A compact radial shearing interferometer based on the law of refraction.
Common path interferometer, using two fresnel zone plates for diffraction beam splitting, is applied to the testing of unit magnification optics
DIFFRACTION PATH↗
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Results for “Fresnel diffraction”
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Calculation of Diffraction Effects on the Average Phase of an Optical Field
The present paper reports on algorithms for the computation of the average phase of a beam over a detector in the near field.
diffraction diffraction modeling space interferome↗
Fresnel Lenses for Wide-Aperture Optical Receivers
Wide-aperture receivers for freespace optical communication systems would utilize Fresnel lenses instead of conventional telescope lenses, according to a proposal. Fresnel lenses weigh and cost much less than conventional lenses having equal aperture widths. Plastic Fresnel lenses are commercially available in diameters up to 5 m large enough to satisfy requirements for aperture widths of the order of meters for collecting sufficient light in typical long-distance free-space optical communication systems. Fresnel lenses are not yet suitable for high-quality diffraction-limited imaging, especially in polychromatic light. However, optical communication systems utilize monochromatic light, and there is no requirement for high-quality imaging; instead, the basic requirement for an optical receiver is to collect the incoming monochromatic light over a wide aperture and concentrate the light onto a photodetector. Because of lens aberrations and diffraction, the light passing through any lens is focused to a blur circle rather than to a point. Calculations for some representative cases of wide-aperture non-diffraction-limited Fresnel lenses have shown that it should be possible to attain blur-circle diameters of less than 2 mm. Preferably, the blur-circle diameter should match the width of the photodetector. For most high-bandwidth communication applications, the required photodetector diameters would be about 1 mm. In a less-preferable case in which the blur circle was wider than a single photodetector, it would be possible to occupy the blur circle with an array of photodetectors. As an alternative to using a single large Fresnel lens, one could use an array of somewhat smaller lenses to synthesize the equivalent aperture area. Such a configuration might be preferable in a case in which a single Fresnel lens of the requisite large size would be impractical to manufacture, and the blur circle could not be made small enough. For example one could construct a square array of four 5-m-diameter Fresnel lenses to obtain the same light-collecting area as that of a single 10-m-diameter lens. In that case (see figure), the light collected by each Fresnel lens could be collimated, the collimated beams from the four Fresnel lenses could be reflected onto a common offaxis paraboloidal reflector, and the paraboloidal reflector would focus the four beams onto a single photodetector. Alternatively, detected signal from each detector behind each lens would be digitized before summing the signals.
Hemmati, Hamid↗
The Milli-Arc-Second Structure Imager, MASSIM: A New Concept for a High Angular Resolution X-ray Telescope
MASSIM, the Milli-Arc-Second Structure Imager, is a mission that has been proposed for study within the context of NASA's "Astrophysics Strategic Mission Concept Studies" program. It uses a set of achromatic diffractive-refractive Fresnel lenses on an optics spacecraft to focus 5-11 keV X-rays onto detectors on a second spacecraft flying in formation 1000 km away. It will have a point-source sensitivity comparable with that of the current generation of major X-ray observatories (Chandra, XMM-Newton) but an angular resolution some three orders of magnitude better. MASSIM is optimized for the study of jets and other phenomena that occur in the immediate vicinity of black holes and neutron stars. It can also be used for studying other astrophysical phenomena on the milli-arc-second scale, such as those involving proto-stars, the surfaces and surroundings of nearby active stars and interacting winds. After introducing the principle of diffractive imaging in the x-ray/gamma-ray regime, the MASSIM mission concept and baseline design will be described along with a discussion of the options and trade-offs within the X-ray optics design.
Skinner, Gerry↗
The analysis of radar echoes from the moon.
Geometric optics used with Fresnel coefficients to interpret data on radar echoes from Moon
FRESNEL DIFFRACTION↗
MASSIM, the Milli-Arc-Second Structure Imager
The MASSIM (Milli-Arc-Second Structure Imager) mission will use a set of achromatic diffractive-refractive Fresnel lenses to achieve imaging in the X-ray band with unprecedented angular resolution. It has been proposed for study within the context of NASA's "Astrophysics Strategic Mission Concept Studies" program. Lenses on an optics spacecraft will focus 5-11 keV X-rays onto detectors on a second spacecraft flying in formation 1000 km away. It will have a point-source sensitivity comparable with that of the current generation of major X-ray observatories (Chandra, XMM-Newton) but an angular resolution some three orders of magnitude better. MASSIM is optimized for the study of jets and other phenomena that occur in the immediate vicinity of black holes and neutron stars. It can also be used for studying other phenomena on the milli-arc-second scale, such as those involving proto-stars, the surfaces and surroundings of nearby active stars and interacting winds.
Skinner, Gerry↗
High Accuracy Coronagraph Flight Model For WFIRST–CGI Raw Contrast Sensitivity Analysis
A high-accuracy high-fidelity flight wavefront control (WFC) model is developed for detailed raw contrast sensitivity analysis of WFIRST-CGI. Built upon features of recently testbed validated model, it is further refined to combine a full Fresnel propagation diffraction model for high accuracy contrast truth evaluation, and an economical compact model for WFC purposes. Extensive individual raw contrast error sensitivities are evaluated systematically, both as known imperfections and as unknown calibration errors, for both spectroscopy mode and wide field-of-view mode with shaped pupil coronagraph. More than 90 distinct error items were identified, including system aberrations, optical misalignment, component manufacturing error, telescope interface related errors, etc. The result forms the basis for raw contrast error budget flow down to a sub-system level, where detailed specifications needed to aid in component design and manufacturing, mechanical alignment and instrument integration, and verification and validation operations. Evaluations are mostly automated, making it relatively easy for repeat runs of revised design or at new desired error quantity. Top error sensitivities and contrast floor contributors are discussed and several observations are noted.
Poberezhskiy, Ilya↗
The dyadic diffraction coefficient for a curved edge
A compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edge formed by perfectly conducting curved or plane surfaces is obtained. This diffraction coefficent remains valid in the transition regions adjacent to shadow and reflection boundaries, where the diffraction coefficients of Keller's original theory fail. The method is on Keller's method of the canonical problem, which in this case is the perfectly conducting wedge illuminated by plane, cylindrical, conical, and spherical waves. When the proper ray fixed coordinate system is introduced, the dyadic diffraction coefficient for the wedge is found to be the sum of only two dyads, and it is shown that this is also true for the dyadic diffraction coefficients of higher order edges. One dyad contains the acoustic soft diffraction coefficient; the other dyad contains the acoustic hard diffraction coefficient. The expressions for the acoustic wedge diffraction coefficients contain Fresnel integrals, which ensure that the total field is continuous at shadow and reflection boundaries. The diffraction coefficients have the same form for the different types of edge illumination; only the arguments of the Fresnel integrals are different. Since diffraction is a local phenomenon, and locally the curved edge structure is wedge shaped, this result is readily extended to the curved edge.
Kouyoumjian, R. G.↗
COMMON PATH INTERFEROMETER USING FRESNEL ZONE PLATES
Common path interferometer using two fresnel zone plates for diffraction beam splitting, is applied to the testing of unit magnification optics
OPTICAL PATH↗
Profiling Saturn's rings by radio occultation
The development of reconstruction algorithms that correct for diffraction effects in radio occultation measurements is described. The reciprocal Fresnel transform relationship between the complex amplitude of the observed coherent signal and the complex microwave transmittance of the rings is derived using the Huygens-Fresnel formulation of the diffraction problem. The effects of the finite data segment width, the uncertainties in the Fresnel scale, systematic phase errors in the kernel of the inverse transform, reference oscillator instabilities, and random noise measurements on the resolution of the reconstructed transmittance are analyzed. Examples of reconstructed opacity profiles for some regions of Saturn's rings derived by applying the reconstruction theory to Voyager 1 at Saturn data are presented.
Marouf, Essam A.↗
Planar techniques for fabricating X-ray diffraction gratings and zone plates
The state of current planar techniques in the fabrication of Fresnel zone plates and diffraction gratings is reviewed. Among the fabrication techniques described are multilayer resist techniques; scanning electron beam lithography; and holographic lithography. Consideration is also given to: X-ray lithography; ion beam lithography; and electroplating. SEM photographs of the undercut profiles obtained in a type AZ 135OB photoresistor by holographic lithography are provided.
Smith, H. I.↗
A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface
A compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edge formed by perfectly conducting curved or plane surfaces is obtained. This diffraction coefficient remains valid in the transition regions adjacent to shadow and reflection boundaries, where the diffraction coefficients of Keller's original theory fail. Our method is based on Keller's method of the canonical problem, which in this case is the perfectly conducting wedge illuminated by plane, cylindrical, conical, and spherical waves. When the proper ray-fixed coordinate system is introduced, the dyadic diffraction coefficient for the wedge is found to be the sum of only two dyads, and it is shown that this is also true for the dyadic diffraction coefficients of higher order edges. One dyad contains the acoustic soft diffraction coefficient; the other dyad contains the acoustic hard diffraction coefficient. The expressions for the acoustic wedge diffraction coefficients contain Fresnel integrals, which ensure that the total field is continuous at shadow and reflection boundaries.
Kouyoumjian, R. G.↗
Optimization of Coherent Lidar Performance Using Graded- Reflectance Transmitter Resonator Optics in the Low Equivalent Fresnel Number Region
Using a diffractive eigenmode treatment to model the laser output, we show that graded-reflectance resonator optics offer significant efficiency benefits over conventional hard-edge coupled unstable resonators in the context of coherent detection lidar applications. Extending previous work pertinent to the high equivalent Fresnel number regime, we have modelled the optimum performance of a notional super-Gaussian coupled cavity as a function of the key resonator parameters in the low equivalent Fresnel number regime.
lidar graded-reflectance transmitter resonator↗
Interior impedance wedge diffraction with surface waves
The exact impedance wedge solution is evaluated asymptotically using the method of steepest descents for plane wave illumination at normal incidence. Uniform but different impedances on each face are considered for both soft and hard polarizations. The asymptotic solution isolates the incident, singly reflected, multiply reflected, diffracted, and surface wave fields. Multiply reflected fields of any order are permitted. The multiply reflected fields from the exact solution are written as ratios of auxiliary Maliuzhinets functions, whereas a geometrical analysis gives the reflected fields as products of reflection coefficients. These two representations are shown to be identical in magnitude, phase and the angular range over which they exist. The diffracted field includes four Fresnel transition functions as in the perfect conductor case, and the expressions for the appropriate discontinuities at the shadow boundaries are presented. The surface wave exists over a finite angular range and only for certain surface impedances. A surface wave transition field is included to retain continuity. Computations are presented for interior wedge diffractions although the formulation is valid for both exterior and interior wedges.
Balanis, Constantine A.↗
Shielding Characteristics Using an Ultrasonic Configurable Fan Artificial Noise Source to Generate Modes - Experimental Measurements and Analytical Predictions
An Ultrasonic Configurable Fan Artificial Noise Source (UCFANS) was designed, built, and tested in support of the NASA Langley Research Center's 14x22 wind tunnel test of the Hybrid Wing Body (HWB) full 3-D 5.8% scale model. The UCFANS is a 5.8% rapid prototype scale model of a high-bypass turbofan engine that can generate the tonal signature of proposed engines using artificial sources (no flow). The purpose of the program was to provide an estimate of the acoustic shielding benefits possible from mounting an engine on the upper surface of a wing; a flat plate model was used as the shielding surface. Simple analytical simulations were used to preview the radiation patterns - Fresnel knife-edge diffraction was coupled with a dense phased array of point sources to compute shielded and unshielded sound pressure distributions for potential test geometries and excitation modes. Contour plots of sound pressure levels, and integrated power levels, from nacelle alone and shielded configurations for both the experimental measurements and the analytical predictions are presented in this paper.
Artifical Noise↗
Near field antenna patterns of obstructed Cassegrainian telescopes
The near field antenna pattern of an obstructed optical transmitter, such as a Cassegrainian telescope, has been computed using the Fresnel approximation to the scalar diffraction integral. A number of cases have been considered. These include uniformly illuminated, obstructed circular apertures, and apertures coherently illuminated with a divergent gaussian beam wave. Other beam profiles that may be derived by energy redistribution of the laser beam have also been considered. The techniques used for the numerical evaluation of the Fresnel integral are discussed and results for the optical systems to be used on the High Altitude Aircraft Optical Communications Experiment are presented.
Webb, W. E.↗
Diffraction hardware testbed and model validation
Optical systems, which operate over a wide range of Fresnel numbers, are often times performance-limited by diffraction effects. In order to characterize such effects at the 40-100 picometer level, a diffraction testbed has been built which has the capability of measuring diffraction effects at this level. Concurrently, mathematical diffraction modeling tools have been developed that propagate an input wavefront through an optical train, while retaining amplitude and phase information at a grid resolution sufficient for yielding picometer-resolution diffraction test data. This paper contains a description of this diffraction hardware testbed, the diffraction modeling approach, and a comparison of the modeled and hardware test results, which then serves as validation of the diffraction modeling methodology.
optical↗
Complex space monofilar approximation of diffraction currents on a conducting half plane
Simple approximation of diffraction surface currents on a conducting half plane, due to an incoming plane wave, is obtained with a line current (monofile) in complex space. When compared to an approximating current at the edge, the diffraction pattern is seen to improve by an order of magnitude for a minimal increase of computation effort. Thus, the inconvient Fresnel integral functions can be avoided for quick calculations of diffracted fields and the accuracy is good in other directions than along the half plane. The method can be applied to general problems involving planar metal edges.
Lindell, I. V.↗