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All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

Surface wave diffraction by a truncated dielectric slab recessed in a perfectly conducting surface

The diffraction of a TM sub 0 surface wave by a terminated dielectric slab which is flush mounted in a perfectly conducting surface is studied. The incident surface wave gives rise to waves reflected and diffracted by the termination; these reflected and diffracted fields may be expressed in terms of the geometrical theory of diffraction by introducing surface wave reflection and diffraction coefficients which are associated with the termination. In this investigation the surface wave reflection and diffraction coefficients have been deduced from a formally exact solution to this canonical problem. The solution is obtained via a combination of the generalized scattering matrix technique and the Wiener-Hopf procedure. Expressions for the reflection and diffraction coefficients contain integrals which can be evaluated numerically.

Pathak, P. H.↗
NASA NTRS1987

Radar cross section of an open-ended circular waveguide Calculation of second-order diffraction terms

The radar cross section of an open-ended, semi-infinite circular waveguide is calculated by the geometrical theory of diffraction and the equivalent-current (EC) method. Both single- and double-diffraction terms are included. It is found that the double-diffraction term is stronger than the single-diffraction term for the horizontal polarization at wide-angle incidence. Its inclusion is necessary in order to check with experimental data and the asymptotic expansion of the exact Wiener-Hopf solution. The EC method is used for the single diffraction. On the other hand the double-diffraction term is obtained by using the EC method for axial incidence and geometrical theory of diffraction for wide-angle incidence. These two solutions are matched with a proper matching function. This technique is computationally more efficient than the matching technique of integration over the equivalent currents.

Lee, C. S.↗
NASA NTRS1994

Wavelength-division multiplexed optical integrated circuit with vertical diffraction grating

A semiconductor optical integrated circuit for wave division multiplexing has a semiconductor waveguide layer, a succession of diffraction grating points in the waveguide layer along a predetermined diffraction grating contour, a semiconductor diode array in the waveguide layer having plural optical ports facing the succession of diffraction grating points along a first direction, respective semiconductor diodes in the array corresponding to respective ones of a predetermined succession of wavelengths, an optical fiber having one end thereof terminated at the waveguide layer, the one end of the optical fiber facing the succession of diffraction grating points along a second direction, wherein the diffraction grating points are spatially distributed along the predetermined contour in such a manner that the succession of diffraction grating points diffracts light of respective ones of the succession of wavelengths between the one end of the optical fiber and corresponding ones of the optical ports.

Lang, Robert J.↗
NASA NTRS1994

MANN: A program to transfer designs for diffractive optical elements to a MANN photolithographic mask generator

There are two basic areas of interest for diffractive optics. In the first, the property of wavefront division is exploited for achieving optical fanout, analogous to the more familiar electrical fanout of electronic circuitry. The basic problem here is that when using a simple uniform diffraction grating the energy input is divided unevenly among the output beams. The other area of interest is the use of diffractive elements to replace or supplement standard refractive elements such as lenses. Again, local grating variations can be used to control the amount of bending imparted to optical rays, and the efficiency of the diffractive element will depend on how closely the element can be matched to the design requirements. In general, production restrictions limit how closely the element approaches the design, and for the common case of photolithographic production, a series of binary masks is required to achieve high efficiency. The actual design process is much more involved than in the case of elements for optical fanout, as the desired phase of the optical wavefront over some reference plane must be specified and the phase alteration to be introduced at each point by the diffraction element must be known. This generally requires the utilization of a standard optical design program. Two approaches are possible. In the first approach, the diffractive element is treated as a special type of lens and the ordinary optical design equations are used. Optical design programs tend to follow a second approach, namely, using the equations of optical interference derived from holographic theory and then allowing the introduction of phase front corrections in the form of polynomial equations. By using either of these two methods, diffractive elements can be used not only to compensate for distortions such as chromatic or spherical aberration, but also to perform the work of a variety of other optical elements such as null correctors, beam shapers, etc. The main focus of the project described in this report is how the design information from the lens design program is incorporated into the photolithographic process. It is shown that the MANN program, a photolithographic mask generator, fills the need for a link between lens design programs and mask generation controllers.The generated masks can be used to expose a resist-coated substrate which is etched and then must be re-coated, re-exposed, and re-etched for making copies, just as in the electronics industry.

Matthys, Donald R.↗
NASA NTRS2008

Transmissive Diffractive Optical Element Solar Concentrators

Solar-thermal-radiation concentrators in the form of transmissive diffractive optical elements (DOEs) have been proposed as alternatives to mirror-type solar concentrators now in use. In comparison with functionally equivalent mirror-type solar concentrators, the transmissive, diffractive solar concentrators would weigh and cost less, and would be subject to relaxed mechanical tolerances. A DOE concentrator would be made from a thin, flat disk or membrane of a transmissive material having a suitable index of refraction. By virtue of its thinness, the DOE concentrator would have an areal mass density significantly less than that of a functionally equivalent conventional mirror. The DOE concentrator would have a relatively wide aperture--characterized by a focal-length/aperture-diameter ratio ('f number') on the order of 1. A kinoform (a surface-relief phase hologram) of high diffractive order would be microfabricated onto one face of the disk. The kinoform (see figure) would be designed to both diffract and refract incident solar radiation onto a desired focal region, without concern for forming an image of the Sun. The high diffractive order of this kinoform (in contradistinction to the low diffractive orders of some other kinoforms) would be necessary to obtain the desired f number of 1, which, in turn, would be necessary for obtaining a desired concentration ratio of 2,500 or greater. The design process of optimizing the concentration ratio of a proposed DOE solar concentrator includes computing convolutions of the optical bandwidth of the Sun with the optical transmission of the diffractive medium. Because, as in the cases of other non-imaging, light-concentrating optics, image quality is not a design requirement, the process also includes trading image quality against concentration ratio. A baseline design for one example calls for an aperture diameter of 1 m. This baseline design would be scalable to a diameter as large as 10 m, or to a smaller diameter for a laboratory test article. Initial calculations have indicated that the characteristics of the test article would be readily scalable to a full-size unit.

Baron, Richard↗
NASA NTRS2009

Suppressing Ghost Diffraction in E-Beam-Written Gratings

A modified scheme for electron-beam (E-beam) writing used in the fabrication of convex or concave diffraction gratings makes it possible to suppress the ghost diffraction heretofore exhibited by such gratings. Ghost diffraction is a spurious component of diffraction caused by a spurious component of grating periodicity as described below. The ghost diffraction orders appear between the main diffraction orders and are typically more intense than is the diffuse scattering from the grating. At such high intensity, ghost diffraction is the dominant source of degradation of grating performance. The pattern of a convex or concave grating is established by electron-beam writing in a resist material coating a substrate that has the desired convex or concave shape. Unfortunately, as a result of the characteristics of electrostatic deflectors used to control the electron beam, it is possible to expose only a small field - typically between 0.5 and 1.0 mm wide - at a given fixed position of the electron gun relative to the substrate. To make a grating larger than the field size, it is necessary to move the substrate to make it possible to write fields centered at different positions, so that the larger area is synthesized by "stitching" the exposed fields.

Wilson, Daniel↗
NASA NTRS2018

Amorphous Phase Characterization Through X-Ray Diffraction Profile Modeling: Implications for Amorphous Phases in Gale Crater Rocks and Soils

The CheMin X-ray diffraction instrument on the Mars Science Laboratory rover has analyzed 18 rock and soil samples in Gale crater. Diffraction data allow for the identification of major crystalline phases based on the positions and intensities of well-defined peaks and also provides information regarding amorphous and poorly-ordered materials based on the shape and positions of broad scattering humps. The combination of diffraction data, elemental chemistry from APXS (Alpha Particle X-ray Spectrometer) and evolved gas analyses (EGA) from SAM (Sample Analysis at Mars) help constrain possible amorphous materials present in each sample (e.g., glass, opal, iron oxides, sulfates) but are model dependent. We present a novel method to characterize amorphous material in diffraction data and, through this approach, aim to characterize the phases collectively producing the amorphous profiles in CheMin diffraction data. This method may be applied to any diffraction data from samples containing X-ray amorphous materials, not just CheMin datasets, but we re-strict our discussion to Martian-relevant amorphous phases and diffraction data measured by CheMin or CheMin-like instruments.

Achilles, C. N.↗
NASA NTRS1974

TM surface wave diffraction by a truncated dielectric slab recessed in a perfectly conducting surface

The diffraction of a TM sub o surface wave by a terminated dielectric slab which is flush mounted in a perfectly conducting surface is studied. The incident surface wave gives rise to waves reflected and diffracted by the termination; these reflected and diffracted fields may be expressed in terms of the geometrical theory of diffraction by introducing surface wave reflection and diffraction coefficients which are associated with the termination. In this investigation, the surface wave reflection and diffraction coefficients have been deduced from a formally exact solution to this canonical problem. The solution is obtained by a combination of the generalized scattering matrix technique and function theoretic methods.

Pathak, P. H.↗
NASA NTRS1978

On the use of classical and conical diffraction mountings for XUV gratings

A description is given of the properties of plane diffraction gratings used in conical diffraction. Formulas are given for computing the direction of the diffracted orders. Experiments were performed to investigate the behavior of gratings used on conical diffraction mountings. Comparisons made with classical diffraction mountings show a significant increase in the efficiency of the -1 order. An empirical formula to predict the efficiencies of gratings used in conical diffraction mountings has been verified by the measurements.

Neviere, M.↗
NASA NTRS1979

Applications of diffraction theory to aeroacoustics

A review is given of the fundamentals of diffraction theory and the application of the theory to several problems of aircraft noise generation, propagation, and measurement. The general acoustic diffraction problem is defined and the governing equations set down. Diffraction phenomena are illustrated using the classical problem of the diffraction of a plane wave by a half-plane. Infinite series and geometric acoustic methods for solving diffraction problems are described. Four applications of diffraction theory are discussed: the selection of an appropriate shape for a microphone, the use of aircraft wings to shield the community from engine noise, the reflection of engine noise from an aircraft fuselage and the radiation of trailing edge noise.

Lansing, D. L.↗
NASA NTRS1979

Applications of diffraction theory to aeroacoustics

The fundamentals of diffraction theory were reviewed and applied to several problems of aircraft noise generation, propagation, and measurement. The general acoustic diffraction problem is defined and the governing equations were set down. Diffraction phenomena are illustrated using the classical problem of the diffraction of a plane wave by a half-plane. Infinite series and geometric acoustic methods for solving diffraction problems are described. Four applications of diffraction theory are discussed: the selection of an appropriate shape for a microphone, the use of aircraft wings to shield the community from engine noise, the reflection of engine noise from an aircraft fuselage, and the radiation of trailing edge noise.

Lansing, D. L.↗
NASA NTRS1987

Dihedral corner reflector backscatter using higher order reflections and diffractions

The uniform theory of diffraction (UTD) plus an imposed edge diffraction extension is used to predict the backscatter cross sections of dihedral corner reflectors which have right, obtuse, and acute included angles. The UTD allows individual backscattering mechanisms of the dihedral corner reflectors to be identified and provides good agreement with experimental cross-section measurements in the azimuthal plane. Multiply reflected and diffracted fields of up to third-order are included in the analysis for both horizontal and vertical polarizations. The coefficients of the uniform theory of diffraction revert to those of the geometrical theory of diffraction (GTD) in far-field cross-section analyses, but finite cross sections can be obtained everywhere by considering mutual cancellation of diffractions from parallel edges. Analytic calculations are performed using UTD coefficients; hence the accuracy required in angular measurements is more critical as the distance increases. The common far-field approximation that all rays to the observation point are parallel is too gross an approxiation for the angular parameters in the UTD coefficients in the far field.

Griesser, Timothy↗
NASA NTRS1993

An extended UTD analysis for the scattering and diffraction from cubic polynomial strips

Spline and polynomial type surfaces are commonly used in high frequency modeling of complex structures such as aircraft, ships, reflectors, etc. It is therefore of interest to develop an efficient and accurate solution to describe the scattered fields from such surfaces. An extended Uniform Geometrical Theory of Diffraction (UTD) solution for the scattering and diffraction from perfectly conducting cubic polynomial strips is derived and involves the incomplete Airy integrals as canonical functions. This new solution is universal in nature and can be used to effectively describe the scattered fields from flat, strictly concave or convex, and concave convex boundaries containing edges. The classic UTD solution fails to describe the more complicated field behavior associated with higher order phase catastrophes and therefore a new set of uniform reflection and first-order edge diffraction coefficients is derived. Also, an additional diffraction coefficient associated with a zero-curvature (inflection) point is presented. Higher order effects such as double edge diffraction, creeping waves, and whispering gallery modes are not examined. The extended UTD solution is independent of the scatterer size and also provides useful physical insight into the various scattering and diffraction processes. Its accuracy is confirmed via comparison with some reference moment method results.

Constantinides, E. D.↗
NASA NTRS1994

A uniform geometrical optics and an extended uniform geometrical theory of diffraction for evaluating high frequency EM fields near smooth caustics and composite shadow boundaries

A uniform geometrical optics (UGO) and an extended uniform geometrical theory of diffraction (EUTD) are developed for evaluating high frequency electromagnetic (EM) fields within transition regions associated with a two and three dimensional smooth caustic of reflected rays and a composite shadow boundary formed by the caustic termination or the confluence of the caustic with the reflection shadow boundary (RSB). The UGO is a uniform version of the classic geometrical optics (GO). It retains the simple ray optical expressions of classic GO and employs a new set of uniform reflection coefficients. The UGO also includes a uniform version of the complex GO ray field that exists on the dark side of the smooth caustic. The EUTD is an extension of the classic uniform geometrical theory of diffraction (UTD) and accounts for the non-ray optical behavior of the UGO reflected field near caustics by using a two-variable transition function in the expressions for the edge diffraction coefficients. It also uniformly recovers the classic UTD behavior of the edge diffracted field outside the composite shadow boundary transition region. The approach employed for constructing the UGO/EUTD solution is based on a spatial domain physical optics (PO) radiation integral representation for the fields which is then reduced using uniform asymptotic procedures. The UGO/EUTD analysis is also employed to investigate the far-zone RCS problem of plane wave scattering from two and three dimensional polynomial defined surfaces, and uniform reflection, zero-curvature, and edge diffraction coefficients are derived. Numerical results for the scattering and diffraction from cubic and fourth order polynomial strips are also shown and the UGO/EUTD solution is validated by comparison to an independent moment method (MM) solution. The UGO/EUTD solution is also compared with the classic GO/UTD solution. The failure of the classic techniques near caustics and composite shadow boundaries is clearly demonstrated and it is shown that the UGO/EUTD results remain valid and uniformly reduce to the classic results away from the transition regions. Mathematical details on the asymptotic properties and efficient numerical evaluation of the canonical functions involved in the UGO/EUTD expressions are also provided.

Constantinides, E. D.↗
NASA NTRS1993

A UGO/EUTD Solution for the Scattering and Diffraction from Cubic Polynomial Strips

A uniform geometrical optics (UGO) and an extended uniform geometrical theory of diffraction (EUTD) solution is developed for the scattering and diffraction from perfectly conducting cubic polynomial strips. The new solution overcomes the difficulties of the classic GO/UTD solution near caustics and composite shadow boundaries. The approach for constructing the UGO/EUTD solution is based on a spatial domain physical optics (PO) radiation integral representation for the scattered field which is then reduced using a uniform asymptotic procedure. New uniform reflection, zero-curvature diffraction, and edge diffraction coefficients are derived and involve the ordinary and incomplete Airy integrals as canonical functions. Higher order effects such as double edge diffraction, edge-excited creeping waves, and whispering gallery modes are not examined in this work. The UGO/EUTD solution is very efficient and provides useful physical insight into the various scattering and diffraction processes. It is also universal in nature and can be used to effectively describe the scattered fields from flat, strictly concave or convex, and concave-convex boundaries containing edges. Its accuracy is confirmed via comparison with some reference moment method (MM) results.

Constantinides, Evagoras D.↗
NASA NTRS1999

X-Ray Diffraction Techniques for a Field Instrument: Patterns of Lithologic Provences

Future exploration of Mars will attempt to shed light on the mineralogy of surface materials. Instruments deployed from remote platforms should have the capability to conduct both intensive analyses as well as rapid, reconnaissance surveys while they function in the martian environment as surrogate geologists. In order to accommodate the reconnaissance mode of analysis and to compensate for analytical limitations imposed by the space-flight conditions, data analysis methods are being developed that will permit interpretation of data by recognition of signatures or "fingerprints". Specifically, we are developing a technique which will allow interpretation of diffraction patterns by recognition of characteristic signatures of different lithologic provences. This technique allows a remote vehicle to function in a rapid-scan mode using the lithologic signature to determine where a more thorough analysis is needed. An x-ray diffraction pattern is characterized by the angular positions of diffracted x-rays, x-ray intensity levels and background radiation levels. These elements may be used to identify a generalized x-ray signature. Lithologic signatures are being developed in two ways. A signature is composed using the ideal powder diffraction indices from the mineral assembledge common to a specific lithologic provence. This is then confirmed using a laboratory diffraction pattern of a whole rock powder. Preliminary results comparing the diffraction signatures of the major mineral assembledges common to basalt, carbonate, and evaporite basin deposits indicate that lithologies are differentiable as a "fingerprint". Statistical analyses are being performed to establish the confidence levels of this technique.

Marshall, J.↗
NASA NTRS2002

Diffraction Effects in a Grating Spectrometer

This paper describes a numerical study of diffraction effects in the AIRES optical system using GLAD by Applied Optics Research. AIRES (or Airborne Infrared Echelle Spectrometer) employs two gratings in series. The small, first-order (i.e., predisperser) grating sorts orders for the large, high-order echelle grating, thus providing moderately high spectral resolution over 3.6 octaves in wavelength. The AIRES' optical design includes three field stops (i.e., a circular aperture and two long, narrow slits) and four pupil stops. A detailed diffraction analysis is required to evaluate critical trade-offs between spectral resolution, optical throughput, detector background, scattered light, and system size and weight. Such an analysis must consider diffraction effects at the pupil stops (edge diffraction), at the field stops (spatial filtering), and at intermediate positions where other optical elements are located. The effects of slit width, slit length, oversizing of the second slit relative to the first, baffling at the Lyot stop and subsequent pupil stops, and the necessity for oversizing other optical elements are presented and discussed. It is found that for narrow slits, the downstream energy distribution is significantly broadened relative to that for large slits, where telescope diffraction dominates, leading to significantly more light loss than anticipated, unless other key optical elements are oversized. The importance of performing a proper diffraction analysis is emphasized and the suitability of GLAD for this task is discussed.

Haas, Michael R.↗
NASA NTRS2006

Optimizing Crystal Volume for Neutron Diffraction

Neutron diffraction is uniquely sensitive to hydrogen positions and protonation state. In that context structural information from neutron data is complementary to that provided through X-ray diffraction. However, there are practical obstacles to overcome in fully exploiting the potential of neutron diffraction, Le. low flux and weak scattering. Several approaches are available to overcome these obstacles and we have investigated the simplest: increasing the diffracting volume of the crystals. Volume is a quantifiable metric that is well suited for experiment design and optimization techniques. By using response surface methods we have optimized xylose isomerase crystal volume, enabling neutron diffraction while we determined the crystallization parameters with the minimum of experiments. Our results suggest a systematic means of enabling neutron diffraction studies for a larger number of samples that require information on hydrogen position and/or protonation state.

Snell, Edward H.↗