# Review of 3D Imaging by Coded Aperture Correlation Holography (COACH) +
## 2 System Architectures
### Coded Aperture Digital Holography
#### 2.1.5 Partial Aperture Imaging System  
Partial aperture imaging is a technique to image objects through a part of the aperture area with as close as possible resolution capabilities of the full aperture. In this section, the partial aperture imaging  
Figure 14: Image of the (**a**) stitched PSH and (**b**) zero padded object hologram. Figure 13: Optical configuration of I-COACH for FOV extension. CPM—Coded phase mask; \(L_{1}\), \(L_{2}\)—Refractive lenses; \(P\)—Polarizer; SLM—Spatial light modulator; QPM—Quadratic phase mask. Figure 15: Reconstruction results using (**a**) regular PSH and (**b**) synthetic PSH. capabilities of I-COACH is summarized and compared with equivalent direct imaging systems. The I-COACH systems with partial apertures are denoted as partial aperture imaging systems (PAISs) [61]. In order to retain the resolution of the full aperture, annular apertures are considered. In the design of PAIS, an annular CPM is first synthesized using the GSA. As shown in Figure 16, the constraint on the camera plane is a uniform magnitude over a limited desired area, and the constraint on the CPM plane is a pure annular phase distribution and a zero transparency outside the ring. The obtained CPM is multiplied by an annular diffractive lens (DL) to satisfy the Fourier transform relation between the SLM and the camera planes. As shown in Figure 17, additional phase functions containing quadratic and linear phases are introduced in the aperture plane to deflect and concentrate the light incident outside the annular region away from the image sensor. The scheme of the laboratory imaging system is shown in Figure 18. The hologram recording and reconstruction are similar to those of a regular I-COACH. The light emitted from an object is collected and collimated using lens \(L_{2}\). The collimated beam is modulated by the annular CPM and Fourier transformed on the sensor plane by the annular DL. The light incident outside the CPM is deflected away from the sensor by the diffractive elements. Like any COACH system, also in PAIS, a training stage is necessary to record the PSH library. An experiment demonstrating PAIS was carried out [61] by a single optical channel to image an NBS object with 14 _lp/mm_. Three intensity patterns were recorded using three different annular CPMs synthesized from three different initial random phase profiles and composed into a complex hologram using phase shifts \(\theta_{1,2,3}=0,2\pi/3\) and \(4\pi/3\). PAIS was trained using a pinhole with a diameter of 25 \(\upmu\)m with the same three CPMs. Direct imaging was compared against PAIS results using only the annular diffractive lens. The recorded intensity patterns for the point object, object, reconstructions and direct imaging results for different thicknesses (160, 80 and 40 \(\upmu\)m of the annular CPMs corresponding to different partial aperture ratios 0.06, 0.03 and 0.014) are shown in Figure 19.  
Figure 16: Modified GSA for the synthesis of an annular CPM to render a uniform magnitude over a limited area on the sensor plane. Figure 17: Design of the aperture function for deflecting the light incident outside the annular CPM away from the image sensor; DOE—Diffractive optical element. The experiment was repeated for two plane objects made of two NBS targets 14 _lp/mm_ and 16 _lp/mm_ separated by 1 cm. The averaged reconstruction results of PAIS with 17 CPM sets were compared with that of direct imaging for annular CPM widths of 40, 80 and 160 \(\upmu\)m, respectively, as shown in Figure 20. PAIS has demonstrated better performances compared to direct imaging, and the images could be perceived even with an aperture ratio of only 1.4%, whereas direct imaging fails to provide an image with an aperture ratio of 6%. Figure 18: Optical configuration of PAIS. CPM—Coded phase mask; \(L_{1}\), \(L_{2}\)—Refractive lenses; \(P\)—Polarizer; SLM—Spatial light modulator; Blue arrows indicate polarization orientations.