# Review of 3D Imaging by Coded Aperture Correlation Holography (COACH) +
## 2 System Architectures
### Coded Aperture Digital Holography
#### 2.1.3 Single Camera Shot I-COACH  
One of the disadvantages of I-COACH is the requirement of several camera shots to reconstruct an object with an acceptable SNR. As mentioned above, the noise reduction techniques in I-COACH  
Figure 8: Reconstruction results of I-COACH for (**a**) NBS chart and (**b**) USAF chart. Figure 7: Optical configuration of I-COACH. CPM—Coded phase mask; \(L_{1}\), \(L_{2}\)—Refractive lenses; \(P\)—Polarizer; SLM—Spatial light modulator; Blue arrows indicate polarization orientations. are implemented at various levels, starting from the design of the CPMs, reconstructing images by phase-only filtering and recording a few holograms for averaging. The averaging technique reduces the time resolution of the system. In this section, the averaging technique is replaced with a method of recording the holograms with a single camera shot. This method is denoted as the single camera shot I-COACH (SCS-I-COACH) [56]. The Fourier-based GSA (see Figure 4) used in I-COACH for synthesizing the CPM was constrained to yield a uniform magnitude on part of the sensor plane. However, because the image sensor was not located at the Fourier plane of the CPM in the experimental setup, the Fourier relation between the CPM and the sensor plane was not satisfied in the experiment. This means that the Fourier-based GSA does not match the experimental setup, and hence the noise has not been reduced as expected. Therefore, an additional diffractive lens was multiplexed into the CPM and the image sensor was positioned at the focal plane of this lens to fulfill the Fourier relations between the CPM and the sensor plane in the GSA. Although the above modification improved the SNR, the system still required at least two camera shots for creating bipolar holograms. In SCS-I-COACH, bipolar holograms are indeed recorded but the two shots recorded in time are replaced by two shots recorded in space using additional diffractive masks. The integration of two CPMs in the aperture plane using linear and quadratic phase functions is shown in Figure 9. The optical configuration of SCS-I-COACH is shown in Figure 10. An additional constraint is used in the GSA to limit the area of the intensity pattern in the sensor plane. It should be noted that the space sharing of two raw holograms on the sensor area reduces the FOV of the imaging system. Hence, in SCS-I-COACH, the single-shot capability is obtained at the expense of a reduction in FOV and some reduction of SNR. Figure 10: Optical configuration of SCS-I-COACH. \(L_{1}\), \(L_{2}\)—Refractive lenses; \(P\)—Polarizer; SLM—Spatial light modulator; Blue arrows indicate polarization orientations. Figure 9: Engineering the aperture of SCS-I-COACH using linear and quadratic phase functions added to the two CPMs. In the SCS-I-COACH setup, there are two image responses to the single object point. Therefore, there are two Fourier transforms for CPM1 and CPM2 centered at (_U_/4,0) and (-_U_/4,0), respectively, where \(U\) is the height of the sensor plane. The intensity in the sensor plane is given by,  
\[I(u,v)=G_{1}(u-U/4,v)+G_{2}(u+U/4,v) \tag{6}\]  
where \(G_{1}=\left|\Im\{\exp(i\Phi_{CPM1})\}\right|^{2}\) and \(G_{2}=\left|\Im\{\exp(i\Phi_{CPM2})\}\right|^{2}\). The two intensity patterns \(G_{1}\) and \(G_{2}\), corresponding to CPM1 and CPM2, respectively, are recorded, extracted and subtracted from each other. The resulting intensity pattern is a bipolar PSH given by \(H_{PSH}(z=0)=G_{1}(u,v)-G_{2}(u,v)\). A library of PSHs is created as described earlier by moving the pinhole to various axial locations. Next, the object hologram is recorded for an object placed within the axial boundaries of the PSH library. The object is considered as a collection of independent incoherent source points.