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Peer Reviewed

Diffractive Optical Networks

Mengu, Deniz
Advisor(s): Ozcan, Aydogan

UCLA Electronic Theses and Dissertations (2022)

Deep learning has been revolutionizing information processing in many fields of science and engineering owing to the massively growing amounts of data and the advances in deep neural network architectures. As these neural networks are expanding their capabilities towards achieving state-of-the-art solutions for demanding statistical inference tasks in various applications, there appears to be a global need for low-power, scalable and fast computing hardware beyond what existing electronic systems can offer. Optical computing might potentially address some of these demands with its inherent parallelism, power efficiency, and high speed. Recent advances in optical materials, fabrication, and optimization techniques have significantly enriched the design capabilities in optics and photonics, leading to various successful demonstrations of guided-wave and free-space computing hardware for accelerating machine learning tasks using light. While integrated waveguide-based photonic approaches mainly aims to replace the current electronic computing hardware with better alternatives, free-space optical neural network architectures and related computing techniques offer unique advantages particularly for inference tasks in visual computing applications, where the information is already in the optical domain.This dissertation introduces diffractive optical networks that are designed based on Diffractive Deep Neural Networks (D2NN) framework using deep learning to tackle various challenges in computational machine vision by providing power-efficient, fast, scalable and massively parallel all-optical solutions. First, a series of design advances were devised to improve the statistical inference accuracy of diffractive object classifiers. Second, hybrid (optical-electronic) neural network systems, which uses diffractive optical networks as front-end optical processors preceding back-end electronic neural networks, were investigated to enable task-specific camera systems that can perform object classification with fewer pixels, thus with less memory and power consumption. In addition, D2NN framework was extended to mitigate the adverse impact of possible physical error sources, termed as vaccinated-D2NN (v-D2NN). The success of v-D2NN was experimentally demonstrated at THz wavelengths by comparing the classification accuracies of 3D-printed nonvaccinated and vaccinated diffractive handwritten digit classifiers under the presence of layer-to-layer misalignments. Next, a diffractive all-optical object classifier was designed to provide inference accuracy that is invariant under random changes on the scale, position and orientation of the input objects with respect to the diffractive surfaces. Furthermore, the all-optical information processing capacity of diffractive optical networks was studied to prove that the dimensionality of the solution space representing the set of all-optical transformations established by a diffractive network increases linearly with the number of diffractive surfaces, up to a limit determined by the size of the input/output fields-of-view. In parallel, the diffractive optical networks were shown to all-optically perform arbitrary complex-valued linear transformations, including space-variant operations, noninvertible and nonunitary matrices, with negligibly small errors provided that the total number of diffractive neurons is sufficiently large to satisfy space-bandwidth product demands on input and output fields-of-view. A diffractive permutation network that can all-optically implement 625 interconnects between its input and output was fabricated using 3D printing and its performance was demonstrated at THz wavelengths. Beyond the outlined optical computing and machine learning applications, diffractive optical networks can also be utilized to all-optically solve challenging inverse problems in computational imaging. Highlighting this aspect, diffractive optical networks that can all-optically perform phase retrieval to reveal the quantitative phase image (QPI) of weakly scattering objects were devised. Based on the conducted analysis, these diffractive QPI networks can resolve subwavelength features, ~0.67λ, of an input phase object, with λ denoting the wavelength of illumination. Finally, in certain application scenarios, spatial overlap between phase objects poses an irreversible information loss due to the superposition of individual phase delays. It was demonstrated that diffractive optical networks can be trained to solve this challenging problem to infer the classes of spatially overlapping phase objects. Moreover, when these diffractive phase object classifiers are combined with electronic deep neural networks, the individual phase images of the objects spatially overlapping within the input field-of-view can be recovered based on the all-optically synthesized class scores, despite the phase ambiguity. All the studies presented in this dissertation demonstrating the success of diffractive optical networks in various general-purpose computing, statistical inference and inverse computational imaging tasks can potentially lead them to largely replace conventional optical components in the next-generation, task-specific machine vision designs that can achieve a given task with fewer pixels, leading to faster, more memory- and power-efficient systems.

$Cover page: Diffractive Optical Networks$

Article
Peer Reviewed

Ensemble learning of diffractive optical networks

UCLA Previously Published Works (2021)

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 that 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 object classification, the spectral encoding of information, optical pulse shaping and imaging. Here, we substantially improve the inference performance of diffractive optical networks using feature engineering and ensemble learning. After independently training 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 improved the 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 ± 0.23% and 62.13 ± 0.05%, 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 leap to extend the application space of diffractive optical image classification and machine vision systems.

$Cover page: Ensemble learning of diffractive optical networks$

Creative Commons 'BY' version 4.0 license

Article
Peer Reviewed

Pyramid diffractive optical networks for unidirectional image magnification and demagnification

UCLA Previously Published Works (2024)

Diffractive deep neural networks (D²NNs) are composed of successive transmissive layers optimized using supervised deep learning to all-optically implement various computational tasks between an input and output field-of-view. Here, we present a pyramid-structured diffractive optical network design (which we term P-D²NN), optimized specifically for unidirectional image magnification and demagnification. In this design, the diffractive layers are pyramidally scaled in alignment with the direction of the image magnification or demagnification. This P-D²NN design creates high-fidelity magnified or demagnified images in only one direction, while inhibiting the image formation in the opposite direction-achieving the desired unidirectional imaging operation using a much smaller number of diffractive degrees of freedom within the optical processor volume. Furthermore, the P-D²NN design maintains its unidirectional image magnification/demagnification functionality across a large band of illumination wavelengths despite being trained with a single wavelength. We also designed a wavelength-multiplexed P-D²NN, where a unidirectional magnifier and a unidirectional demagnifier operate simultaneously in opposite directions, at two distinct illumination wavelengths. Furthermore, we demonstrate that by cascading multiple unidirectional P-D²NN modules, we can achieve higher magnification factors. The efficacy of the P-D²NN architecture was also validated experimentally using terahertz illumination, successfully matching our numerical simulations. P-D²NN offers a physics-inspired strategy for designing task-specific visual processors.

$Cover page: Pyramid diffractive optical networks for unidirectional image magnification and demagnification$

Article
Peer Reviewed

Polarization multiplexed diffractive computing: all-optical implementation of a group of linear transformations through a polarization-encoded diffractive network

UCLA Previously Published Works (2022)

Research on optical computing has recently attracted significant attention due to the transformative advances in machine learning. Among different approaches, diffractive optical networks composed of spatially-engineered transmissive surfaces have been demonstrated for all-optical statistical inference and performing arbitrary linear transformations using passive, free-space optical layers. Here, we introduce a polarization-multiplexed diffractive processor to all-optically perform multiple, arbitrarily-selected linear transformations through a single diffractive network trained using deep learning. In this framework, an array of pre-selected linear polarizers is positioned between trainable transmissive diffractive materials that are isotropic, and different target linear transformations (complex-valued) are uniquely assigned to different combinations of input/output polarization states. The transmission layers of this polarization-multiplexed diffractive network are trained and optimized via deep learning and error-backpropagation by using thousands of examples of the input/output fields corresponding to each one of the complex-valued linear transformations assigned to different input/output polarization combinations. Our results and analysis reveal that a single diffractive network can successfully approximate and all-optically implement a group of arbitrarily-selected target transformations with a negligible error when the number of trainable diffractive features/neurons (N) approaches [Formula: see text], where N_i and N_o represent the number of pixels at the input and output fields-of-view, respectively, and N_p refers to the number of unique linear transformations assigned to different input/output polarization combinations. This polarization-multiplexed all-optical diffractive processor can find various applications in optical computing and polarization-based machine vision tasks.

$Cover page: Polarization multiplexed diffractive computing: all-optical implementation of a group of linear transformations through a polarization-encoded diffractive network$

Article
Peer Reviewed

Data‐Class‐Specific All‐Optical Transformations and Encryption

UCLA Previously Published Works (2023)

Diffractive optical networks provide rich opportunities for visual computing tasks. Here, data-class-specific transformations that are all-optically performed between the input and output fields-of-view (FOVs) of a diffractive network are presented. The visual information of the objects is encoded into the amplitude (A), phase (P), or intensity (I) of the optical field at the input, which is all-optically processed by a data-class-specific diffractive network. At the output, an image sensor-array directly measures the transformed patterns, all-optically encrypted using the transformation matrices preassigned to different data classes, i.e., a separate matrix for each data class. The original input images can be recovered by applying the correct decryption key (the inverse transformation) corresponding to the matching data class, while applying any other key will lead to loss of information. All-optical class-specific transformations covering A → A, I → I, and P → I transformations using various image datasets are numerically demonstrated. The feasibility of this framework is also experimentally validated by fabricating class-specific I → I transformation diffractive networks and is successfully tested at different parts of the electromagnetic spectrum, i.e., 1550 nm and 0.75 mm wavelengths. Data-class-specific all-optical transformations provide a fast and energy-efficient method for image and data encryption, enhancing data security and privacy.

Article
Peer Reviewed

Spectrally encoded single-pixel machine vision using diffractive networks

UCLA Previously Published Works (2021)

We demonstrate optical networks composed of diffractive layers trained using deep learning to encode the spatial information of objects into the power spectrum of the diffracted light, which are used to classify objects with a single-pixel spectroscopic detector. Using a plasmonic nanoantenna-based detector, we experimentally validated this single-pixel machine vision framework at terahertz spectrum to optically classify the images of handwritten digits by detecting the spectral power of the diffracted light at ten distinct wavelengths, each representing one class/digit. We also coupled this diffractive network-based spectral encoding with a shallow electronic neural network, which was trained to rapidly reconstruct the images of handwritten digits based on solely the spectral power detected at these ten distinct wavelengths, demonstrating task-specific image decompression. This single-pixel machine vision framework can also be extended to other spectral-domain measurement systems to enable new 3D imaging and sensing modalities integrated with diffractive network-based spectral encoding of information.

$Cover page: Spectrally encoded single-pixel machine vision using diffractive networks$

Article
Peer Reviewed

Terahertz pulse shaping using diffractive surfaces

UCLA Previously Published Works (2021)

Recent advances in deep learning have been providing non-intuitive solutions to various inverse problems in optics. At the intersection of machine learning and optics, diffractive networks merge wave-optics with deep learning to design task-specific elements to all-optically perform various tasks such as object classification and machine vision. Here, we present a diffractive network, which is used to shape an arbitrary broadband pulse into a desired optical waveform, forming a compact and passive pulse engineering system. We demonstrate the synthesis of various different pulses by designing diffractive layers that collectively engineer the temporal waveform of an input terahertz pulse. Our results demonstrate direct pulse shaping in terahertz spectrum, where the amplitude and phase of the input wavelengths are independently controlled through a passive diffractive device, without the need for an external pump. Furthermore, a physical transfer learning approach is presented to illustrate pulse-width tunability by replacing part of an existing network with newly trained diffractive layers, demonstrating its modularity. This learning-based diffractive pulse engineering framework can find broad applications in e.g., communications, ultra-fast imaging and spectroscopy.

$Cover page: Terahertz pulse shaping using diffractive surfaces$

Article
Peer Reviewed

All-optical image denoising using a diffractive visual processor.

UCLA Previously Published Works (2024)

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 that axially spans <250 × λ, where λ is the wavelength of light. 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.

$Cover page: All-optical image denoising using a diffractive visual processor.$