## 2 Method
### Ensemble Deep-Learning Network  
The hologram-classifier employed in this paper is EDL-IOHC. The approach in the articles [18, 19] opens a new paradigm for digital hologram recognition directly by wavefront analysis. The choice of EDL-IOHC is due to its robustness and high accuracy under noisy conditions with occlusion compared to its predecessors in [18, 19]. For clarity of explanation, the hologram-classifier EDL-IOHC, a complex wavefront recognition system, is outlined below. In reference to Figure 2a, which shows the structure of EDL-IOHC in [6] for recognizing digital holograms with the powerful capability to handle occluded objects contaminated with speckle noise. The input of the network is the reconstructed hologram with both magnitude and phase information, as shown in Figure 2a. The first and second CNN, known as the Magnitude CNN and the Phase CNN, accept the magnitude and phase components of the digital hologram, which is structurally the same but trained with different components' information. The architecture of both CNNs, as shown in Figure 2b, can be divided into three sections. Sections 1 and 2 have identical structures but different hyper-parameters, containing a convolution layer for local feature extraction, max-pooling, and dropout layers. Section 3 is a shared section for both the CNNs, and it is a \"Concatenate Unit\" to ensemble output information from the two CNNs. The concatenate unit ensembles all the extracted phase features and magnitude features into a combined flatten features vector before fitting into the \"Output Dense Layer\" for the decision unit to output the identity of the input digital hologram. This study employs the hologram-classifier EDL-IHC to identify the tissue object wavefronts (digital holograms) reconstructed from the raw intensity fringe patterns. Fringe pattern intensity is referred to as a raw hologram; \(\Gamma\) is a real number quantity and can be obtained as the result of measuring the intensity that results from the linear superposition of a diffracted object wavefront 'O' and a reference wavefront 'R'. Mathematically, the recorded intensity image can be expressed as follows:  
\[\Gamma(m,n)=\left\|R(m,n)+O(m,n)\right\|^{2} \tag{1}\]  
where \(\Gamma(m,n)\) is the intensity of the captured hologram with a size of M columns \(\times\) N rows. \(R(m,n)\) is the reference wavefront, and \(O(m,n)\) is the object wavefront. Expanding Equation (1) is as follows:  
\[ \begin{split}\Gamma(m,n)=&\|R(m,n)\|^{2}+\left\|O(m, n)\right\|^{2}\\ &+O(m,n)R^{*}(m,n)+O^{*}(m,n)R(m,n)\end{split}  \tag{2}\]  
where \({}^{*}\) is the complex conjugate operation for complex numbers, \(\left\|R(m,n)\right\|^{2}\) is the square magnitude of the reference wavefront, and \(\left\|O(m,n)\right\|^{2}\) is the square magnitude of the object  
Figure 1: Schematic diagram of the single-shot off-axis digital holographic interferometer. wavefront. \(\Gamma\) is a set of dark and bright fringes that embeds the amplitude and the phase information of the corresponding complex object wavefront. Discrete Fourier Transform (DFT) is performed on the off-axis raw hologram and generates the four terms in the frequency domain. The DFT transforms the raw hologram from the spatial domain to the frequency domain in a discrete manner. After performing DFT on Equation (2) and getting Equation (3), as below. \[ \begin{split} H(u,v)=& A^{2}MN\delta(u,v)+DFT\Big{\{} \|O(m,n)\|^{2}\Big{\}}\\ &+DFT\{O(m,n)R^{*}(m,n)+O^{*}(m,n)R(m,n)\}\end{split}  \tag{3}\]  
where \(u,v\) are the frequency axis, \(\delta(*)\) is the delta function, and \(A\) is the reference wave's amplitude. In the frequency domain, the spectral locations of the frequency components separated by the recorded off-axis hologram provide easy means to separate specific wavefront information in the Fourier space. The spectrum in the third term is extracted by a masking method, and the zero-order low-frequency spectrum and the twin image spectrum are removed.