurement of these sensors depends heavily on signal-to-noise (SNR) of the incoming signal and the subsequent processing algorithms. A detailed understanding of the statistical distributions of the measurement parameters is crucial for accurate distance measurement analysis especially in low SNR scenarios. In this paper, we provide explicit noise models for the three parameters of amplitude, phase and intensity. The proposed stochastic model helps in investigating the effect of noise on signal and classifying range data reliability in TOF cameras. The model is used for prediction of errors in a TOF camera under various SNR conditions. Experimental verification confirms the validity of the model using real data for range error classification under different noise conditions.