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We review ray-optical methods of analyzing short-wavelength propagation in random media. The advantages and limitations of ray methods are discussed, and results of the statistical theory of ray segment fluctuations pertinent to ray tracing are summarized. The standard method of Monte Carlo ray tracing is compared to a new method which takes into account recent results on the statistics of ray segment fluctuations.
A method is developed for predicting the radiant heat flux distribution produced by tungsten filament, tubular fused-quartz envelope heating systems with reflectors. The method is an application of Monte Carlo simulation, which takes the form of a random walk or ray tracing scheme. The method is applied to four systems of increasing complexity, including a single lamp without a reflector, a single lamp with a Hat reflector, a single lamp with a parabolic reflector, and up to six lamps in a six-lamp contoured-reflector heating unit. The application of the Monte Carlo method to the simulation of the thermal radiation generated by these systems is discussed. The procedures for numerical implementation are also presented. Experiments were conducted to study these quartz heating systems and to acquire measurements of the corresponding empirical heat flux distributions for correlation with analysis. The experiments were conducted such that several complicating factors could be isolated and studied sequentially. Comparisons of the experimental results with analysis are presented and discussed. Good agreement between the experimental and simulated results was obtained in all cases. This study shows that this method can be used to analyze very complicated quartz heating systems and can account for factors such as spectral properties, specular reflection from curved surfaces, source enhancement due to reflectors and/or adjacent sources, and interaction with a participating medium in a straightforward manner.
The method for calculating the pitch angle diffusion coefficient is investigated for cosmic rays in a static random magnetic field, using the resonance integral method. The pitch angle diffusion coefficient may be derived from the Vlasov equation via ensemble averaging.
Statistics of electromagnetic rays in a random medium are studied numerically by the Monte Carlo method. Two dimensional random surfaces with prescribed correlation functions are used to simulate the random media. Rays are then traced in these sample media. Statistics of the ray properties such as the ray positions and directions are computed. Histograms showing the distributions of the ray positions and directions at different points along the ray path as well as at given points in space are given. The numerical experiment is repeated for different cases corresponding to weakly and strongly random media with isotropic and anisotropic irregularities. Results are compared with those derived from theoretical investigations whenever possible.
An equation is derived to compute the amount of diffuse light reflected by a particulate surface, such as on Mars or an asteroid. The method traces the paths of rays within an ensemble of randomly shaped grains and finds the eventual probability of emission. The amount of diffuse, unpolarized emitted light is obtained in terms of the real index of refraction, the imaginary index, and the average diameter of particles making up the surface. The equation is used to compute the empirical rule for obtaining the planetary albedo from the slope of its polarization curve. Accuracy of the equation, estimated at + or - 4%, seems justified because of quantitative agreement with experimental measures of the empirical rule. It is also shown that the equation can be applied to bubble-enclosing surfaces such as volcanic foams. Results for the indices of the moon, Mars, Io, and Europa are obtained and compared with other data.
Critical assessment of two versions of a procedure for calculating the pitch angle diffusion coefficient for cosmic rays in a static random magnetic field using the 'resonance integral' method of Hasselmann and Wiberenz (1968) and Jokipii (1972). One of these versions is shown to represent the physics of the situation more accurately than the other.
We have investigated a new approach to deriving a diffusion equation for charged particles in a static, random magnetic field. Our method incorporates essential effects of the magnetic fluctuations in the lowest order particle orbits. Significant corrections to the usual quasilinear diffusion coefficient for cosmic rays with pitch angles near 90 deg are a consequence. Monte Carlo results bear out the validity of our theory.
Spherical or spheroidal air bubbles are generally trapped in the formation of rapidly growing ice crystals. In this study the single-scattering properties of inhomogeneous ice crystals containing air bubbles are investigated. Specifically, a computational model based on an improved geometric-optics method (IGOM) has been developed to simulate the scattering of light by randomly oriented hexagonal ice crystals containing spherical or spheroidal air bubbles. A combination of the ray-tracing technique and the Monte Carlo method is used. The effect of the air bubbles within ice crystals is to smooth the phase functions, diminish the 22deg and 46deg halo peaks, and substantially reduce the backscatter relative to bubble-free particles. These features vary with the number, sizes, locations and shapes of the air bubbles within ice crystals. Moreover, the asymmetry factors of inhomogeneous ice crystals decrease as the volume of air bubbles increases. Cloud reflectance lookup tables were generated at wavelengths 0.65 m and 2.13 m with different air-bubble conditions to examine the impact of the bubbles on retrieving ice cloud optical thickness and effective particle size. The reflectances simulated for inhomogeneous ice crystals are slightly larger than those computed for homogenous ice crystals at a wavelength of 0.65 microns. Thus, the retrieved cloud optical thicknesses are reduced by employing inhomogeneous ice cloud models. At a wavelength of 2.13 microns, including air bubbles in ice cloud models may also increase the reflectance. This effect implies that the retrieved effective particle sizes for inhomogeneous ice crystals are larger than those retrieved for homogeneous ice crystals, particularly, in the case of large air bubbles.
Studies are reported of the slow variability of SMC X-1 and its spectrum. An analysis of red-noise random variability is based on a method discussed by Deeter and Boynton (1982). The 0.7 s X-ray pulsar SMC X-1 is in a 3.89 day eclipsing binary system with a B0 I supergiant companion. Observations of the pulsar were conducted with the aid of the UCSD/MIT instrument on HEAO 1 from 1977 August through 1979 January. A light curve was constructed for the period 1977 September to 1978 December. The apparent tendency of SMC X-1 to be in one of two states, high or low, suggests the acquisition of average spectra separately for each state. The total (steady plus pulsed) emission from SMC X-1 displays a continuum spectrum with a dominant exponential form which implies a temperature of 17 keV for thin thermal bremsstrahlung emission or 5 keV if the other limit of a Wien spectrum is assumed.
Using a model that combines single-scattering properties for spheroidal and hexagonal ice crystals, the thermal infrared radiative properties of cirrus clouds have been investigated. Infrared scattering and absorption properties for randomly oriented spheroids and hexagons are parameterized based on the anomalous diffraction theory and a geometric ray-tracing method, respectively. Using observed ice crystal size distributions, upwelling radiances at the top of cirrus cloudy atmospheres have been computed. Results show that the presence of small ice crystals can produce significant brightness temperature differences between two infrared wavelengths in the 10-micron window. Theoretical results have been compared with observed brightness temperature differences between 8.35 and 11.16 microns and between 11.16 and 12 microns. The observed values were obtained from the high-spectral resolution interferometer sounder. It is shown that the use of the present nonspherical model for ice crystals in radiative transfer calculations leads to a significantly better interpretation of the observed data than does the use of the spherical model.
Direct emission from individual grains and multiple scattering between regolith particles are encompassed by the present model of particulate planetary surface thermal emission, whose randomly positioned spherical grains are large relative to the emission's wavelength scale. A Monte Carlo ray-tracing method is used to calculate the spectral and directional emissivity of the surface and the polarization of the emitted radiation, for 7-16 micron wavelengths. The effects of roughness at the scale of individual grains and scattering are separated to elucidate how each affects the emitted radiation. Implications of these results for planetary remote sensing are discussed.
Magnetometers and gyroscopes have been shown to provide very accurate attitudes for a variety of spacecraft. These results have been obtained, however, using a batch-least-squares algorithm and long periods of data. For use in onboard applications, attitudes are best determined using sequential estimators such as the Kalman filter. When a filter is used to determine attitudes using magnetometer and gyroscope data for input, the resulting accuracy is limited by both the sensor accuracies and errors inherent in the Earth magnetic field model. The Kalman filter accounts for the random component by modeling the magnetometer and gyroscope errors as white noise processes. However, even when these tuning parameters are physically realistic, the rate biases (included in the state vector) have been found to show systematic oscillations. These are attributed to the field model errors. If the gyroscope noise is sufficiently small, the tuned filter 'memory' will be long compared to the orbital period. In this case, the variations in the rate bias induced by field model errors are substantially reduced. Mistuning the filter to have a short memory time leads to strongly oscillating rate biases and increased attitude errors. To reduce the effect of the magnetic field model errors, these errors are estimated within the filter and used to correct the reference model. An exponentially-correlated noise model is used to represent the filter estimate of the systematic error. Results from several test cases using in-flight data from the Compton Gamma Ray Observatory are presented. These tests emphasize magnetometer errors, but the method is generally applicable to any sensor subject to a combination of random and systematic noise.
The DebriSat project is a collaboration effort with the NASA Orbital Debris Program Office, the U.S. Space Force Space Systems Command Center, The Aerospace Corporation, and the University of Florida. To date, over 200,000 fragments from this ground-based, hypervelocity impact experiment have been collected, and processing is underway to determine their physical characteristics, such as material, shape, color, characteristic length, and average cross-sectional area. The x-ray process is primarily used to identify the location of the fragments and estimated size for extraction, so that these physical characteristics can be assessed. This paper proposes a machine learning-based approach to characterize materials from x-ray images of debris fragments embedded in soft-catch foam used in the DebriSat project. The novel methodology discussed in this paper will highlight the use of x-ray imagery data to characterize these fragments without extraction or a human-in-the-loop. Both supervised and unsupervised machine learning techniques are utilized with this approach to infer the physical parameters of the fragments embedded in the soft-catch foam panels used in the impact experiment based on x-ray images of the foam panels. Additionally, 3D reconstructions of the extracted fragments are created with images taken from two different angles using the structure from motion (SfM) method. The characteristic lengths and shape from the 3D reconstruction, alongside the physical characteristics of the debris, are used in the inference of the material type. To develop and test the approach, a dataset of x-ray images of debris fragments of varying sizes and materials is collected. Supervised learning methods such as convolutional neural networks (CNNs), support vector machines (SVM), decision trees, and random forest classifiers are used due to the high-dimensional feature spaces of the debris and nonlinear decision boundaries for material categorization. Given the limited pre-labeled data of embedded debris materials smaller than 10 mm, unsupervised machine learning techniques such as clustering algorithms and autoencoders are used, in addition to supervised learning methods. The clustering algorithms group similar fragments together based on their physical properties, and autoencoders reduce the dimensionality of the x ray images and extract relevant features. The performance of the proposed approach's is analyzed using a range of statistical methods, including confusion matrices, receiver operating characteristic curves, and precision-recall curves. The results are compared with those obtained using a baseline approach that relies on manual identification and classification of debris fragments. To evaluate the effectiveness of different machine learning methods, statistical tests such as t-tests, ANOVA, and cross-validation are performed, comparing the performance of CNNs, SVMs, clustering algorithms, and autoencoders. Additional analysis needs to be conducted to identify any sources of bias or variability that may affect the results, such as variations in imaging conditions or fragmentation patterns. Other topics explored are limitations, refinements, and the potential use of semi-supervised learning techniques, such as self-training to label unlabeled datasets and co-training using x-ray images taken from two different angles as two different models.
The DebriSat project is a collaboration effort with the NASA Orbital Debris Program Office, the U.S. Space Force Space Systems Command Center, The Aerospace Corporation, and the University of Florida. To date, over 200,000 fragments from this ground-based, hypervelocity impact experiment have been collected, and processing is underway to determine their physical characteristics, such as material, shape, color, characteristic length, and average cross-sectional area. The x-ray process is primarily used to identify the location of the fragments and estimated size for extraction, so that these physical characteristics can be assessed. This paper proposes a machine learning-based approach to characterize materials from x-ray images of debris fragments embedded in soft-catch foam used in the DebriSat project. The novel methodology discussed in this paper will highlight the use of x-ray imagery data to characterize these fragments without extraction or a human-in-the-loop. Both supervised and unsupervised machine learning techniques are utilized with this approach to infer the physical parameters of the fragments embedded in the soft-catch foam panels used in the impact experiment based on x-ray images of the foam panels. Additionally, 3D reconstructions of the extracted fragments are created with images taken from two different angles using the structure from motion (SfM) method. The characteristic lengths and shape from the 3D reconstruction, alongside the physical characteristics of the debris, are used in the inference of the material type. To develop and test the approach, a dataset of x-ray images of debris fragments of varying sizes and materials is collected. Supervised learning methods such as convolutional neural networks (CNNs), support vector machines (SVM), decision trees, and random forest classifiers are used due to the high-dimensional feature spaces of the debris and nonlinear decision boundaries for material categorization. Given the limited pre-labeled data of embedded debris materials smaller than 10 mm, unsupervised machine learning techniques such as clustering algorithms and autoencoders are used, in addition to supervised learning methods. The clustering algorithms group similar fragments together based on their physical properties, and autoencoders reduce the dimensionality of the x ray images and extract relevant features. The performance of the proposed approach's is analyzed using a range of statistical methods, including confusion matrices, receiver operating characteristic curves, and precision-recall curves. The results are compared with those obtained using a baseline approach that relies on manual identification and classification of debris fragments. To evaluate the effectiveness of different machine learning methods, statistical tests such as t-tests, ANOVA, and cross-validation are performed, comparing the performance of CNNs, SVMs, clustering algorithms, and autoencoders. Additional analysis needs to be conducted to identify any sources of bias or variability that may affect the results, such as variations in imaging conditions or fragmentation patterns. Other topics explored are limitations, refinements, and the potential use of semi-supervised learning techniques, such as self-training to label unlabeled datasets and co-training using x-ray images taken from two different angles as two different models.
This presentation discusses fractured leads on field-programmable gate array (FPGA) during flight vibration. Actions taken to determine root cause and resolution of the failure include finite element analysis (FEA) and vibration testing and scanning electron microscopy (with X-ray microanalysis) and energy dispersive spectrometry (SEM/EDS) failure assessment. Bonding methods for surface mount parts is assessed, including critical analysis and assessment of random fatigue damage. Regarding ceramic quad flat pack (CQFP) lead fracture, after disassembling the attitude control electronics (ACE) configuration, photographs showed six leads cracked on FPGA RTSX72SU-1 CQ208B package located on the RWIC card. An identical package (FPGA RTSX32SU-1 CQ208B) mounted on the RWIC did not results in cracked pins due to vibration. FPGA lead failure theories include workmanship issues in the lead-forming, material defect in the leads of the FPGA packages, and the insecure mounting of the board in the card guides, among other theories. Studies were conducted using simple calculations to determine the response and fatigue life of the package. Shorter packages exhibited more response when loaded by out-of-plane displacement of PCB while taller packages exhibit more response when loaded by in-plane acceleration of PCB. Additionally, under-fill did not contribute to reducing stress in leads due to out-of-plane PCB loading or from component twisting, as much as corner bonding. The combination of corner bond and under-fill is best to address mechanical and thermal S/C environment. Test results of bonded parts showed reduced (dampened) amplitude and slightly shifted peaks at the un-bonded natural frequency and an additional response at the bonded frequency. Stress due to PCBB out-of-plane loading was decreased on in the corners when only a corner bond was used. Future work may address CQFP fatigue assessment, including the investigation of discrepancy in predicted fatigue damage, as well as comparing fatigue life and fatigue damage cycle ration computed using FEA and Miner's rule to results from a fatigue assessment software program.
Markov random fields have been used for image segmentation since their introduction in the1980s. This work applies a method from Principal Component Thermography to enhance thecontrast in damage regions in 3D images derived from X-ray computed tomography (CT)inspections. The developed method is applied to sizing of small cracks in thin Inconel tubes designed as probability of detection (POD) samples for radiographic inspection.Misclassification errors arising from artifacts due to beam-hardening are reduced by fitting the boundary of the segmented damage region with the arc of an ellipse. Results are comparedagainst those obtained through manual inspection.
We find that dim gamma-ray bursts (GRBs) are softer than bright GRBs, as indicated on average by data from the Burst and Transient Source Experiment (BATSE) on board the Compton Gamma Ray Observatory (CGRO). We show that this correlation is statistically significant with respect to variations due to random differences between GRBs. This effect is discernible using a variety of methods and data sets, including public domain data. We analyze several types of systematic errors and selection effects in the BATSE data and conclude that the observed effect is not dominated by any of them. We therefore assert that this dim/soft effect is a real property of GRBs. It is possible that this correlation is a consequence of the time dilation and that the burst sources are located at cosmological distances.
Statistical procedures taken from the field of survival analysis have been adapted to astronomical usage and have been applied to a sample of stars in the B-V color range between 0.1 and 0.5 with measured soft X-ray luminosities and projected equatorial velocities. The two-sample problem and linear regression problem with arbitrarily censored data were studied. A new method for determining the linear regression between two random variables in the presence of arbitrary censoring has been developed which can also be used for a likelihood-ratio test for the independence of two random variables and for principal-component analysis in the presence of arbitrary censoring. The required numerical computations can be carried out straightforwardly and rapidly.