arXiv subjects

Md Sadman Sakib Rahman

Publications and source records attributed to Md Sadman Sakib Rahman.

16 recordsLinked to original sources

arXiv2026

Universal Function Approximation via Diffractive Optical Processors: Physical Limits, Error Bounds, and Learnability

We present a unified theoretical framework connecting classical universal approximation theory, Fourier-feature approximation, and diffractive optical processors. We show that phase-encoded diffractive processors implement finite Fourier-feature expansions whose mathematical completeness follows from Fourier/Stone-Weierstrass arguments, while their physical realizability is governed by finite coefficient synthesis through optimized spatially varying coherent point-spread functions (PSFs). Our analyses derive approximation-error bounds that separate Fourier truncation, PSF-synthesis, input phase error, optical hardware, readout, and noise contributions; establish scaling relationships linking approximation complexity to optical degrees of freedom and input/output space-bandwidth products; derive photon-budget and throughput limits imposed by photon statistics; formulate finite-class statistical learnability bounds for phase-quantized diffractive function approximators; and analyze the impact of spatially incoherent illumination. We further analyze coherent optical cascadability and show that quadratic feature expansion through coherent mixing and optical readout provides a mechanism for enhanced representation while remaining fundamentally distinct from the depth-separation results established for digital neural networks. Our analyses provide a rigorous theoretical foundation for diffractive nonlinear function approximation and establish quantitative relationships among mathematical expressivity, optical hardware resources, statistical learning, and physical performance limits, thereby offering general design principles for large-scale analog optical computing systems.

physics.optics↗

arXiv2026

Breaking the Cascade: Compact Nonlinear Optical Computing with Single-Layer Encoder-Decoder Co-Localization

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.

physics.optics↗

arXiv2026

Large-scale nonlinear optical computing with incoherent light via linear diffractive systems

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.

physics.optics↗

arXiv2026

Compressive single-pixel imaging via a wavelength-multiplexed spatially incoherent diffractive optical processor

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.

physics.optics↗

arXiv2025

Programming of refractive functions

Snell's law dictates the phenomenon of light refraction at the interface between two media. Here, we demonstrate arbitrary programming of light refraction through an engineered material where the direction of the output wave can be set independently for different directions of the input wave, covering arbitrarily selected permutations of light refraction between the input and output apertures. Formed by a set of cascaded transmissive layers with optimized phase profiles, this refractive function generator (RFG) spans only a few tens of wavelengths in the axial direction. In addition to monochrome RFG designs, we also report wavelength-multiplexed refractive functions, where a distinct refractive function is implemented at each wavelength through the same engineered material volume, i.e., the permutation of light refraction is switched from one desired function to another function by changing the illumination wavelength. As experimental proofs of concept, we demonstrate permutation and negative refractive functions at the terahertz part of the spectrum using 3D-printed materials. Arbitrary programming of refractive functions enables new design capabilities for optical materials, devices and systems.

physics.optics↗

arXiv2025

Massively parallel and universal approximation of nonlinear functions using diffractive processors

Nonlinear computation is essential for a wide range of information processing tasks, yet implementing nonlinear functions using optical systems remains a challenge due to the weak and power-intensive nature of optical nonlinearities. Overcoming this limitation without relying on nonlinear optical materials could unlock unprecedented opportunities for ultrafast and parallel optical computing systems. Here, we demonstrate that large-scale nonlinear computation can be performed using linear optics through optimized diffractive processors composed of passive phase-only surfaces. In this framework, the input variables of nonlinear functions are encoded into the phase of an optical wavefront, e.g., via a spatial light modulator (SLM), and transformed by an optimized diffractive structure with spatially varying point-spread functions to yield output intensities that approximate a large set of unique nonlinear functions, all in parallel. We provide proof establishing that this architecture serves as a universal function approximator for an arbitrary set of bandlimited nonlinear functions, also covering multi-variate and complex-valued functions. We also numerically demonstrate the parallel computation of one million distinct nonlinear functions, accurately executed at wavelength-scale spatial density at the output of a diffractive optical processor. Furthermore, we experimentally validated this framework using in situ optical learning and approximated 35 unique nonlinear functions in a single shot using a compact setup consisting of an SLM and an image sensor. These results establish diffractive optical processors as a scalable platform for massively parallel universal nonlinear function approximation, paving the way for new capabilities in analog optical computing based on linear materials.

physics.optics↗

arXiv2025

Universal point spread function engineering for 3D optical information processing

Point spread function (PSF) engineering has been pivotal in the remarkable progress made in high-resolution imaging in the last decades. However, the diversity in PSF structures attainable through existing engineering methods is limited. Here, we report universal PSF engineering, demonstrating a method to synthesize an arbitrary set of spatially varying 3D PSFs between the input and output volumes of a spatially incoherent diffractive processor composed of cascaded transmissive surfaces. We rigorously analyze the PSF engineering capabilities of such diffractive processors within the diffraction limit of light and provide numerical demonstrations of unique imaging capabilities, such as snapshot 3D multispectral imaging without involving any spectral filters, axial scanning or digital reconstruction steps, which is enabled by the spatial and spectral engineering of 3D PSFs. Our framework and analysis would be important for future advancements in computational imaging, sensing and diffractive processing of 3D optical information.

physics.optics↗

arXiv2024

Unidirectional imaging with partially coherent light

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.

physics.optics↗

arXiv2024

Integration of Programmable Diffraction with Digital Neural Networks

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.

physics.optics↗

arXiv2024

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.

physics.optics↗

arXiv2023

Complex-valued universal linear transformations and image encryption using spatially incoherent diffractive networks

As an optical processor, a Diffractive Deep Neural Network (D2NN) utilizes engineered diffractive surfaces designed through machine learning to perform all-optical information processing, completing its tasks at the speed of light propagation through thin optical layers. With sufficient degrees-of-freedom, D2NNs can perform arbitrary complex-valued linear transformations using spatially coherent light. Similarly, D2NNs can also perform arbitrary linear intensity transformations with spatially incoherent illumination; however, under spatially incoherent light, these transformations are non-negative, acting on diffraction-limited optical intensity patterns at the input field-of-view (FOV). Here, we expand the use of spatially incoherent D2NNs to complex-valued information processing for executing arbitrary complex-valued linear transformations using spatially incoherent light. Through simulations, we show that as the number of optimized diffractive features increases beyond a threshold dictated by the multiplication of the input and output space-bandwidth products, a spatially incoherent diffractive visual processor can approximate any complex-valued linear transformation and be used for all-optical image encryption using incoherent illumination. The findings are important for the all-optical processing of information under natural light using various forms of diffractive surface-based optical processors.

physics.optics↗

arXiv2023

Learning Diffractive Optical Communication Around Arbitrary Opaque Occlusions

Free-space optical systems are emerging for high data rate communication and transfer of information in indoor and outdoor settings. However, free-space optical communication becomes challenging when an occlusion blocks the light path. Here, we demonstrate, for the first time, a direct communication scheme, passing optical information around a fully opaque, arbitrarily shaped obstacle that partially or entirely occludes the transmitter's field-of-view. In this scheme, an electronic neural network encoder and a diffractive optical network decoder are jointly trained using deep learning to transfer the optical information or message of interest around the opaque occlusion of an arbitrary shape. The diffractive decoder comprises successive spatially-engineered passive surfaces that process optical information through light-matter interactions. Following its training, the encoder-decoder pair can communicate any arbitrary optical information around opaque occlusions, where information decoding occurs at the speed of light propagation. For occlusions that change their size and/or shape as a function of time, the encoder neural network can be retrained to successfully communicate with the existing diffractive decoder, without changing the physical layer(s) already deployed. We also validate this framework experimentally in the terahertz spectrum using a 3D-printed diffractive decoder to communicate around a fully opaque occlusion. Scalable for operation in any wavelength regime, this scheme could be particularly useful in emerging high data-rate free-space communication systems.

physics.optics↗

arXiv2023

Universal Linear Intensity Transformations Using Spatially-Incoherent Diffractive Processors

Under spatially-coherent light, a diffractive optical network composed of structured surfaces can be designed to perform any arbitrary complex-valued linear transformation between its input and output fields-of-view (FOVs) if the total number (N) of optimizable phase-only diffractive features is greater than or equal to ~2 Ni x No, where Ni and No refer to the number of useful pixels at the input and the output FOVs, respectively. Here we report the design of a spatially-incoherent diffractive optical processor that can approximate any arbitrary linear transformation in time-averaged intensity between its input and output FOVs. Under spatially-incoherent monochromatic light, the spatially-varying intensity point spread functon(H) of a diffractive network, corresponding to a given, arbitrarily-selected linear intensity transformation, can be written as H(m,n;m',n')=|h(m,n;m',n')|^2, where h is the spatially-coherent point-spread function of the same diffractive network, and (m,n) and (m',n') define the coordinates of the output and input FOVs, respectively. Using deep learning, supervised through examples of input-output profiles, we numerically demonstrate that a spatially-incoherent diffractive network can be trained to all-optically perform any arbitrary linear intensity transformation between its input and output if N is greater than or equal to ~2 Ni x No. These results constitute the first demonstration of universal linear intensity transformations performed on an input FOV under spatially-incoherent illumination and will be useful for designing all-optical visual processors that can work with incoherent, natural light.

physics.optics↗

arXiv2022

Time-lapse image classification using a diffractive neural network

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.

physics.optics↗

arXiv2021

Computer-free, all-optical reconstruction of holograms using diffractive networks

Reconstruction of in-line holograms of unknown objects in general suffers from twin-image artifacts due to the appearance of an out-of-focus image overlapping with the desired image to be reconstructed. Computer-based iterative phase retrieval algorithms and learning-based methods have been used for the suppression of such image artifacts in digital holography. Here we report an all-optical hologram reconstruction method that can instantly retrieve the image of an unknown object from its in-line hologram and eliminate twin-image artifacts without using a digital processor or a computer. Multiple transmissive diffractive layers are trained using deep learning so that the diffracted light from an arbitrary input hologram is processed all-optically, through light-matter interaction, to reconstruct the image of an unknown object at the speed of light propagation and without the need for any external power. This passive all-optical processor composed of spatially-engineered transmissive layers forms a diffractive network, which successfully generalizes to reconstruct in-line holograms of unknown, new objects and exhibits improved diffraction efficiency as well as extended depth-of-field at the hologram recording distance. This all-optical hologram processor and the underlying design framework can find numerous applications in coherent imaging and holographic display-related applications owing to its major advantages in terms of image reconstruction speed and computer-free operation.

physics.optics↗

arXiv2020

Ensemble learning of diffractive optical networks

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.

cs.NE↗