# Review of 3D Imaging by Coded Aperture Correlation Holography (COACH) +
## 3 System Applications
### Super-resolution Imaging by Coded FINCH Technique  
The image resolution of a general optical system is governed by two parameters, namely, wavelength and the NA [62]. Improving the resolution using shorter wavelengths is not always feasible or practical. A more practical way to improve the image resolution is to increase the NA. Increasing the NA requires increasing the diameter of the system aperture or alternatively using special techniques to enhance the resolution without changing aperture diameter. In the following, the lateral resolution enhancement of COACH is discussed. The following technique of resolution enhancement is based on the idea that a scattering mask positioned between the observed object and the entrance of an imaging system can increase the effective NA of the system, and thus can improve the resolution. An early implementation of this idea was proposed by [PERSON] et al. [63]. A modern version of this technique, with the ability to control the size of the effective NA, is termed coded FINCH (C-FINCH) and is actually a combination between COACH and FINCH [64]. C-FINCH was designed in order to improve the lateral resolution beyond the inherent limit of FINCH. Moreover, C-FINCH was planned in order to maintain any of the basic advantages of both COACH and FINCH, such as motionless, compactness and the use of a single optical channel. The optical configuration of the proposed C-FINCH system is shown in Figure 23[64]. A laser light emitted from a point object is incident on SLM\({}_{1}\) on which a CPM is displayed. The scattering degree of the CPM is calibrated by the GSA. When as much of the area of the CPM spectrum is constrained to be wider, the scattering degree becomes higher [64]. The scattering degree is defined as \(\sigma=B/B_{max}\), where \(B\) and \(B_{max}\) are the constrained area and maximal area in the spectral domain of the GSA, respectively. The scattering mask displayed on the SLM\({}_{1}\) scatters the incident light and acquires the high spatial frequencies discarded by the system without the CPM, due to the limited NA. The scattered light is collected by lens \(L_{1}\) and directed into the dual lens FINCH setup. Polarizers \(P_{1}\) and \(P_{2}\) are used  
Figure 21: Experimental setup of I-COACH for recording 3D objects. BS\({}_{1}\) and BS\({}_{2}\)—Beam splitters; BPF—Band pass filter; SLM—Spatial light modulator; \(L_{\rm IA}\) and \(L_{\rm IB}\)—identical refractive lenses; CPM—Coded phase mask; LED1 and LED2—identical Light emitting diodes; \(P_{1}\)—Polarizer; \(\bullet\)—Polarization direction perpendicular to the plane of the page. Figure 22: 3D imaging reconstruction results of I-COACH (**a**) Two one-cent coins, (**b**) LED and (**c**) Stapler pins. for the polarization multiplexing scheme in FINCH [27]. A refractive lens \(L_{2}\) with a focal length of \(f_{0}\) after the SLM\({}_{2}\) is used for implementing the dual lens FINCH [31]. DL with a focal length of \(f_{d}\) is displayed on SLM\({}_{2}\). As a result of the CPM on SLM\({}_{1}\), the two interfering waves are distorted due to the scattering characteristic of the CPM. The two chaotic waves propagate to the image sensor located at a distance of \(z_{h}\) from the SLM\({}_{2}\) and create an interference pattern recorded by the sensor. The bias and twin image terms are removed using the phase shifting procedure as in ordinary FINCH [23]. The three recorded raw holograms for \(\theta_{1,2,3}=0^{\circ}\), \(120^{\circ}\) and \(240^{\circ}\) are superposed to obtain a complex hologram. The magnitude of the PSH recorded using a pinhole with a diameter of 5 \(\upmu\)m, for different values of the scattering degree \(\sigma\), is shown in Figure 24.  
The relation between the sensor plane and SLM\({}_{1}\) (CPM) can be approximated to a Fourier relation with a scaling factor of \(\lambda d_{1}z_{h}/f_{0}\), where \(\lambda\) is the central wavelength of the illumination [64].