## 2 Analysis of Imaging Properties of HDOE in Wide-Bandwidth Spectrum
### Deep Dense Zoned Multipath Residual Network  
In SHDICS, we built a multi-task network model for image restoration and super-resolution, in order to recover the degradation of diffraction imaging and improve the imaging capability of the system, because data-driven image restoration and super-resolution processing have the same inherent process. The process is to find the optimal intrinsic relationship in the pixel-to-pixel correspondence of the input image with the output image and to remove only the unwanted content, while carefully preserving the desired spatial details. Therefore, we reconceptualized image restoration and super-resolution reconstruction as two tasks performed simultaneously within a process. Accordingly, the imaging degradation procedure in SHDCI can be expressed as:  
\[L=h\otimes(H\downarrow_{s})+n, \tag{11}\]  
where \(L\) is the low quality image captured by the sensor, \(H\) is the ground truth, \(h\) is the degradation function of HDOE derived in Section 2.2, which can also be called fuzzy kernel, \(\downarrow_{s}\) represents the downsampling process, and \(n\) is noise generated by the system. The residual network framework can build very deep networks to perform multi-image tasks [16,26]. Consequently, based on the residual network and the image quality degradation model of HDOE, we designed the deep dense zoned multipath residual (DDZMR) network. The main components of DDZMR network are: the image regional division and channel selection module; the double residual tandem spatial attention block (DRTSAB); the residual dense concatenation block (RDCB); an upsampling module. These components are combined in an end-to-end architecture for DDZMR learning; the network model is shown in Figure 4.  
Figure 3: **(a)** The PSF distribution of the harmonic diffractive lens with a wavelength of 500–600 nm on the focal plane; **(b)** PSF estimation experiment of harmonic diffraction imaging system; **(c)** The PSF distribution of the imaging system measured experimentally. The image regional division and channel selection module divides the image into 25 \(128\times 128\) pixel subimages. The pixel overlap for adjacent subimages is 32 pixels. Each subimages learns a subregion-specific degradation process along its own independent channel. Since the performance of PSF in HDOE is different on different field of views, the region partitioning strategy can make the DDZMR network better learn the sub-image computational reconstruction process. The subimages maintain the original resolution features along the network hierarchy, thereby minimizing the loss of precise spatial detail. The reconstructed subimages are finally stitched together into a reconstructed full-frame image. DRTSAB consists of two sets of convolutional (Conv) and spatial attention module (SAM) layers, as shown in Figure 5, and the input and output of each layer are connected to subsequent layers for local residual learning.The SAM is connected to the residual block to filter out blur caused by chromatic aberration and loss of detail caused by stray light, and optimize the network size. The SAM independently applies global average pooling and max pooling operations to feature extraction in the channel dimension, and concatenates the outputs to form feature maps. It aims to exploit the spatial interdependence of convolutional features to generate spatial attention feature maps, which are used to recalibrate the incoming feature space [26]. Figure 4: Deep dense zoned multipath residual network. Figure 5: Double residual tandem spatial attention block (DRTSAB). The components of RDCB are three dense skip-connected DRTSABs to propagate low-level features to subsequent residual blocks. The purpose of the dense skip connections is to further facilitate the back propagation of gradients, to reuse low level features to increase the potential of the final reconstructed features [26], and to facilitate information flow during learning.