## 1 Introduction  
In our daily life, there are many scattering mediums, such as milk, cloud fog, and human tissue, to name a few. The light wave surface is disturbed due to the random scattering of light in the scattering medium, so it is difficult to directly achieve optical focusing and imaging for its internal targets, which is the main restricting factor for imaging depth and resolution in medical diagnosis and treatment [1; 2; 3; 4; 5]. In order to control the scattered wavefront and suppress the light scattering, researchers proposed wavefront shaping [6; 7; 8; 9], transmission matrix [10; 11; 12; 13], phase conjugate [14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26], and other techniques. Among them, the optical phase conjugate technique uses the phase conjugate modulation of the optical wave surface to realize the time reversal of the light wave, so that the wavefront distortion is compensated in a targeted manner, and the scattering effect is suppressed to achieve focusing as well as imaging. The response speed of the optical phase conjugate technique is fast, and its real-time performance is strong, and these features make it the current research hotspot in related fields [14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. Generally, the optical phase conjugation can be divided into analog modulation [14; 15; 16] and digital modulation [17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. Analog modulation uses crystals as an optical modulation as well as recovery medium. Digital modulation realizes optical phase recording and recovery by a camera and a spatial light modulator (SLM). Compared with analog modulation, digital modulation has stronger controllability, higher sensitivity, shorter exposure time, and it also has no wavelength and light intensity limitation, so that it has wider application prospects. In 2010, [PERSON] et al. first established the digital optical phase conjugation (DOPC), which used a four-step phase-shifting method to measure the speckle phase and realized the phase conjugate focusing through the scattering medium [17]. Since then, DOPC has been deeply researched for focusing imaging of the scattering medium. In 2012, [PERSON] et al. reduced the alignment complexity of a COMS (complementary metal oxide semiconductor) camera and SLM by improving the system design of DOPC, and fluorescence imaging inside the scattering medium was also realized by using ultrasonic modulation [18]. In the same year, [PERSON] et al. also realized fluorescence imaging of the isotropic medium in the three-dimensional restricted area of light [19]. [PERSON] et al. presented a reference-free digital optical phase conjugation (DOPC) method that is sensitive enough to detect very weak fluorescent signals and works for light that is both spatially and temporally incoherent [20]. In 2013, [PERSON] et al. presented a simple and robust digital optical phase conjugation implementation for suppressing multiple scattering. They experimentally demonstrated wide-field imaging through a highly scattered sample using DOPC employing a ring interferometer configuration [21]. In 2014, [PERSON] et al. realized the ultrasonic-encoded digital optical phase conjugate in the reflection mode for the first time, further promoting the practical application of the DOPC system [22]. In 2015, [PERSON] et al. demonstrated the realization of a one-wave optical phase conjugation mirror using a spatial light modulator. Their method is simple, alignment free, and fast while allowing high-power throughput in the time reversed wave [23]. In the same year, [PERSON] et al. presented a new technique, known as time-reversed ultrasound microbubble encoded (TRUME) optical focusing, which focuses light with improved efficiency and sub-ultrasound wavelength resolution [24]. In 2016, [PERSON] et al. further realized the variable focus and three-dimensional imaging of transmitting scattering medium, which improved the controllability of phase conjugate focusing imaging [25]. In 2017, [PERSON] et al.