Optical implementation of an iterative algorithm for matrix inversion

Rajbenbach, H.; Fainman, Y.; Lee, Sing H.

doi:10.1364/ao.26.001024

Cited by 44 publications

(34 citation statements)

References 12 publications

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“…Matrix-vector and matrixmatrix multiplications can often be implemented as optical systems. Such systems have been used for matrix-matrix multiplication [Athale and Collins 1982], matrix inversion [Rajbenbach et al 1987], as well as computing eigenvectors [Vijaya Kumar and Casasent 1981]. Of particular interest to our paper is the optical computing of the light transport operator using Krylov subspace methods [O'Toole and Kutulakos 2010].…”

Section: Prior Workmentioning

confidence: 99%

KRISM—Krylov Subspace-based Optical Computing of Hyperspectral Images

Saragadam

Sankaranarayanan

2019

ACM Trans. Graph.

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Relative intensity Wavelength (nm) KRISM Spectrometer spatial code measured spectrum S-polarized light polarizing beam splitter LCoS SLM diffraction grating P-polarization S-polarization operator #1. spatially-coded spectrum measurement spectral code measured spatial image P-polarized light operator #2. spectrally-coded spatial measurement 1 1 Fig. 1.Hyperspectral imagers resolve scenes at high spatial and spectral resolutions. We propose a novel architecture called KRISM that provides the ability to implement two operators: a spatially-coded spectrometer and a spectrally-coded spatial imager. By iterating between the two, we can acquire a low rank approximation of the hyperspectral image in a light efficient manner with very few measurements. The left image shows optical schematics for implementing the two operators. On the right, we show a hyperspectral image of a scene illuminated with a compact fluorescent lamp (CFL) acquired using our lab prototype. The proposed method enables high spatial and spectral resolution as observed in the zoomed-in image patches and CFL peaks, respectively.We present an adaptive imaging technique that optically computes a lowrank approximation of a scene's hyperspectral image, conceptualized as a matrix. Central to the proposed technique is the optical implementation of two measurement operators: a spectrally-coded imager and a spatially-coded spectrometer. By iterating between the two operators, we show that the top singular vectors and singular values of a hyperspectral image can be adaptively and optically computed with only a few iterations. We present an optical design that uses pupil plane coding for implementing the two operations and show several compelling results using a lab prototype to demonstrate the effectiveness of the proposed hyperspectral imager.

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Section: Prior Workmentioning

confidence: 99%

KRISM—Krylov Subspace-based Optical Computing of Hyperspectral Images

Saragadam

Sankaranarayanan

2019

ACM Trans. Graph.

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“…Optical processors were also designed for many other operations such as matrix operations 126 , or for systolic array processing 127 and neural network processors 128 .…”

Section: Optical Information Processing Optical Pattern Recognitionmentioning

confidence: 99%

A short history of optical computing: rise, decline, and evolution

Ambs

2009

SPIE Proceedings

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This paper gives a brief historical review of the development of optical computing from the early years, 60 years ago, until today. All the major inventions in the field were made in the sixties, generating a lot of enthusiasm. However it is between 1980 and 2000, that optical computing had its golden age with numerous new technologies and innovating optical processors been designed and constructed for real applications. Today the field of optical computing has evolved and its results benefit to new research topics such as nanooptics, biophotonics, or communication systems.

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“…These methods exploited the parallelism of optics supported by the richness of the modal continuum of free space and a variety of optoelectronic devices that were developed in support of these applications and systems. The constructed information processing systems and concepts were used for image processing, 1 " 4 pattern recognition, 5 ' 6 neural networks, 7 and linear algebra calculus 8 -to name a few. However with rapid advancements of the speed and, therefore, the information processing throughput of digital computers, the optical signal processing systems were not able to support these applications in a broad sense due to high cost, lesser accuracy, and lack of user-friendly interfaces.…”

Section: Introductionmentioning

confidence: 99%

Nanophotonics for Information Systems

Luryi

Zaslavsky

2010

Future Trends in Microelectronics

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Optics has the potential to solve some of the most exing problems in computing hardware. It promises crosstalk-free interconnects with essentially unlimited bandwidth, long-distance data transmission without skew and without power-and time-consuming regeneration, miniaturization, parallelism, and efficient implementation of important algorithms such as Fourier transforms. Yet, optical computing and processing in space and time has so far failed to move out of the lab. The free-space and guided-wave devices are costly, bulky, and fragile in their alignment. They are also difficult to integrate with electronic systems, both in terms of the fabrication process and in terms of delivery and retrieval of the massive volumes of data the optical elements can process. Moreover, there exist applications that rely on our ability in interfacing optical devices and systems with other signal modalities such as for example biological and biochemical processes. These applications led us recently to establishing a new research area that we call optofluidics, where fluids are used to create adaptive optical elements, control them, and establish efficient interfaces with biochemical systems.Things may be changing, however. More recent work emphasizes the construction of optical subsystems directly on-chip, with the same lithographic tools as the surrounding electronics. This has been made possible by the advances in these tools, which can now create features significantly smaller than the optical wavelength; experts predict lithographic resolution as fine as 16 nm by year 2020. Arranged in a regular pattern, subwavelength features act as a metamaterial whose optical properties are controlled by the density and geometry of the pattern and its constituents. Lenses, polarizers, chromatic dispersers, diffraction gratings, and other optical processing devices can now be implemented on-chip using metamaterials wherever natural materials with similar properties either do not exist, or (more frequently) would not be compatible with lithographic fabrication.To advance this technology, investigations of nanostructures and their interaction with electromagnetic field are critical. Engineers also need appropriate modeling and design tools, new fabrication recipes, and test instruments capable of characterizing on-chip components. The design of integrated photonic systems is a challenging task as it not only involves the accurate solution of electromagnetic equations, but also the need to incorporate the material and quantum physics equations to enable the investigation and analysis of near field interactions. These studies need to be integrated with device fabrication and characterization to verify device concepts and optimize device designs. In this talk, we discuss some of the CMOS-compatible SOI metamaterials and devices recently demonstrated. These include graded-index lenses, birefringent elements that utilize a combination of geometry and material properties to separate light into orthogonal polarizations, frequency-selective resonators ...

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Optical implementation of an iterative algorithm for matrix inversion

Cited by 44 publications

References 12 publications

KRISM—Krylov Subspace-based Optical Computing of Hyperspectral Images

KRISM—Krylov Subspace-based Optical Computing of Hyperspectral Images

A short history of optical computing: rise, decline, and evolution

Nanophotonics for Information Systems

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