Speaker:  Itay Horev

M.Sc. student under the supervision of Dr. Ofer Amrani

Wednesday, May 29, 2019 at 15:00

Room 011, Kitot Bldg., Faculty of Engineering

LIDAR Detection in the Few-Photon Regime 

 
Abstract

Lidar (Light Detection and Ranging) is a method used for measuring distance to a target by illuminating the target with pulses of (laser) light and measuring the reflected light pulses with a sensor sensitive to light, a.k.a photo detector. This work considers the low photon count regime and provides methods for determining photon time of arrival (TOA) assuming a non-ideal detector array.

This problem was previously treated using the maximum likelihood criterion while referring to correlation type filter and a matched filter as an ideal solution.

Apriori-knowledge or a good characterization of all possible detector outputs used in a matched filters bank is the optimal solution in a minimum square error (MSE) sense. Unfortunately,  the hardware (HW) complexity and memory requirements entailed by such implementation make it inefficient when moving into the real-time domain, as encountered in Lidar applications.

In Lidar applications, 'hidden' targets, e.g. when located behind a camouflage net, increase the complexity of such a problem and make it necessary to find another simple yet generic solution more suitable for HW realization.

The detector used in this work consists of 20x20 sensor elements. Each element can be triggered independently, it has no constant optical threshold , i.e. optical energy level, that results with an output pulse (voltage measured at the sensor output). Rather, the probability that a sensor produces an electrical output pulse is a probabilistic function of the number of impinging photons. Note that each sensor can be considered a binary component in the sense that it emits an electrical pulse whose properties are fixed, or otherwise, it emits nothing.

The probability that a light pulse does not trigger a sensor-array-based detector depends on the transmitted pulse energy, channel transmission and detection efficiency, but finally, it depends on the actual received optical pulse characteristics. In practice, a small number of photons are received, and the objective is to identify the exact moment when a photon triggered (at least) one sensor element in an array.  The probability P of obtaining an electrical output pulse increases as the energy of the optical signal at the detector input increases. However, when a pulse is received, it may interfere with previous (or following) pulses due to the behavior of the sensor array.

Expectation–maximization (EM) algorithm [3] was introduced for image restoration based on  penalized likelihood formulated in the wavelet domain. The algorithm takes advantage of the sparsity of wavelet representations; as such, it is shown to provide good fit for the case of the low photon count regime. A similar approach of using an EM algorithm was reported in [4] for range discrimination. We use the EM approach as a baseline for solving all the above mentioned difficulties associated with a practical  detector array. 

The current work provides a complete algorithmic, and easy to implement solution which was also tested on a real-world data. It consists of two main parts:

1. an EM algorithmic approach properly tailored for (few-photon) pulse detection, pulse-separation and target image reconstruction;  and

2. a neural network approach employed as a system-level pre-processing filter for distinguishing between "real", "fake" (false) or "complex" targets.