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We present a case study for a time-of-flight (ToF) 3D imaging system using single-pixel imaging (SPI) approach based on compressive sensing (CS), accompanied by the Time-of-flight (ToF) principle applied to four reference points of the 2D image created and then mapped to the rest of the SPI generated virtual pixels. In this analysis we have developed a mathematical model of the system and evaluated three different scenarios considering different performance issues based on signal-to-noise ratio, different levels of background illumination, distance, spatial resolution, and material reflectivity presented by the objects in the scene. To be able to reduce the background photon shot noise and enable the correct functionality of the system also in harsh environments (in presence of micrometer size particles such as rain, snow, fog or smoke) we propose using near infra-red (NIR) active illumination with a peak wavelength of 1550 nm. The SPI principle is based here on an array of NIR emitting LEDs and the Thorlab FGA015 InGaAs single photodiode. For the system modelling and analysis, we considered the maximum background illumination intensity of up to 100 klux, different reflection coefficients of the target material to be detected, and measurement distances between 1 and 10 m. Using the ToF principle, we evaluated the direct ToF using both, pulsed laser NIR source as well as an array of NIR emitting LEDs combined with a single InGaAs photodiode on the one side, and an InGaAs single-photon avalanche diode (SPAD) on the other. Using the model developed, we estimated the spatial resolution (standard deviation from the distance measured) the proposed system might reach for each of the ToF methods analyzed and combining different system elements. Finally, we propose a SPI-ToF 3D imaging and ranging system for drone outdoors applications.
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