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At least 415 records · Page 23

Role of hot electrons in shock ignition constrained by experiment at the National Ignition Facility

Shock ignition is a scheme for direct drive inertial confinement fusion that offers the potential for high gain with the current generation of laser facility; however, the benefits are thought to be dependent on the use of low adiabat implosions without laser–plasma instabilities reducing drive and generating hot electrons. A National Ignition Facility direct drive solid target experiment was used to calibrate a 3D Monte Carlo hot-electron model for 2D radiation-hydrodynamic simulations of a shock ignition implosion. The α = 2.5 adiabat implosion was calculated to suffer a 35% peak areal density decrease when the hot electron population with temperature T ℎ = 55 keV and energy E ℎ = 13 kJ was added to the simulation. Optimizing the pulse shape can recover ~1/3 of the peak areal density lost due to a change in shock timing. Here, despite the harmful impact of laser–plasma instabilities, the simulations indicate shock ignition as a viable method to improve performance and broaden the design space of near ignition high adiabat implosions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A microstructural lattice model for strain oriented problems: A combined Monte Carlo finite element technique

A specialized, microstructural lattice model, termed MCFET for combined Monte Carlo Finite Element Technique, was developed which simulates microstructural evolution in material systems where modulated phases occur and the directionality of the modulation is influenced by internal and external stresses. In this approach, the microstructure is discretized onto a fine lattice. Each element in the lattice is labelled in accordance with its microstructural identity. Diffusion of material at elevated temperatures is simulated by allowing exchanges of neighboring elements if the exchange lowers the total energy of the system. A Monte Carlo approach is used to select the exchange site while the change in energy associated with stress fields is computed using a finite element technique. The MCFET analysis was validated by comparing this approach with a closed form, analytical method for stress assisted, shape changes of a single particle in an infinite matrix. Sample MCFET analytical for multiparticle problems were also run and in general the resulting microstructural changes associated with the application of an external stress are similar to that observed in Ni-Al-Cr alloys at elevated temperature.

Gayda, J.↗

Extinction-to-Backscatter Ratios of Lofted Aerosol Layers Observed During the First Three Months of CALIPSO Measurements

Case studies from the first three months of the Cloud and Aerosol Lidar and Infrared Pathfinder Spaceborne Observations (CALIPSO) measurements of lofted aerosol layers are analyzed using transmittance [Young, 1995] and two-wavelength algorithms [Vaughan et al., 2004] to determine the aerosol extinction-to-backscatter ratios at 532 and 1064 nm. The transmittance method requires clear air below the layer so that the transmittance through the layer can be determined. Suitable scenes are selected from the browse images and clear air below features is identified by low 532 nm backscatter signal and confirmed by low depolarization and color ratios. The transmittance and two-wavelength techniques are applied to a number of lofted layers and the extinction-to-backscatter ratios are compared with values obtained from the CALIPSO aerosol models [Omar et al., 2004]. The results obtained from these studies are used to adjust the aerosol models and develop observations based extinction-to-backscatter ratio look-up tables and phase functions. Values obtained by these techniques are compared to Sa determinations using other independent methods with a goal of developing probability distribution functions of aerosol type-specific extinction to backscatter ratios. In particular, the results are compared to values determined directly by the High Spectral Resolution Lidar (HSRL) during the CALIPSO CloudSat Validation Experiments (CCVEX) and Sa determined by the application of the two-wavelength lidar Constrained Ratio Aerosol Model-fit (CRAM) retrieval approach [Cattrall et al., 2005; Reagan et al., 2004] to the HSRL data. The results are also compared to values derived using the empirical relationship between the multiple-scattering fraction and the linear depolarization ratio by using Monte Carlo simulations of water clouds [Hu et al., 2006].

Omar, Ali H.↗

Analysis and Compensation of Tx and Rx IQ Imbalances in Uplink IM-OFDMA Systems

Index modulation-based orthogonal division multiple access (IM-OFDMA) has recently been proposed as a potential technique for future wireless communication systems due to its superior spectral efficiency and error performance over conventional multiple access schemes. However, its performance is still under investigation by researchers in light of a variety of scenarios and assumptions. Following this direction, in this Article, the individual and joint effects of the transmitter (Tx) and receiver (Rx) in-phase and quadrature imbalances (IQI) on the bit-error-rate (BER) performance of the uplink IM-OFDMA scheme are investigated by considering whether each user's RF front-end is identical or not. Moreover, to reduce the detrimental effect of IQI, a preamble-based estimation and compensation method is proposed for IM-OFDMA. Closed-form expressions for the average BER of IM-OFDMA are obtained by considering the physical effect of the Tx and Rx IQI. Also, using Monte Carlo simulations, the derived expressions are verified under different system configurations. Furthermore, analytical and simulation results reveal that Tx and Rx IQI cause an error floor in the BER performance of IM-OFDMA schemes. However, the proposed estimation and compensation method not only reduces the impact of IQI but also leads to a better BER performance compared to the case of no IQI, which mainly refers to the frequency diversity caused by the IQI.

42 ENGINEERING↗

Monte Carlo studies of ocean wind vector measurements by SCATT: Objective criteria and maximum likelihood estimates for removal of aliases, and effects of cell size on accuracy of vector winds

The scatterometer on the National Oceanic Satellite System (NOSS) is studied by means of Monte Carlo techniques so as to determine the effect of two additional antennas for alias (or ambiguity) removal by means of an objective criteria technique and a normalized maximum likelihood estimator. Cells nominally 10 km by 10 km, 10 km by 50 km, and 50 km by 50 km are simulated for winds of 4, 8, 12 and 24 m/s and incidence angles of 29, 39, 47, and 53.5 deg for 15 deg changes in direction. The normalized maximum likelihood estimate (MLE) is correct a large part of the time, but the objective criterion technique is recommended as a reserve, and more quickly computed, procedure. Both methods for alias removal depend on the differences in the present model function at upwind and downwind. For 10 km by 10 km cells, it is found that the MLE method introduces a correlation between wind speed errors and aspect angle (wind direction) errors that can be as high as 0.8 or 0.9 and that the wind direction errors are unacceptably large, compared to those obtained for the SASS for similar assumptions.

Pierson, W. J.↗

Aerothermodynamics of Pyrolizing Surfaces in Hypersonic Rarefied Flows

Direct simulation Monte Carlo (DSMC) calculations of rarefied flows about entry bodies typically employ a fixed surface temperature or a radiative-equilibrium energy balance to compute that temperature. Such boundary conditions neglect any effects of heat capacitance and heat conduction in the spacecraft heat shield and, therefore, provide an upper bound for the surface temperature. Such calculations also neglect pyrolysis from the heat shield which can be significant for a high-energy incident flow at very low densities. Accurate prediction of both heating and aerodynamic forces requires including pyrolysis and surface heat transfer in the models for gas-surface interaction employed in DSMC methods. Although these physical models have long appeared in various continuum flow calculation codes, they have only recently appeared in DSMC codes which are required to simulate rarefied flows during entry at high altitudes. In the current implementation, routines from the widely distributed Charring Material Thermal Response and Ablation (CMA) program are coupled into a DSMC code to calculate the one-dimensional heat transfer into the carbon phenolic heat shield at each point on a vehicle surface. Temperature-dependent material properties, surface re-radiation, and in-depth pyrolysis were included in the calculation, but surface ablation was neglected. Sample calculations for entry of the Galileo probe into the atmosphere of Jupiter demonstrate that including pyrolysis in the model leads to significant differences in predicted aerodynamics. Granted, the drag coefficient does not depend strongly on the surface temperature which can itself be significantly below the radiative equilibrium value during entry. However, the surface mass flux due to pyrolysis of the material is significant once the probe drops to altitudes characterized by transition flow. This leads to a noticeable increase in drag and a decrease in heating compared to a body without pyrolysis.

Haas, Brian L.↗

Trajectory Engineering with Modular Patched Conics for Entry Systems and TPS (TEMPEST)

Brief Presenter Biography (35 word limit): Bohdan Wesely is an Aerospace Engineer in the Entry Systems and Technology Division at Ames. He has worked on a variety of projects for NASA including integrated TPS (thermal protection system) flight hardware deliveries and testing services for commercial partners. Introduction: TEMPEST is a new trajectory analysis framework that is designed to fill the gap between dedicated flight mechanics tools and aerothermal and TPS sizing tools. The project started as an SJSU master’s thesis and has since evolved into a general conceptual design tool capable of studying a wide variety of entry problems. Development is ongoing in the Entry Systems and Technology Division at NASA ARC. Why TEMPEST: Space missions involving entry into a planetary atmosphere involve a series of unique requirements across multiple disciplines. Whether it is traditional entry descent and landing (EDL), or aerocapture, the vehicle must navigate to its target landing location or orbit state, and the TPS must protect the payload during entry. The design process typically involves iterative handoffs between various flight mechanics, flow solver, and material response level tools. During the early conceptual phase, a wide variety of feasible trajectories are simulated in a Monte Carlo scenario which broadly satisfy the mission or landing requirements. Next, computational fluid dynamics (CFD), direct simulation Monte Carlo (DSMC), and other flow solver analyses are performed at various key trajectory points to generate an aero-database, heating and TPS design requirements also emerge at this stage. At this point, with updated aerodynamics from the various flow solvers, trajectories can be re-run, this in turn can change the required freestream conditions for the CFD tools, and as a project progresses, these analyses converge, and uncertainty is reduced. However, there is always a “hand-off” occurring between two inherently coupled phenomena. Analysis Description: One of the goals with TEMPEST is to use a variety of first principles estimation methods coupled with an atmosphere model to predict vehicle aerothermodynamics across the entire flight regime while propagating a 3 or 6 degree of freedom (DoF) trajectory. Aerodynamics methods include modified Newtonian, Maxwell and Cercignani- Lampis-Lord (CLL) for continuum, transitional, and free molecular flow regimes. Aerothermodynamics include boundary layer and reference enthalpy methods, and Mutation++ for non-equilibrium chemistry modeling. TEMPEST is also capable of stitching multiple trajectory segments together to study mission scenarios like multi-pass aerocapture and aero-gravity assists. Most of the program is implemented in MATLAB using modern system objects, it relies on several C++ shared libraries for supporting tools like Gmsh, the Global Reference Atmospheric Model (GRAM), and Mutation++. The various first principles aerothermal estimation methods are discretized across either a structured axisymmetric panel mesh or an unstructured tri-mesh generated from an open-source tool such as Gmsh, this allows solutions on the same mesh to be compared across tools such as CB-Aero. CFD Coupling. A physics-aware, gaussian process CFD anchoring scheme is proposed to adjust the various first principles methods as a CFD database is populated. One goal for this anchoring module is to inform the project where CFD should be run. Full knowledge of the entire trajectory, atmosphere, and aerothermodynamics allows for easier identification of high sensitivity areas and uncertainty quantification. While the first principles effects are well known and proven accurate in existing tools such as CB- Aero and Cart3D, a physics aware CFD anchoring scheme increases tool credibility across a project lifecycle. Material Response Modeling. Correct TPS sizing is critical for optimizing mass for science payloads and ensuring mission success. The process typically involves a thermal analysis along the trajectory with surface heating environments as a boundary condition. Several design constraints are maximum bondline temperature and maximum recession with various margining techniques. The material response tool FIAT, developed out of NASA Ames, is currently being integrated into the TEMPEST environment. TPS recession, shape change, mass loss, and mass property alteration are all factors that can perturb an entry trajectory. For missions like Mars 2020, recession was minimal and was safely handled separately as a post process. For missions such as Jupiter Galileo with a high TPS mass fraction or asteroid entries, recession plays a major role. The proposed fully coupled scheme is to use an epoch-based approach where the trajectory integration is halted after a recession threshold, the energy balance and FIAT are solved at each panel, the mesh, aerodynamics, and mass properties are updated, and the trajectory continues. Several computational tradeoffs have been made during the development of TEMPEST to limit the cost of a single trajectory and preserve its utility as a conceptual, rapid iteration tool. Conclusion: Development of TEMPEST is ongoing and the project is still in its infancy. This talk aims to showcase its unique capabilities to support future NASA entry systems missions.

Bohdan O Wesely↗

Path Toward a Unifid Geometry for Radiation Transport

The Direct Accelerated Geometry for Radiation Analysis and Design (DAGRAD) element of the RadWorks Project under Advanced Exploration Systems (AES) within the Space Technology Mission Directorate (STMD) of NASA will enable new designs and concepts of operation for radiation risk assessment, mitigation and protection. This element is designed to produce a solution that will allow NASA to calculate the transport of space radiation through complex computer-aided design (CAD) models using the state-of-the-art analytic and Monte Carlo radiation transport codes. Due to the inherent hazard of astronaut and spacecraft exposure to ionizing radiation in low-Earth orbit (LEO) or in deep space, risk analyses must be performed for all crew vehicles and habitats. Incorporating these analyses into the design process can minimize the mass needed solely for radiation protection. Transport of the radiation fields as they pass through shielding and body materials can be simulated using Monte Carlo techniques or described by the Boltzmann equation, which is obtained by balancing changes in particle fluxes as they traverse a small volume of material with the gains and losses caused by atomic and nuclear collisions. Deterministic codes that solve the Boltzmann transport equation, such as HZETRN [high charge and energy transport code developed by NASA Langley Research Center (LaRC)], are generally computationally faster than Monte Carlo codes such as FLUKA, GEANT4, MCNP(X) or PHITS; however, they are currently limited to transport in one dimension, which poorly represents the secondary light ion and neutron radiation fields. NASA currently uses HZETRN space radiation transport software, both because it is computationally efficient and because proven methods have been developed for using this software to analyze complex geometries. Although Monte Carlo codes describe the relevant physics in a fully three-dimensional manner, their computational costs have thus far prevented their widespread use for analysis of complex CAD models, leading to the creation and maintenance of toolkit-specific simplistic geometry models. The work presented here builds on the Direct Accelerated Geometry Monte Carlo (DAGMC) toolkit developed for use with the Monte Carlo N-Particle (MCNP) transport code. The workflow for achieving radiation transport on CAD models using MCNP and FLUKA has been demonstrated and the results of analyses on realistic spacecraft/habitats will be presented. Future work is planned that will further automate this process and enable the use of multiple radiation transport codes on identical geometry models imported from CAD. This effort will enhance the modeling tools used by NASA to accurately evaluate the astronaut space radiation risk and accurately determine the protection provided by as-designed exploration mission vehicles and habitats

Lee, Kerry↗

Monte Carlo simulation of a near-continuum shock-shock interaction problem

A complex shock interaction is calculated with direct simulation Monte Carlo (DSMC). The calculation is performed for the near-continuum flow produced when an incident shock impinges on the bow shock of a 0.1 in. radius cowl lip for freestream conditions of approximately Mach 15 and 35 km altitude. Solutions are presented both for a full finite-rate chemistry calculation and for a case with chemical reactions suppressed. In each case, both the undisturbed flow about the cowl lip and the full shock interaction flowfields are calculated. Good agreement has been obtained between the no-chemistry simulation of the undisturbed flow and a perfect gas solution obtained with the viscous shock-layer method. Large differences in calculated surface properties when different chemical models are used demonstrate the necessity of adequately representing the chemistry when making surface property predictions. Preliminary grid refinement studies make it possible to estimate the accuracy of the solutions.

Carlson, Ann B.↗

Predicting the Phase Stability of Multicomponent High-Entropy Compounds

A generic method to estimate the relative feasibility of formation of high-entropy compounds in a single phase, directly from first principles, is developed. As a first step, the relative formation abilities of 56 multicomponent, AO, oxides were evaluated. These were constructed from five cation combinations chosen from A = {Ca, Co, Cu, Fe, Mg, Mn, Ni, Zn}. Candidates for multicomponent oxides are predicted from descriptors related to the enthalpy and configurational entropy obtained from the mixing enthalpies of two-component oxides. The utility of this approach is evaluated by comparing the predicted combinations with the experimentally realized entropy-stabilized oxide, (MgCoCuNiZn)O. In the second step, Monte Carlo simulations are utilized to investigate the phase composition and local ionic segregation as a function of temperature. This approach allows for the evaluation of potential secondary phases, thereby making realistic predictions of novel multicomponent compounds that can be synthesized.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Pairing Correlations across the Superfluid Phase Transition in the Unitary Fermi Gas

In the two-component Fermi gas with a contact interaction, a pseudogap regime can exist at temperatures between the superfluid critical temperature $T_c$ and a temperature $T^\ast > T_c$. This regime is characterized by pairing correlations without superfluidity. However, in the unitary limit of infinite scattering length, the existence of this regime is still debated. To help address this, we have applied finite-temperature auxiliary-field quantum Monte Carlo (AFMC) methods to study the thermodynamics of the superfluid phase transition and signatures of the pseudogap in the spin-balanced homogeneous unitary Fermi gas. We present results at finite filling factor $\textit{ν}$ ≃ 0.06 for the condensate fraction, an energy-staggering pairing gap, the spin susceptibility, and the heat capacity, and compare them to experimental data when available. In contrast to previous AFMC simulations, our model space consists of the complete first Brillouin zone of the lattice, and our calculations are performed in the canonical ensemble of fixed particle number. The canonical ensemble AFMC framework enables the calculation of a model-independent gap, providing direct information on pairing correlations without the need for numerical analytic continuation. We use finite-size scaling to estimate $T_c$ at the corresponding filling factor. In this work, we find that the energy-staggering pairing gap vanishes above $T_c$, showing no pseudogap effects, and that the spin susceptibility shows a substantially reduced signature of a spin gap compared to previously reported AFMC simulations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Efficient Sequential Attitude Estimation from Vector Observations

This paper presents a computationally efficient, sequential method for attitude matrix estimation using gyro and vector measurements. The method is based on a recently introduced, minimal-parameter third-order method for solving the orthogonal matrix differential equation in R(sup n). In the three-dimensional case, these third-order attitude parameters can be interpreted as temporal-integrals of the body-frame angular velocity components. A nonlinear algorithm is developed, which uses this minimal set of three parameters to estimate the nine-parameter direction-cosine matrix. Having an extremely simple kinematic equation, these parameters render the resulting estimator highly computationally efficient. An orthogonalization procedure, incorporated into the measurement processing stage, enhances the accuracy and stability of the resulting algorithm, yet retains reasonable simplicity. The performance of the estimator is demonstrated via a Monte Carlo simulation study.

Oshman, Yaakov↗

Examination of synthetic gas puff imaging diagnostic data from a gyrokinetic turbulence code

A synthetic gas puff imaging (GPI) diagnostic has been developed for the purpose of validating the three-dimensional gyrokinetic turbulence code XGC. The synthetic diagnostic is described and applied to XGC simulations of two Alcator C-Mod discharges. The turbulence characteristics deduced from the resulting simulated GPI frames, using analysis techniques similar to those applied to experimental data, are compared with locally derived characteristics extracted directly from the XGC output. The comparison of the two is shown to be potentially impacted by misalignment between the GPI view and the magnetic field, the dependence of the light emission on the electron density and temperature, and spatial and temporal variations in the neutral gas cloud induced by the turbulent plasma fluctuations. We conclude that quantitative and, in some cases even qualitative, validation of turbulence simulations need to account for these effects. While we cannot directly compare our results with experimental data due to the absence of high quality GPI data from the shots and times simulated by XGC, we do relate the overall characteristics obtained from the synthetic GPI analysis to published Alcator C-Mod GPI data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Robust verification of stochastic simulation codes

We introduce a robust verification tool for computational codes, which we call Stochastic Robust Extrapolation based Error Quantification (StREEQ). Unlike the prevalent Grid Convergence Index (GCI) [1] method, our approach is suitable for both stochastic and deterministic computational codes and is generalizable to any number of discretization variables. Building on ideas introduced in the Robust Verification [2] approach, we estimate the converged solution and orders of convergence with uncertainty using multiple fits of a discretization error model. In contrast to Robust Verification, we perform these fits to many bootstrap samples yielding a larger set of predictions with smoother statistics. Here, bootstrap resampling is performed on the lack-of-fit errors for deterministic code responses, and directly on the noisy data set for stochastic responses. This approach lends a degree of robustness to the overall results, capable of yielding precise verification results for sufficiently resolved data sets, and appropriately expanding the uncertainty when the data set does not support a precise result. For stochastic responses, a credibility assessment is also performed to give the analyst an indication of the trustworthiness of the results. Furthermore, this approach is suitable for both code and solution verification, and is particularly useful for solution verification of high-consequence simulations..

97 MATHEMATICS AND COMPUTING↗

Rotational symmetry relation for efficient response function generation in the coarse mesh transport method COMET

The coarse mesh transport code COMET is a continuous energy hybrid stochastic-deterministic neutronics solver with high fidelity and formidable computation speed in solving reactor core problems. Its method is based on the incident flux expansion theory. In this work, we take advantage of the local geometric symmetry in many reactor cores lattices (e.g., fuel lattices and reflector blocks) to develop relations among the flux response expansion coefficients for symmetric surfaces to further improve the computational efficiency of the COMET response function generation tool (method). This is done by a rigorous derivation of the transformation matrices for the angular and spatial expansion moments resulting from a rotation of a coarse mesh by an arbitrary angle. The relations for the response coefficients for the symmetric surfaces can be then written as the Kronecker product of those transformation matrices. The method is implemented into COMET and tested on two advanced high temperature reactor (AHTR) full-length single assembly benchmark problems. The COMET results using the response function library based on the symmetry relations were compared to those using the library directly generated by continuous energy Monte Carlo for all surfaces. It was found that the eigenvalues and stripe-wise fission densities using the two libraries are in statistical agreement as expected. This indicates that the new method maintains the high fidelity of the original COMET method while improving the computational efficiency in the response function generation by 270% to 400%, depending on the local geometric symmetry. This method also reduces the size of the response function library by the same magnitude (270% to 400%). (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

An intermediate model for fitting triplet–triplet annihilation in phosphorescent organic light emitting diode materials

Triplet–triplet annihilation (TTA) is one of the primary contributors to efficiency roll-off and permanent material degradation in phosphorescent organic light-emitting diodes. Here, the two limiting case models typically used to quantify this quenching mechanism are multi-step Dexter and single-step Förster, which, respectively, assume ideal Fickian diffusion or perfect trapping of triplet excitons. For device-relevant guest doping levels (typically 5–12 vol. %), both significant diffusion of excitons and trapping due to spatial and energetic disorder exist, so neither conventional model fits experimental data well. We develop and validate an intermediate TTA model, which is a weighted average of the limiting cases of pure radiative decay (no TTA) and multi-step Dexter based TTA that returns an effective TTA rate constant and a parameter quantifying the portion of well-isolated excitons. Kinetic Monte-Carlo simulations and time-resolved photoluminescence measurements of an archetype host–guest system demonstrate that our intermediate model provides significantly improved fits with more realistic physical values, is more robust to variations in experimental conditions, and provides an analysis framework for the effects of trapping on TTA.

30 DIRECT ENERGY CONVERSION↗

Deciphering the Scattering of Mechanically Driven Polymers Using Deep Learning

Here, we present a deep learning approach for analyzing two-dimensional scattering data of semiflexible polymers under external forces. In our framework, scattering functions are compressed into a three-dimensional latent space using a Variational Autoencoder (VAE), and two converter networks establish a bidirectional mapping between the polymer parameters (bending modulus, stretching force, and steady shear) and the scattering functions. The training data are generated using off-lattice Monte Carlo simulations to avoid the orientational bias inherent in lattice models, ensuring robust sampling of polymer conformations. The feasibility of this bidirectional mapping is demonstrated by the organized distribution of polymer parameters in the latent space. By integrating the converter networks with the VAE, we obtain a generator that produces scattering functions from given polymer parameters and an inferrer that directly extracts polymer parameters from scattering data. While the generator can be utilized in a traditional least-squares fitting procedure, the inferrer produces comparable results in a single pass and operates 3 orders of magnitude faster. This approach offers a scalable automated tool for polymer scattering analysis and provides a promising foundation for extending the method to other scattering models, experimental validation, and the study of time-dependent scattering data.

Ding, Lijie [Oak Ridge National Laboratory (ORNL),↗

CTRANS: A Monte Carlo program for radiative transfer in plane parallel atmospheres with imbedded finite clouds: Development, testing and user's guide

The program called CTRANS is described which was designed to perform radiative transfer computations in an atmosphere with horizontal inhomogeneities (clouds). Since the atmosphere-ground system was to be richly detailed, the Monte Carlo method was employed. This means that results are obtained through direct modeling of the physical process of radiative transport. The effects of atmopheric or ground albedo pattern detail are essentially built up from their impact upon the transport of individual photons. The CTRANS program actually tracks the photons backwards through the atmosphere, initiating them at a receiver and following them backwards along their path to the Sun. The pattern of incident photons generated through backwards tracking automatically reflects the importance to the receiver of each region of the sky. Further, through backwards tracking, the impact of the finite field of view of the receiver and variations in its response over the field of view can be directly simulated.

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