Advanced Photonics, Volume. 1, Issue 1, 016004(2019)
End-to-end deep learning framework for digital holographic reconstruction
Figures & Tables(14)
Fig. 1. (a) Schematic of the deep learning workflow and the structure of HRNet. It consists of three functional blocks: input, feature extraction, and reconstruction. In the first block, the input is a hologram of either an amplitude object (top), a phase object (middle), or a two-sectional object (bottom). The third block is the reconstructed output image according to the specific input. The second block shows the structure of HRNet; (b) and (c) elaborate the detailed structures of the residual unit and the subpixel convolutional layer, respectively.
Fig. 2. (a) The USAF test target and its local areas as amplitude objects. (b) A customized groove on an optical wafer as the phase object. (c) A homemade two-sectional object consisting of a transparent triangle and a rectangle located at different axial positions.
Fig. 3. Experimentally collected testing holograms of amplitude objects.
Fig. 4. (a)–(d) Ground-truth images and reconstructed images of holograms in
Fig. 5. Experimentally collected testing holograms of the phase object.
Fig. 6. (a)–(d) Ground-truth images and reconstructed quantitative phase images of holograms in
Fig. 7. Experimentally collected testing holograms of the two-sectional object.
Fig. 8. Ground-truth: (a)–(d) EFI and (e)–(h) DM. HRNet, reconstructed: (i)–(l) EFI and (m)–(p) DM. Entropy, reconstructed: (q)–(t) EFI and (u)–(x) DM. T-gradient, reconstructed: (y)–(ab) EFI and (ac)–(af) DM. Variance, reconstructed: (ag)–(aj) EFI and (ak)–(an) DM. The color bar shows the depth in DM; the unit is mm.
Fig. 9. (a) and (b) Holograms. (c) and (d) Frequency spectra. (e) and (f) Reconstructed images under different angles.
Fig. 10. Holograms [(a) and (b)] and reconstructed images [(c) and (d)] under different axial distances.
Table 1. Comparison of reconstruction performance for the amplitude object among ASM, CONV, and HRNet.
View tableView in ArticleTable 1. Comparison of reconstruction performance for the amplitude object among ASM, CONV, and HRNet.
Measure Methods Amplitude dataset Validation Test PSNR (dB) ASM 17.66 19.64 CONV 19.68 20.54 HRNet 25.99 24.62 SSIM ASM 0.20 0.19 CONV 0.26 0.26 HRNet 0.92 0.91 Time (s) ASM 1.56 1.49 CONV 1.35 1.72 HRNet 1.14 1.21
Table 2. Comparison of reconstruction performance for the phase object among PCA, DE, and HRNet.
View tableView in ArticleTable 2. Comparison of reconstruction performance for the phase object among PCA, DE, and HRNet.
Measure Methods Phase dataset Validation Test PSNR (dB) PCA 10.12 9.53 DE 8.94 8.68 HRNet 30.35 30.49 SSIM PCA 0.13 0.11 DE 0.12 0.10 HRNet 0.96 0.96 Time (s) PCA 1.96 1.93 DE 2.09 2.15 HRNet 1.06 1.20
Table 3. Comparison of EFI and DM reconstruction performance for the two-sectional object among SEN, VRA, TEN, and HRNet.
View tableView in ArticleTable 3. Comparison of EFI and DM reconstruction performance for the two-sectional object among SEN, VRA, TEN, and HRNet.
Measure Methods EFI DM Validation Test Validation Test PSNR (dB) SEN 16.82 15.92 12.66 12.78 VAR 15.44 14.69 12.78 11.92 TEN 16.03 15.86 11.82 12.24 HRNet 35.64 35.72 37.81 36.70 SSIM SEN 0.28 0.27 0.80 0.80 VAR 0.10 0.11 0.82 0.82 TEN 0.14 0.10 0.80 0.80 HRNet 0.97 0.97 0.97 0.98 Time (s) SEN 380.30 392.68 390.03 391.36 VAR 384.38 386.52 390.58 388.82 TEN 376.76 383.66 398.29 394.37 HRNet 1.35 1.30 1.04 1.42
Table 4. Detailed description of the layers and parameters of the proposed HRNet (biases are ignored in the computation).
View tableView in ArticleTable 4. Detailed description of the layers and parameters of the proposed HRNet (biases are ignored in the computation).
Layer number Layer type Configuration Number of parameters Layer 1 2-D convolution 3 × 3 × 32 + BN + ReLU 3 × 3 × 32 = 288 Layer 2 ResUnit (64) Max-pooling: 2 × 2 3 × 3 × 64 + BN + ReLU 3 × 3 × 64 + BN + ReLU Parameter-free 3 × 3 × 32 × 64 = 18,432 3 × 3 × 64 × 64 = 36,864 Layer 3 ResUnit (64) 3 × 3 × 64 + BN + ReLU 3 × 3 × 64 + BN + ReLU 3 × 3 × 64 × 64 = 36,864 3 × 3 × 64 × 64 = 36,864 Layer 4 ResUnit (128) Max-pooling: 2 × 2 3 × 3 × 128 + BN + ReLU 3 × 3 × 128 + BN + ReLU Parameter-free 3 × 3 × 64 × 128 = 73,728 3 × 3 × 128 × 128 = 147,456 Layer 5 ResUnit (128) 3 × 3 × 128 + BN + ReLU 3 × 3 × 128 + BN + ReLU 3 × 3 × 128 × 128 = 147,456 3 × 3 × 128 × 128 = 147,456 Layer 6 ResUnit (256) Max-pooling: 2 × 2 3 × 3 × 256 + BN + ReLU 3 × 3 × 256 + BN + ReLU Parameter-free 3 × 3 × 128 × 256 = 294,912 3 × 3 × 256 × 256 = 589,824 Layer 7 ResUnit (256) 3 × 3 × 256 + BN + ReLU 3 × 3 × 256 + BN + ReLU 3 × 3 × 256 × 256 = 589,824 3 × 3 × 256 × 256 = 589,824 Layer 8 Subpixel convolution 3 × 3 × 64 + BN + ReLU + periodic shuffling 3 × 3 × 256 × 64 = 147,456 Total parameters 2,857,248
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Zhenbo Ren, Zhimin Xu, Edmund Y. Lam, "End-to-end deep learning framework for digital holographic reconstruction," Adv. Photon. 1, 016004 (2019)
Paper Information
Category: Research Articles
Received: Jun. 6, 2018
Accepted: Nov. 14, 2018
Published Online: Feb. 18, 2019
The Author Email: Lam Edmund Y. (elam@eee.hku.hk)
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