Abstract
Imaging through diffusers presents a challenging problem with various digital image reconstruction solutions demonstrated to date using computers. Here, we present a computer-free, all-optical image reconstruction method to see through random diffusers at the speed of light. Using deep learning, a set of transmissive diffractive surfaces are trained to all-optically reconstruct images of arbitrary objects that are completely covered by unknown, random phase diffusers. After the training stage, which is a one-time effort, the resulting diffractive surfaces are fabricated and form a passive optical network that is physically positioned between the unknown object and the image plane to all-optically reconstruct the object pattern through an unknown, new phase diffuser. We experimentally demonstrated this concept using coherent THz illumination and all-optically reconstructed objects distorted by unknown, random diffusers, never used during training. Unlike digital methods, all-optical diffractive reconstructions do not require power except for the illumination light. This diffractive solution to see through diffusers can be extended to other wavelengths, and might fuel various applications in biomedical imaging, astronomy, atmospheric sciences, oceanography, security, robotics, autonomous vehicles, among many others.
Highlights
Imaging through scattering and diffusive media has been an important problem for many decades, with numerous solutions reported so far [1–19]
The output image (See figure on page.) Fig. 1 All-optical imaging through diffusers using diffractive surfaces. a Training and design schematic of a 4-layered diffractive system that can see through unknown/new randomly generated phase diffusers. b Sample images showing the image distortion generated by random diffusers
To further demonstrate the generalization of the alloptical image reconstructions achieved by trained diffractive networks, Additional file 1: Fig. S5 reports the reconstruction of unknown test objects that were seen through a new diffuser, which had a smaller correlation length (~5λ) compared to the training diffusers (~10λ); stated differently, the randomly generated test diffuser was not used as part of the training, and it included much finer phase distortions compared to the diffusers used in the training
Summary
Imaging through scattering and diffusive media has been an important problem for many decades, with numerous solutions reported so far [1–19]. There is no simple solution to accurately obtain the transmission matrix of a diffuser [34]. The transmission matrix will significantly deviate from its measured function if there are changes in the scattering medium [35], partially limiting the utility of such measurements to see through unknown, new diffusers. With significant advances in wave-front shaping [37–40], wide-field real-time imaging through turbid media became possible [8, 41]. These algorithmic methods are implemented digitally using a computer and require guide-stars or known reference objects, which introduce additional complexity to an imaging system. Digital deconvolution using the memory effect [42, 43] with iterative algorithms is another important
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