Uncertainty quantification (UQ) is the study of the effects of uncertainty on the values of analytical results and the predictions of scientific models. Sources of uncertainty include imprecise knowledge of the exact values of parameters, lack of confidence in the physical models, use of imperfectly calibrated models, and irreducible uncertainties due to physical characteristics. The Air Force Research Laboratory has undertaken the challenge of understanding, developing and analyzing the techniques of UQ as they apply to Laser Beam Control. This paper proposes a simple methodology and simple results with our first attempt of applying UQ as a new analysis tool. The software toolkit which was chosen was an analytical group of algorithms from a Sandia National Laboratory (SNL) package called DAKOTA (Design Analysis Kit for Optimization and Terascale Applications). The specific application of interest to the Air Force Research Laboratory (AFRL) is the analytical prediction of the performance of a Laser Beam Control systems under various scenarios, conditions, and missions. The application of rigorous UQ techniques to the models used to predict beam control performance could greatly improve our confidence in these predictions and also improve the acceptance of advanced Laser Beam Control systems within the science and engineering communities1,2. The proposed work would follow a multi-step approach, analyzing the more easily quantified sources of uncertainty, and then including increasingly complicated physical phenomena as the work progresses. Will present the initial results, and the first steps in the incorporation of UQ into our Laser Beam Control Modeling and Simulation environments.
The beam control system of a high energy laser (HEL) application can typically experience error amplification due to disturbance measurements that are associated with the non-common path of the optical train setup. In order to address this error, conventional schemes require offline identification or a calibration process to determine the non-common path error portion of a measured sequence that contains both common and non-common path disturbances. However, not only is it a challenging to model the properties of the non-common path disturbance alone but also a stationary model may not guarantee consistent jitter control performance and repeated calibration may be necessary. The paper first attempts to classify the non-common path error problem into two categories where the designer is only given one measurement or two measurements available for real-time processing. For the latter case, an adaptive correlated pre-filter is introduced here to provide in situ determination of the non-common path disturbance through an adaptive correlation procedure. Contrasting features and advantages of this algorithm will be demonstrated alongside a baseline approach of utilizing notch filters to bypass the non-common portion of the combined sequence.
Small MEMS (Micro-Electro-Mechanical Systems) deformable mirror (DM) technology is of great interest to the adaptive optics (AO) community. These new, MEMS-DM's are being considered for many conventional AO applications since they posses some advantages over conventional DM's. The MEMS-DM technology is driven by the expectation of achieving improved performance with lower costs, low electrical power, high number of actuators, high production rates, and large reductions in structural mass and volume. In addition to the imaging community, the directed energy community is also interested in taking advantages of some of the characteristics which MEMS-DM's offer.
The Air Force Research Laboratory has undertaken the challenge of developing and analyzing several continuous face-sheet MEMS-DM's designs. This paper proposes a simple controls loop computer model for a typical continuous reflective face-sheet MEMS-DM. There are a variety of MEMS-DM's which are being developed for the Air Force Research Laboratory. Data from a typical continuous reflective face-sheet MEMS-DM has been acquired and analyzed. From this data a model for a typical MEMS-DM device could be developed and verified. This MEMS-DM's data can be compared to previous design models which were developed in previous articles. In addition a feedback, closed adaptive optics loop can be designed and analyzed. The research goal is to get a realistic idea of the behavior and performance of these new, innovative devices.
Small Micro-Electro-Mechanical Systems (MEMS) deformable mirror (DM) technology is of great interest to the adaptive optics (AO) community. These MEMS-DM's are being considered for many conventional AO applications since they posses some advantages over conventional DM's. The MEMS-DM technology is driven by the expectation of achieving improved performance with lower costs, low electrical power, high number of actuators, high production rates, and large reductions in structural mass and volume. In addition to the imaging community, the directed energy community is also interested in taking advantage of the characteristics which MEMS-DM's offer.
Unlike imaging, the optical fill-factor of a high-energy laser DM, has to be essentially 100 percent! Many modern MEMS-DM designs consist of small, lightweight, segmented mirrors that can be precisely controlled. For high-energy laser applications, the MEMS DM's should have a continuous reflective face-sheet with no gaps. This continuous reflective face-sheet must include high-energy laser coatings, which render the face sheet very stiff. This is a new challenge for MEMS-DM's, which has not previously been addressed. The Air Force Research Laboratory has proposed to meet this challenge with several continuous face-sheet high-energy laser MEMS-DM's designs. This paper will give a generic description of a MEMS-DM computer model. The research goal is to develop a MEMS-DM model for closed loop control of a high-energy laser, MEMS-DM adaptive optics application.
The Air Force Research Laboratory/Directed Energy Directorate (AFRL/DE) via the ALVA (Applications of Lidars for Vehicles with Analysis) program installed in late 2000 a wideband, 12 J 15 Hz CO2 laser radar (ladar) on the 3.67 meter aperture AEOS (Advanced Electro-Optics System) telescope. This system is part of the Maui Space Surveillance System (MSSS), on the summit of Haleakala, Maui, HI. This ladar adopts the technology successfully demonstrated by the first generation HI-CLASS (High Performance CO2) Ladar Surveillance Sensor) operating on the nearby 0.6 meter aperture Laser Beam Director (LBD) and developed under the Field Ladar Demonstration program, jointly sponsored by AFRL/DE and the Army's Space and Missile Defense Command. The moderate power (approximately 180 watts) HI-CLASS/AEOS system generates multiple, coherent waveforms for precision satellite tracking and characterization of space objects for 1 m2 targets at ranges out to 10,000 km. This system also will be used to track space objects smaller than30 cm at ranges to 2,000 km. A third application of this system is to provide data for developing satellite identification, characterization, health and status techniques. This paper will discuss the operating characteristics and innovative features of the new system. The paper will also review recent results in support of AF needs, demonstrations, experiments, as well as planned activities that directly support applications in the DoD, scientific, and commercial arenas.
The Air Force Research Laboratory (AFRL) is exploring the feasibility of large-aperture, deployable, space-based membrane telescopes operating in the visible and/or near- infrared spectral regions. One of the near-term goals of this work is to develop an understanding of available and achievable membrane materials, specifically concentrating on practical techniques to form large aperture membranes with the necessary surface quality and economy. When this research began a little more than three years ago, the conceptual design was based upon a totally inflatable structure. An inflatable structure has been used for space solar power collection and radio frequency antennas. This totally inflatable lenticular design is simple and relatively easy to demonstrate, but maintaining inflation during an extended lifetime in near-earth orbit may not be feasible. Recently, a new concept for a membrane telescope has emerged which does not depend on sustained inflation during operation. Thin membranes on the order of 10 to 100 micrometer thick will be packaged and deployed, maintaining their surface figure by means other than inflation. Given the fact that the sub- wavelength level surface tolerances required of imaging telescopes will probably not be practical with a membrane- based telescope, such systems will probably rely on real-time holography or some other wavefront correction or compensation technique. We will discuss the primary experimental work ongoing in the AFRL Membrane Mirror Laboratory, and in doing so, some of the issues relevant to demonstrating a practical, large-aperture membrane mirror system.
Thin membrane inherently require a certain minimum amount of strain to adequately perform as optical elements. This minimum strain can be established by simultaneously considering the effects of strain on the reflective surface, film thickness variations, and the corrective range of the adaptive optics (AO) scheme. To show how strain and the optimal optical surface are related, 75 and 125-micron thick polyimide films were examined under various strain conditions. Thickness variations were also mapped and correlated. The limits of the AO correction scheme set the films surface topography requirement. Our results will help to partially define an optical quality membrane, which is an important initial step toward the manufacturing of such a film.
The Air Force Research Laboratory is developing a large space-based optical membrane telescope. When this research began a little more than three years ago, the conceptual design was based upon a totally inflatable structure. An inflatable structure has been used for space solar power collection and radio-frequency antennas. To place the development of the membrane optical telescope in perspective, a short history of past inflatables will be presented. The totally inflatable lenticular design used in a variety of space-based applications in radio and radar antennae, solar power for propulsion applications and solar shields is of particular interest. Recently, a new version of a membrane telescope has emerged. Thin membranes on the order of 10 to 100 micrometers thick will be packaged and deployed without using inflation to maintain the surface figure. The move away from a pure inflatable is driven by several factors, including wavelength-level tolerances required of optical telescopes, even when real-time holography is invoked as the adaptive optics correction technique. Issues that led us to de-emphasize an inflatable, lenticular design and concentrate on a near-net shape film using stress coatings and dual boundary edge control are discussed.
The feasibility of forming very thin (approximately 100 um), flexible membranes into low-cost, low-mass, large diameter optical elements is being explored. While spherical or parabolic shapes are the ultimate goal for imaging and other light-gathering applications, there are potential applications for large, planar surfaces. Also, knowledge gained while working with planar membranes is being applied to concave structures. Recent efforts have concentrated on measuring and understanding the behavior of currently available materials. This paper discusses experimental results, and describes measurement techniques and membrane materials used. Highlighted are our most recent results on a 11-inch diameter membrane mirror which we measured to be flat to approximately 0.1 um rms.
The surface of an initially planar membrane, which is subsequently subjected to a pressure difference, can be manipulated into a variety of shapes. This report discusses two methods by which optically desirable deterministic shapes might be achieved. The first involves pre-straining of the membrane, a technique which has already been demonstrated to reduce the spherical aberration in such a mirror. However, near-parabolic shapes at low f-numbers appear not to be achievable with this method, i.e., using pressure differences and pre-strain alone. The second technique is a somewhat novel one involving the use of a plunger to translate the central region of the membrane along the optical axis. Preliminary results suggest that attainment of a near-parabolic shape over a substantial area of the membrane may indeed be possible with this method. The experiments described here use an aluminum coated 125 micron thick polyimide membrane with a clear aperture of 11 inches.
Thin flexible membranes with curvature are gaining favor as lightweight optical components. The Surveillance Technologies Branch of the Air Force Research Laboratory has demonstrated that membranes can yield a near diffraction limited image when combined with real-time holography as the wavefront correction method. Researchers at the University of Strathclyde in Glasgow, Scotland are using large membrane mirrors in a volumetric imaging project, while others at the Vavilov Laser Physics Institute in Saint Petersburg, Russia are investigating the use of real-time holography to correct membrane mirror aberrations. Existing membranes, however, have not been designed with optical imaging as the intended application. Thus, there is a need to design and construct optical quality membranes.
Thin membranes with curvature are investigated as mirror substrates for use in large optical telescopes. These films are mounted on an optically flat circular ring and stretched over a smaller optically flat circular ring where pressure or vacuum is applied to create the doubly curved surface as shown in figure 1. The films may vary in thickness from 20 to 200 microns. This particular experiment examines an aluminum coated 125 micron thick homogeneous, planar, isotropic membrane with a clear aperture of 28 centimeters. The nature of a flexible membrane implies that the surface curvature will result in an assorted array of gross surface figure issues associated with deterministic shape limits, probabilistic imperfections, nonlinear constitutive effects, and long-time- dependent effects. This report will focus on the empirical deterministic shape limits of a doubly curved membrane. Theoretical work on thin films inflated or evacuated into a doubly curved surface has a long history, and remains an active area of research. A number of articles [1,2,3,4,7] include summaries of this history, and offer insight on the deterministic membrane shapes.
Space-based inflatable technology is of current interest to NASA, DOD, and in particular to the Air Force Research Laboratory. Potentially large gains in lowering launch costs, through reductions in structural mass and volume are driving this activity. Diverse groups are researching and developing this technology for radio and radar antennae, optical telescopes, and solar power and propulsion applications. Regardless of the use, one common requirement for successful application is the accuracy of the inflated surface figure. This paper gives a very cursory description of the research being performed at the Air Force Research Laboratory in the fields of membrane mirrors and real time holography. First, the article will show a shape modification method for the membrane mirror, achieved through enforced boundary displacements. The membrane mirror shape modification, resulted in moving the inflated membrane shape towards a desired optical profile. Minimization of the optical figure error is further discussed. Next, the optical requirements levied from the membrane mirror to an optically addressed spatial light modulator performing real time holographic correction are discussed. A proposed optical configuration in which a real time holographic optical element could be combined with the membrane mirror to achieve near diffraction limited optical performance is discussed.
An important difference between biological vision systems and their electronic counterparts is the large number of feedback signals controlling each aspect of the image collection process. For every forward path of information in the brain, from sensor to comprehension, there appears to be several neural bundles which send information back to the sensor to modify the way the information is collected. In this paper we will examine the role of such feedback signals and suggest algorithms for intelligent processing of images directly on the focal plane, using feedback. We consider first what form these signals might take and how they can be used to implement functions common to conventional image processing with the objective of moving the computation out of the digital domain and place much of its on the focal plane, or analog processing close to the focal plane. While this work falls under the general heading of artificial neural networks, it goes beyond the static processing of signals suggested by the McCulloch and Pitts model of the neuron and the Laplacian image processing suggested by Carver Mead by including the dynamics of temporal encoding in the analysis process.
Optical aberrations are characterized by orthogonal basis functions composed of discretized Zernike polynomials. The coefficients associated with each Zemike polynomial can be measured using a Phase Diversity wave front sensing technique. Nonlinear optimization techniques are utilized to calculate the Zernike coefficients in a serial manner. Even though this traditional method is attractive, it is computationally a very formidable task to calculate several Zernike coefficients for a given system. Hence the method is not applicable in a real time image reconstruction scheme. In this paper we first show that each Zemike coefficient can be calculated independently in a parallel fashion from each other. Our method uses nonlinear optimization of a single variable only. We use a modified Gonsalves error metric function involving only a single unknown aberration coefficient. Next, we describe an implementation of the algorithm on the IBM SP2 parallel computer. We used the PVM software for parallelizing the computational tasks across the processors in a "master/slave" fashion. We will show that the computation can be performed in an efficient manner using this strategy.
Key Words: optical aberration; Zernike polynomials; Zernike coefficients; phase diversity; parallel computation
Unlike biological vision, most techniques for computer image processing are not robust over large samples of imagery. Natural systems seem unaffected by variation in local illumination and textures which interfere with conventional analysis. While change detection algorithms have been partially successful, many important tasks like extraction of roads and communication lines remain unsolved. The solution to these problems may lie in examining architectures and algorithms used by biological imaging systems. Pulsed oscillatory neural network design, based on biomemetics, seem to solve some of these problems. Pulsed oscillatory neural networks are examined for application to image analysis and segmentation of multispectral imagery from the Satellite Pour l'Observation de la Terre. Using biological systems as a model for image analysis of complex data, a pulsed coupled networks using an integrate and fire mechanism is developed. This architecture, based on layers of pulsed coupled neurons is tested against common image segmentation problems. Using a reset activation pulse similar to that generated by sacatic motor commands, an algorithm is developed which demonstrates the biological vision could be based on adaptive histogram techniques. This architecture is demonstrated to be both biologically plausible and more effective than conventional techniques. Using the pulse time-of-arrival as the information carrier, the image is reduced to a time signal, temporal encoding of imagery, which allows an intelligent filtering based on expectation. This technique is uniquely suited to multispectral/multisensor imagery and other sensor fusion problems.
This paper describes a method to compute the optical transfer function, in terms of Zernike polynomials, one coefficient at a time using a neural network and gradiant decent. Neural networks, which are a class of self-tutored non-linear transfer functions, are shown to be appropriate for this problem as a closed form solution does not exist. A neural network provides an approximation to the optical transfer function computed from examples using gradient descent methods. Orthogonality of the Zernike polynomials allow image wavefront aberrations to be described as an ortho-normal set of coefficients. Atmospheric and system distortion of astronomical observations can introduce an unknown phase error with the observed image. This phase distortion can be described by a set of coefficients of the Zernike polynomials. This orthogonality is shown to contribute to the simplicity of the neural network method of computation. Two paradigms are used to determine the coefficient description of the wave front error to provide to a compensation system. The first uses a phase diverse image as input to a feedforward backpropagation network for generation of a single coefficient. The second method requires the transfer function to be computed in the Fourier domain. Architecture requirements are investigated and reported together with saliency determination of each input the the network to optimize computation and system requirements.
We present the preliminary results of a laboratory experiment using phase diversity as a wavefront sensor. Computer simulations of this experiment were also performed. The phase diversity algorithm used the ordinary finite-difference method to solve the transport equation of intensity and phase. This method of phase diversity retrieves the phase directly and may prove to be useful for low light level applications and for extended objects. This entertains the possibility of using phase diversity as an on-line wavefront sensor for adaptive optics.
A theoretical description of Phase Diversity is done in some detail to lay the foundations for the experimental effort. The Phase Diversity algorithm is formulated in the context of nonlinear programming where a metric is developed and then minimized. This development will show how the Zernike coefficients can be solved for directly using nonlinear optimization techniques. Computer simulations are used to validate the algorithms and techniques. The results of the computer simulations are shown. Once the confidence of the algorithms and techniques are established in the computer simulations, they are used on actual laboratory data. Detailed discussion of the laboratory implementation will be described and the laboratory results will be shown.
We present the results of some laboratory experiments of the use of electro-optical (EO) devices to control the optical path length (OPL) of an interferometric array. One of the most important problems in interferometric beam combination is the control of the path length; this is coupled with the need for partial wavefront compensation in order to increase the sensitivity of the interferometer. Traditional approaches to such problems are often very expensive and sometimes impractical. For this reason we started an effort, both theoretically and experimentally, in order to investigate if less costly and more effective techniques can be applied. In our experiments we used single-cell LCDs in order to eliminate piston terms in a two- aperture interferometer. We used phase diversity techniques for extracting the phase information. Although the experimental results are still partial we believe that there is enough evidence that such devices can be used for the OPL control and partial wavefront compensation. Further testing is needed in order to assess the real capabilities of commercially available LCDs and the need, if any, of customization.
In this paper we present (1) the optical system design and operational overview, (2) laboratory evaluation spectra, and (3) a sample of the first observational data taken with HYSAT. The hyperspectral sensor systems which are being developed and whose utility is being pioneered by the Phillips Laboratory are applicable to several important SOI (space object identification), military, and civil applications including (1) spectral signature simulations, satellite model validation, and satellite database observations and (3) simultaneous spatial/spectral observations of booster plumes for strategic and surrogate tactical missile signature identification. The sensor system is also applicable to a wide range of other applications, including astronomy, camouflage discrimination, smoke chemical analysis, environmental/agricultural resource sensing, terrain analysis, and ground surveillance. Only SOI applications will be discussed here.
An image restoration problem will be formulated in the context of nonlinear programming using the conjugate gradient algorithm. The formulation of the objective function used in the conjugate gradient routine is presented. Situations may occur when there is a great deal already known about a certain object of interest which have been optically blurred because of the atmosphere or system imperfections. This paper shows a new and innovative way to incorporate a priori, perfect, partial knowledge of an object into the nonlinear optimization procedure. The topics discussed include the steps which led to the development of this procedure, the incorporation of the a priori knowledge into the nonlinear optimization problem, an analytical, mathematical approach which shows how the improvement should occur, and finally, data from simulated results which demonstrate the improvement using the developed diagnostic metrics.
This paper shows the development of the imaging restoration problem entirely in the frequency domain, then solves for the analytical solution. The analytical solution is found to be ill-posed, thus, a good approach for the solution is via nonlinear optimization. The image recovery problem is thus formulated in the context of nonlinear optimization using Fourier data. Several examples are shown using unconstrained optimization techniques with the incorporation of the conjugate gradient algorithm. These examples basically are the inverse filter solutions. Three main diagnostic metrics are shown and discussed as possible candidates for evaluation of the results.
KEYWORDS: Telescopes, Control systems, Data modeling, Phased arrays, Optical telescopes, Mathematical modeling, Space telescopes, Digital signal processing, System identification, Signal processing
A phased-array telescope is formed by combining a number of optical telescopes to yield the resolution of a single much larger telescope. One such telescope, the Multipurpose Multiple Telescope Testbed (MMTT), consists of four 20-cm-aperture telescopes phased together with a 30-arcmin field of view. This paper illustrates the model identification of the MMTT system. Each of the 4 channels of the system consists of over 30 subsystems and/or components. Various experimental tests were set up for the MMTT components using a white Gaussian noise source on a spectrum analyzer. The input/output signals for each experimental set up were measured and an ASCII file was created on a personal computer. The transfer function of each subsystem was identified using either the spectrum analyzer and/or through standard system identification software on an AT-class PC. The model thus identified can be used to study system's behavior by simulation as well as designing various controllers for tilt, piston, and pupil geometry control purposes.
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