# Detection of Underwater Targets Using Polarization Laser Assisted Echo Detection Technique
## 2 Underwater Target Polarization Detection Mechanism  
As known from physics, light is an electromagnetic wave; electromagnetic waves are a kind of wave with vector characteristics, which includes electric field vector component E and magnetic field vector component B, two components [10]. The dominant quantity that can play a light-sensitive role is the electric field vector component E so that the electric field vector E is usually called the light vector, the vibration of this vector is usually called light vibration, and the direction of vibration of this vector as the direction of vibration of light. From the optics part of physics, it is known that the light in the ordinary light source is generated by the vibration of a large number of molecules or atoms that make up the light source. The light atoms or molecules in either of these light processes are intermittent; they are re-emitting or re-emitting at each time. The phase and the direction of vibration will change some so that the light of the ordinary light source contains vibrations in all directions and this vibration in each direction with equal probability of occurrence. This instantaneous light-emitting process in the plane perpendicular to the direction of light propagation appears in the statistical distribution of mathematical probability, is equal to the probability distribution and is called natural light, the sun, life in fluorescent lamps, tungsten lamps, etc., issued by the light belongs to the natural light. If a beam of light only in a certain direction vibration or vibration dominance, using mathematical probability statistics to explain the probability of occurrence in a certain direction is equal to one or the probability of occurrence in a certain direction is greater than the probability of occurrence in other directions, this light is called polarized light. There are four kinds of light with polarization state: partially polarized light, linearly polarized light, elliptically polarized light and circularly polarized light. When a beam of light irradiates an object, the object will act on the light, let the outgoing beam is \(E_{out}\), the incident beam is \(E_{in}\), then the four Stokes parameters \(E_{out}\) will be respectively with the four corresponding parameters \(E_{in}\) into a linear function of the relationship [11], if the matrix can be written in the form of Equation (1). \[S_{\text{out}}\ =M\times S_{\text{in}} \tag{1}\]  
where represents the Stokes vector parameter \(S_{out}\) of the outgoing light \(E_{out}\), \(S_{in}\) represents the Stokes vector parameter of the incoming light \(E_{in}\), and \(M\) is a Mueller matrix of (4 \(\times\) 4) order [12], by which the properties and characteristic orientation of the medium of such an irradiated object can be represented. A polarization device is an object that allows light to pass through if a beam of light irradiates the polarization device and passes through the polarization device. The change in the Stokes vector between the incident and outgoing light can be considered as the result of the role of the polarization device; the resulting effect is represented by the matrix \(M\). By analogy, if the light beam \(E_{in}\) passes through several such devices in turn, the properties of the outgoing light \(E_{out}\) can be calculated by knowing the properties of the devices through which the light passes and the properties of the light itself. If \(L\) optical elements are passed \(E_{in}\) in turn, the total effect can be expressed by Equation (2). \[M_{\text{comb}}\ =M_{L}M_{L-1}\cdots M_{2}M_{1} \tag{2}\]  
The above equation \(M_{L}\) represents the M-matrix of the \(E_{in}\) action of the \(L\)th element pair, with the elements passing through the order from 1 to \(L\).