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At least 253 records · Page 14

Develop advanced nonlinear signal analysis topographical mapping system

The Space Shuttle Main Engine (SSME) has been undergoing extensive flight certification and developmental testing, which involves some 250 health monitoring measurements. Under the severe temperature, pressure, and dynamic environments sustained during operation, numerous major component failures have occurred, resulting in extensive engine hardware damage and scheduling losses. To enhance SSME safety and reliability, detailed analysis and evaluation of the measurements signal are mandatory to assess its dynamic characteristics and operational condition. Efficient and reliable signal detection techniques will reduce catastrophic system failure risks and expedite the evaluation of both flight and ground test data, and thereby reduce launch turn-around time. The basic objective of this contract are threefold: (1) develop and validate a hierarchy of innovative signal analysis techniques for nonlinear and nonstationary time-frequency analysis. Performance evaluation will be carried out through detailed analysis of extensive SSME static firing and flight data. These techniques will be incorporated into a fully automated system; (2) develop an advanced nonlinear signal analysis topographical mapping system (ATMS) to generate a Compressed SSME TOPO Data Base (CSTDB). This ATMS system will convert tremendous amount of complex vibration signals from the entire SSME test history into a bank of succinct image-like patterns while retaining all respective phase information. High compression ratio can be achieved to allow minimal storage requirement, while providing fast signature retrieval, pattern comparison, and identification capabilities; and (3) integrate the nonlinear correlation techniques into the CSTDB data base with compatible TOPO input data format. Such integrated ATMS system will provide the large test archives necessary for quick signature comparison. This study will provide timely assessment of SSME component operational status, identify probable causes of malfunction, and indicate feasible engineering solutions. The final result of this program will yield an ATMS system of nonlinear and nonstationary spectral analysis software package integrated with the Compressed SSME TOPO Data Base (CSTDB) on the same platform. This system will allow NASA engineers to retrieve any unique defect signatures and trends associated with different failure modes and anomalous phenomena over the entire SSME test history across turbo pump families.

Source record↗

Conversion-Integration of MSFC Nonlinear Signal Diagnostic Analysis Algorithms for Realtime Execution of MSFC's MPP Prototype System

NASA's advanced propulsion system Small Scale Magnetic Disturbances/Advanced Technology Development (SSME/ATD) has been undergoing extensive flight certification and developmental testing, which involves large numbers of health monitoring measurements. To enhance engine safety and reliability, detailed analysis and evaluation of the measurement signals are mandatory to assess its dynamic characteristics and operational condition. Efficient and reliable signal detection techniques will reduce the risk of catastrophic system failures and expedite the evaluation of both flight and ground test data, and thereby reduce launch turn-around time. During the development of SSME, ASRI participated in the research and development of several advanced non- linear signal diagnostic methods for health monitoring and failure prediction in turbomachinery components. However, due to the intensive computational requirement associated with such advanced analysis tasks, current SSME dynamic data analysis and diagnostic evaluation is performed off-line following flight or ground test with a typical diagnostic turnaround time of one to two days. The objective of MSFC's MPP Prototype System is to eliminate such 'diagnostic lag time' by achieving signal processing and analysis in real-time. Such an on-line diagnostic system can provide sufficient lead time to initiate corrective action and also to enable efficient scheduling of inspection, maintenance and repair activities. The major objective of this project was to convert and implement a number of advanced nonlinear diagnostic DSP algorithms in a format consistent with that required for integration into the Vanderbilt Multigraph Architecture (MGA) Model Based Programming environment. This effort will allow the real-time execution of these algorithms using the MSFC MPP Prototype System. ASRI has completed the software conversion and integration of a sequence of nonlinear signal analysis techniques specified in the SOW for real-time execution on MSFC's MPP Prototype. This report documents and summarizes the results of the contract tasks; provides the complete computer source code; including all FORTRAN/C Utilities; and all other utilities/supporting software libraries that are required for operation.

Jong, Jen-Yi↗

Possible radio emission from Uranus at 0.5 MHz

Radio emission from the direction of Uranus has been detected in data from the Goddard radio astronomy experiment on the IMP-6 spacecraft. Previously, emission from the direction of Jupiter and Saturn had been observed by IMP-6 at a number of frequencies near 1 MHz and were identified through an analysis of the phase of the observed modulated signal detected from the spinning dipole antenna. This technique was applied to the direction of Uranus with possible positive results. Over the approximately 500 days of data, three to six bursts with unique spectral characteristics have been found. The events persisted less than 3 minutes and are strongest in intensity near 0.5 MHz. Identification with Uranus is confused by the likely presence of low-level terrestrial and solar emission. Because of the unfavorable angular separation of earth and Uranus, there is a possibility that the bursts are atypical terrestrial magnetospheric phenomena, although the uniqueness of the set of events indicates the probable detection of radiation from Uranus.

Brown, L. W.↗

Vertical Axis Rotational Motion Cues in Hovering Flight Simulation

A previous study that examined how yaw motion affected a pilot's ability to perform realistic hovering flight tasks indicated that any amount of pure yaw motion had little-to-no effect on pilot performance or opinion. In that experiment, pilots were located at the vehicle's center of rotation; thus lateral or longitudinal accelerations were absent. The purpose of the new study described here was to investigate further these unanticipated results for additional flight tasks, but with the introduction of linear accelerations associated with yaw rotations when the pilot is not at the center of rotation. The question of whether a yaw motion degree-of-freedom is necessary or not is important to government regulators who specify what simulator motions are necessary according to prescribed levels of simulator sophistication. Currently, specifies two levels of motion sophistication for flight simulators: full 6-degree-of-freedom and 3-degree-of-freedom. For the less sophisticated simulator, the assumed three degrees of freedom are pitch, roll, and heave. If other degrees of freedom are selected, which are different f rom these three, they must be qualified on a case-by-case basis. Picking the assumed three axes is reasonable and based upon experience, but little empirical data are available to support the selection of critical axes. Thus, the research described here is aimed at answering this question. The yaw and lateral degrees of freedom were selected to be examined first, and maneuvers were defined to uncouple these motions from changes in the gravity vector with respect to the pilot. This approach simplifies the problem to be examined. For this experiment, the NASA Ames Vertical Motion Simulator was used in a comprehensive investigation. The math model was an AH-64 Apache in hover, which was identified from flight test data and had previously been validated by several AH-64 pilots. The pilot's head was located 4.5 ft in front of the vehicle center of gravity, which is representative of the AH-64 pilot location. Six test pilots flew three tasks that were specifically designed to represent a broad class of situations in which both lateral and yaw motion cues may be useful. For the first task, the pilot controlled only the yaw axis and was required to rapidly acquire a North heading from 15 deg yaw offsets to either the East or West. This task allowed for full, or 1:1, motion to be used in all axes (yaw, lateral, and longitudinal). The second task was a 10 sec., 180 deg. pedal turn over a runway, but with the pilot only controlling the yaw degree-of-freedom. The position of the vehicle's center-of-mass remained fixed. This maneuver was taken from a current U.S. Army rotary wing design standard5 and is representative of a maneuver performed for acceptance of military helicopters; however, it does not allow for full 1:1 motion, since the simulator cab cannot rotate 180 deg. The third task required the pilot to perform a rapid 9 ft climb at a constant heading. This task was challenging, because rapid collective lever movement in the unaugmented AH64 results in a substantial yawing moment (due to engine torque) that must be countered by the pilot. This task also had full motion in all axes, but, in this case, the pilot had two axes to control simultaneously, rather than one as in the previous tasks. Four motion configurations were examined for each task: full motion (except for the 180 deg turn, for which the motion system was configured to provide as much motion as possible), full linear with no yaw motion, full yaw with no linear motion, and no motion. Each configuration was flown four times in a randomized test matrix, and the pilots were not informed of the configuration given. Vehicle state data were recorded for objective performance comparisons, and pilots provided subjective comments and ratings. As part of the pilots' evaluation, they were asked to rate the compensation required, the overall fidelity of the motion as compared to real flight, and whether motion was detected or not in each of the six degrees of freedom. In addition, the pilots provided a numerical level-of confidence rating, between 1 and 7, corresponding to how sure they were whether or not motion was present in each degree-of-freedom. The latter rating allow classical signal detection analysis to be performed.

Schroeder, Jeffrey A.↗

Determination of a Limited Scope Network's Lightning Detection Efficiency

This paper outlines a modeling technique to map lightning detection efficiency variations over a region surveyed by a sparse array of ground based detectors. A reliable flash peak current distribution (PCD) for the region serves as the technique's base. This distribution is recast as an event probability distribution function. The technique then uses the PCD together with information regarding: site signal detection thresholds, type of solution algorithm used, and range attenuation; to formulate the probability that a flash at a specified location will yield a solution. Applying this technique to the full region produces detection efficiency contour maps specific to the parameters employed. These contours facilitate a comparative analysis of each parameter's effect on the network's detection efficiency. In an alternate application, this modeling technique gives an estimate of the number, strength, and distribution of events going undetected. This approach leads to a variety of event density contour maps. This application is also illustrated. The technique's base PCD can be empirical or analytical. A process for formulating an empirical PCD specific to the region and network being studied is presented. A new method for producing an analytical representation of the empirical PCD is also introduced.

Rompala, John T.↗

Nonenzymatic catalytic signal amplification for nucleic acid hybridization assays

Devices, methods, and kits for amplifying the signal from hybridization reactions between nucleic acid probes and their cognate targets are presented. The devices provide partially-duplexed, immobilized probe complexes, spatially separate from and separately addressable from immobilized docking strands. Cognate target acts catalytically to transfer probe from the site of probe complex immobilization to the site of immobilized docking strand, generating a detectable signal. The methods and kits of the present invention may be used to identify the presence of cognate target in a fluid sample.

Fan, Wenhong↗

Improving Balance Function Using Low Levels of Electrical Stimulation of the Balance Organs

Crewmembers returning from long-duration space flight face significant challenges due to the microgravity-induced inappropriate adaptations in balance/sensorimotor function. The Neuroscience Laboratory at JSC is developing a method based on stochastic resonance to enhance the brain's ability to detect signals from the balance organs of the inner ear and use them for rapid improvement in balance skill, especially when combined with balance training exercises. This method involves a stimulus delivery system that is wearable/portable and provides imperceptible electrical stimulation to the balance organs of the human body. Stochastic resonance (SR) is a phenomenon whereby the response of a nonlinear system to a weak periodic input signal is optimized by the presence of a particular non-zero level of noise. This phenomenon of SR is based on the concept of maximizing the flow of information through a system by a non-zero level of noise. Application of imperceptible SR noise coupled with sensory input in humans has been shown to improve motor, cardiovascular, visual, hearing, and balance functions. SR increases contrast sensitivity and luminance detection; lowers the absolute threshold for tone detection in normal hearing individuals; improves homeostatic function in the human blood pressure regulatory system; improves noise-enhanced muscle spindle function; and improves detection of weak tactile stimuli using mechanical or electrical stimulation. SR noise has been shown to improve postural control when applied as mechanical noise to the soles of the feet, or when applied as electrical noise at the knee and to the back muscles. SR using imperceptible stochastic electrical stimulation of the vestibular system (stochastic vestibular stimulation, SVS) applied to normal subjects has shown to improve the degree of association between the weak input periodic signals introduced via venous blood pressure receptors and the heart-rate responses. Also, application of SVS over 24 hours improves the long-term heart-rate dynamics and motor responsiveness as indicated by daytime trunk activity measurements in patients with multi-system atrophy, Parkinson s disease, or both, including patients who were unresponsive to standard therapy for Parkinson s disease. Recent studies conducted at the NASA JSC Neurosciences Laboratories showed that imperceptible SVS, when applied to normal young healthy subjects, leads to significantly improved balance performance during postural disturbances on unstable compliant surfaces. These studies have shown the benefit of SR noise characteristic optimization with imperceptible SVS in the frequency range of 0-30 Hz, and amplitudes of stimulation have ranged from 100 to 400 microamperes.

Bloomberg, Jacob↗

Evaluating Biosignatures for Life Detection

The goal here is to develop a conceptual framework for evaluating the ability of different biosignatures to provide evidence for the presence of life in planned missions or observational studies. The focus is on intrinsic characteristics of biosignatures in a given space environment rather than on their detection, which depends on the current state of technology. Suitable evaluation procedures are based on an extensive body of previous work on related problems in which different options are evaluated to make decisions in business, engineering, medical fields and social or political arena. In these cases, three approaches have proven to be particularly useful. Two of them, signal detection theory (SDT) and Bayesian hypothesis testing are based on probabilities. The third approach, multi-attribute utility (MAU) is based on utility theory.

Pohorille, Andrew↗

Polymers in solar energy utilization

A laser photoacoustic technique (LPAT) has been verified for performing accelerated life testing of outdoor photooxidation of polymeric materials used in solar energy applications. Samples of the material under test are placed in a chamber with a sensitive microphone, then exposed to chopped laser radiation. The sample absorbs the light and converts it to heat by a nonradiative deexcitation process, thereby reducing pressure fluctuations within the cell. The acoustic signal detected by the microphone is directly proportional to the amount of light absorbed by the specimen. Tests were performed with samples of ethylene/methylacrylate copolymer (EMA) reprecipitated from hot cyclohexane, compressed, and molded into thin (25-50 microns) films. The films were exposed outdoors and sampled by LPAT weekly. The linearity of the light absorbed with respect to the acoustic signal was verified.Correlations were established between the photoacoustic behavior of the materials aged outdoors and the same kinds of samples cooled and heated in a controlled environment reactor. The reactor tests were validated for predicting outdoor exosures up to 55 days.

Liang, R. H.↗

A theoretical analysis of the MSFC holographic correlation system

A theoretical analysis was completed for the correlation output signal for the MSFC holographic correlation filtering system. Under appropriate assumptions, the correlation output was derived as a function of the roughness of the tested surface, the displacement of the illuminated area of the test surface, the characteristics of the optical components used in the system, and the system configuration. In addition, an approximate relationship between the displacement of the detected signal (which is focused on the photomultiplier tube) and the displacement of the illuminated area on the test surface was also derived.

Liu, H. K.↗

On Certain New Methodology for Reducing Sensor and Readout Electronics Circuitry Noise in Digital Domain

NASA Hubble Space Telescope (HST) and upcoming cosmology science missions carry instruments with multiple focal planes populated with many large sensor detector arrays. These sensors are passively cooled to low temperatures for low-level light (L3) and near-infrared (NIR) signal detection, and the sensor readout electronics circuitry must perform at extremely low noise levels to enable new required science measurements. Because we are at the technological edge of enhanced performance for sensors and readout electronics circuitry, as determined by thermal noise level at given temperature in analog domain, we must find new ways of further compensating for the noise in the signal digital domain. To facilitate this new approach, state-of-the-art sensors are augmented at their array hardware boundaries by non-illuminated reference pixels, which can be used to reduce noise attributed to sensors. There are a few proposed methodologies of processing in the digital domain the information carried by reference pixels, as employed by the Hubble Space Telescope and the James Webb Space Telescope Projects. These methods involve using spatial and temporal statistical parameters derived from boundary reference pixel information to enhance the active (non-reference) pixel signals. To make a step beyond this heritage methodology, we apply the NASA-developed technology known as the Hilbert- Huang Transform Data Processing System (HHT-DPS) for reference pixel information processing and its utilization in reconfigurable hardware on-board a spaceflight instrument or post-processing on the ground. The methodology examines signal processing for a 2-D domain, in which high-variance components of the thermal noise are carried by both active and reference pixels, similar to that in processing of low-voltage differential signals and subtraction of a single analog reference pixel from all active pixels on the sensor. Heritage methods using the aforementioned statistical parameters in the digital domain (such as statistical averaging of the reference pixels themselves) zeroes out the high-variance components, and the counterpart components in the active pixels remain uncorrected. This paper describes how the new methodology was demonstrated through analysis of fast-varying noise components using the Hilbert-Huang Transform Data Processing System tool (HHT-DPS) developed at NASA and the high-level programming language MATLAB (Trademark of MathWorks Inc.), as well as alternative methods for correcting for the high-variance noise component, using an HgCdTe sensor data. The NASA Hubble Space Telescope data post-processing, as well as future deep-space cosmology projects on-board instrument data processing from all the sensor channels, would benefit from this effort.

Kizhner, Semion↗

Possible radio emission from Uranus at 0.5 MHz

Radio emission from the direction of Uranus was detected in data from the radio astronomy experiment on the IMP-6 spacecraft. Previously, emission from the direction of Jupiter and Saturn was observed by the IMP-6 at a number of frequencies near 1 MHz during the period April 1971 to October 1972. These radio bursts were identified in the IMP-6 data through an analysis of the phase of the observed modulated signal detected from the spinning dipole antenna. This technique was applied to the direction of the planet Uranus with possible positive results. Over the approximately 500 days of data, three to six bursts with unique spectral characteristics were found. Identification with Uranus is confused by the likely presence of low level terrestrial and solar emission. The observed events persisted less than three minutes and are strongest in intensity near 0.5 MHz.

Brown, L. W.↗

Acoustic space occupancy: Combining ecoacoustics and lidar to model biodiversity variation and detection bias across heterogeneous landscapes

There is global interest in quantifying changing biodiversity in human-modified landscapes. Ecoacoustics may offer a promising pathway for supporting multi-taxa monitoring, but its scalability has been hampered by the sonic complexity of biodiverse ecosystems and the imperfect detectability of animal-generated sounds. The acoustic signature of a habitat, or soundscape, contains information about multiple taxa and may circumvent species identification, but robust statistical technology for characterizing community-level attributes is lacking. Here, we present the Acoustic Space Occupancy Model, a flexible hierarchical framework designed to account for detection artifacts from acoustic surveys in order to model biologically relevant variation in acoustic space use among community assemblages. We illustrate its utility in a biologically and structurally diverse Amazon frontier forest landscape, a valuable test case for modeling biodiversity variation and acoustic attenuation from vegetation density. We use complementary airborne lidar data to capture aspects of 3D forest structure hypothesized to influence community composition and acoustic signal detection. Our novel analytic framework permitted us to model both the assembly and detectability of soundscapes using lidar-derived estimates of forest structure. Our empirical predictions were consistent with physical models of frequency-dependent attenuation, and we estimated that the probability of observing animal activity in the frequency channel most vulnerable to acoustic attenuation varied by over 60%, depending on vegetation density. There were also large differences in the biotic use of acoustic space predicted for intact and degraded forest habitats, with notable differences in the soundscape channels predominantly occupied by insects. This study advances the utility of ecoacoustics by providing a robust modeling framework for addressing detection bias from remote audio surveys while preserving the rich dimensionality of soundscape data, which may be critical for inferring biological patterns pertinent to multiple taxonomic groups in the tropics. Our methodology paves the way for greater integration of remotely sensed observations with high-throughput biodiversity data to help bring routine, multi-taxa monitoring to scale in dynamic and diverse landscapes.

Airborne lidar↗

The NASA SETI program at JPL

The NASA All Sky Survey strategy for detecting signals of extraterrestrial origin is examined. The All Sky Survey observes the entire celestial sphere, covers a frequency range of 1-10 Ghz, and has spatial direction and frequency coverage. The survey time is dependent on the area of the sky surveyed, the telescope diameter, scan rate, the angular separation of the scans, the bandwidth of the receiver, and the frequency coverage. The distance at which a transmitter can be detected for a given sensitivity is analyzed. The interaction between scan strategy and various accumulation strategies and its effect on the sensitivity of the survey are investigated using field tests. A diagram of the SETI Sky Survey observational system is provided.

Gulkis, Sam↗

Improving Balance Function Using Low Levels of Electrical Stimulation of the Balance Organs

Crewmembers returning from long-duration space flight face significant challenges due to the microgravity-induced inappropriate adaptations in balance/ sensorimotor function. The Neuroscience Laboratory at JSC is developing a method based on stochastic resonance to enhance the brain s ability to detect signals from the balance organs of the inner ear and use them for rapid improvement in balance skill, especially when combined with balance training exercises. This method involves a stimulus delivery system that is wearable/portable providing imperceptible electrical stimulation to the balance organs of the human body. Stochastic resonance (SR) is a phenomenon whereby the response of a nonlinear system to a weak periodic input signal is optimized by the presence of a particular non-zero level of noise. This phenomenon of SR is based on the concept of maximizing the flow of information through a system by a non-zero level of noise. Application of imperceptible SR noise coupled with sensory input in humans has been shown to improve motor, cardiovascular, visual, hearing, and balance functions. SR increases contrast sensitivity and luminance detection; lowers the absolute threshold for tone detection in normal hearing individuals; improves homeostatic function in the human blood pressure regulatory system; improves noise-enhanced muscle spindle function; and improves detection of weak tactile stimuli using mechanical or electrical stimulation. SR noise has been shown to improve postural control when applied as mechanical noise to the soles of the feet, or when applied as electrical noise at the knee and to the back muscles.

Bloomberg, Jacob↗

Carrier synchronization and detection of polyphase signals.

Digital communication networks used for the distribution of high-speed digital information are currently the subject of design studies for many civil and military applications. This paper presents results that are useful in such studies as well as in network planning. In particular, the paper is concerned with the problems of carrier synchronization and noisy reference detection of polyphase signals. Reconstruction of coherent references for the detection of polyphase signals is considered and analyzed for three carrier reconstruction loops, namely, Nth power (multiply-and-divide) loops, generalized Costas (I-Q) loops, and extensions of data-aided (modulation wipeoff) loops. General expressions for the error probability are developed when the reconstructed reference signals are noisy.

Lindsey, W. C.↗

Greenhouse Gas Concentration Data Recovery Algorithm for a Low Cost, Laser Heterodyne Radiometer

The goal of a coordinated effort between groups at GWU and NASA GSFC is the development of a low-cost, global, surface instrument network that continuously monitors three key carbon cycle gases in the atmospheric column: carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), as well as oxygen (O2) for atmospheric pressure profiles. The network will implement a low-cost, miniaturized, laser heterodyne radiometer (mini-LHR) that has recently been developed at NASA Goddard Space Flight Center. This mini-LHR is designed to operate in tandem with the passive aerosol sensor currently used in AERONET (a well established network of more than 450 ground aerosol monitoring instruments worldwide), and could be rapidly deployed into this established global network. Laser heterodyne radiometry is a well-established technique for detecting weak signals that was adapted from radio receiver technology. Here, a weak light signal, that has undergone absorption by atmospheric components, is mixed with light from a distributed feedback (DFB) telecommunications laser on a single-mode optical fiber. The RF component of the signal is detected on a fast photoreceiver. Scanning the laser through an absorption feature in the infrared, results in a scanned heterodyne signal io the RF. Deconvolution of this signal through the retrieval algorithm allows for the extraction of altitude contributions to the column signal. The retrieval algorithm is based on a spectral simulation program, SpecSyn, developed at GWU for high-resolution infrared spectroscopies. Variations io pressure, temperature, composition, and refractive index through the atmosphere; that are all functions of latitude, longitude, time of day, altitude, etc.; are modeled using algorithms developed in the MODTRAN program developed in part by the US Air Force Research Laboratory. In these calculations the atmosphere is modeled as a series of spherically symmetric shells with boundaries specified at defined altitudes. Temperature, pressure, and species mixing ratios are defined at these boundaries. Between the boundaries, temperature is assumed to vary linearly with altitude while pressure (and thus gas density) vary exponentially. The observed spectrum at the LHR instrument will be the integration of the contributions along this light path. For any absorption measurement the signal at a particular spectral frequency is a linear combination of spectral line contributions from several species. For each species that might absorb in a spectral region, we have pre-calculated its contribution as a function of temperature and pressure. The integrated path absorption spectrum can then by calculated using the initial sun angle (from location, date, and time) and assumptions about pressure and temperature profiles from an atmospheric model. The modeled spectrum is iterated to match the experimental observation using standard multilinear regression techniques. In addition to the layer concentrations, the numerical technique also provides uncertainty estimates for these quantities as well as dependencies on assumptions inherent in the atmospheric models.

Miller, J. Houston↗

On the detectability of infrared echo arcs around supernova 1987A

The ring-like interstellar visual echoes of radii 33 and 54 arcsec detected around SN 1987A should coincide with infrared echoes (thermal reradiation) from dust at T approximately equal to 15 to 30 K. Whether these infrared echoes are detectable at present is considered. They will be brightest at approximately 100 microns, the range of the Texas infrared photometer. Detectability depends on the ratio zeta congruent to tan(sub a)/tan(sub s)P(theta), where tan(sub a) and tan(sub s) are the visual absorption and scattering optical thicknesses of the echo layer, and P is the phase function function for small-angle scattering (theta approximately equal to 2 to 4 degrees). Zeta approximately greater than 1 is needed for a detectable signal (approximately 0.3 Jy), but zeta cannot be much less than 1; otherwise the visual echoes could not be as bright as they are. Typical dust mixtures of Mathis-Rumpl-Nordsieck type have zeta much less than 1. Zeta remains small even if a population of very small grains with power-law index as steep as approximately 5.5 is added. A population with even more small grains and/or fewer large grains could have a zeta similar to 1 and be detectable at present, but this seems unlikely. The echoes will move, but should remain accessible for many years and should be detected eventually.

Felten, James E.↗