## 1 Introduction  
In the past few decades, wireless sensor networks (WSNs), which are composed of numerous nodes randomly distributed over a given region to collect information, have been successfully applied in various applications, such as environmental monitoring, medical care and intelligent households, _etc._[1]. The sensor nodes form a large scale, multi-hop self-organizing system, communicating their readings to the base station (BS). This type of network has played a significant role in the advancement of ubiquitous computing and mobile communication. Conventionally, research on WSNs has focused on nodes that transmit data via radio frequency (RF). The signal is transmitted omnidirectionally, so the network is generally modeled as a geometric random graph (GRG). Two nodes, \(S_{i}\) and \(S_{j}\), can establish a bi-directional link if they are within a fixed communication radius \(r\). However, the RF-based sensor networks (RFSNs) suffer from many potential issues, such as severe signal interference, attenuation and collision. As one of the candidate technologies, free space optical sensor networks (FSOSNs) that are based on directed broad-beam free space optics (FSO), show favorable merits over RFSNs. These merits include the increased spatial reuse for communications, smaller node size, ultra-high bandwidths, enhanced security, and the reduction in interference, _etc._[2]. An increasing number of studies have been focused on FSO-based sensor network systems [3, 4, 5, 6]. Just as nodes in RFSNs, nodes in FSOSNs are also generally designed to be small, light and cheap. Typically, a node is equipped with a sensing device (_i.e._, sensor), tiny battery, simple processor as the control unit, and communication device. What makes nodes in FSOSNs different from those in RFSNs is that their communication device integrates a receiver, an active transmitter, and a passive transmitter based on corner cube retro-reflector (CCR) instead of only a transceiver. Figure 1 shows the general node architecture of FSOSNs. The active transmitter usually assembles a semiconductor laser, collimating lens and beam steering, which is in charge of unidirectional transmission [4]. However, the passive transmitter does not have a light source. Its main component, CCR, consists of three mutually orthogonal mirrors of gold-coated polysilicon that form a concave corner. This CCR has the property that any incident ray of light can be reflected back to the source. Thus, by modulating the reflected beam, it is able to set up a bi-directional link with the light source using a negligible amount of energy consumption [7]. The third part of the communication device is the receiver that is built upon a photo-detector. It can receive signals from most directions. Figure 1: Node architecture. Based on the special node architecture, the establishment of a hierarchical FSOSN is initiated by the BS via scanning the entire area with an interrogating beam of light. Any node in the network that shares a direct line-of-sight (LOS) path with the BS can set up bi-directional path with it using CCR. These nodes are called cluster heads (CHs). All other nodes, known as general sensors (GSs), have to contact the BS through one or multi-hops to the closest CH using active transmitters. Figure 2(a) shows an example of FSOSN, and Figure 2(b) is the corresponding hierarchical network structure. Note that _S1, S3, S10_ are CHs while other nodes are GSs. It is observed that the CHs form the middle layer that acts as a bridge between the BS and GSs with fare energy consumption: the passive transmitter is used when contacting the BS while the active transmitter is applied when contacting the GSs. Compared with the RFSNs, which use omnidirectional communication, the main limitation of FSOSNs is the requirement of a LOS path between a sender and a receiver. With an active transmitter, a node in the FSOSNs transmits data by scanning a directional modulated visible or infrared (IR) beam over a \"pie-shaped\" angular sector.