Subwavelength Imaging using a Solid-Immersion Diffractive Optical Processor

Phase imaging is widely used in biomedical imaging, sensing, and material characterization, among other fields. However, direct imaging of phase objects with subwavelength resolution remains a challenge. Here, we demonstrate subwavelength imaging of phase and amplitude objects based on all-optical diffractive encoding and decoding. To resolve subwavelength features of an object, the diffractive imager uses a thin, high-index solid-immersion layer to transmit high-frequency information of the object to a spatially-optimized diffractive encoder, which converts/encodes high-frequency information of the input into low-frequency spatial modes for transmission through air. The subsequent diffractive decoder layers (in air) are jointly designed with the encoder using deep-learning-based optimization, and communicate with the encoder layer to create magnified images of input objects at its output, revealing subwavelength features that would otherwise be washed away due to diffraction limit. We demonstrate that this all-optical collaboration between a diffractive solid-immersion encoder and the following decoder layers in air can resolve subwavelength phase and amplitude features of input objects in a highly compact design. To experimentally demonstrate its proof-of-concept, we used terahertz radiation and developed a fabrication method for creating monolithic multi-layer diffractive processors. Through these monolithically fabricated diffractive encoder-decoder pairs, we demonstrated phase-to-intensity transformations and all-optically reconstructed subwavelength phase features of input objects by directly transforming them into magnified intensity features at the output. This solid-immersion-based diffractive imager, with its compact and cost-effective design, can find wide-ranging applications in bioimaging, endoscopy, sensing and materials characterization.

All-optical image denoising using a diffractive visual processor

Image denoising, one of the essential inverse problems, targets to remove noise/artifacts from input images. In general, digital image denoising algorithms, executed on computers, present latency due to several iterations implemented in, e.g., graphics processing units (GPUs). While deep learning-enabled methods can operate non-iteratively, they also introduce latency and impose a significant computational burden, leading to increased power consumption. Here, we introduce an analog diffractive image denoiser to all-optically and non-iteratively clean various forms of noise and artifacts from input images - implemented at the speed of light propagation within a thin diffractive visual processor. This all-optical image denoiser comprises passive transmissive layers optimized using deep learning to physically scatter the optical modes that represent various noise features, causing them to miss the output image Field-of-View (FoV) while retaining the object features of interest. Our results show that these diffractive denoisers can efficiently remove salt and pepper noise and image rendering-related spatial artifacts from input phase or intensity images while achieving an output power efficiency of ~30-40%. We experimentally demonstrated the effectiveness of this analog denoiser architecture using a 3D-printed diffractive visual processor operating at the terahertz spectrum. Owing to their speed, power-efficiency, and minimal computational overhead, all-optical diffractive denoisers can be transformative for various image display and projection systems, including, e.g., holographic displays.

Cycle Consistency-based Uncertainty Quantification of Neural Networks in Inverse Imaging Problems

Uncertainty estimation is critical for numerous applications of deep neural networks and draws growing attention from researchers. Here, we demonstrate an uncertainty quantification approach for deep neural networks used in inverse problems based on cycle consistency. We build forward-backward cycles using the physical forward model available and a trained deep neural network solving the inverse problem at hand, and accordingly derive uncertainty estimators through regression analysis on the consistency of these forward-backward cycles. We theoretically analyze cycle consistency metrics and derive their relationship with respect to uncertainty, bias, and robustness of the neural network inference. To demonstrate the effectiveness of these cycle consistency-based uncertainty estimators, we classified corrupted and out-of-distribution input image data using some of the widely used image deblurring and super-resolution neural networks as testbeds. The blind testing of our method outperformed other models in identifying unseen input data corruption and distribution shifts. This work provides a simple-to-implement and rapid uncertainty quantification method that can be universally applied to various neural networks used for solving inverse problems.

eFIN: Enhanced Fourier Imager Network for generalizable autofocusing and pixel super-resolution in holographic imaging

The application of deep learning techniques has greatly enhanced holographic imaging capabilities, leading to improved phase recovery and image reconstruction. Here, we introduce a deep neural network termed enhanced Fourier Imager Network (eFIN) as a highly generalizable framework for hologram reconstruction with pixel super-resolution and image autofocusing. Through holographic microscopy experiments involving lung, prostate and salivary gland tissue sections and Papanicolau (Pap) smears, we demonstrate that eFIN has a superior image reconstruction quality and exhibits external generalization to new types of samples never seen during the training phase. This network achieves a wide autofocusing axial range of 0.35 mm, with the capability to accurately predict the hologram axial distances by physics-informed learning. eFIN enables 3x pixel super-resolution imaging and increases the space-bandwidth product of the reconstructed images by 9-fold with almost no performance loss, which allows for significant time savings in holographic imaging and data processing steps. Our results showcase the advancements of eFIN in pushing the boundaries of holographic imaging for various applications in e.g., quantitative phase imaging and label-free microscopy.

GedankenNet: Self-supervised learning of hologram reconstruction using physics consistency

The past decade has witnessed transformative applications of deep learning in various computational imaging, sensing and microscopy tasks. Due to the supervised learning schemes employed, most of these methods depend on large-scale, diverse, and labeled training data. The acquisition and preparation of such training image datasets are often laborious and costly, also leading to biased estimation and limited generalization to new types of samples. Here, we report a self-supervised learning model, termed GedankenNet, that eliminates the need for labeled or experimental training data, and demonstrate its effectiveness and superior generalization on hologram reconstruction tasks. Without prior knowledge about the sample types to be imaged, the self-supervised learning model was trained using a physics-consistency loss and artificial random images that are synthetically generated without any experiments or resemblance to real-world samples. After its self-supervised training, GedankenNet successfully generalized to experimental holograms of various unseen biological samples, reconstructing the phase and amplitude images of different types of objects using experimentally acquired test holograms. Without access to experimental data or the knowledge of real samples of interest or their spatial features, GedankenNet's self-supervised learning achieved complex-valued image reconstructions that are consistent with the Maxwell's equations, meaning that its output inference and object solutions accurately represent the wave propagation in free-space. This self-supervised learning of image reconstruction tasks opens up new opportunities for various inverse problems in holography, microscopy and computational imaging fields.

Fourier Imager Network : A deep neural network for hologram reconstruction with superior external generalization

Deep learning-based image reconstruction methods have achieved remarkable success in phase recovery and holographic imaging. However, the generalization of their image reconstruction performance to new types of samples never seen by the network remains a challenge. Here we introduce a deep learning framework, termed Fourier Imager Network (FIN), that can perform end-to-end phase recovery and image reconstruction from raw holograms of new types of samples, exhibiting unprecedented success in external generalization. FIN architecture is based on spatial Fourier transform modules that process the spatial frequencies of its inputs using learnable filters and a global receptive field. Compared with existing convolutional deep neural networks used for hologram reconstruction, FIN exhibits superior generalization to new types of samples, while also being much faster in its image inference speed, completing the hologram reconstruction task in ~0.04 s per 1 mm^2 of the sample area. We experimentally validated the performance of FIN by training it using human lung tissue samples and blindly testing it on human prostate, salivary gland tissue and Pap smear samples, proving its superior external generalization and image reconstruction speed. Beyond holographic microscopy and quantitative phase imaging, FIN and the underlying neural network architecture might open up various new opportunities to design broadly generalizable deep learning models in computational imaging and machine vision fields.