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DOE OSTI2026

Allometric and Mobile Terrestrial LiDAR Modeling of Aboveground Woody Biomass of Populus in Coppice Production

Poplars ( Populus spp.) and their hybrids are increasingly being grown in coppice production to generate bioenergy feedstocks at frequent intervals. Allometric equations are re-quired to predict aboveground biomass (AGB) of coppiced individuals with minimal field measurements. Likewise, remote sensing tools like LiDAR (light detection and ranging) can be used if models are available to predict AGB from point cloud data. Therefore, this study sought to develop equations to predict dry woody AGB from field measurements and LiDAR data from coppiced poplar field trials containing eastern cottonwood ( P. del-toides ) and hybrid poplar taxa. We found that taxa-specific allometric models containing the summed basal area of the three largest stems in the coppice provided the best predictive model, with stem height and stem count failing to provide additional explanatory power. The best predictive LiDAR-based model was independent of taxa but had slightly lower adjusted R 2 and higher RMSE than the allometric model. It contained four parameters including crown volume, leaf area index, variance of height returns, and the top point density (i.e., density metric 9 or the proportion of points in the highest point interval when the point cloud is evenly divided into ten vertical intervals). In total, these models can be used to quickly and efficiently estimate dry woody AGB of Populus coppice systems for bioenergy feedstock production.

AGB↗

DOE OSTI2023

Efficient Reliability Analysis using Generalized Multifidelity Modeling and Explainable Active Learning

To assess the reliability of critical technologies like nuclear plants and infrastructure systems and improve the robustness of design, engineers have to quantify the uncertainties surrounding the system behavior accurately. However, the complexity of the problem can make standard reliability analysis algorithms prohibitively expensive, primarily due to the high computational cost of estimating the system response at each iteration. This cost can be greatly reduced by using multi-fidelity modeling and machine learning to build a surrogate model to replace the expensive response function. We propose a general and robust method for building surrogates from multiple Low Fidelity (LF) models coupled with machine learning to retain accuracy. Our framework first constructs “Corrected Low Fidelity models” (CLFs) by coupling a High Fidelity (HF) model inferred Gaussian Process correction term with each of the LF models. It then uses the correction terms to assign model probabilities to each of these CLFs in an explainable way before using them to assemble the final surrogate. No assumptions are made about the type of the LF models or their correlation with the HF model. The proposed surrogate modeling framework is used within the subset simulation algorithm (a variance-reduced MCMC-based reliability analysis algorithm) for enhanced efficiency. Additionally, an active learning step is added to the algorithm to adaptively decide when the surrogate is not sufficiently accurate, at which point the HF model is called and used to refine the surrogate. Through a frame buckling example, our method is shown to be highly efficient at reducing the expensive HF model calls while accurately estimating the failure probability.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Global variation of transpiration and soil evaporation and the role of their major climate drivers

Although global variation in actual evapotranspiration has been widely investigated, it remains unclear how its two major components, transpiration and soil evaporation, are driven by climate drivers across global land surface. This paper uses a well-validated, process-based model that estimates transpiration and soil evaporation, and for the first time investigates and quantifies how the main global drivers, associated to vegetation process and the water and energy cycle, drive the spatiotemporal variation of the two components. The results show that transpiration and soil evaporation dominate the variance of actual evapotranspiration in wet and dry regions, respectively. Dry southern hemisphere from 13°S to 27°S is highlighted since it contributes to 21% global soil evaporation variance, with only 11% global land area. In wet regions, particularly in the humid tropics, there are strong correlations between transpiration, actual evapotranspiration, and potential evapotranspiration, with precipitation playing a relatively minor role, and available radiative energy is the major contributor to the interannual variability in transpiration and actual evapotranspiration in Amazonia. Conversely in dry regions, there are strong correlations between soil evaporation, actual evapotranspiration, and precipitation. Lastly, our findings highlight that ecohydrological links are highly related to climate regimes, and the small region such as Australia has important contribution to interannual variation in global soil evaporation and evapotranspiration, and anthropogenic activities strongly influence the variances in irrigation regions

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2014

Sequential Monte Carlo sampling in hidden Markov models of nonlinear dynamical systems

We investigate the issue of which state functionals can have their uncertainty estimated efficiently in dynamical systems with uncertainty. Because of the high dimensionality and complexity of the problem, sequential Monte Carlo (SMC) methods are used. We investigate SMC methods where the proposal distribution is computed by maximum likelihood or by a linearization approach. We prove that the variance of the SMC method is bounded linearly in the number of time steps when the proposal distribution is truncated normal distribution. We also show that for a moderate large number of steps the error produced by approximation of dynamical systems linearly accumulates on the condition that the logarithm of the density function of noise is Lipschitz continuous. This finding is significant because the uncertainty in many dynamical systems, in particular, in chemical engineering systems, can be assumed to have this nature. We demonstrate our findings for a simple test case from chemical engineering. The theoretical findings provide a foundation for the parallel software SISTOS.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

A Piecewise Local Partial Least Squares (PLS) Method for the Quantitative Analysis of Plutonium Nitrate Solutions

We have developed a piecewise local (PL) partial least squares (PLS) analysis method for total plutonium measurements by absorption spectroscopy in nitric acid-based nuclear material processing streams. Instead of using a single PLS model that covers all expected solution conditions, the method selects one of several local models based on an assessment of solution absorbance, acidity, and Pu oxidation state distribution. The local models match the global model for accuracy against the calibration set, but were observed in several instances to be more robust to variations associated with measurements in the process. The improvements are attributed to the relative parsimony of the local models. Not all of the sources of spectral variation are uniformly present at each part of the calibration range. Thus, the global model is locally overfitting and susceptible to increased variance when presented with new samples. A second set of models quantifies the relative concentrations of Pu(III), (IV), and (VI). Standards containing a mixture of these species were not at equilibrium due to a disproportionation reaction. Therefore, a separate principal component analysis is used to estimate of the concentrations of the individual oxidation states in these standards in the absence of independent confirmatory analysis. The PL analysis approach is generalizable to other systems where the analysis of chemically complicated systems can be aided by rational division of the overall range of solution conditions into simpler sub-regions.

47 OTHER INSTRUMENTATION↗

DOE OSTI2016

SU-F-T-323: A Post-Mastectomy Radiation Therapy Dose Distribution Study Using Nanodots and Films

Purpose: In post-mastectomy radiation therapy (RT), skin dose must be accurately estimated to assess skin reactions such as erythema, desquamation and necrosis. Planning systems cannot always provide accurate dosimetry for target volumes distal to skin. Therefore, in-vivo dosimetry is necessary. A female anthropomorphic phantom was used with optically stimulated luminescence dosimeters (nanoDots) to measure dose to chest wall skin. In addition, EBT2 films was employed to measure dose to left lung and heart in post-mastectomy RT. Methods: Films and nanoDots were calibrated under full buildup conditions at 100cm SAD for 6MV photons. Five pieces of films were placed between slabs of Rando phantom to assess dose to left lung and heart. Two layers of 0.5cm thick bolus were used to cover the whole left chest. Six pairs of nanoDots were placed at medical and lateral aspects on the bolus surface, between the 0.5cm bolus layers, and under the bolus. Three control nanoDots were placed on chest wall to quantify imaging dose. The phantom was CT scanned with all dosimeters in place, and treatment planning was performed with tangential fields (200cGy). All dosimeters were contoured on CT and dose was extracted. NanoDots were read using nanoDot reader and films were scanned using film scanner. The measured and calculated doses were tabulated. Results: Dose to 12 nanoDots were evaluated. Dose variance for surface nanoDots were +3.8%, +2.7%, −5% and −9.8%. Those at lateral positions, with greater beam obliquity had larger variance than the medial positions. A similar trend was observed for other nanoDots (Table1). Point doses from films for heart and the left lung were 112.7cGy and 108.7cGy, with +10.2% and +9.04% deviation from calculated values, respectively. Conclusion: Dosimetry provided by the advanced planning system was verified using NanoDots and films. Both nanoDots and films provided good estimation of dose distribution in post-mastectomy RT.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

Progress in the development of the neutron flux monitoring system of the French GEN-IV SFR: simulations and experimental validations [ANIMMA--2015-IO-392]

France has a long experience of about 50 years in designing, building and operating sodium-cooled fast reactors (SFR) such as RAPSODIE, PHENIX and SUPER PHENIX. Fast reactors feature the double capability of reducing nuclear waste and saving nuclear energy resources by burning actinides. Since this reactor type is one of those selected by the Generation IV International Forum, the French government asked, in the year 2006, CEA, namely the French Alternative Energies and Atomic Energy Commission, to lead the development of an innovative GEN-IV nuclear- fission power demonstrator. The major objective is to improve the safety and availability of an SFR. The neutron flux monitoring (NFM) system of any reactor must, in any situation, permit both reactivity control and power level monitoring from startup to full power. It also has to monitor possible changes in neutron flux distribution within the core region in order to prevent any local melting accident. The neutron detectors will have to be installed inside the reactor vessel because locations outside the vessel will suffer from severe disadvantages; radially the neutron shield that is also contained in the reactor vessel will cause unacceptable losses in neutron flux; below the core the presence of a core-catcher prevents from inserting neutron guides; and above the core the distance is too large to obtain decent neutron signals outside the vessel. Another important point is to limit the number of detectors placed in the vessel in order to alleviate their installation into the vessel. In this paper, we show that the architecture of the NFM system will rely on high-temperature fission chambers (HTFC) featuring wide-range flux monitoring capability. The definition of such a system is presented and the justifications of technological options are brought with the use of simulation and experimental results. Firstly, neutron-transport calculations allow us to propose two in-vessel regions, namely the above-core and under-core structures. We verify that they comply with the main objective, that is the neutron power and flux distribution monitoring. HTFC placed in these two regions can detect an inadvertent control rod withdrawal that is a postulated initiating event for safety demonstration. Secondly, we show that the HTFC reliability is enhanced thanks to a more robust physical design and the fact that it has been justified that the mineral insulation is insensitive to any increase in temperature. Indeed, the HTFC insulation is subject to partial discharges at high temperature when the electric field between their electrodes is greater than about 200 V/mm or so. These discharges give rise to signals similar to the neutron pulses generated by a fission chamber itself, which may bias the HTFC count rate at start-up only. However, as displayed in Figure 1, we have experimentally verified that one can discriminate neutron pulses from partial discharges using online estimation of pulse width. Thirdly, we propose to estimate the count rate of a HTFC using the third order cumulant of its signal that is described by a filtered Poisson process. For such a statistic process, it is known that any cumulant, also called cumulative moment, is proportional to the process intensity that is here the count rate of a fission chamber. One recalls that the so-called Campbelling mode of such a detector is actually based on the signal variance, which is the second-order cumulant as well. The use of this extended Campbelling mode based on the third-order cumulant will permit to ensure the HTFC response linearity over the entire neutron flux range using a signal processing technique that is simple enough to satisfy design constraints on electric devices important for nuclear safety. We also show that this technique, named high order Campbelling method (HOC), is significantly more robust than another technique based on the change in the HTFC filling gas, which consists in adding a few percent of nitrogen. Finally, we also present an experimental campaign devoted to the required calibration process of the so-called HOC method. The Campbelling results show a good agreement with the simple pulse counting estimation at low count rates. It is also shown that the HOC technique provides a linear estimation of the count rates at higher power levels as well.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2014

Analog neutron transport for nuclear instrumentation applications with the Monte-Carlo code TRIPOLI-4 - Paper 3

Monte-Carlo codes simulating particle transport usually make use of well-known variance reduction techniques, leading to more efficient simulations. Even in configurations which do not deal with deep-penetration, some of these techniques, such as the implicit capture, are actually often used by default. The statistical weight of the simulated particles is then modified in order to take into account the modification of the sampling without introducing any bias in the estimation process. For instance, the implicit capture decreases the statistical weight of the particles at each collision, whereas the sampling of a single outgoing particle increases this statistical weight in case of scattering reactions producing multiple neutrons. In addition, Russian roulette and splitting operations, which are usually also played at each collision, lead to other modifications of the statistical weights. As a result, Monte-Carlo codes provide particle histories that are valid on average, but collect statistical weights which differ from 1, when tallying the estimation of the quantities of interest. Yet, some nuclear instrumentation calculations inherently need to work with statistical weights equal to 1, since either individual events have to be collected (such as the arrival of a particle at a detector, the measurement of a time of flight, etc), or the coincidence of events or also correlations between individual events have to be taken into account. To address these specific applications with Monte-Carlo simulation codes, users need a full analog simulation mode. The continuous-energy Monte-Carlo code TRIPOLI4{sup R} is mainly dedicated to shielding, reactor physics and criticality safety calculations. Its capabilities have recently been extended to widen its use to nuclear instrumentation with the possibility of γ-spectrometry calculations and the simulation of photonuclear reactions for instance. Other features needed by nuclear instrumentation applications have been available in TRIPOLI-4 for a long time, such as the sampling of the time variable and the possibility of tallying in a time grid for most of the available tallies (fluxes, reaction rates, dose equivalent rates, energy depositions, etc). In TRIPOLI-4, the transport between two consecutive collisions is analog if no variance reduction technique is requested by the user to handle deep-penetration configurations. However, up to the version 9 of the code, the collision itself is sampled in a non-analog way. This paper presents a first implementation of a full analog neutron transport mode in TRIPOLI-4, preliminary verification results and an application of this functionality to the simulation of the Nucifer detector located in Saclay, France. It should be noted that only neutron transport is dealt with in this work and that all nuclear data come from JEFF-3.1.1 or ENDF/B-VII.0 evaluations, including fission data when needed. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2023

Urban Flood Modeling: Uncertainty Quantification and Physics‐Informed Gaussian Processes Regression Forecasting

Abstract Estimating uncertainty in flood model predictions is important for many applications, including risk assessment and flood forecasting. We focus on uncertainty in physics‐based urban flooding models. We consider the effects of the model's complexity and uncertainty in key input parameters. The effect of rainfall intensity on the uncertainty in water depth predictions is also studied. As a test study, we choose the Interconnected Channel and Pond Routing (ICPR) model of a part of the city of Minneapolis. The uncertainty in the ICPR model's predictions of the floodwater depth is quantified in terms of the ensemble variance using the multilevel Monte Carlo (MC) simulation method. Our results show that uncertainties in the studied domain are highly localized. Model simplifications, such as disregarding the groundwater flow, lead to overly confident predictions, that is, predictions that are both less accurate and uncertain than those of the more complex model. We find that for the same number of uncertain parameters, increasing the model resolution reduces uncertainty in the model predictions (and increases the MC method's computational cost). We employ the multilevel MC method to reduce the cost of estimating uncertainty in a high‐resolution ICPR model. Finally, we use the ensemble estimates of the mean and covariance of the flood depth for real‐time flood depth forecasting using the physics‐informed Gaussian process regression method. We show that even with few measurements, the proposed framework results in a more accurate forecast than that provided by the mean prediction of the ICPR model.

Kohanpur, Amir H.↗

NASA NTRS1994

Comments on the statistical analysis of excess variance in the COBE differential microwave radiometer maps

Cosmic anisotrophy produces an excess variance sq sigma(sub sky) in the Delta maps produced by the Differential Microwave Radiometer (DMR) on cosmic background explorer (COBE) that is over and above the instrument noise. After smoothing to an effective resolution of 10 deg, this excess sigma(sub sky)(10 deg), provides an estimate for the amplitude of the primordial density perturbation power spectrum with a cosmic uncertainty of only 12%. We employ detailed Monte Carlo techniques to express the amplitude derived from this statistic in terms of the universal root mean square (rms) quadrupole amplitude, (Q sq/RMS)(exp 0.5). The effects of monopole and dipole subtraction and the non-Gaussian shape of the DMR beam cause the derived (Q sq/RMS)(exp 0.5) to be 5%-10% larger than would be derived using simplified analytic approximations. We also investigate the properties of two other map statistics: the actual quadrupole and the Boughn-Cottingham statistic. Both the sigma(sub sky)(10 deg) statistic and the Boughn-Cottingham statistic are consistent with the (Q sq/RMS)(exp 0.5) = 17 +/- 5 micro K reported by Smoot et al. (1992) and Wright et al. (1992).

Wright, E. L.↗

NASA NTRS1994

Martian aerosols: Near-infrared spectral properties and effects on the observation of the surface

Imaging sprectroscopic measurements (ISM) of Mars acquired by the ISM instrument on Phobos-2 are used to investigate the NIR spectral properties of aerosols and the effects of atmospheric scattering on inferred mineralogy of the surface. Estimates of aerosols spectra between 0.77 and 2.6 micrometers are derived above Tharsis and Ophir Planum. The spectral continua are consistent with the particle size distribution derived using data from the solar occultation experiment on-board the spacecraft (effective radius approximately = 1.2 micrometers, with an effective variance approximately = 0.2). The aerosols spectra contain water-ice absorption features and possibly absorptions due to clay and/or sulfates. The largest effect of the aerosols on surface spectra is in dark regions, where the continuum spectral slope becomes more negative and the 1-micrometers absorption due to Fe in pyroxene is shifted toward longer wavelengths. The effects of aerosols on spectra of bright regions are insufficiently large to change mineralogic interpretations based on ISM data, i.e., that bright regions in Tharsis are dominated spectrally by hematite, but that additional ferric minerals are probably present in other areas including Arabia.

Erard, Stephane↗

NASA NTRSDate not supplied

End-To-End Uncertainty Quantification with Analytical Derivatives for Design Under Uncertainty

Uncertainty quantification (UQ) is a rapidly growing and evolving discipline, especially within the aerospace community. Performing analysis with UQ can provide decision makers with a wealth of information about a candidate design. However, the value of UQ is fully realized when the information gained during UQ analysis is leveraged in a feedback loop of a design optimization process, often referred to as design under uncertainty. Although design under uncertainty can be a powerful risk mitigation technique, there are a number of roadblocks that prevent its implementation. Two primary factors are computational costs and added complexity of the analysis. High fidelity simulations on the order tens of uncertain variables quickly become computationally infeasible. Also, implementing UQ into an existing multidisciplinary design and optimization (MDO) process often requires extensive knowledge of the UQ methods and careful treatment of the problem formulation. The objective of this work is to address these two primary roadblocks and enable practitioners to efficiently perform design under uncertainty with limited knowledge of the UQ discipline. Methods outlined in this paper demonstrate MDO incorporating UQ into the design process, leveraging an analytic derivative tool chain through the entire optimization. The proposed approach leverages machine learning techniques to generate a differentiable confidence interval output from polynomial chaos models. This technique, coupled with the incorporation of analytical derivatives through the Polynomial Chaos Expansion (PCE) process, eliminates the need to estimate derivatives which are usually obtained from finite difference, complex step, or similar methods. Developing a differentiable confidence interval allows mixed uncertainty problems (both epistemic and aleatory) to be modeled. Without such modeling, these problems cannot accurately predict objective functions containing statistical quantities such as mean and variance. The addition of analytic derivatives to a polynomial chaos-based UQ method decreases the computational costs of performing design under uncertainty by orders of magnitude in comparison with methods such as complex step. The method and codes developed are modular in nature and are a drop-in solution for design under uncertainty within existing MDO problems. A low-fidelity analytical multidisciplinary optimization under uncertainty for a wing design in OpenMDAO is detailed in this paper. This demonstration case will include both objective functions and constraints which are influenced by uncertain parameters.

Ben D Phillips↗

NASA NTRSDate not supplied

End-To-End Uncertainty Quantification with Analytical Derivatives for Design Under Uncertainty

Ben Phillips↗

DOE OSTI2019

Development of control quality factor for HVAC control loop performance assessment I—Methodology (ASHRAE RP-1587)

This article is the second paper from the ASHRAE research project RP-1587, focusing on the methodology of obtaining a control quality factor (CQF). This article presents a development of two CQFs for assessing the heating, ventilation, and air-conditioning (HVAC) control loop performance. Both CQFs are able to detect whether the control loop is able to maintain the setpoint and identify the loop's ability to handle disturbances. In addition, the reversal behaviors are assessed as well. The first CQF (CQF-Harris) is proposed based on the normalized Harris index using the recursive least squares method. This recursive least squares method is selected because of its computational efficiency compared with the maximum likelihood estimation method. The second CQF (CQF-EWMA) is based on the exponentially weighted moving average of the error ratio. The assessment scale of excellent, good, fair, bad, and failed, which indicates the quality of the HVAC control loops, is established as well. The sensitivity analysis for both CQFs is also conducted, and it provides insights on choosing the appropriate parameters to compute such CQFs. Such parameters include the sampling frequency, the length of the moving window, and the variance of the unmeasured disturbance. The field evaluations and tests of the proposed CQFs for simulated control loops and real control loops can be found in the companion paper with the title 'Development of Control Quality Factor for HVAC Control Loop Performance Assessment - III: Field Testing and Results (ASHRAE RP-1587).'

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

NASA NTRS2016

Satellite-Based Spatiotemporal Trends in PM2.5 Concentrations: China 2004-2013

Three decades of rapid economic development is causing severe and widespread PM2.5(particulate matter (is) less than 2.5 ) pollution in China. However, research on the health impacts of PM2.5 exposure has been hindered by limited historical PM2.5 concentration data. We estimated ambient PM2.5 concentrations from 2004 to 2013 in China at 0.1 deg resolution using the most recent satellite data and evaluated model performance with available ground observations. We developed a two-stage spatial statistical model using the Moderate Resolution Imaging Spectroradiometer (MODIS) Collection 6 aerosol optical depth (AOD) and assimilated meteorology, land use data, and PM2.5 concentrations from China's recently established ground monitoring network. An inverse variance weighting (IVW) approach was developed to combine MODIS Dark Target and Deep Blue AOD to optimize data coverage. We evaluated model predicted PM2.5 concentrations from 2004 to early 2014 using ground observations. The overall model cross-validation R(sup 2) and relative prediction error were 0.79 and 35.6%, respectively. Validation beyond the model year (2013) indicated that it accurately predicted PM(sub 2.5) concentrations with little bias at the monthly (R(sup 2) = 0.73), regression slope = 0.91) and seasonal (R(sup 2) = 0.79), regression slope = 0.92) levels. Seasonal variations revealed that winter was the most polluted season and that summer was the cleanest season. Analysis of predicted PM2.5 levels showed a mean annual increase of 1.97 micro-g/cu cm between 2004 and 2007 and a decrease of 0.46 micro-g/cu cm between 2008 and 2013. Our satellite-driven model can provide reliable historical PM2.5 estimates in China at a resolution comparable to those used in epidemiologic studies on the health effects of long-term PM2.5 exposure in North America. This data source can potentially advance research on PM2.5 health effects in China.

satellite remote sensing↗

NASA NTRS1992

Estimates of tropical analysis differences in daily values produced by two operational centers

To assess the uncertainty of daily synoptic analyses for the atmospheric state, the intercomparison of three First GARP Global Experiment level IIIb datasets is performed. Daily values of divergence, vorticity, temperature, static stability, vertical motion, mixing ratio, and diagnosed diabatic heating rate are compared for the period of 26 January-11 February 1979. The spatial variance and mean, temporal mean and variance, 2D wavenumber power spectrum, anomaly correlation, and normalized square difference are employed for comparison.

Kasahara, Akira↗

DOE OSTI2013

A Model-Free No-arbitrage Price Bound for Variance Options

We suggest a numerical approximation for an optimization problem, motivated by its applications in finance to find the model-free no-arbitrage bound of variance options given the marginal distributions of the underlying asset. A first approximation restricts the computation to a bounded domain. Then we propose a gradient projection algorithm together with the finite difference scheme to solve the optimization problem. We prove the general convergence, and derive some convergence rate estimates. Finally, we give some numerical examples to test the efficiency of the algorithm.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Detection of correlated fragments in a sequence of images by superimposed Fourier holograms

The problem of detecting correlated fragments in a sequence of images recorded by the superimposing holograms within the Fourier holography scheme with angular multiplication of a spatially modulated reference beam is considered. The approach to the solution of this problem is based on the properties of the variance of the image sum. It is shown that this problem can be solved by providing a constant distance between the signal and reference images when recording superimposed holograms and a partial mutual correlatedness of reference images. The detection efficiency is analysed from the point of view of estimated image data capacity, the degree of mutual correlation of reference images, and the hologram recording conditions. The results of a numerical experiment under the most complicated conditions (representation of images by realisations of homogeneous random fields) confirm the theoretical conclusions. (holographic memory)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗