## 1 Introduction  
The issue of laser beam propagation in atmospheric turbulence has been explored widely over the past decades. It is well-known that atmospheric turbulence induces random variations in the phase, propagating direction and intensity of beams, which are characterized by beam spreading, beam wander and scintillation [1; 2; 3]. These phenomena have negative effects on the laser transport performance. In contrast to fully coherent beams, partially coherent beams are better at resisting the negative effects induced by atmospheric turbulence, and this has been verified in several experiments [4; 5]. Thus, partially coherent beams are expected to improve the performance of laser communication systems [6; 7]. The Gaussian Schell-model (GSM) beam [8; 9] is a representative partially coherent beam, whose intensity and spectral degree of coherence satisfy Gaussian distributions, and much attention has been paid to its transmission properties in free space or random media. Several relevant research methods have been proposed [10; 11; 12]. Although researchers have made many efforts on the subject of GSM beam propagation through atmospheric turbulence [13; 14; 15; 16; 17], most studies have been limited to scalar fields without considering the vector properties of light. The degree of polarization represents the relevance of two rectangular components of the electric field at one single point [18; 19; 20]. In 2003, a unified theory of coherence and polarization was proposed [21], and this is highly advantageous for in-depth study of the spectrum, coherence and polarization of the beam [22; 23; 24]. The electromagnetic Gaussian Schell-model (EGSM) beam is a classical partially coherent vector beam and any point in this field has the same polarization [25; 26; 27; 28; 29; 30]. In recent years, a number of researchers have increasingly focused on the propagation of EGSM beams in free space and in random media [31; 32; 33; 34; 35; 36; 37; 38]. In comparison with the GSM beam, under appropriate conditions, the EGSM beam can significantly reduce the light fluctuations caused by atmospheric turbulence, and this conclusion has been well verified [39; 40; 41]. There are numerous studies on the effect of atmospheric turbulence on the coherence degree and polarization state of an EGSM beam [42; 43; 44; 45; 46]. Many experimental and theoretical studies have demonstrated that EGSM beams have significant applications in many areas such as free-space optical communications, remote sensing, LIDAR systems, and optical illumination [47; 48; 49]. In an active bistatic LIDAR system, the returned beam passing through atmospheric turbulence aggravates the system noise, and then, the detection accuracy and efficiency is reduced. Many studies have found that the properties of laser beams are affected by the transmission medium, besides target scattering [50; 51; 52; 53; 54]. Accordingly, it is necessary to study the combined action of the atmospheric turbulence and target scattering on laser beams with the object embedded in atmospheric turbulence. In previous work, attention has been focused on the forward transmission in atmospheric turbulence. The interaction of the EGSM beam with a semi-rough target located in atmospheric turbulence was explored in [39]; the paper qualitatively analyzed the combined effect of the surface roughness and the object size on the coherence and polarization. In this paper, through inversion analysis of the interaction of isotropic EGSM beams with a semi-rough target in atmospheric turbulence, we found that it is possible to quantitatively obtain accurate parameters of the object surface by contrasting the characteristics of the incident beam and its returned beam. We assumed the atmospheric turbulence to be homogeneous and isotropic. Moreover, the surface of the target was set as semi-rough and isotropic. The model of the target consisted of two components: a thin lens with good reflective properties and a thin phase screen to cause phase perturbations [55; 56; 57; 58].