# On Ghost Imaging Studies for Information Optical Imaging
## 3 Ghost Imaging Studies for Information Optical Imaging  
### Mapping Higher-Dimensional Light-Field Information into Lower-Dimensional Domain  
As demonstrated in (11), GI can modulate the object's image information with controllable light fields and map it into lower detectable dimensions through encoding, thus making it possible to realize direct imaging in the high-dimensional light-field domain and enable further-developed imaging capabilities. Typical examples include the GI LiDAR and the GI camera. The principle of GI LiDAR is shown in Figure 2. It was first made public in 2011 [66; 67] and demonstrated to perform three-dimensional (3-D) imaging of natural scenes [68]. GI LiDAR uses light fields with designed spatiotemporal fluctuations, which are generated by modulating a pulse laser with a diffuser to illuminate the object, then acquires the return signal with a bucket detector and retrieves the 3-D spatial-depth image information by the second-order correlation between illuminated light fields and return signals as  
\[\langle\Delta I_{\rm t}(t_{\rm d})\Delta I_{\rm r}(\mathbf{r}_{\rm r})\rangle\propto T (\mathbf{r}_{\rm r},d(t_{\rm d})), \tag{12}\]  
where \(t_{\rm d}\) is the relative time delay of the detection signal. During the detection process, the encoding is performed via the designed light fields to transform the 3-D information into a time-serial signal which is recorded by the bucket detector. Compared with traditional LiDAR systems which only perform encoding on the time-frequency dimension, GI LiDAR essentially extends the encoding domain to higher dimensions including both spatial and temporal domains. Hence, different from traditional LiDAR, which can only measure the distance and velocity, GI LiDAR can simultaneously perform the imaging of scenes of different distances as well as obtaining their depth and velocity information [69], which belong to higher dimensions. For GI LiDAR with incoherent bucket detection, the phase information (which may include the vibration information) of the target is lost when recording. On the contrary, in those GI variants in microwave bands (e.g., the correlated imaging), the micro-vibration information of the target can be obtained when performing imaging. This is mainly owing to the utilization of the coherent detection method for signal recording since it is the first-order field correlation that is involved there [44; 45; 46]. Recently, with the development of coherent optical communication [70] and fiber optical time-frequency transmission [71], coherent detection methods for optical-waveband signals have been largely developed. Thus, they have also been introduced into GI LiDAR at optical wavebands, leading to coherent detection GI LiDAR [72; 73; 74] which has the ability to acquire the information in a higher dimension (e.g., the micro-Doppler vibration information) and enable a stronger anti-interference capability. In this scheme, a long-pulse laser is modulated in the spatial-temporal/spatial-frequency domains to illuminate the object, and the return signal is detected via a typical coherent detection approach. Then, by combining the second-order correlation with time-frequency analysis techniques, 3-D spatial-depth image information as well as the spatial distribution information of velocity and vibration of the target can be retrieved together. Different from GI LiDAR with active illumination, the GI camera [75] is a passive (using natural lights only) GI scheme inspired by near-field diffraction speckle phenomena [76; 77], proposed via utilizing the ergodicity of thermal light fields to extract image information from the second-order correlation in the spatial domain rather than the original temporal domain. The principle of a representative GI spectral camera is shown in Figure 3. The object illuminated by natural lights is firstly imaged by a front imaging module, then diffracted by a spatial random phase modulator (SRPM) and finally recorded by a detector as a pattern of intensity distribution \(I_{t}(\mathbf{r}_{t})\).