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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS2014

Space-Based Reconfigurable Software Defined Radio Test Bed Aboard International Space Station

The National Aeronautical and Space Administration (NASA) recently launched a new software defined radio research test bed to the International Space Station. The test bed, sponsored by the Space Communications and Navigation (SCaN) Office within NASA is referred to as the SCaN Testbed. The SCaN Testbed is a highly capable communications system, composed of three software defined radios, integrated into a flight system, and mounted to the truss of the International Space Station. Software defined radios offer the future promise of in-flight reconfigurability, autonomy, and eventually cognitive operation. The adoption of software defined radios offers space missions a new way to develop and operate space transceivers for communications and navigation. Reconfigurable or software defined radios with communications and navigation functions implemented in software or VHDL (Very High Speed Hardware Description Language) provide the capability to change the functionality of the radio during development or after launch. The ability to change the operating characteristics of a radio through software once deployed to space offers the flexibility to adapt to new science opportunities, recover from anomalies within the science payload or communication system, and potentially reduce development cost and risk by adapting generic space platforms to meet specific mission requirements. The software defined radios on the SCaN Testbed are each compliant to NASA's Space Telecommunications Radio System (STRS) Architecture. The STRS Architecture is an open, non-proprietary architecture that defines interfaces for the connections between radio components. It provides an operating environment to abstract the communication waveform application from the underlying platform specific hardware such as digital-to-analog converters, analog-to-digital converters, oscillators, RF attenuators, automatic gain control circuits, FPGAs, general-purpose processors, etc. and the interconnections among different radio components.

Communications↗
NASA NTRS2017

Hardware Interface Description for the Integrated Power, Avionics, and Software (iPAS) Space Telecommunications Radio Ssystem (STRS) Radio

The Space Telecommunications Radio System (STRS) provides a common, consistent framework for software defined radios (SDRs) to abstract the application software from the radio platform hardware. The STRS standard aims to reduce the cost and risk of using complex, configurable and reprogrammable radio systems across NASA missions. To promote the use of the STRS architecture for future NASA advanced exploration missions, NASA Glenn Research Center (GRC) developed an STRS-compliant SDR on a radio platform used by the Advance Exploration System program at the Johnson Space Center (JSC) in their Integrated Power, Avionics, and Software (iPAS) laboratory. The iPAS STRS Radio was implemented on the Reconfigurable, Intelligently-Adaptive Communication System (RIACS) platform, currently being used for radio development at JSC. The platform consists of a Xilinx ML605 Virtex-6 FPGA board, an Analog Devices FMCOMMS1-EBZ RF transceiver board, and an Embedded PC (Axiomtek eBox 620-110-FL) running the Ubuntu 12.4 operating system. Figure 1 shows the RIACS platform hardware. The result of this development is a very low cost STRS compliant platform that can be used for waveform developments for multiple applications.The purpose of this document is to describe how to develop a new waveform using the RIACS platform and the Very High Speed Integrated Circuits (VHSIC) Hardware Description Language (VHDL) FPGA wrapper code and the STRS implementation on the Axiomtek processor.

Flight Computer↗
NASA NTRS2017

Waveform Developer's Guide for the Integrated Power, Avionics, and Software (iPAS) Space Telecommunications Radio System (STRS) Radio

The Space Telecommunications Radio System (STRS) provides a common, consistent framework for software defined radios (SDRs) to abstract the application software from the radio platform hardware. The STRS standard aims to reduce the cost and risk of using complex, configurable and reprogrammable radio systems across NASA missions. To promote the use of the STRS architecture for future NASA advanced exploration missions, NASA Glenn Research Center (GRC) developed an STRS-compliant SDR on a radio platform used by the Advance Exploration System program at the Johnson Space Center (JSC) in their Integrated Power, Avionics, and Software (iPAS) laboratory. The iPAS STRS Radio was implemented on the Reconfigurable, Intelligently-Adaptive Communication System (RIACS) platform, currently being used for radio development at JSC. The platform consists of a Xilinx(Trademark) ML605 Virtex(Trademark)-6 FPGA board, an Analog Devices FMCOMMS1-EBZ RF transceiver board, and an Embedded PC (Axiomtek(Trademark) eBox 620-110-FL) running the Ubuntu 12.4 operating system. The result of this development is a very low cost STRS compliant platform that can be used for waveform developments for multiple applications. The purpose of this document is to describe how to develop a new waveform using the RIACS platform and the Very High Speed Integrated Circuits (VHSIC) Hardware Description Language (VHDL) FPGA wrapper code and the STRS implementation on the Axiomtek processor.

Software Defined Radio↗
NASA NTRS2004

Formation Control of the MAXIM L2 Libration Orbit Mission

The Micro-Arcsecond Imaging Mission (MAXIM), a proposed concept for the Structure and Evolution of the Universe (SEU) Black Hole Imaging mission, is designed to make a ten million-fold improvement in X-ray image clarity of celestial objects by providing better than 0.1 microarcsecond imaging. To achieve mission requirements, MAXIM will have to improve on pointing by orders of magnitude. This pointing requirement impacts the control and design of the formation. Currently the architecture is comprised of 25 spacecraft, which will form the sparse apertures of a grazing incidence X-ray interferometer covering the 0.3-10 keV bandpass. This configuration will deploy 24 spacecraft as optics modules and one as the detector. The formation must allow for long duration continuous science observations and also for reconfiguration that permits re-pointing of the formation. In this paper, we provide analysis and trades of several control efforts that are dependent upon the pointing requirements and the configuration and dimensions of the MAXIM formation. We emphasize the utilization of natural motions in the Lagrangian regions that minimize the control efforts and we address both continuous and discrete control via LQR and feedback linearization. Results provide control cost, configuration options, and capabilities as guidelines for the development of this complex mission.

Folta, David↗
NASA NTRS2013

Space Communication and Navigation SDR Testbed, Overview and Opportunity for Experiments

NASA has developed an experimental flight payload (referred to as the Space Communication and Navigation (SCAN) Test Bed) to investigate software defined radio (SDR) communications, networking, and navigation technologies, operationally in the space environment. The payload consists of three software defined radios each compliant to NASAs Space Telecommunications Radio System Architecture, a common software interface description standard for software defined radios. The software defined radios are new technology developments underway by NASA and industry partners launched in 2012. The payload is externally mounted to the International Space Station truss to conduct experiments representative of future mission capability. Experiment operations include in-flight reconfiguration of the SDR waveform functions and payload networking software. The flight system will communicate with NASAs orbiting satellite relay network, the Tracking and Data Relay Satellite System at both S-band and Ka-band and to any Earth-based compatible S-band ground station. The system is available for experiments by industry, academia, and other government agencies to participate in the SDR technology assessments and standards advancements.

Reinhart, Richard C.↗
NASA NTRS1993

Semi-Markov Unreliability Range Evaluator

Semi-Markov Unreliability Range Evaluator, SURE, computer program is software tool for analysis of reconfigurable, fault-tolerant systems. Traditional reliability analyses based on aggregates of fault-handling and fault-occurrence models. SURE provides efficient means for calculating accurate upper and lower bounds for probabilities of death states for large class of semi-Markov mathematical models, and not merely those reduced to critical-pair architectures.

Butler, Ricky W.↗
NASA NTRS2007

Optical Phased Array Antennas using Coupled Vertical Cavity Surface Emitting Lasers

High data rate communication links are needed to meet the needs of NASA as well as other organizations to develop space-based optical communication systems. These systems must be robust to high radiation environments, reliable, and operate over a wide temperature range. Highly desirable features include beam steering capability, reconfigurability, low power consumption, and small aperture size. Optical communication links, using coupled vertical cavity surface emitting laser radiating elements are promising candidates for the transmit portion of these communication links. In this talk we describe a mission scenario, and how the antenna requirements are derived from the mission needs. We describe a potential architecture for this type of antenna, and outline the advantages and drawbacks of this approach relative to competing technologies. The technology we are proposing used coupled arrays of 1550 nm vertical cavity surface emitting lasers for transmission. The feasibility of coupling these arrays together, to form coherent high-power beams that can be modulated at data rates exceeding 1 Gbps, will be explored. We will propose an architecture that enables electronic beam steering, thus mitigating the need for ancillary acquisition, tracking and beam pointing equipment such as needed for current optical communicatin systems. The beam-steering capability we are proposing also opens the possibility of using this technology for inter-satellite communicatin links, and satellite-to-surface links.

Mueller, Carl H.↗
NASA NTRS2008

Electronic Switch Arrays for Managing Microbattery Arrays

Integrated circuits have been invented for managing the charging and discharging of such advanced miniature energy-storage devices as planar arrays of microscopic energy-storage elements [typically, microscopic electrochemical cells (microbatteries) or microcapacitors]. The architecture of these circuits enables implementation of the following energy-management options: dynamic configuration of the elements of an array into a series or parallel combination of banks (subarrarys), each array comprising a series of parallel combination of elements; direct addressing of individual banks for charging/or discharging; and, disconnection of defective elements and corresponding reconfiguration of the rest of the array to utilize the remaining functional elements to obtain the desited voltage and current performance. An integrated circuit according to the invention consists partly of a planar array of field-effect transistors that function as switches for routing electric power among the energy-storage elements, the power source, and the load. To connect the energy-storage elements to the power source for charging, a specific subset of switches is closed; to connect the energy-storage elements to the load for discharging, a different specific set of switches is closed. Also included in the integrated circuit is circuitry for monitoring and controlling charging and discharging. The control and monitoring circuitry, the switching transistors, and interconnecting metal lines are laid out on the integrated-circuit chip in a pattern that registers with the array of energy-storage elements. There is a design option to either (1) fabricate the energy-storage elements in the corresponding locations on, and as an integral part of, this integrated circuit; or (2) following a flip-chip approach, fabricate the array of energy-storage elements on a separate integrated-circuit chip and then align and bond the two chips together.

Mojarradi, Mohammad↗
NASA NTRS1987

An innovative design for autonomous backup attitude control of the Gamma Ray Observatory

The Gamma Ray Observatory is a NASA funded three-axis stabilized spacecraft which will carry four scientific instruments to observe gamma ray phenomena. The requirement to protect the scientific mission from system failures led to the attitude control and determination system design described in this paper. The design employs nine control modes with error detection, hardware substitution, and autonomous mode switching. The system architecture evolved to eliminate cross-dependence between the primary on-board computer (OBC) and the backup control processor electronics. Cross strapping of sensors and actuators and separation of the input/output electronics ensure that a reliable set of sensors and actuators will be available for backup mode operation. The OBC software includes failure detection, hardware reconfiguration, and mode switching logic which provide the ability to autonomously transfer, upon anomaly, to a reliable backup mode. Verification of this mode transition design is done in four test programs: at the unit level, by analytical simulation, by a hybrid breadboard electronics-simulation setup, and by a flight hardware-simulation test.

Tai, F.↗
NASA NTRS2012

NASA Tech Briefs, April 2012

Topics include: Computational Ghost Imaging for Remote Sensing; Digital Architecture for a Trace Gas Sensor Platform; Dispersed Fringe Sensing Analysis - DFSA; Indium Tin Oxide Resistor-Based Nitric Oxide Microsensors; Gas Composition Sensing Using Carbon Nanotube Arrays; Sensor for Boundary Shear Stress in Fluid Flow; Model-Based Method for Sensor Validation; Qualification of Engineering Camera for Long-Duration Deep Space Missions; Remotely Powered Reconfigurable Receiver for Extreme Environment Sensing Platforms; Bump Bonding Using Metal-Coated Carbon Nanotubes; In Situ Mosaic Brightness Correction; Simplex GPS and InSAR Inversion Software; Virtual Machine Language 2.1; Multi-Scale Three-Dimensional Variational Data Assimilation System for Coastal Ocean Prediction; Pandora Operation and Analysis Software; Fabrication of a Cryogenic Bias Filter for Ultrasensitive Focal Plane; Processing of Nanosensors Using a Sacrificial Template Approach; High-Temperature Shape Memory Polymers; Modular Flooring System; Non-Toxic, Low-Freezing, Drop-In Replacement Heat Transfer Fluids; Materials That Enhance Efficiency and Radiation Resistance of Solar Cells; Low-Cost, Rugged High-Vacuum System; Static Gas-Charging Plug; Floating Oil-Spill Containment Device; Stemless Ball Valve; Improving Balance Function Using Low Levels of Electrical Stimulation of the Balance Organs; Oxygen-Methane Thruster; Lunar Navigation Determination System - LaNDS; Launch Method for Kites in Low-Wind or No-Wind Conditions; Supercritical CO2 Cleaning System for Planetary Protection and Contamination Control Applications; Design and Performance of a Wideband Radio Telescope; Finite Element Models for Electron Beam Freeform Fabrication Process Autonomous Information Unit for Fine-Grain Data Access Control and Information Protection in a Net-Centric System; Vehicle Detection for RCTA/ANS (Autonomous Navigation System); Image Mapping and Visual Attention on the Sensory Ego-Sphere; HyDE Framework for Stochastic and Hybrid Model-Based Diagnosis; and IMAGESEER - IMAGEs for Education and Research.

Source record↗
NASA NTRS2013

Orbiting Rainbows: Optical Manipulation of Aerosols and the Beginnings of Future Space Construction

Our objective is to investigate the conditions to manipulate and maintain the shape of an orbiting cloud of dust-like matter so that it can function as an ultra-lightweight surface with useful and adaptable electromagnetic characteristics, for instance, in the optical, RF, or microwave bands. Inspired by the light scattering and focusing properties of distributed optical assemblies in Nature, such as rainbows and aerosols, and by recent laboratory successes in optical trapping and manipulation, we propose a unique combination of space optics and autonomous robotic system technology, to enable a new vision of space system architecture with applications to ultra-lightweight space optics and, ultimately, in-situ space system fabrication. Typically, the cost of an optical system is driven by the size and mass of the primary aperture. The ideal system is a cloud of spatially disordered dust-like objects that can be optically manipulated: it is highly reconfigurable, fault-tolerant, and allows very large aperture sizes at low cost. See Figure 1 for a scenario of application of this concept. The solution that we propose is to construct an optical system in space in which the nonlinear optical properties of a cloud of micron-sized particles are shaped into a specific surface by light pressure, allowing it to form a very large and lightweight aperture of an optical system, hence reducing overall mass and cost. Other potential advantages offered by the cloud properties as optical system involve possible combination of properties (combined transmit/receive), variable focal length, combined refractive and reflective lens designs, and hyper-spectral imaging. A cloud of highly reflective particles of micron-size acting coherently in a specific electromagnetic band, just like an aerosol in suspension in the atmosphere, would reflect the Sun's light much like a rainbow. The only difference with an atmospheric or industrial aerosol is the absence of the supporting fluid medium. This new concept is based on recent understandings in the physics of optical manipulation of small particles in the laboratory and the engineering of distributed ensembles of spacecraft clouds to shape an orbiting cloud of micron-sized objects. In the same way that optical tweezers have revolutionized micro- and nano-manipulation of objects, our breakthrough concept will enable new large scale NASA mission applications and develop new technology in the areas of Astrophysical Imaging Systems and Remote Sensing because the cloud can operate as an adaptive optical imaging sensor. While achieving the feasibility of constructing one single aperture out of the cloud is the main topic of this work, it is clear that multiple orbiting aerosol lenses could also combine their power to synthesize a much larger aperture in space to enable challenging goals such as exoplanet detection. Furthermore, this effort could establish feasibility of key issues related to material properties, remote manipulation, and autonomy characteristics of cloud in orbit. There are several types of endeavors (science missions) that could be enabled by this type of approach, i.e. it can enable new astrophysical imaging systems, exoplanet search, large apertures allow for unprecedented high resolution to discern continents and important features of other planets, hyperspectral imaging, adaptive systems, spectroscopy imaging through limb, and stable optical systems from Lagrange-points. Future micro-miniaturization might hold promise of a further extension of our dust aperture concept to other more exciting smart dust concepts with other associated capabilities.

Space Construction↗
NASA NTRS2013

Space Communication and Navigation Testbed Communications Technology for Exploration

NASA developed and launched an experimental flight payload (referred to as the Space Communication and Navigation Test Bed) to investigate software defined radio, networking, and navigation technologies, operationally in the space environment. The payload consists of three software defined radios each compliant to NASAs Space Telecommunications Radio System Architecture, a common software interface description standard for software defined radios. The software defined radios are new technology developed by NASA and industry partners. The payload is externally mounted to the International Space Station truss and available to NASA, industry, and university partners to conduct experiments representative of future mission capability. Experiment operations include in-flight reconfiguration of the SDR waveform functions and payload networking software. The flight system communicates with NASAs orbiting satellite relay network, the Tracking, Data Relay Satellite System at both S-band and Ka-band and to any Earth-based compatible S-band ground station.

Reinhart, Richard↗
NASA NTRS1992

Implementation of an intelligent control system

A laboratory testbed facility which was constructed at NASA LeRC for the development of an Intelligent Control System (ICS) for reusable rocket engines is described. The framework of the ICS consists of a hierarchy of various control and diagnostic functions. The traditional high speed, closed-loop controller resides at the lowest level of the ICS hierarchy. Above this level resides the diagnostic functions which identify engine faults. The ICS top level consists of the coordination function which manages the interaction between an expert system and a traditional control system. The purpose of the testbed is to demonstrate the feasibility of the OCS concept by implementing the ICS as the primary controller in a simulation of the Space Shuttle Main Engine (SSME). The functions of the ICS which are implemented in the testbed are as follows: an SSME dynamic simulation with selected fault mode models, a reconfigurable controller, a neural network for sensor validation, a model-based failure detection algorithm, a rule based failure detection algorithm, a diagnostic expert system, an intelligent coordinator, and a user interface which provides a graphical representation of the event occurring within the testbed. The diverse nature of the ICS has led to the development of a distributed architecture consisting of specialized hardware and software for the implementation of the various functions. This testbed is made up of five different computer systems. These individual computers are discussed along with the schemes used to implement the various ICS components. The communication between computers and the timing and synchronization between components are also addressed.

Simon, D. L.↗
NASA NTRS2019

The Space Communications and Navigation Testbed aboard International Space Station: Seven Years of Space-based Reconfigurable Software Defined Communications, Navigation, and Networking

The adoption of software defined radios offers space missions a new way to develop and operate space transceivers for communications and navigation.The SCaN Testbed on-board the ISS led groundbreaking efforts to champion use of software defined radios for space communications. The SCaN Testbed has allowed NASA, industry, academia, and international partners to pursue their respective interests in joint collaboration with NASA, and move this technology and it's applications to the space domain. Launched in 2012, The SCaN Testbed has logged over 4000 hours of operation exploring the development, reconfiguration, and operation of software defined radios and their software applications. Over the past seven years, experimenters and organizations from across the United States and around the world, have advanced the applications of software defined radios and networks using the SCaN Tested. Some of SCaN Testbed's successful experiments include the demonstration of the first Ka-band full duplex space transceiver, which became an R&D 100 award winning technology, and was inducted into the Space Technology Hall of Fame, following the launch and space deployment of a successful commercial product line based on the Testbed radios.Experiments have focused on new software development and operations concepts for understanding how to manage and apply this relatively new technology to space to improve communications and navigation for space science and exploration missions. The advanced capabilities of the software radios allow for multiple applications or functions (e.g., communication and navigation) to operate from the same radio platform. Multiple software waveform applications enable software component reuse and improve efficiency for multiple applications operating over different mission phases. The new capabilities of software defined radios such as on-orbit reconfiguration, also present new challenges such as increased operational complexity. Experiments of the SCaN testbed include more intelligent or cognitive applications to improve communications efficiency and manage the complexity of the radios, the communication channels, and the network itself. The software defined radios on the SCaN Testbed are each compliant to NASA's Space Telecommunications Radio System (STRS) Architecture. The STRS Architecture provides commonality among radio developments from different providers and different mission applications, and is designed to reduce the cost, risk, and complexity of unique and custom radio developments. This radio architecture standard defines common waveform software interfaces, methods of instantiation, operation, and documentation. As the SCaN Testbed concludes its operations on ISS, this presentation explores the advancements and accomplishments made to advance software defined radio technology and its applications for exploration. The accomplishments cover a number of experiment areas in Ka-band and S-band communications with TDRS, high rate communications, adaptive waveform operation, navigation using both GPA and Galileo constellations, complex networking and disruptive tolerant link protocols, user initiative service, and initial experiments with intelligent and cognitive applications which demonstrate the significant potential of software defined and cognitive radios.

Mortensen, Dale↗
NASA NTRSDate not supplied

Reconfiguring COSSIR for the Next Generation of Cloud and Precipitation Science

NASA originally developed the Compact Scanning Sub-millimeter Imaging Radiometer (CoSSIR) in the early 2000s, where it was own in the CRYSTAL-FACE and TC4 field experiments. With renewed interest in sub-millimeter remote sensing motivated by the upcoming launch of the EUMETSAT-sponsored Ice Cloud Imager (ICI), along with its potential for inclusion as part of the NASA Decadal Survey Aerosols, CLouds, Convection, and Precipitation (ACCP) observing architecture, CoSSIR is being refurbished to prepare for routine suborbital submillimeter measurements this decade. Upgrades include hardware (procurement of shared parts so that CoSMIR and CoSSIR can fly concurrently) and a change to the channels, with a focus on differential scattering and polarization at eight frequencies ranging from 170 to 640 GHz. As part of the refurbishment, the instrument name has been changed to Configurable Scanning Sub-millimeter Instrument/Radiometer, retaining the same acronym, in order to emphasize the science objectives that are enabled by CoSSIR's unique scanning geometry and channel set. These anticipated capabilities include two-dimensional pro ling of clouds and precipitation and characterization of the geometry (shape and orientation) of large cloud and precipitating ice particles.

Radiometry↗
NASA NTRS2013

Analyses Made to Order: Using Transformation to Rapidly Configure a Multidisciplinary Environment

Aerospace problems are highly multidisciplinary. Four or more major disciplines are involved in analyzing any particular vehicle. Moreover, the choice of implementation technology of various subsystems can lead to a change of leading domain or reformation of the driving equations. An excellent example is the change of expertise required to consider aircraft built from composite or metallic structures, or those propelled by chemical or electrical thrusters. Another example is in the major reconfiguration of handling and stability equations with different control surface configuration (e.g., canards, t-tail v four-post tail). Combinatorial problems are also commonplace anytime that a major system is to be designed. If there are only 5 attributes of a design to consider with 4 different options, this is already 1024 options. Adding just 5 more dimensions to the study explodes the space to over one million. Even generous assumptions like the idea that only 10% of the combinations are physically feasible can only contain the problem for so long. To make matters worse, the simple number of combinations is only the beginning. Combining the issue of trade space size with the need to reformulate the design problem for many of the possibilities makes life exponentially more difficult. Advances in software modeling approaches have led to the development of model-driven architecture. This approach uses the transformation of models into inferred models (e.g. inferred execution traces from state machines) or the skeletons for code generation. When the emphasis on transformation is applied to aerospace, it becomes possible to exploit redundancy in the information specified in multiple domain models into a unified system model. F1urther, it becomes possible to overcome the combinatorial nature of specifying integrated system behavior by manually combining the equations governing a given component technology. Transformations from a system specification combined with a system-analysis mapping specification enable one-click combination of domain analyses. This is a flexibility that has been missing from many engineering codes, which often entangle design specification and physical examination much more than is required to conduct the analysis. This capability has been investigated and cultivated within the DARPA F6 program by a team of JPL and Phoenix Integration engineers building the Adapatable Systems Design and Analysis (ASDA) framework. By embracing system modeling with SysML and the Query-View-Transformation (QVT) language, the ASDA team has been able to build a flexible, easily reconfigurable framework for building up and solving large tradespaces. Examples of application and lessons learned in building the framework will be described in this paper. In addition, the motivation will be laid for various tool vendors to develop open model description standards while being able to maintain competitive advantage through proprietary algorithms and approaches. These standards will also be compared to the underpinnings of model-driven architecture and the OMG standards of the Meta-Object Facility (MOF), SysML, and QVT.

Cole, Bjorn↗
NASA NTRS1993

Dynamically reconfigurable optical morphological processor and its applications

An innovative optically implemented morphological processor is introduced. With the use of a large space-bandwidth-product Dammann grating and a high-speed shutter spatial light modulator, effective structuring element with large size and arbitrary shape can be constructed with dynamic reconfigurability. This reconfigurability is a major improvement over the conventional correlator-based morphological processor in which fixed holographic filters are used as structuring elements (Casasent and Botha, 1988). A novel two-dimensional thresholding photodetector array, capable of performing parallel thresholding and feedback, is utilized in this system and makes possible the implementation of many complex morphological operations requiring iterative feedbacks and full programmability. The optical architecture and the principle of operation are presented. Experimental demonstration of binary image morphological erosion, dilation, opening, and closing are also demonstrated. A technique for extending this technique to gray-scale image using thresholding decomposition technique is also discussed.

Chao, Tien-Hsin↗