**Bin Zhuang 1,2, Chengfang Xu 1,2, Yi Geng 1,2, Guangzhi Zhao 1,2, Hui Chen 1,2, Zhengquan He <sup>1</sup> and Liyong Ren 1,\***


Received: 13 May 2018; Accepted: 23 June 2018; Published: 25 June 2018

**Abstract:** Imaging an object hidden behind a highly scattering medium is difficult since the wave has gone through a round-trip distortion: On the way in for the illumination and on the way out for the detection. Although various approaches have recently been proposed to overcome this seemingly intractable problem, they are limited to two-dimensional (2D) intensity imaging because the phase information of the object is lost. In such a case, the morphological features of the object cannot be recovered. Here, based on the round-trip optical transmission matrix of the scattering medium, we propose an imaging method to recover the complex amplitude (both the amplitude and the phase) information of the object. In this way, it is possible to achieve the three-dimensional (3D) complex amplitude imaging. To preliminarily verify the effectiveness of our method, a simple virtual complex amplitude object has been tested. The experiment results show that not only the amplitude but also the phase information of the object can be recovered directly from the distorted output optical field. Our method is effective to the thick scattering medium and does not involve scanning during the imaging process. We believe it probably has potential applications in some new fields, for example, using the scattering medium itself as an imaging sensor, instead of a barrier.

**Keywords:** round-trip imaging; scattering media; 3D imaging; transmission matrix
