# Review of 3D Imaging by Coded Aperture Correlation Holography (COACH) +
## 2 System Architectures
### Coded Aperture Digital Holography
#### 2.1.2 Interferenceless Coded Aperture Correlation Holography  
The entire incoherent digital holography techniques discussed so far are based on two-beam interference. In general, two beam interferometers suffer from several limitations, such as the need for vibration isolation, power loss of more than half of the incident optical power and the need to minimize the optical path difference between the optical channels. Two-beam interference is essential in FINCH to read the phase of the wave emitted from each object point. Only the phase function contains the information of an object point location, whereas the wave magnitude is uniform and thus lacks any information. Unlike FINCH, in COACH, the information of a single point location is encoded in both the phase and the magnitude distributions. Both functions have chaotic distributions that can be reconstructed by a cross-correlation with the corresponding PSH. However, to record the phase, self-interference is needed, whereas to record the magnitude, a direct detection of the light intensity is  
Figure 6: Reconstruction results using (**a**) matched filter, (**b**) phase-only filter. Phase-only filter and averaging with (**c**) 5 samples, (**d**) 10 samples, (**e**) 15 samples and (**f**) 20 samples.  
enough. Therefore, COACH has the capability to image a 3D scene without two-wave interference. This version of COACH without two-wave interference is termed interferenceless COACH (I-COACH) [54], and it is implemented without splitting the object beam to two beams.  
I-COACH is not much different from a direct single-channel imaging system but has the capability to record and reconstruct 3D information in one or a few camera shots. The relaxation of the interference condition improves the SNR during reconstruction and the power efficiency of the imaging process is increased. At this point, it should be mentioned that imaging with a phase-coded aperture has already been proposed by [PERSON] and [PERSON] [55]. However, Ref. [55] has avoided an imaging 3D scene and because of lack of any noise reduction mechanism, the presented results suffer from substantial background noise. The optical configuration of I-COACH is shown in Figure 7. The polarizer P is oriented along the active axis of the SLM such that all the incident light is modulated. In I-COACH, three CPMs are synthesized from three initial independent random phase profiles and the corresponding intensity patterns are recorded for a point object. Each of the recorded patterns is multiplied by one of the phase constants with the values \(\theta_{1,2,3}=0\), \(2\pi/3\) and \(4\pi/3\), and the three matrices are combined into a single complex hologram. The same procedure is repeated for the object hologram. The object image is reconstructed by a cross-correlation between the above two holograms.  
The experimental results of I-COACH are shown in Figure 8 for a two plane object constructed from element 8 _lp/mm_ of the NBS chart and elements 5 and 6 of Group 2 of the USAF chart [54]. The NBS and USAF are separated from each other by 1 cm. The \(H_{PSH}\) is recorded at the two planes of the object as with COACH followed by the recording of the \(H_{\text{OBJ}}\). Even though the SNR is improved in the case of I-COACH compared to COACH, the technique still needs additional procedures to reduce the background noise. In the present experiment, both phase-only filtering and averaging technique (20 samples) were implemented. The simplicity of the optical configuration without interference but with a unique capability to record and reconstruct 3D information makes I-COACH an attractive candidate for 3D imaging.