Extended depth-of-field in holographic image reconstruction using deep learning based auto-focusing and phase-recovery

Abstract: Holography encodes the three dimensional (3D) information of a sample in the form of an intensity-only recording. However, to decode the original sample image from its hologram(s), auto-focusing and phase-recovery are needed, which are in general cumbersome and time-consuming to digitally perform. Here we demonstrate a convolutional neural network (CNN) based approach that simultaneously performs auto-focusing and phase-recovery to significantly extend the depth-of-field (DOF) in holographic image reconstruction. For this, a CNN is trained by using pairs of randomly de-focused back-propagated holograms and their corresponding in-focus phase-recovered images. After this training phase, the CNN takes a single back-propagated hologram of a 3D sample as input to rapidly achieve phase-recovery and reconstruct an in focus image of the sample over a significantly extended DOF. This deep learning based DOF extension method is non-iterative, and significantly improves the algorithm time-complexity of holographic image reconstruction from O(nm) to O(1), where n refers to the number of individual object points or particles within the sample volume, and m represents the focusing search space within which each object point or particle needs to be individually focused. These results highlight some of the unique opportunities created by data-enabled statistical image reconstruction methods powered by machine learning, and we believe that the presented approach can be broadly applicable to computationally extend the DOF of other imaging modalities.

• The paper introduces HIDEF, a deep learning framework utilizing CNNs for simultaneous non-iterative auto-focusing and phase-recovery from single holograms.
• Experiments show HIDEF achieves robust phase-recovery and auto-focusing across significant axial ranges with dramatically reduced inference times compared to conventional techniques.
• This deep learning approach overcomes computational limitations of conventional holographic reconstruction and suggests potential for wider application in other imaging modalities requiring extended depth of field.

Extended Depth-of-Field in Holographic Image Reconstruction Using Deep Learning Techniques

The paper authored by Wu et al. presents a convolutional neural network (CNN) based method termed HIDEF (Holographic Imaging using Deep learning for Extended Focus) to address key limitations in holographic imaging modalities. Holography inherently captures comprehensive 3D information of samples through intensity recordings that encapsulate, albeit indirectly, both amplitude and phase data. The recovery of this information, crucial for accurate image reconstruction from holograms, requires complex processes including phase-recovery and auto-focusing, traditionally characterized by their iterative and computationally expensive nature.

Methodology

The authors propose a non-iterative deep-learning framework leveraging CNNs. The architecture draws upon U-Net structures to facilitate simultaneous auto-focusing and phase-recovery from single back-propagated holograms. By training on defocused holographic images paired with their corresponding in-focus phase-recovered counterparts, the neural network learns to reconstruct in-focus images, effectively extending the depth-of-field (DOF) without iterative computational burdens.

Upon completion of the training phase, the network operates with a time complexity reduction from O(nm) to O(1), signifying substantial improvement in computational efficiency. The algorithm's ability to handle extensive DOFs suggests its broader applicability across various imaging systems, potentially extending its utility to modalities like fluorescence microscopy.

Findings

Wu et al. report promising results from their experiments using aerosol samples. The HIDEF framework achieved robust phase-recovery and auto-focusing across substantial axial ranges (~0.2 mm defocusing). Remarkably, despite training with depth-specific patches, the CNN successfully generalized to diverse samples with variable depth distributions without requiring precise sample positioning during testing. Such adaptability highlights the neural network's ability not only to extract spatial features across different scales but also to filter in-focus from out-of-focus components efficiently.

Comparative analysis against multi-height phase-recovery techniques revealed that HIDEF achieves comparable, if not superior, results with significantly lower inference times—less than 0.3 seconds per sample, a striking reduction from traditional methods which may require up to 6.4 seconds per field of view.

Implications and Future Perspectives

The innovation presented by Wu et al. opens avenues for improving holographic imaging modalities by overcoming limitations associated with conventional reconstruction methods. This research underscores how deep learning models can transcend traditional physics-based algorithms by statistically modeling spatial characteristics to enhance imaging capabilities. The potential applications extend beyond holography into other fields demanding extended DOF and computational efficiency.

Future research could explore enhancements to network architecture to further expand the axial DOF range. Investigating larger datasets or advanced network designs might push modeling capabilities further, allowing for more diverse imaging scenarios. Additionally, consideration of noise, sample complexity, and imaging environments could refine the robustness and applicability of such deep learning approaches.

In summary, the paper offers substantive contributions to holographic imaging through robust deep learning methods, presenting a framework that not only accelerates computational performance but also widens DOF, offering a pragmatic pathway for advancement in both applied and theoretical imaging sciences.