Fig. 1. (Top row) Simplified schematic of in-line digital holographic microscopy. The complex-valued transmittance of a tissue sample of type k is converted into a hologram on a sensor array, with system parameters including wavelength (λ), numerical aperture (NA), magnification (M), propagation distance (d), and pixel size (p). (Bottom row) Framework of the proposed method. The backpropagated hologram displays obscured structural features with interference-related artifacts, enabling generalization across tissue types. For the training of our DL network, we employed a self-supervised training scheme using the refined forward model with effective reparameterization. This reparameterization enabled the representation of the hologram space using only two variables (peff and deff), instead of the original five variables (λ, NA, M, d, and p), thereby enhancing adaptability across various imaging configurations. Finally, our DL network reconstructs the complex-valued field from a single backpropagated hologram, demonstrating robust holographic reconstruction performance across various imaging scenarios.

Fig. 2. Comparison of sampling results of hologram space using conventional and refined forward models. (a) Sampling results using the conventional forward model, where pixel size (2 to 10μm), propagation distance (5 to 20 mm), NA (0.1 to 0.4), and magnification (5× to 20×) were randomly sampled 10,000 times from a uniform distribution for each parameter, with a fixed wavelength of 532 nm. The sampled values were converted to effective pixel size (peff) and effective distance (deff) and plotted. The orange dotted box highlights the region corresponding to the sampling range used in the refined forward model for our experiments. (b) Sampling results using the refined forward model, where peff and deff were randomly sampled 10,000 times from uniform distributions with ranges of 0.05 to 0.25 and 1.3 to 5.4, respectively.

Fig. 3. Effect of the backpropagation operator. Contrastive learning was applied to complex-valued fields from five tissue types: rectum, colon, small bowel, breast, and appendix, across three data categories: “in-focused field,” “propagated field,” and “backpropagated hologram,” as shown in the left panels. The upper row shows the real values, and the lower row shows the imaginary values for each data category. “In-focused field” refers to complex-valued fields captured via off-axis interferometry. Propagated field was generated through numerical propagation of the in-focused field. Backpropagated hologram was simulated by numerically backpropagating the intensity map of propagated field. Both propagated field and backpropagated hologram were simulated with a propagation distance of 15 mm. Middle panels show 2D visualizations obtained from the SimCLR network, where dimensionality reduction of the 512D intermediate vectors was performed using t-SNE. The right panels display FDs between rectum tissue and other tissue types, representing statistical distances within the 512D latent space of the SimCLR network. Scale bar: 20μm.

Fig. 4. Demonstration of enhanced generalization capability for OOD tissue types. Rectum tissue, used for training both the baseline and proposed models, represents the in-distribution data. In contrast, colon, small bowel, breast, and appendix tissues represent OOD tissue types that were not encountered during training. (a) Holographic reconstruction results from both the baseline and proposed methods. The input holograms were captured with an image-to-sensor distance (propagation distance) of 20 mm. (b) Mean PCC scores of reconstructed images across a distance range of 5 to 20 mm. Each bar in panel (b) is accompanied by an error bar indicating the standard deviation, derived from 375 distinct 512pixel×512pixel patches for each tissue type (25 patches per distance). Scale bar: 20μm.

Fig. 5. Demonstration of enhanced generalization capability for OOD imaging configurations. The schematic on the left displays the imaging systems used for capturing the holograms. System 1, which has identical imaging configurations to the rectum training data, represents the in-distribution imaging configuration with peff value of 0.1466. Systems 2 to 4 represent OOD imaging configurations with peff values of 0.1833, 0.1466, and 0.0677, respectively. The ground truth phase and the holographic reconstruction results for the baseline and proposed methods are shown on the right, using holograms with propagation distances of 20 mm (5.413), 12 mm (5.075), 15 mm (4.06), and 12 mm (5.075) for systems 1 to 4, respectively. The values in parentheses are corresponding effective distances for each configuration. Scale bar: 30μm.

Fig. 6. Generalization capability for OOD holograms with distinct tissue types and imaging configurations. The test holograms were captured from OOD tissues (appendix and colon) and OOD imaging systems (objective lens with 10× magnification and 0.25 NA) and evaluated using networks trained on the baseline and proposed methods with rectum data captured from imaging systems equipped with a 20×, 0.4 NA objective lens, and 6.5μm pixel size. (a) Holographic reconstruction results of the appendix with a pixel size of 6.5μm at different propagation distances. The upper row displays the results from the baseline method, whereas the lower row shows the results from the proposed method, at increasing propagation distances. (b) Holographic reconstruction results of the colon with a pixel size of 2.4μm at different propagation distances. Scale bar: 20μm.

Fig. 7. Robust phase reconstruction of colorectal cancer tissues across diverse imaging configurations using the proposed method. (a) Schematic of the training and testing process. Normal rectum tissue images, captured with a 20× objective lens, 0.4 NA, and a sensor with a 6.5μm pixel size, were used for training. The trained model was tested on cancerous rectum tissue holograms acquired using imaging systems with varying configurations (5× to 20× objective lenses, 0.1 to 0.4 NA, and a sensor with a 6.5μm pixel size). (b) Holographic reconstruction results for holograms of cancerous tissues. Ground-truth phase images and the corresponding reconstruction results by the proposed method are shown for systems with 5×/0.1 NA, 10×/0.25 NA, and 20×/0.4 NA. Blue dotted boxes in the low-magnification images (5× and 10×) indicate the corresponding fields of view seen at higher magnification images (10× and 20×, respectively). Yellow dotted boxes in the 20× images indicate the zoomed-in regions of interest, highlighting areas of dirty necrosis in the cancerous tissue. White arrows in the zoomed-in regions point to cell nuclei within these areas.