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Mirror Surface Contamination Specification Derived from Coronagraphy Scatter Error Budget Allocation

Near-Angle Scatter (NAS) of the host star’s light may limit the ability of a potential Habitable Worlds Observatory (HWO) to detect and characterize an Earth-like planet around a Sun-like star via coronagraphy. NAS from each optical surface before the coronagraph’s focal plane mask produces an E-field across the dark hole that is coherent. These E-fields sum and could be as large or larger than the coronagraph mask leakage E-field. This paper assumes an error budget allocation for scatter of 20 ppt. NAS E-fields contribute to the dark hole noise floor via both shot noise and heterodyne amplification of the wavefront instability. While previous papers have developed specifications for scatter from surface scatter, this paper develops specifications for scatter from surface contamination and micrometeoroid impacts. The development process utilizes an expression that predicts scatter throughput into the dark hole based on surface BRDF. Analysis does not include scatter from coating columnar structure, edges, contamination, micrometeoroid impacts, or polarization.

near angle scatter↗

DOE OSTI2025

Deciphering the small-angle scattering of polydisperse hard spheres using deep learning

We introduce a deep learning approach for analyzing the scattering function of the polydisperse hard sphere system. We use a variational autoencoder-based neural network to learn the bidirectional mapping between the scattering function and the system parameters, including the volume fraction and polydispersity. Such that the trained model serves both as a generator that produces a scattering function from the system parameters and an inferrer that extracts system parameters from the scattering function. We first generate a scattering dataset by carrying out molecular dynamics simulations of the polydisperse hard spheres modeled by the truncated-shifted Lennard-Jones model, then analyze the scattering function dataset using singular value decomposition to confirm the feasibility of dimensional compression. Then, we split the dataset into training and testing sets and train our neural network on the training set only. Our generator model produces a scattering function with significantly higher accuracy compared to the traditional Percus–Yevick approximation and β correction, and the inferrer model can extract the volume fraction and polydispersity with much higher accuracy than traditional model functions.

Ding, Lijie [ORNL] (ORCID:0000000227454606)↗

DOE OSTI2025

Imaging Valence Electron Rearrangement in a Chemical Reaction Using Hard X-Ray Scattering

We have observed the signatures of valence electron rearrangement in photoexcited ammonia using ultrafast hard x-ray scattering. Time-resolved x-ray scattering is a powerful tool for imaging structural dynamics in molecules because of the strong scattering from the core electrons localized near each nucleus. Such core-electron contributions generally dominate the differential scattering signal, masking any signatures of rearrangement in the chemically important valence electrons. Ammonia represents an exception to the typically high core-to-valence electron ratio. Here, we measured 9.8 keV x-ray scattering from gas-phase deuterated ammonia following photoexcitation via a 200 nm pump pulse to the 3s Rydberg state. We observed changes in the recorded scattering patterns due to the initial photoexcitation and subsequent deuterium dissociation. Ab initio calculations confirm that the observed signal is sensitive to the rearrangement of the single photoexcited valence electron as well as the interplay between adiabatic and nonadiabatic dissociation channels. The use of ultrafast hard x-ray scattering to image the structural rearrangement of single valence electrons constitutes an important advance in tracking valence electronic structure in photoexcited atoms and molecules.

Gabalski, Ian [SLAC National Accelerator Laborator↗

DOE OSTI2025

Theory of resonant x-ray scattering with ultrafast intense pulses

Here, we present a time-dependent Schrödinger equation approach within a nonrelativistic quantum electrodynamics framework to investigate resonant x-ray scattering driven by intense x-ray pulses. This method enables us to explore how coherent x-ray electron dynamics influence scattering signals from Ne + . We account for both resonance fluorescence and elastic scattering channels, while also considering competing photoionization and inner-shell decay processes. By computing the angular distribution and energy spectrum of scattered photons, we uncover interference effects between elastic scattering and resonance fluorescence pathways. Notably, this interference results in a small asymmetry in the energy spectrum. We discuss the experimental potential for detecting signatures of interference. Our findings demonstrate that the x-ray Rabi dynamics can be used to control scattering responses and provide insights into interference mechanisms and scattering efficiency in high-intensity x-ray regimes.

Venkatesh, Akilesh [Argonne National Laboratory (A↗

NASA NTRS1972

X-ray scattering study

A soft X-ray glancing incidence telescope mirror and a group of twelve optical flat samples were used to study the scattering of X-rays. The mirror was made of Kanigen coated beryllium and the images produced were severely limited by scattering of X-rays. The best resolution attained was about fifteen arc seconds. The telescope efficiency was found to be 0.0006. The X-ray beam reflected from the twelve optical flat samples was analyzed by means of a long vacuum system of special design for these tests. The scattering then decreased with increasing angle of incidence until a critical angle was passed. At larger angles the scattering increased again. The samples all scattered more at 44 A than at 8 A. Metal samples were found to have about the same scattering at 44 A but greater scattering at 8 A than glass samples.

Wriston, R. S.↗

NASA NTRS1972

One-phonon transitions observed in the scattering of He atoms from a LiF/001/ surface.

For the scattering of a nearly monoenergetic beam of thermal-energy He atoms from a cleaved (001)LiF crystal surface, speed distributions of the reflected atoms are measured at suitably spaced scattering angles within the plane of incidence. From the measurements, elastic and one-phonon inelastic scattering processes are identified. Elastically scattered atoms distribute themselves in a set of sharp diffraction peaks. One-phonon inelastically scattered atoms are dispersed about each diffraction peak. The most probable velocities of the inelastically scattered atoms exhibit a characteristic sawtooth variation with scattering angle which, to first approximation, corresponds to conservation of the component of atom momentum tangent to the surface.-

Fisher, S. S.↗

NASA NTRS1972

Electromagnetic inverse scattering

A three-dimensional electromagnetic inverse scattering identity, based on the physical optics approximation, is developed for the monostatic scattered far field cross section of perfect conductors. Uniqueness of this inverse identity is proven. This identity requires complete scattering information for all frequencies and aspect angles. A nonsingular integral equation is developed for the arbitrary case of incomplete frequence and/or aspect angle scattering information. A general closed-form solution to this integral equation is developed, which yields the shape of the scatterer from such incomplete information. A specific practical radar solution is presented. The resolution of this solution is developed, yielding short-pulse target resolution radar system parameter equations. The special cases of two- and one-dimensional inverse scattering and the special case of a priori knowledge of scatterer symmetry are treated in some detail. The merits of this solution over the conventional radar imaging technique are discussed.

Bojarski, N. N.↗

NASA NTRS1974

Bistatic scatter from rain

An experimental investigation of bistatic scatter from rain was conducted, using a 143-km scatter path at frequencies of 4.5 and 7.7 GHz. The ratio of transmitted to received power (transmission loss) was measured for scattering angles ranging from 6 to 130 deg. Simultaneous weather radar observations were made at a frequency of 1.3 GHz. Transmission loss estimates for the bistatic scatter path were computed, using the weather radar data, the bistatic radar equation, and a model for the scattering cross section per unit volume of rain based upon Rayleigh scattering by an ensemble of water spheres. The measured and estimated transmission loss values were compared to test the use of the scattering model for the estimation of interference. The averaged ratio of measured-to-calculated transmission loss for the 4.5 GHz data is 1.2 plus or minus 0.4 dB. The averaged ratio for the 7.7 GHz data is -1.6 plus or minus 0.5 dB.

Crane, R. K.↗

NASA NTRS1974

Lectures on the scattering of light

The exact (Mie) theory for the scattering of a plane wave by a dielectric sphere is presented. Since this infinite series solution is computationally impractical for large spheres, another formulation is given in terms of an integral equation valid for a bounded, but otherwise general array of scatterers. This equation is applied to the scattering by a single sphere, and several methods are suggested for approximating the scattering cross section in closed form. A tensor scattering matrix is introduced, in terms of which some general scattering theorems are derived. The application of the formalism to multiple scattering is briefly considered.

Saxon, D. S.↗

NASA NTRS1977

The 2 deg/90 deg laboratory scattering photometer

A scattering photometer for measuring the light scattered by particles in a hydrosol at substantially 2 deg and 90 deg simultaneously is described. Light from a source is directed by a first optical system into a scattering cell containing the hydrosol under study. Light scattered at substantially 90 deg to the incident beam is focused onto a first photoelectric detector to generate an electrical signal indicative of the amount of scattered light at substantially 90 deg. Light scattered at substantially 2 deg to the incident beam is directed through an annular aperture symmetrically located about the axis of the illuminating beam which is linearly transmitted undeviated through the hydrosol and focused onto a second photoelectric detector to generate an electrical signal indicative of the amount of light scattered at substantially 2 deg.

Mccluney, W. R.↗

NASA NTRS1978

Model potentials for electron scattering - Converged close coupling calculations for the differential cross section for e/-/N2 at 30-50 eV

A calculation has been made of the elastic scattering and rotational excitation cross sections for e(-)-N2 scattering at 30 and 50 eV using quantum chemical techniques specially designed to be applicable to elastic and inelastic electron scattering by general polyatomic molecules. The angle dependence of the sum of the elastic and rotational excitation differential cross sections is in good agreement with experiment at all scattering angles at both energies, but at 50 eV the difference from experiment exceeds the experimental uncertainty at small scattering angles and near the minimum of the differential cross section. At large scattering angles the rotational excitation cross sections are predicted to exceed the elastic scattering cross sections. The absolute cross sections agree with experiment at some angles but at other angles are as much as 51% (30 eV) or 90% (50 eV) higher; this may be due at least in part to the difficulty of putting the experimental results on an absolute scale.

Onda, K.↗

NASA NTRS1980

Light scattering by randomly oriented spheroidal particles

A study of the light scattering properties of randomly oriented, identical spheroidal particles is presented. A computation method was developed to integrate the Asano and Yamomoto solution (1975) for scattering from a homogeneous spheroid over all particle orientations; the extinction and scattering cross-sections, the asymmetry factor, and scattering matrix elements are calculated for randomly oriented prolate and oblate spheroids and compared with the calculations for spheres and laboratory measurements. The angular scattering behavior of spheroids is found to be different from that of the spheres for side scattering to backscattering directions, and prolate and oblate spheroids of the same shape parameter have similar angular scattering patterns.

Asano, S.↗

NASA NTRS1980

Gravitational scattering of electromagnetic radiation

The scattering of electromagnetic radiation by linearized gravitational fields is studied to second order in a perturbation expansion. The incoming electromagnetic radiation can be of arbitrary multipole structure, and the gravitational fields are also taken to be advanced fields of arbitrary multipole structure. All electromagnetic multipole radiation is found to be scattered by gravitational monopole and time-varying dipole fields. No case has been found, however, in which any electromagnetic multipole radiation is scattered by gravitational fields of quadrupole or higher-order multipole structure. This lack of scattering is established for infinite classes of special cases, and is conjectured to hold in general. The results of the scattering analysis are applied to the case of electromagnetic radiation scattered by a moving mass. It is shown how the mass and velocity may be determined by a knowledge of the incident and scattered radiation.

Brooker, J. T.↗

NASA NTRS1983

Fresnel zone considerations for reflection and scatter from refractive index irregularities

Several different echoing mechanisms are proposed to explain VHF/UHF scatter from clear air; (1) anisotropic scatter; (2) Fresnel reflection, and (3) Fresnel scatter, in order to account for the spatial (angle and range) and temporal dependence of the echoes. The term diffuse reflection describes the echoing mechanism when both scatter and reflection coexist. A unifying formulation is presented incorporating a statistical approach that embraces all mechanisms the above mechanisms and gives conditions under which reflection or scatter dominates. A distinction between Fraunhofer and Fresnel scatter and a criterion is presented under which Fresnel scatter is important.

Doviak, R. J.↗

NASA NTRS1984

Surface scattering effects at different spectral regions

The development of theoretical models of rough surface scattering in different frequency regions is reviewed. The applications of the models to four different types of rough surface scattering are presented. The four categories of surface roughness effects are: (1) where the angular distribution of first-order average incoherent scattered power is proportional to the roughness spectrum of the surface; (2) where the horizontal roughness scale is less than the incident wavelength; (3) where both the horizontal and vertical roughness scales are large compared to the incident wavelength; and (4) scattering in the specular direction is dominated by large-scale roughness, and scattering in the opposite direction is dominated by small-scale roughness. Acoustic, optical and microwave scattering measurements from rough surfaces are presented which illustrate the four types of scattering behavior.

Fung, A. K.↗

NASA NTRS1985

A study of the polarization of light scattered by vegetation

This study was undertaken in order to better understand the factors that govern the polarization of light scattered from vegetation and soils. The intensity and polarization of light scattered by clover and grass in vivo and soil were measured at a number of different angles of incidence and reflectance. Both individual leaves and natural patches of leaves were measured. The light transmitted through the leaves was found to be negatively polarized. The light scattered from the upper leaf surface was found to be positively polarized in a manner which could be accounted for qualitatively but not quantitatively by the Fresnel reflection coefficients modified by a shadowing function of the form cos sup2 (g/2), where g is the phase angle. Findings indicate that the polarization of light scattered by vegetation is a more complex process than previously thought, and that besides the surface-scattered component of light, the volume-scattered and multiply-scattered components also contribute significantly to the polarization.

Woessner, P. N.↗

NASA NTRS1988

The scattered solar X-ray background in low earth orbit

In order to interpret X-ray observations of the sun-lit earth obtained with the IPC, a detailed model is developed that treats the radiative transfer of solar X-rays in single scattering approximation and employs the relevant scattering processes (elastic Thomson scattering and inelastic fluorescent scattering). The X-ray-bright earth, one of the strongest soft X-ray sources seen by the IPC, can then be understood in terms of solar X-rays scattered in the upper atmosphere. Using the CIRA 1972 Reference Atmosphere, it is possible to account for the observed 'bright earth' X-ray light curves under a variety of different viewing geometries. It is argued that the observed changes in hardness ratio of the scattered radiation can be interpreted as an indication of a change in the ratio of Thomson and fluorescently scattered photons as a function of zenith angle. The relevance of bright earth X-ray observations is further discussed in the context of operating X-ray telescopes in low-earth orbit, as well as in a broader astrophysical context.

Fink, H. H.↗

NASA NTRS1989

Hybrid method in light scattering by an arbitrary particle

A hybrid method for light scattering by an arbitrary particle using the scattering-order formulation of the coupled dipole method is described. An arbitrary particle is divided into two or more segments, and the field scattered by the particle is obtained from the fields scattered by each segment together with the field due to interactions among segments. An exact or approximate theory is used to calculate the scattered field from each segment, and interactions are included using the scattering-order formulation of the coupled dipole method. Calculations show that for certain particles, this hybrid approach can require fewer computations and give more accurate results than the scattering-order method.

Singham, Shermila Brito↗