Non-line of Sight imaging by SPAD​

Introduction

Silicon single photon avalanche detector (Si SPAD) has become a hot topic today for its single photon sensitivity, pico-second timing resolution and CMOS compatibility and low cost. Because of its unique properties, it becomes a tool to capture transient imaging for computer vision industry. One of applications enabled by transient imaging is non-line of sight problem, usually being referred to "look around the corner", where using Si SPAD, we could locate, track and recognize the shape of objects around the corner without directly seeing it.

The object of our project is to simulate Si SPAD response in non-line of sight imaging using ray tracing and verify its algorithm to track position of "hidden" object.

There have been multiple papers published on this topic. The one we have studied is “Detection and tracking of moving objects hidden from view”. It was published last year on nature photonics. The scenario they provided is as follow. First they have the SPAD and laser light source hang at the wall. Then the laser and SPAD would first hit the ground. And these two regions at the ground are our starting point and the end point.

This remains a hot area for recently years. The one we focus on is "“Detection and tracking of moving objects hidden from view".

Background

Difference between APD and SPAD

Traditional avalanche photo detector (APD) and SPAD both use avalanche effect to amplify signal. However, they are very different in circuit configuration and performance. APD is often reversely biased to have a gain around 10-100, while SPAD is biased above breakdown voltage with a gain above $10^6$ or even up to infinity. In timing response, APD usually have a time resolution of sub nanoseconds while SPAD have a time resolution of pico-seconds. The bandwidth of APD is limited by RC delay and timing resolution. On the other hand, SPAD is constrained by dead time, where it has to rest for a while before being sensitive to next arrival photon.

Work principle of SPAD

Because of dead time, the measurement method for using SPAD is time-correlated single photon counting (TCSPC). We would like to use bio-fluorescence as a working example. In these experiments as shown in Fig 1, the fluorescence response with regards to excitation laser is often recorded. The experiment begin by repeating excitation laser pulses with many cycles and sometimes fluorophore will emit photons. For each cycle, the emitted photon may be captured by SPAD and get registered or it may be missing. Si SPAD will also take note in photon arrival time. After repeating a certain times, a histogram of photon arrival time could be drawn and this distribution will be asymptotic to fluorescence emission response, denoted by red curve in Fig 1.

Imaging model of SPAD

With SPAD work principle in mind, SPAD imaging model is built upon Poisson distribution as it comes from discrete nature of photons and SPAD triggering response (trigger or no trigger). In equations below, h is actual measurement result, $A,\mu ,\tau ,d$ are matrix in time domain. $d$ denotes dark count rate (DCR), which is the number of counts without any photon impinging on SPAD due to detector noise. $\mu \tau$ is expected response of how many photons are injected, absorbed and successfully trigger SPAD. $\mu \tau +d$ represents timing response of photon from the environment and this has to convolve with $A$, SPAD timing response itself. The final measurement results are Poisson distribution with expected tming response from $A\times (\mu \tau +d))$.

Results

1) Ray optic distribution 2) distance relationship 3) ray optics distribution verification 4) volumetric reconstruction verification

Results 4.1

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Example of two iterations of the meanshift algorithm