## 2 Methods
### Synthesis of CgH  
The CGH synthesis for near-eye holographic content is explained on the basis of the wave optics and [PERSON]'s holographic model in the system schematically illustrated in Figure 4[10; 11; 12]. We assume that the distance (\(D_{1}\)) between the holographic display and the eye lens is equal to the focal length (\(f_{1}\)) of the field lens. When the size of eyeball and the focal length of eye lens are given as \(D_{2}\) and \(f_{2}\), we also assume that the hologram plane (\(x_{1}\),\(y_{1}\)) near the field lens and the retinal plane (\(x_{2}\), \(y_{2}\)) of the user are located in parallel with the eye lens plane (\(u\),\(v\)). The optical field at the display panel with size of \(X\times Y\) and that of retinal domain of the observer are denoted as \(F(x_{1},\ y_{1})\) and \(G(x_{2},\ y_{2})\), respectively. These fields are related to the following equation, called a cascaded Fresnel transform [24; 25]:  
\[G(x_{2},y_{2})=a(x_{2},\ y_{2})\iint\biggl{[}e^{\frac{i\pi}{A}(\frac{1}{T_{1}} +\frac{1}{T_{2}}-\frac{1}{T_{2}})(u^{2}+v^{2})}\iint h(x_{1},y_{1},u,v)F(x_{1},y_{1})dx_{1}dy_{1}\biggr{]}\times e^{-\frac{3\pi i}{A}(x_{2}u+y_{2}v)}dudv, \tag{1}\]  
where \(a(x_{2},\ y_{2})=-e^{\frac{2i\pi(D_{1}+D_{2})}{A}}e^{\frac{i\pi(x_{2}^{2}+y_{2 }^{2})}{A\Omega_{2}}}\), and \(h(x_{1},y_{1},u,v)=rect(\frac{x_{1}}{X},\frac{y_{1}}{Y})\times e^{\frac{i\pi}{ A\Omega_{1}}(x_{1}^{2}+y_{1}^{2})}\)\(e^{-\frac{3\pi i}{A\Omega_{1}}(x_{1}u+y_{1}v)}\).  
While an image formed at the retinal plane is analyzed using the direct cascaded Fresnel transform, as given in Equation (1), making the desired image formation the optical field input at the display plane (\(x_{1}\),\(y_{1}\)) is calculated using an inverse cascaded Fresnel transform. On the basis of Equation (1), the desired hologram field \(H(x_{1},\ y_{1})\) in the display domain is synthesized after a process of superposition of a reference wave field with the initially calculated optical field \(F(x_{1},\ y_{1})\). It is assumed that the reference wave field is the complex amplitude of the illumination wave from the backlight unit that is collimated, normally incident with a constant amplitude. In addition to the reference wave, we superimpose an off-axis carrier wave \(C(x_{1},\ y_{1})\) on the calculated optical field \(F(x_{1},\ y_{1})\) so that the desired signal function may shift from the noise terms, such as the DC term, and the twin-conjugate image. Through direct observation tests of each eye from H3D reconstructions, we experimentally derived the optimized conditions for the carrier wave format of \(C(x_{1},\ y_{1})=e^{[\pi i(x_{1}+y_{1})]}\), with \(a\) = 0.048 and \(b\) = 0.128, in applying the current-considered optical geometry (see Figure 4). Therefore, we could finally synthesize the signal function for the digital hologram \(H(x,\ y)\); the signal function contains complex numbers in general, and can be expressed by \(H(x,\ y)=|H(x,\ y)|e^{i\Phi(x,\ y)}\), where \(|H(x,\ y)|\) is the amplitude of \(H(x,y)\) and \(\Phi(x,y)\) is its phase. Here, the CGH's original function must  
Figure 3: Geometry for extracting RGB and depth map information and examples of RGB and depth map images: geometry in a perspective view (**a**) and in a camera-lens view (**b**). (**c,d**) are a set for the left eye, and (**e,f**) are for the right eye. Each image of FHD resolution is extracted at a given view from a virtual camera set to capture the RGB color and depth map images.  
be converted into an appropriate representation, that is, amplitude-modulating hologram data suitable for the study, because we use the amplitude-modulating SLM in our system.