All-Optical Synthesis of an Arbitrary Linear Transformation Using Diffractive Surfaces

• URL: http://arxiv.org/abs/2108.09833v1
• Date: Sun, 22 Aug 2021 20:40:35 GMT
• Title: All-Optical Synthesis of an Arbitrary Linear Transformation Using Diffractive Surfaces
• Authors: Onur Kulce, Deniz Mengu, Yair Rivenson, Aydogan Ozcan
• Abstract summary: We report the design of diffractive surfaces to all-optically perform arbitrary complex-valued linear transformations between an input (N_i) and output (N_o) We also consider a deep learning-based design method to optimize the transmission coefficients of diffractive surfaces by using examples of input/output fields corresponding to the target transformation. Our analyses reveal that if the total number (N) of spatially-engineered diffractive features/neurons is N_i x N_o or larger, both design methods succeed in all-optical implementation of the target transformation, achieving negligible error.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We report the design of diffractive surfaces to all-optically perform arbitrary complex-valued linear transformations between an input (N_i) and output (N_o), where N_i and N_o represent the number of pixels at the input and output fields-of-view (FOVs), respectively. First, we consider a single diffractive surface and use a matrix pseudoinverse-based method to determine the complex-valued transmission coefficients of the diffractive features/neurons to all-optically perform a desired/target linear transformation. In addition to this data-free design approach, we also consider a deep learning-based design method to optimize the transmission coefficients of diffractive surfaces by using examples of input/output fields corresponding to the target transformation. We compared the all-optical transformation errors and diffraction efficiencies achieved using data-free designs as well as data-driven (deep learning-based) diffractive designs to all-optically perform (i) arbitrarily-chosen complex-valued transformations including unitary, nonunitary and noninvertible transforms, (ii) 2D discrete Fourier transformation, (iii) arbitrary 2D permutation operations, and (iv) high-pass filtered coherent imaging. Our analyses reveal that if the total number (N) of spatially-engineered diffractive features/neurons is N_i x N_o or larger, both design methods succeed in all-optical implementation of the target transformation, achieving negligible error. However, compared to data-free designs, deep learning-based diffractive designs are found to achieve significantly larger diffraction efficiencies for a given N and their all-optical transformations are more accurate for N < N_i x N_o. These conclusions are generally applicable to various optical processors that employ spatially-engineered diffractive surfaces.

Related papers

• Compositional Generative Inverse Design [69.22782875567547]
  Inverse design, where we seek to design input variables in order to optimize an underlying objective function, is an important problem. We show that by instead optimizing over the learned energy function captured by the diffusion model, we can avoid such adversarial examples. In an N-body interaction task and a challenging 2D multi-airfoil design task, we demonstrate that by composing the learned diffusion model at test time, our method allows us to design initial states and boundary shapes.
  arXiv  Detail & Related papers  (2024-01-24T01:33:39Z)
• Complex-valued universal linear transformations and image encryption using spatially incoherent diffractive networks [0.0]
  As an optical processor, a Diffractive Deep Neural Network (D2NN) utilizes engineered diffractive surfaces designed through machine learning to perform all-optical information processing. We show that a spatially incoherent diffractive visual processor can approximate any complex-valued linear transformation and be used for all-optical image encryption using incoherent illumination.
  arXiv  Detail & Related papers  (2023-10-05T08:43:59Z)
• Entropy Transformer Networks: A Learning Approach via Tangent Bundle Data Manifold [8.893886200299228]
  This paper focuses on an accurate and fast approach for image transformation employed in the design of CNN architectures. A novel Entropy STN (ESTN) is proposed that interpolates on the data manifold distributions. Experiments on challenging benchmarks show that the proposed ESTN can improve predictive accuracy over a range of computer vision tasks.
  arXiv  Detail & Related papers  (2023-07-24T04:21:51Z)
• VTAE: Variational Transformer Autoencoder with Manifolds Learning [144.0546653941249]
  Deep generative models have demonstrated successful applications in learning non-linear data distributions through a number of latent variables. The nonlinearity of the generator implies that the latent space shows an unsatisfactory projection of the data space, which results in poor representation learning. We show that geodesics and accurate computation can substantially improve the performance of deep generative models.
  arXiv  Detail & Related papers  (2023-04-03T13:13:19Z)
• Universal Linear Intensity Transformations Using Spatially-Incoherent Diffractive Processors [0.0]
  Under spatially-incoherent light, a diffractive optical network can be designed to perform arbitrary complex-valued linear transformations. We numerically demonstrate that a spatially-incoherent diffractive network can be trained to all-optically perform any arbitrary linear intensity transformation.
  arXiv  Detail & Related papers  (2023-03-23T04:51:01Z)
• Oracle-Preserving Latent Flows [58.720142291102135]
  We develop a methodology for the simultaneous discovery of multiple nontrivial continuous symmetries across an entire labelled dataset. The symmetry transformations and the corresponding generators are modeled with fully connected neural networks trained with a specially constructed loss function. The two new elements in this work are the use of a reduced-dimensionality latent space and the generalization to transformations invariant with respect to high-dimensional oracles.
  arXiv  Detail & Related papers  (2023-02-02T00:13:32Z)
• Retrieving space-dependent polarization transformations via near-optimal quantum process tomography [55.41644538483948]
  We investigate the application of genetic and machine learning approaches to tomographic problems. We find that the neural network-based scheme provides a significant speed-up, that may be critical in applications requiring a characterization in real-time. We expect these results to lay the groundwork for the optimization of tomographic approaches in more general quantum processes.
  arXiv  Detail & Related papers  (2022-10-27T11:37:14Z)
• Massively Parallel Universal Linear Transformations using a Wavelength-Multiplexed Diffractive Optical Network [8.992945252617707]
  deep learning-based design of a massively parallel broadband diffractive neural network for all-optically performing a large group of transformations. Massively parallel, wavelength-multiplexed diffractive networks will be useful for designing high- throughput intelligent machine vision systems.
  arXiv  Detail & Related papers  (2022-08-13T07:59:39Z)
• Polarization Multiplexed Diffractive Computing: All-Optical Implementation of a Group of Linear Transformations Through a Polarization-Encoded Diffractive Network [0.0]
  We introduce a polarization multiplexed diffractive processor to all-optically perform arbitrary linear transformations. A single diffractive network can successfully approximate and all-optically implement a group of arbitrarily-selected target transformations. This processor can find various applications in optical computing and polarization-based machine vision tasks.
  arXiv  Detail & Related papers  (2022-03-25T07:10:47Z)
• Revisiting Transformation Invariant Geometric Deep Learning: Are Initial Representations All You Need? [80.86819657126041]
  We show that transformation-invariant and distance-preserving initial representations are sufficient to achieve transformation invariance. Specifically, we realize transformation-invariant and distance-preserving initial point representations by modifying multi-dimensional scaling. We prove that TinvNN can strictly guarantee transformation invariance, being general and flexible enough to be combined with the existing neural networks.
  arXiv  Detail & Related papers  (2021-12-23T03:52:33Z)
• Channel-Directed Gradients for Optimization of Convolutional Neural Networks [50.34913837546743]
  We introduce optimization methods for convolutional neural networks that can be used to improve existing gradient-based optimization in terms of generalization error. We show that defining the gradients along the output channel direction leads to a performance boost, while other directions can be detrimental.
  arXiv  Detail & Related papers  (2020-08-25T00:44:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.