Far-field diffraction pattern for corner reflectors with complex reflection coefficients
Far field diffraction pattern of corner reflector for normally incident monochromatic light, considering polarization characteristics
Alley, C. O.↗
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The far field diffraction pattern for corner reflectors with complex reflection coefficients
The far field diffraction pattern of a geometrically perfect corner reflector is examined analytically for normally incident monochromatic light. The states of polarization and the complex amplitudes of the emerging light are expressed through transformation matrices in terms of those of the original incident light for each sextant of the face in a single coordinate system. The analytic expression of the total diffraction pattern is obtained for a circular face. This expression consists of three component functions in addition to the basic Airy function. The coefficient of each function is expressed in terms of complex coefficients of reflectance of the reflecting surface. Some numerical results for different reflecting surfaces, including total internal reflection, are presented. The iso-intensity contours of the diffraction pattern evaluated from the analytical expressions for an uncoated solid corner reflector are also presented along with the photographs of the pattern.
Chang, R. F.↗
Investigation Of Far-Field Diffraction
Report describes experimental investigation of far-field diffracton by normally illuminated circular apertures with diameters of several wavelengths of incident light. Purpose of investigation to determine whether Keller's "geometrical" theory of diffraction valid for diffraction phenomena of this kind.
Wang, Yaujen↗
Identify the Limits of Geometric Optics Ray Tracing by Numerically Solving the Vector Kirchhoff Integral
The properties of a pencil of light as defined approximately in the geometric optics ray tracing method are investigated. The vector Kirchhoff integral is utilized to accurately compute the electromagnetic near field in and around the pencil of light with various beam base sizes, shapes, propagation directions and medium refractive indices. If a pencil of light has geometric mean cross section size of the order p times the wavelength, it can propagate independently to a distance p2 times the wavelength, where most of the beam energy diffuses out of the beam region. This is consistent with a statement that van de Hulst made in a classical text on light scattering. The electromagnetic near fields in the pencil of light are not uniform, have complicated patterns within short distances from the beam base, and the fields tend to converge to Fraunhofer diffraction fields far away from the base.
Far field diffraction↗
Test results from LAGEOS-2 optical characterization using pulsed lasers
The Laser Geodynamic Satellite-2 (LAGEOS-2) has undergone extensive optical testing at NASA Goddard Space Flight Center during 1989. The techniques included measuring the far field diffraction pattern using cw and pulsed lasers. In the pulsed measurement technique, response of the satellite was studied by measuring the far-field diffraction pattern (FFDP) as a function of pulsewidth, wavelength, polarization, position in the FFDP, detector/processing techniques, and satellite orientation. The purpose of the pulsed laser testing was two-fold: (1) to characterize the satellite optical response with the detector and signal processing electronics currently used in most SLR stations using the portable laser ranging standard, and (2) to characterize the satellite response for various conditions using the highest bandwidth optical detector (streak camera) available for the next generation of satellite laser ranging (SLR) technology. The portable ranging standard employed multiple measurement devices and an optical calibration scheme to eliminate range-dependent and amplitude-dependent systematics. These precautions were taken to eliminate/minimize instrumental errors and provide maximum accuracy. For LAGEOS orbit (6000 Km), ground stations are located 34 to 38 Mu radians off the axis of the return signal from the satellite; therefore, an optical mask was used to restrict the field of view (FOV) of detection to this annular region of the FFDP. The two measurement techniques were implemented using an aperture sharing scheme and complemented each other by providing mutual verification.
Varghese, Thomas K.↗
Prelaunch optical characterization of the Laser Geodynamic Satellite (LAGEOS 2)
The optical range correction (the distance between the apparent retroreflective skin of the satellite and the center of mass) of the LAGEOS 2 was determined using computer analysis of theoretical and experimentally measured far field diffraction patterns, and with short pulse lasers using both streak camera-based range receivers and more conventional PMT-based range receivers. The three measurement techniques yielded range correction values from 248 to 253 millimeters dependent on laser wavelength, pulsewidth, and polarization, location of the receiver in the far field diffraction pattern and detection technique (peak, half maximum, centroid, or constant fraction). The Lidar cross section of LAGEOS 2 was measured at 4 to 10 million square meters, comparable to the LAGEOS 1.
Minott, Peter O.↗
Nanotechnology Infrared Optics for Astronomy Missions
We have used the "MicroStripes" code (Flomerics, Inc.) to perform full-, near- and far-field diffraction modeling of metal mesh performance on substrates. Our Miles Code software, which approximates the full calculation in a quick, gui-based window, is useful as an iterative device by adjusting the input parameters (index of refraction, thickness, etc.) to provide agreement with the full calculation. However, despite the somewhat extravagant claims by the MicroStripes manufacturer, this code is also not perfect because numerous free parameters must be set. Key among these, as identified in our earlier papers and proposal documents, is the high frequency (i.e., far IR) character of the real and imaginary parts of the index of refraction of the metal mesh, the high frequency character of the real and imaginary parts of the index of refraction of the substrate, and the character of the interface between the mesh and the substrate material, and in particular the suppression (or possible enhancement) of surface effects at the interface.
Frogel, Jay↗
Cube corner retroreflector test and analysis
Cube corner retroreflectors with nominal dihedral angles of 90 deg 0 min 1.5 sec were fabricated, tested, and analyzed to determine the return energy in the annular ring of the far field diffraction pattern required by the Laser Geodynamic Satellite. Performance was assessed for variations in the dihedral angles, optical surfaces, and thermal environment. Despite relatively high independent axial and radial sensitivities, the changes caused by the anticipated thermal environment were found to be negligible; however, there were substantial variations between the analytical predictions and measured performance.-
Zurasky, J. L.↗
Cube-Corner Retroreflector Modeling
Collection of computer programs analyzes arrays of optical cube corners used in laser ranging. Programs compute impulse-response and interference effects of reflected pulses from optical cube corners and calculates interference-effects histogram and far-field diffraction patterns.
Kirk, J. G.↗
Study of hollow corner retroreflectors for use in a synchronous orbit
The performance of a hollow corner cube retroreflector made up of three mutually perpendicular optically flat mirrors when undergoing the thermal-mechanical strains induced by a spacecraft environment was studied. Of particular interest was a device of 200 square centimeter optical aperture used on a satellite in a synchronous orbit. It was assumed that the reflector always faces the earth. The effects of direct solar irradiance, earthshine, and albedo were considered. The results included the maximum mirror surface temperature during the orbit as well as the worst-case loss of optical performance due to thermally-induced mirror distortions. It was concluded that a device made of three suitably coated flat ULE mirrors, optically contacted to each other and supported mechanically in a nonrigid mount, would be expected to concentrate over 80 percent of the theoretical maximum energy in the central of the far field diffraction pattern. Continued development of the device through a detailed design, fabrication, and test phase was recommended.
Yoder, P. R., Jr.↗
Single-color laser ranging with a cube-corner-retroreflector array
Lidar cross section of some typical types of cube-corner retroreflectors (CCRs) having a three corner mirror system is investigated for the case that the CCR is tilted from the normal illumination axis. Analytic expressions for the effective aperture area for the two typical window types (circular and hexagonal) of CCRs are obtained for the case that the CCR is tilted. The range of incidence angle in which only the total reflection occurs at all three uncoated corner mirrors has been found to vary considerably with the orientation of CCR and the refractive index of the CCR prism. The analytical expression for the far-field diffraction pattern of a tilted CCR is obtained by taking different polarization transformation of the six sectors of the effective reflecting aperture into account. This expression is essential when evaluating the lidar cross section of a moving CCR which is tilted in general. Formulas for the angles defining the six sectors have also been obtained.
Song, G. Hugh↗
Optical Characterization of Laser Retroreflector Arrays for Lunar Landers
Laser Retroreflector Array for Lunar Landers (LRALL) is a small optical instrument designed to provide a target for precision laser ranging from a spacecraft in lunar orbit, enabling geolocation of the lander and its instrument suite and establishing a fiducial maker on the lunar surface. Here we describe the optical performance of LRALL at visible and near-infrared wavelengths. Individual corner cube reflectors (CCRs) within LRALL were tested for surface flatness and dihedral angle values. We also imaged the far-field diffraction patterns of individual CCRs as well as the entire retroreflector array over the range of possible incident angles to extract the optical cross section as a function of viewing angle. We also measured the optical properties of one of the CCRs over the lunar temperature range (100 K to 380 K) and found no significant temperature-dependent variance. The test results show LRALL meets the design criteria and can be ranged to from elevation angles above 30° with respect to the instrument base from an orbital laser altimeter such as the Lunar Orbiter Laser Altimeter (LOLA) on the Lunar Reconnaissance Orbiter (LRO). This work summarizes the test data and serves as a guide for future laser ranging to these retroreflector arrays.
Daniel R Cremons↗
Alignment and Verification Testing of the GPS LRA Test Bed
The LRCTF (Laser Ranging Characterization and Test Facility) is a unique facility built at NASA GSFC to provide thermal-optical testing of the next generation GPS LRA (Global Positioning Satellite’s Laser Retroreflector Array) laser ranging target. The 400mm diameter target is an array consisting of 48 total internal reflection retroreflectors and has an optical cross section requirement of 100 MSM (million square meters). To verify that the array meets this requirement during on-orbit conditions, the LRCTF is equipped with a 400mm test beam, a data product output consisting of full aperture FFDPs (Far Field Diffraction Patterns) and a thermal chamber. The FFDPs are used to calculate the OCS. This paper will describe the facility design, alignment approach, and verification process.
Patricia Lyons↗
Unstable resonator antenna properties in coherent lidar applications - A comparative study
The antenna parameters of a coherent lidar in the far-field diffraction-limited regime, where the lidar transmitter consists of an unstable resonator with a Gaussian reflectivity profile output coupler, are investigated. A figure-of-merit combining lasr transmitter energy extraction efficiency with the far-field attributes of a given cavity configuration has been used to compare the lidar performance and relative merits of such systems as they relate to those of conventional unstable cavities with diffractive output coupling.
Tratt, David M.↗
Diffraction by fractally serrated apertures
An investigation of light diffracted by irregularly serrated apertures yields a closed-form analytical solution that confirms experimental recording of the diffracted patterns. These serrated apertures are modeled by a fractal function. Examples are given for both sinusoidal and fractal aperture perimeters with varying fractal dimension. Relations between the far-zone diffracted fields and the fractal dimension are examined.
Kim, Y.↗
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↗
Infrared Astronomical Satellite (IRAS) analysis, appendix B
Analytical results derived during the development of the PADE program are presented. Near field on-axis diffraction from a circular aperture is analyzed by integrating Kirchhoff's formula, the boundary wave formulation, and the Rayleigh-Sommerfeld theory. Far field on-axis diffraction from obliquely illuminated apertures is described using the angular spectrum approach. Transmission functions and diffracted fields for rectangular, circular, and rotated square apertures are presented.
Source record↗
Mathmatical modeling for diffractive optics
We consider a 'diffractive optic' to be a biperiodic surface separating two half-spaces, each having constant constitutive parameters; within a unit cell of the periodic surface and across the transition zone between the two half-spaces, the constitutive parameters can be a continuous, complex-valued function. Mathematical models for diffractive optics have been developed, and implemented as numerical codes, both for the 'direct' problem and for the 'inverse' problem. In problems of the 'direct' class, the diffractive optic is specified, and the full set of Maxwell's equations is cast in a variational form and solved numerically by a finite element approach. This approach is well-posed in the sense that existence and uniqueness of the solution can be proved and specific convergence conditions can be derived. An example of a metallic grating at a Wood anomaly is presented as a case where other approaches are known to have convergence problems. In problems of the 'inverse' class, some information about the diffracted field (e.g., the far-field intensity) is given, and the problem is to find the periodic structure in some optimal sense. Two approaches are described: phase reconstruction in the far-field approximation; and relaxed optimal design based on the Helmholtz equation. Practical examples are discussed for each approach to the inverse problem, including array generators in the far-field case and antireflective structures for the relaxed optimal design.
Dobson, David↗