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Physical Optics Simulations with GRASP Physical Optics Simulations with GRASP December 07, 2007 General Reflector and Antenna Analysis Program, Ticra Ltd. Free student version including technical documentation available at www.ticra.com. 1 Physical Optics Simulations with GRASP Simulation and measurement of different optical setups at 625 GHz Aberrations from off-axis geometry increase with bend angle. They cannot be modeled with basic Gaussian beam theory. Amplitude [dB] 0 f=625.00 GHz, file: ../iap_01.dat −40 −2 0 −30 −3 0 −40 −40 −2 −20 −3 0 −1 0 y [mm] 0 −1 −30 0 0 −4 −20 −20 −50 −30 0 −4 0 −4 −40 −50 −40 −4 0 −30 −40 0 −3 −20 −30 −40 0 −4 −20 −30 −30 −4 0 −2 0 −30 −40 −3 −40 −30 y [mm] 0 0 −3 −10 −10 −20 −4 −30 0 −30 −30 −40 −30 −20 −3 −10 −3 0 0 −4 −1 −3 0 − −10 20 0 −4 −3 10 0 0 −30 20 −20 10 60 −10 −4 −40 0 −30 0 −40 −4 −30 −2 0 −2 −40 −40 −30 20 Amplitude [dB] 0 f=624.32 GHz, file: abmm.grd 30 −10 −4 0 0 −4 40 0 −4 −30 30 −10 40 −40 −40 −30 −20 −10 0 20 −40 30 10 40 50 −40 −40 −60 −30 −20 −10 0 x [mm] 10 20 30 40 50 −60 x [mm] f=625.00 GHz, file: cm2_01.dat Amplitude [dB] 0 60 f=650.00 GHz, file: cm2_800mm_measurement_plane.txt Amplitude [dB] 0 60 −4 0 −20 −4 −40 −30 0 −3 −20 −30 −50 −40 −40 −10 −40 −3 −10 −20 −4 0 −30 0 0 −1 −30 −40 0 −3 −30 −3 −4 −40 0 −40 −40 −40 −20 −20 −40 −20 −40 −40 0 −30 −40 −40 0 −1 −40 −4 −40 0 −4 0 −3 −10 0 −1 −40 0 −20 −40 −30 −3 0 −20 20 −40 0 −2 −3 −3 −4 −20 −20 y [mm] 0 −3 −3 0 −10 0 −4 0 −40 0 45 40 −4 −10 −4 0 −40 −10 −4 0 −40 −30 −20 z [mm] −40 0 −04 −4 −40 20 −40 −40 40 −20 −40 −40 −40 −50 −60 −60 −60 −40 −20 0 x [mm] 20 40 60 Measurement −60 −60 −40 −20 0 y [mm] 20 40 60 −60 GRASP Simulation 2 Physical Optics Simulations with GRASP Limitations of fundamental Gaussian Beam Mode Analysis I Paraxial approximation I Diffraction at apertures and mirror rims not included I Aberrations at off-axis elements I Polarization effects Solution: Numerical models with less approximations 3 Physical Optics Simulations with GRASP Different Methods for Quasi-Optical Simulations Coherent Field Analysis Incoherent Field Analysis Approximate Source Field Aperture Field Method Rayleigh Rayleigh Sommerfeld Sommerfeld 2 1 Projected Aperture Method Debye (Plane Waves) Boundary Wave Equivalence Theorem Analysis Gabor Modes Method of Moments Geometrical Optics (ray tracing) Modal Analysis Diffraction Integrals Kirchhoff Boundary Element Methods Finite Difference Techniques Physical Optics Gaussian Geometrical Physical Theory of Theory Modes Diffraction Diffraction Hermite Functions Laguerre Functions Stationary Phase 4 Physical Optics Simulations with GRASP Results of different simulation tools Comparison of GRASP with Gaussian Beam Modes (GBM) and other software packages. ESA study by O’Sullivan et al: ”Far-IR Optics Design and Verification”, International Journal of Infrared & Millimeter Waves, pp. 1029-1045, Vol. 23, No. 7, July 2002. 5 Physical Optics Simulations with GRASP General Reflector and Antenna Analysis Program GRASP State-of-the-art commercial software package from Ticra Ltd. I Reflector Surfaces: paraboloid, hyperboloid, ellipsoid, polynomial, tabulated ... I Reflector Materials: ideal conductor, finite conductivity, strip or wire grid, mesh, dielectric ... I Feed Types: Gaussian beam, Potter or corrugated horns, tabulated, spherical wave expansion... Analysis Methods: I 1. Geometrical Optics (GO) 2. Physical Optics (PO) 3. Physical Theory of Diffraction (PTD) 6 Physical Optics Simulations with GRASP Method 1: Geometrical Optics (GO) and Geometrical Theory of Diffraction (GTD) I GO (”Raytracing”) only for λ D I GTD: Diffraction at edges is taken into account. I Much faster than PO for large reflectors, but no accurate near-field results. 7 Physical Optics Simulations with GRASP Method 2: Physical Optics (PO) 1. The reflector is described by a number of surface elements. → − 2. An incoming electromagnetic wave with (mag. field H ) → − induces in every element a surface current J . For the calculation an infinite plane reflector with the same → normal vector − n as the surface element is assumed: → − → − → − J = 2n × H. 3. Integration over all surface elements allows to calculate the electrical and the magnetic vector potential A¯e , A¯m → at any point − r. 4. From Ae and Am the electric and magnetic fields in →− − → − → − → E→ r and H − r in r can be calculated, e.g. at the surface of the next reflector or in the far field. 8 Physical Optics Simulations with GRASP Surface integrals for PO 9 Physical Optics Simulations with GRASP Method 3: Physical Theory of Diffraction (PTD) PO does not describe edge diffraction accurately. PTD corrects for the currents on the reflector edges, which are calculated with the approximation infinite perfectly conducting half plane illuminated by a plane wave. 10 Physical Optics Simulations with GRASP PO Discretization Examples Optimum number and location of the PO points depends on the shape of the reflector. Circular reflector N = 152 Nθ = 19, Nr = 8 Triangular reflector N = 86 Nh = 10, Nb = 12 11 Physical Optics Simulations with GRASP Number of PO Points I Minimum number of PO points depends on λ, D, off-axis angle, accuracy. I Optimum determined by automated convergence tests. PO points depending on convergence level: = -20dB = -60dB + = -100dB 12 Physical Optics Simulations with GRASP GRASP Output Parameters y y R I G 1D cuts or 2D grids I planar or spherical I Near- or far-field I Two orthogonal polarizations (i.g. linear, circular) I Current distribution on the reflectors I Spillover losses at each component G R x R z G R R I=30º G x R z G (a) TI-polarisation (for 0ºdTd60º, 0ºdI<360º) y (b) TI-polarisation (for -60ºdTd60º, I=30º) cx e x co e z (c) Ludwig’s 3rd polarisation y y El e El e x x z Az e (d) El over Az polarisation (for -45ºdEld45º, -45ºdAzd45º) z Az e (e) Az over El polarisation (for -45ºdAzd45º, -45ºdEld45º) Polarization directions on a sphere 13 Physical Optics Simulations with GRASP Scattering at the feed support (struts) 1 1' 2' 2 1. Scattering of the field from the main reflector 2. Scattering of the field from the feed 14 Physical Optics Simulations with GRASP Example for strut scattering f = 30 GHz, D = 500mm, focal length F = 250mm 3 circular struts with 10mm diameter 15 Physical Optics Simulations with GRASP Application example for a shaped reflectors Contoured antenna beams of broadcasting satellites optimize the coverage for a continent. 16 Physical Optics Simulations with GRASP Example: IAP Fortgeschrittenen Praktikum Small Radio Telescope (SRT) I λ = 21 cm H2 line I Parabola D=2.3 m, F=0.87 m SRT On−Axis 30 0deg 90 deg Main Beam 20 Gain [dBi] 10 Diffraction Side Lobes 0 Spillover −10 −20 −30 −180 −135 −90 −45 0 Angle [deg] 45 90 135 180 17