Download Physical Optics Simulations with GRASP

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