Md Sadman Sakib Rahman

Yuntian Wang, Alexander Chen, Md Sadman Sakib Rahman et al.

We demonstrate that nonlinear computing can be achieved with a single linear diffractive surface under coherent illumination. We introduce a compact encoder-decoder co-localization (E+D) architecture in which an input-dependent dynamic encoder and a static optimized decoder are integrated within the same phase-only diffractive plane. Following free-space propagation, coherent interference between the encoder and decoder fields, combined with intensity detection, generates programmable nonlinear input-output mappings without requiring nonlinear optical materials or multiple diffractive layers. We prove that the proposed E+D optical processor is a universal approximator for arbitrary real-valued band-limited nonlinear functions and identify the physical factors governing its approximation fidelity, including the decoder degrees-of-freedom, detector aperture, and axial propagation distance. Crucially, we demonstrate that introducing a trained, frozen phase bias to the encoder region systematically enhances functional expressivity, providing robustness against coarse phase quantization on spatial light modulators. Using this framework, we accurately synthesize diverse nonlinear functions, including commonly used neural network activation functions and complex-valued nonlinear functions. Finally, we experimentally validate the proposed approach using a visible-light optical set-up trained through in situ learning, demonstrating the parallel approximation of 9 nonlinear functions in a single optical forward pass. By collapsing nonlinear optical computation into a single diffractive surface, the E+D architecture substantially reduces hardware and alignment complexity while preserving powerful function-approximation capabilities, providing a compact and scalable framework for analog information processing.

Md Sadman Sakib Rahman, Aydogan Ozcan

Diffractive deep neural networks (D2NNs) define an all-optical computing framework comprised of spatially engineered passive surfaces that collectively process optical input information by modulating the amplitude and/or the phase of the propagating light. Diffractive optical networks complete their computational tasks at the speed of light propagation through a thin diffractive volume, without any external computing power while exploiting the massive parallelism of optics. Diffractive networks were demonstrated to achieve all-optical classification of objects and perform universal linear transformations. Here we demonstrate, for the first time, a "time-lapse" image classification scheme using a diffractive network, significantly advancing its classification accuracy and generalization performance on complex input objects by using the lateral movements of the input objects and/or the diffractive network, relative to each other. In a different context, such relative movements of the objects and/or the camera are routinely being used for image super-resolution applications; inspired by their success, we designed a time-lapse diffractive network to benefit from the complementary information content created by controlled or random lateral shifts. We numerically explored the design space and performance limits of time-lapse diffractive networks, revealing a blind testing accuracy of 62.03% on the optical classification of objects from the CIFAR-10 dataset. This constitutes the highest inference accuracy achieved so far using a single diffractive network on the CIFAR-10 dataset. Time-lapse diffractive networks will be broadly useful for the spatio-temporal analysis of input signals using all-optical processors.

Guangdong Ma, Che-Yung Shen, Jingxi Li et al.

Unidirectional imagers form images of input objects only in one direction, e.g., from field-of-view (FOV) A to FOV B, while blocking the image formation in the reverse direction, from FOV B to FOV A. Here, we report unidirectional imaging under spatially partially coherent light and demonstrate high-quality imaging only in the forward direction (A->B) with high power efficiency while distorting the image formation in the backward direction (B->A) along with low power efficiency. Our reciprocal design features a set of spatially engineered linear diffractive layers that are statistically optimized for partially coherent illumination with a given phase correlation length. Our analyses reveal that when illuminated by a partially coherent beam with a correlation length of ~1.5 w or larger, where w is the wavelength of light, diffractive unidirectional imagers achieve robust performance, exhibiting asymmetric imaging performance between the forward and backward directions - as desired. A partially coherent unidirectional imager designed with a smaller correlation length of less than 1.5 w still supports unidirectional image transmission, but with a reduced figure of merit. These partially coherent diffractive unidirectional imagers are compact (axially spanning less than 75 w), polarization-independent, and compatible with various types of illumination sources, making them well-suited for applications in asymmetric visual information processing and communication.

Xiao Wang, Yiyang Wu, Yuntian Wang et al.

Despite offering high sensitivity, a high signal-to-noise ratio, and a broad spectral range, single-pixel imaging (SPI) is limited by low measurement efficiency and long data-acquisition times. To address this, we propose a wavelength-multiplexed, spatially incoherent diffractive optical processor combined with a compact/shallow digital artificial neural network (ANN) to implement compressive SPI. Specifically, we model the bucket detection process in conventional SPI as a linear intensity transformation with spatially and spectrally varying point-spread functions. This transformation matrix is treated as a learnable parameter and jointly optimized with a shallow digital ANN composed of 2 hidden nonlinear layers. The wavelength-multiplexed diffractive processor is then configured via data-free optimization to approximate this pre-trained transformation matrix; after this optimization, the diffractive processor remains static/fixed. Upon multi-wavelength illumination and diffractive modulation, the target spatial information of the input object is spectrally encoded. A single-pixel detector captures the output spectral power at each illumination band, which is then rapidly decoded by the jointly trained digital ANN to reconstruct the input image. In addition to our numerical analyses demonstrating the feasibility of this approach, we experimentally validated its proof-of-concept using an array of light-emitting diodes (LEDs). Overall, this work demonstrates a computational imaging framework for compressive SPI that can be useful in applications such as biomedical imaging, autonomous devices, and remote sensing.

Alexander Chen, Yuntian Wang, Md Sadman Sakib Rahman et al.

Nonlinear computation is essential for various information processing tasks. Optical implementations are attractive because passive light propagation can manipulate high-dimensional signals with extreme throughput and parallelism; yet realizing nonlinear mappings in optical hardware remains challenging due to the weak nonlinearity of optical materials and the large intensities required to induce nonlinear interactions. This challenge is further amplified in many systems that operate with incoherent illumination, motivating a coherence-aware framework for scalable optical nonlinear processing. Here, we show that linear optical systems, in particular, optimized diffractive processors comprising passive surfaces, can perform large-scale nonlinear function approximation under spatially incoherent or partially coherent illumination, when preceded by intensity-only input encoding. We quantify how the accuracy of the nonlinear function approximation varies with the degree of parallelism, the number of diffractive layers, and the number of trainable diffractive features. Numerical results demonstrate snapshot computation of up to one million distinct nonlinear functions in a single forward pass through a diffractive processor, with the function outputs spatially multiplexed and read out using densely packed detectors at the output. We further provide a proof-of-concept experimental demonstration under incoherent illumination from a liquid crystal display (LCD), enabled by a model-free in situ learning strategy that jointly optimizes the diffractive profile and detector readout geometry in the presence of hardware imperfections and misalignments. Our findings establish diffractive processors as a massively parallel universal function approximator for both spatially incoherent and partially coherent illumination.

Jingtian Hu, Kun Liao, Niyazi Ulas Dinc et al.

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.

Md Sadman Sakib Rahman, Aydogan Ozcan

Optical imaging and sensing systems based on diffractive elements have seen massive advances over the last several decades. Earlier generations of diffractive optical processors were, in general, designed to deliver information to an independent system that was separately optimized, primarily driven by human vision or perception. With the recent advances in deep learning and digital neural networks, there have been efforts to establish diffractive processors that are jointly optimized with digital neural networks serving as their back-end. These jointly optimized hybrid (optical+digital) processors establish a new "diffractive language" between input electromagnetic waves that carry analog information and neural networks that process the digitized information at the back-end, providing the best of both worlds. Such hybrid designs can process spatially and temporally coherent, partially coherent, or incoherent input waves, providing universal coverage for any spatially varying set of point spread functions that can be optimized for a given task, executed in collaboration with digital neural networks. In this article, we highlight the utility of this exciting collaboration between engineered and programmed diffraction and digital neural networks for a diverse range of applications. We survey some of the major innovations enabled by the push-pull relationship between analog wave processing and digital neural networks, also covering the significant benefits that could be reaped through the synergy between these two complementary paradigms.

Md Sadman Sakib Rahman, Jingxi Li, Deniz Mengu et al.

A plethora of research advances have emerged in the fields of optics and photonics that benefit from harnessing the power of machine learning. Specifically, there has been a revival of interest in optical computing hardware, due to its potential advantages for machine learning tasks in terms of parallelization, power efficiency and computation speed. Diffractive Deep Neural Networks (D2NNs) form such an optical computing framework, which benefits from deep learning-based design of successive diffractive layers to all-optically process information as the input light diffracts through these passive layers. D2NNs have demonstrated success in various tasks, including e.g., object classification, spectral-encoding of information, optical pulse shaping and imaging, among others. Here, we significantly improve the inference performance of diffractive optical networks using feature engineering and ensemble learning. After independently training a total of 1252 D2NNs that were diversely engineered with a variety of passive input filters, we applied a pruning algorithm to select an optimized ensemble of D2NNs that collectively improve their image classification accuracy. Through this pruning, we numerically demonstrated that ensembles of N=14 and N=30 D2NNs achieve blind testing accuracies of 61.14% and 62.13%, respectively, on the classification of CIFAR-10 test images, providing an inference improvement of >16% compared to the average performance of the individual D2NNs within each ensemble. These results constitute the highest inference accuracies achieved to date by any diffractive optical neural network design on the same dataset and might provide a significant leapfrog to extend the application space of diffractive optical image classification and machine vision systems.