Antenne e componenti passivi
per misure di fondo cosmico
ANTENNE A RIFLETTORE
Fabrizio Villa
INAF / IASF – Bologna
[email protected]
1
Angolo Solido del Beam
2
QUALCHE RIFLESSIONE
• Quali caratteristiche deve avere un’antenna
per fondo cosmico?
• Risoluzione angolare
• Misure di Spettro > 10 gradi
• Misure di Anisotropia e polarizzazione (lensing) - ordine dei
primi d’arco
• bump di polarizzazione modi B ~1 grado
• aberrazioni ottiche contenute
• Bassi lobi laterali -60dB
• Adatta per lavorare alle microonde (GHz – THz)
3
horn e riflettori
Come guadagnare in
risoluzione angolare?
4
horn e riflettori
416 PENCIL-BEAM
AND SIMPLE
FANNED-BEAM
ANTENNAS
~Sm,, 12.2
focus; the coordinates are R, O, +, with O the pola~ angle and I#Jthe
azimuth angle, the latter being measured from the zz-plane.
The reflector is cut off by the “aperture plane” A at z = Zo. The
diameter of the aperture will be designated by D, and iix area by A.
The “shape” of the reflector is specified by the ratio of focal length to
Come guadagnare in
risoluzione angolare?
z
1
1!
/
Y
.
A
v
I
I
I
.f+zo
I
A
FIG. 12. 1.—Geometrical
S.Silver, Microwave Antennas Theory and Design
parameters for the paralmlo idal reflector.
diameter, j/D, or alternatively by the angular aperture T, that is, the
angle subtended at the focus by a radius of the aperture. The relation
between the f/D ratio and the angular aperture is given by
Il modo più semplice è posizionare una sorgente puntiforme nel
fuoco di un sistema ottico (quali un riflettore od una lente) per
produrre un fascio di raggi paralleli
(4b)
5
Figura di diffrazione
6
7
PLANCK, WMAP, BOOMERANG, ECC.
8
UN’ANTENNA SEMPLICE: LA PARABOLA
9
IL RAPPORTO FOCALE
Tipici valori di F#: 0.4 – 1.4
 Angoli: 60 – 20 gradi
10
ILLUMINAZIONE DELLA PARABOLA
Parabola
Livelli di dB
0dB
Fuoco
11
FEED CON DIAGRAMMA UNIFORME
Parabola
Livelli di dB
0dB
Fuoco
12
ILLUMINAZIONE UNIFORME
Parabola
Livelli di dB
0dB
Fuoco
13
DIAGRAMMA DEL FEED “REALE”
Parabola
Livelli di dB
0dB
Fuoco
14
PERDITE PER ILLUMINAZIONE E SPILLOVER
Parabola
Livelli di dB
0dB
Fuoco
15
ANTENNE AD “APERTURA”
Pattern
Illuminazione
16
TIPI DI ILLUMINAZIONI
17
DIAGRAMMA DEL FEED “REALE”
Parabola
Livelli di dB
0dB
Pbordo
Fuoco
Pcentro
18
L’ EDGE TAPER (ET)
Potenza incidente al bordo del Riflettore
ET =
Potenza incidente al centro del Riflettore
ET
( dB )
P bordo
= 10 * Log 10
≤0
P centro
ET = 0
( dB )
ET < 0
( dB )
--> Illuminazione Uniforme
--> Illuminazione NON Uniforme
19
EDGE TAPER (E ALTRO) NEL CASO DI WMAP
20
EFFETTO DELL’ ILLUMINAZIONE
FWHM
(arcmin )
λ
180
= 60 *
[1.149 + 0.0135 * (−ET −10)] *
D
π
D=1500 mm ; f = 30GHz (100GHz)
ET
FWHM
0 dB
23’
–10 dB
26’
– 20 dB
29.4’
– 30 dB
32.5’ (9.8’)
21
EFFETTO DELL’ ILLUMINAZIONE
Caso Reale
Feed Horn at 100
GHz
ET 30 dB @ 22°
Feed Horn at 100
GHz
ET 15 dB @ 22°
Feed Horn at 100
GHz
ET 23 dB @ 22°
Feed Horn at 100
GHz
ET 10 dB @ 22°
22
EFFETTO DELL’ ILLUMINAZIONE
Caso Reale
23
MAIN BEAM E STRAY LIGHT
Main Beam
Sub Spillover
STRAYLIGHT
Potenza proveniente
dal cielo che viene
misurata nei
rivelatori, entro la
loro banda di
frequenza di lavoro, e
Main Spillover che non è originata
dal main beam del
telescopio
Main Spillover
24
COME SI CONTROLLA
L’ILLUMINAZIONE ?
• Scelta accurata del feed
• disegno dell’horn
• Scelta della configurazione dell’ottica
• F#, Doppio o singolo riflettore, ecc...
Il Feed non puo’ essere
disaccoppiato dal riflettore
Il telescopio e’ composto da
Feed + Riflettore
25
“GAUSSIAN BEAM PROPAGATION”
26
CONFIGURAZIONI OTTICHE

In – Asse
 Singolo Riflettore
 Doppio Riflettore

Fuori – Asse
 Singolo Riflettore
 Doppio Riflettore
27
OTTICHE A DOPPIO RIFLETTORE
Si
ottengono combinando riflettori ottenute
da coniche di rivoluzione
 Ellissoidi
 Iperboloidi
 Piani (caso degenere)

Lo scopo e’ di
 Deviare il cammino ottico e cambiare il rapporto
focale del riflettore principale (parabola)
28
ESEMPI DI CONFIGURAZIONI
Configurazione
Primario
Secondario
Gregoriano
Paraboloide
Ellissoide
Cassegrain
Paraboloide
Iperboloide
G. Aplanatico
Ellissoide
Ellissoide
C. Aplanatico
Iperboloide
Iperboloide
29
ANTENNE A RIFLETTORE
F/# basso, feed piccolo
F/# alto, feed grosso
Le configurazioni in asse sono SIMMETRICHE, anche nel
beam pattern, ma l’ostruzione alza i lobi laterali
30
ANTENNE A RIFLETTORE
F/# basso, feed piccolo
F/# alto, feed grosso
Le configurazioni fuori asse sono ASIMMETRICHE,
anche nel beam pattern (aberrazioni) , ma senza
ostruzione
31
PARABOLA FUORI ASSE
32
PARABOLA OFF–AXIS:
PARAMETRI
Illuminazione non
Simmetrica
33
FEED “FUORI ASSE”
34
EDGE TAPER DI PLANCK
35
EDGE TAPER PER PLANCK
Top of the reflector
36
RADIATION PATTERN
Main Beam
Response
Far Sidelobes
Near Sidelobes
Angle from boresight
37
— PG25
ET ⇒ 25.5 dB @ 24°
MS ⇒ -7 dBi
AR ⇒ 10.56 arcmin
— PG27
ET ⇒19 dB @ 24°
MS ⇒ -2 dBi
AR ⇒ 10 arcmin
— PG31
ET ⇒ 15 dB @ 24°
MS ⇒ 3 dBi
AR ⇒ 9.5 arcmin
38
ESEMPIO ANTENNA SINGOLO
RIFL.
39
ORIGIN OF THE FAR SIDE LOBES
40
External straylight (1/2)
Main
Spillover
(a)
MB
Sub
Spillover
(a)
Main
Spillover
(b)
Sub Spillover (b)
41
DISTORSIONI DEL BEAM
 Degrado
della risoluzione
angolare
 Statistica falsata
 Degrado della purezza in
polarizzazione
 Difficoltà nel combinare più
beam
42
Possiamo Simmetrizzare il beam si ottiche
fuori asse?
43
DRAGONE – MIZUGUCHI (DM)
l’asse di rivoluzione del riflettore secondario e’
inclinato rispetto a quello del riflettore
principale

α: angolo tra l’asse del feed e l’asse
del secondario
β: angolo tra l’asse del primario
e l’asse del secondario
e: eccentricita’ dell’ellissoide
M: ingrandimento del secondario
44
PARABOLA EQUIVALENTE 1/2
La
condizione DM ottimizza la X – pol e la
simmetria del beam relativo al feed posizionato nel
fuoco geometrico
Il telescopio a due riflettori e’ equivalente ad una
parabola in–asse ma senza oscuramento da parte
del feed
45
PARABOLA EQUIVALENTE 2/2
46
PRESTAZIONI OTTICHE DI DM
Configurazione ottica
COBRAS/SAMBA
47
PRESTAZIONI OTTICHE DI DM
Configurazione ottica
COBRAS/SAMBA
48
DIRETTIVITÀ, ANGOLO SOLIDO E FWHM
49
GREGORIANO APLANATICO
Correzione
delle costanti coniche del primario e
del secondario
 Annullare l’aberrazione sferica
 Annullare l’aberrazione di Coma
Beam
pattern piu’ simmetrici rispetto a DM
50
DM Vs APLANATICO
51
DM Vs APLANATICO
52
IL TELESCOPIO DI PLANCK
Primary Mirror:
ellipsoidal, ~ 1.9m x 1.5m
Secondary Mirror:
ellipsoidal, ~ 1m x 1m
Overall Focal Ratio:
F# = 1.1
Field of View:
± 5° x 5°
53
Il Telescopio
 Configurazione
 Gregoriano aplanatico
ottimizzato
 Frequenza
 25 – 1000 GHz
 Temperatura
 40 K and 65 K
 Massa
totale
 < 120 Kg
 Lifetime
 6 years on the ground + 2
years in space
54
54
CODE V package and GRASP8
software (partially ASAP)
 symmetric FPU
 8 HFI Feeds

 (1, 1, 2, 4)

8 LFI Feeds
 (2, 2, 1, 1, 1, 1)

Minimisation of the WFE at the
aperture with gaussian illumination
OUTPUT
“Case1” Design
55
Timeline
(1992) COBRAS
 (1996) Phase A Telescope

 1.3 meter aperture
 Dragone – Mizuguchi (minimizzazione della
polarizzazione al centro del piano focale)

(1998) Carrier Telescope
 Phase A telescope + Extension of the primary
mirror
 1.5 meter aperture

(1999) Architect Study
 Ottimizzazione del Telescopio
56
 Core
 Celle esagonali di fibra di carbonio
 Reflecting
coating
 Adesivo: 5nm di NiCr
 Riflettivo: 550nm di Al
 Protettivo: 30nm PLASIL (silicone)
57
Qualification Model
58
Dove siamo con Planck?
c ESO 2011
!
Astronomy
&
Astrophysics
Planck early results
Special feature
A&A 536, A3 (2011)
DOI: 10.1051/0004-6361/201116480
Planck early results. III. First assessment of the Low Frequency
Instrument in-flight performance!
Bersanelli22,39 ,
Butler38 ,
Curto47 ,
Cuttaia38 ,
Davis50 ,
Dick57 ,
Frailis37 ,
A. Mennella et al.: Planck early results. III.
Fig. 12. Examples (one per frequency channel) of the LFI measured be
computed in the co- and cross-polar basis according to Ludwig’s third de
with respect to the LOS frame. They are referred to the design telescope c
−20 dB from the corresponding power peak. The simulations have been
optics and physical theory of diffraction have been used on both reflector
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22,39
38
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, N. Mandolesi , M. Maris , E. Martínez-González47 , P. R. Meinhold19 , G. Morgante38 , D. Pearson49 ,
F. Perrotta57 , G. Polenta2,36 , T. Poutanen32,16,1 , M. Sandri38 , M. D. Seiffert49,7 , A.-S. Suur-Uski16,32 , D. Tavagnacco37 ,
L. Terenzi38 , M. Tomasi22,39 , J. Valiviita45 , F. Villa38 , R. Watson50 , A. Wilkinson50 , A. Zacchei37 , A. Zonca19 , B. Aja12 ,
E. Artal12 , C. Baccigalupi57 , A. J. Banday62,6,53 , R. B. Barreiro47 , J. G. Bartlett4,49 , N. Bartolo20 , P. Battaglia61 ,
K. Bennett30 , A. Bonaldi35 , L. Bonavera57,5 , J. Borrill52,59 , F. R. Bouchet43 , C. Burigana38 , P. Cabella25 ,
B. Cappellini39 , X. Chen41 , L. Colombo15,49 , M. Cruz13 , L. Danese57 , O. D’Arcangelo48 , R. D. Davies50 ,
G. de Gasperis25 , A. de Rosa38 , G. de Zotti35,57 , C. Dickinson50 , J. M. Diego47 , S. Donzelli39,45 , G. Efstathiou44 ,
T. A. Enßlin53 , H. K. Eriksen45 , M. C. Falvella3 , F. Finelli38 , S. Foley29 , C. Franceschet22 , E. Franceschi38 ,
T. C. Gaier49 , R. T. Génova-Santos46,27 , D. George58 , F. Gómez46 , J. González-Nuevo57 , K. M. Górski49,63 ,
A. Gruppuso38 , F. K. Hansen45 , D. Herranz47 , J. M. Herreros46 , R. J. Hoyland46 , N. Hughes9 , J. Jewell49 , P. Jukkala9 ,
94
96
98
100
A. Mennella et al.: Planck early results. III.
M. Juvela16 , P. Kangaslahti49 , E. Keihänen16 , R. Keskitalo49,16 , V.-H. Kilpia9 , T. S. Kisner52 , J. Knoche53 , L. Knox18 ,
M. Laaninen56 , A. Lähteenmäki1,32 , J.-M. Lamarre51 , R. Leonardi28,30,19 , J. León-Tavares1 , P. Leutenegger61 ,
35 , S. Matarrese20 ,
P. B. Lilje45,8 , M. López-Caniego47 , P. M. Lubin19 , M. Malaspina38 , D. Marinucci26 , M. Massardi
Fig. 12.
Examples (one per frequency channel) of the LFI measured beams compared with simulations. The simulate
53
21
28
61
25
49
14
, P. Natoli
, cross-polar basis according to Ludwig’s third definition (Ludwig 1973), in spherical grids with
F. Matthai , A. Melchiorri , L. Mendes , M. Miccolis , M. Migliaccio , S. Mitra , A. Moss
computed
in the24,2,38
co- and
33
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49
60,7
38
31
37
with
respect
to
the
LOS
frame. They are referred to the design telescope configuration. In each plot the contours are the le
R. Nesti , H. U. Nørgaard-Nielsen , L. Pagano , R. Paladini , D. Paoletti , B. Partridge , F. Pasian ,
57
49
55
7,49
49
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42
dB from
V. Pettorino , D. Pietrobon , M. Pospieszalski , G. Prézeau , M. Prina , P. Procopio −20
, J.-L.
Pugetthe, corresponding power peak. The simulations have been carried out in the transmitting mode using GR
optics
and
physical
25
53
46,27
53
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53
49,7 , theory of diffraction have been used on both reflectors.
, M. Reinecke , S. Ricciardi , G. Robbers , G. Rocha
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50
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94
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the
dipole
and
the
dipole
signal
was weak
G. Umana34 , L. Valenziano38 , J. Varis54 , P. Vielva47 , N. Vittorio25 , L. A. Wade49 , C. Watson29 ,
are ∼4% rms and ∼67% peak-to-peak. T
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Sky [V]
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A. Mennella et al.: Pl
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single pointing period, rather than actual
We can put a limit on the true intrin
Received 9 January 2011 / Accepted 9 May 2011
looking at the variation of the total pow
Sect. 5.1). The small variations in total po
94
96
98
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ABSTRACT
gain96
variations to98
be less than100
1%.
Days
aftersolution
launch based on individua
The gain
The scientific performance of the Planck Low Frequency Instrument (LFI) after one year of in-orbit operation is presented. We describe the main
optical parameters and discuss photometric calibration, white Fig.
noise12.
sensitivity,
and noise
A preliminary
evaluation
of themeasured
impact of the
Examples
(one properties.
per frequency
channel)
of the LFI
beams compared with simulations. The simulated main
beams have beento improve its stability
therefore
Fig. 13. Sky (top), reference
(middle)processed
and difference (bottom) signals
main systematic effects is presented. For each of the performance
parameters,
wecooutline
methods used
to obtain
them from
the flight third
data and
computed
in the
andthe
cross-polar
basis
according
to Ludwig’s
definition (Ludwig 1973), in spherical grids with 301running
× 301 points
defined
59sm
averages
thattohave
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effect
(Affiliations can be found after the references)
Il Futuro: La polarizzazione
• Ottiche “perfette”
• “Tantissimi” rivelatori
• Ingombri e pesi limitati
60
SVILUPPO DI DISEGNI DI OTTICHE
P. Bolli et al 2009 - INAF-IRA IR
#428/2009 (Pre-phase-A study for
the B-POL program
Configurazioni simili a Planck
61
IL FUTURO … INCERTO
 Grandi
Piani focali (~ 10000 rivelatori
 Multi frequenza
 Ottima cross polarizzazione
62
ESEMPIO DI FUTURA MISSIONE (EPIC)
Jamie Bock presentation
63
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64
Comparison of the crossed and the Gregorian
Mizuguchi–Dragone for wide-field millimeter-wave
astronomy
Huan Tran,1,* Adrian Lee,2 Shaul Hanany,3 Michael Milligan,3 and Tom Renbarger4
Space Sciences Laboratory, University of California, Berkeley, California 94720, USA
2
Department of Physics, University of California,
Berkeley,
Q"U
Imaging California
Experiment94720,
[10] useUSA
the crossed con3
figuration.
Here
we
compare
the
relative
School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455,merits
USAof
and crossed
Mizuguchi–Dragone.
4Department of Physics, University of California,the
SanGregorian
Diego, California
92093,
USA
1
Crossed configurations tend to have secondary reflectors similar in size to the primaries. The study is
*Corresponding author: [email protected]
therefore limited to a 1.65 m aperture, as a larger
crossed configuration is mechanically complicated
Received 13 August 2007; accepted
8 September
2007;
due
to the large secondary.
The study is divided into
a
geometric
and
physical-optics
analysis. The geoposted 16 November 2007 (Doc. ID 85684); published 4 January 2008
metric analysis shows that the crossed configuration
has a larger DLFOV than the Gregorian, although
Fig. 2. Strehl ratios across the focal plane, calculated at 150 GHz.
the Gregorian has a large enough DLFOV for most
Crossed shows a clear advantage in terms of DLFOV. A design is
practical applications. The physical-optics analysis
considered diffraction-limited if the Strehl ratio is above 0.8.
show
that both configurations
have adequate
We compare the geometric and physical-optics performancewill
of two
configurations
of offset dual-reflector
cross and instrumental polarization.
antennas that obey the Mizuguchi–Dragone condition. The traditional
Gregorian configuration is comondary with the clearance between the main beam A complete optical system could also include relay
pared with theand
larger
crossedInconfiguration.
These the
configurations
are candidates
experiments
that
optics, depending
on the for
exact
requirements
of the
the receiver.
the Gregorian design,
items
focalParticular
plane technology.
Relay
systems
many posin competition
separation
of the receiver
and
measure the polarization
of are
thethe
cosmic
microwave
background.
attention
is given
to have
wide-field
primary,
the size fidelity.
of the secondary,
andtracer
the obliquedesigns,
andsimulation
hence will not
be included
in this
performance and
polarization
Both a ray
and sible
a physical
optics
package
are used
ness of the primary. The differences between the two
analysis.
to conclude that
the crossedare
configuration
has ina Section
larger 5.
diffraction-limited field of view, but within this
configurations
further explained
The aberrations
both configurations
evallimit both configurations
haveforroughly
the same were
instrumental
polarization
2. Geometric
Optics and both show excellent
uated
by
calculating
the
Strehl
ratios
with
the
ray
cross-polarization levels, with the crossed configuration showing
dB better performance.
© 2008have
The two!10
configurations
chosen for comparison
tracing software. Figure 2 is a plot of the Strehl ratios
the same aperture size and EFL. Since both obey the
Optical Societyasofa America
function of field position. The crossed configuraMizuguchi–Dragone
OCIS codes:tion110.3000,
220.1250,
220.4830,
260.5430. condition, they are also reprehas nearly110.6770,
a factor of 2220.1000,
larger focal
plane diam-
1. Introduction
sented by the same equivalent paraboloid. It is thus
eter. The crossed configuration also has a nearly
expected that the geometric and electrical perfortelecentric focal plane, meaning that chief rays from
mance of both configurations should be similar to a
all field positions arrive nearly parallel at the focal
centered parabola near the central feed. It has been
plane. This makes the use of bare planar arrays of
shown, however, that the performance quickly discalar feedhorns at the telescope focus possible, eliminating the need for relay optics. Nearly all the Greverges from the equivalent parabola as the feed is
gorian systems, on the other hand, require a curved
to the edge
of the field signals
[3]. Serabyn
[11] has
for scanned
the window.
Spurious
from
ground
focal plane or relay optics.
furthermore suggested that conics arranged in the
contamination
seen from
farsmaller
sidelobes
are due
also a major
Increasing demands on sensitivity
have driven the
cross configuration
can have
abberations
3. Physical Optics
concern.
Unobstructed
primary
to cancellation
between the
mirrors. apertures are benefineed for large-format, millimeter-wave
Thepackage
The GRASP9 [14] physicalarrays.
optics software
was To compare the Gregorian and the crossed configcial
used toarrays
evaluate three
copolar
pro-in reducing scattering and diffraction from obcurrent generation of detector
havequantities:
an order
of beam
urations at field positions far from the center, it is
cross-polar profiles, and instrumental polarizastructions
Furthermore,
the expected
1000 elements, about anfiles,
order
of
magnitude
larger
necessaryand
to usesupports.
a more robust
tool than the equivation. To study the effects of the telescope mirrors
lentofparabola.
Here we use
ray CMB
tracing software,
the intensity
ofthethe
to the polarized
than the previous generation.
being
only, anThese
idealizedarrays
feedhorn are
was used,
with zeroratio
cross
Fig. 3. Copolarized beams for both the (a) crossed and (b) GregoZEMAX
[12],
to
compare
the
geometric
performance
of
polarization
and a Gaussian taper
of !12 dB
at the
Diagrams
of two Mizuguchi–Dragone
configurations.
For
rian. Strehl ratio
contours
calculated
independently
ray tracing
gravitational
wave
CMB
signal
is by!90
dB,
placing
actively developedFig.
for1.use
in Sunyaev–Zeldovich
clusedge
primary.
each, the chief
rayof
is the
shown
as the thick black line. The "2° off-axis
the systems.
While
have
advantage
of
for different
points ray
in thetracers
focal plane
are the
superimposed
for com-
65
X-polarizzazione
Fig. 4. Cross polarization across the focal planes. The top two panels are the cross-polarized beams produced by GRASP9. Each feedhorn
was rotated about the boresight to null the cross polarization on the middle of the beam, resulting in a characteristic double-lobe pattern.
The gray scale is in decibels relative to the peak of the copolarization beam. Note that the two color scales are different. The Strehl ratios
66
DOVE CI PORTA IL FUTURO?
67
4pi simulation method: GRASP9 MrGTD
MrGTD computes the scattered field from the reflectors performing a backward ray tracing. The main
difficulty was to understand the contributions that had to be considered, or in other words, to identify the
sequence of diffractions and/or reflections on each scatterer which produce a significant power level in the
resulting radiation pattern.
68
MrGTD: direct and Rs contributions
Left panel: 4pi map of the field due to the rays coming from the feed (direct contribution), together with the field
due to the rays reflected on the subreflector and not intercepted by the main reflector (Rs contribution). Most of
the map is empty (grey colour) since most of the rays are blocked by the baffle. The power peak of the direct
contribution is about -11.64 dBi whereas the power peak of the Rs contribution is about -3.16 dBi. This latter is
the brightest contribution in the far sidelobes.
Right panel: sketch of the optics in the symmetry plane, together with the ray-tracing of these two contributions in
the plane at φbf = 22° (these rays lie in the white dashed cut indicated in the map, where the field is present).
69
MrGTD: Rb contribution
Left panel: 4pi map of the field due to the rays coming from the feed that are reflected by the baffle (Rb
contribution) is shown. The power peak is about -7.58 dBi.
Right panel: sketch of the optics in the symmetry plane is shown together with the ray-tracing of this contribution
in the plane at φbf = 22° (these rays lie in the white dashed cut indicated in the map, where the field is present).
70
MrGTD: RsDm contribution
Left panel: 4pi map of the field due to the rays that are reflected onto the sub reflector and diffracted by the main
reflector (RsDm contribution) is shown. The power peak is about -19.48 dBi, in the main beam direction.
Right panel: sketch of the optics in the symmetry plane is shown together with the ray-tracing of this contribution
in the plane at φbf = 22° (these rays lie in the white dashed cut indicated in the map, where the field is present).
71
MrGTD: total field
72
Far beam at 30 GHz
Co− and cross− polar components of the 4pi beam at 30 GHz (feed horn #27 Y polarised)
The maximum level of the main spillover is about −4.6 dBi at φ ~ 17° and θ ~ 85° for the co−
polar component, and it is about −8.0 dBi at φ ~ 18° and θ ~ 86° for the cross− polar
component.
GSC ⇒ 7.2 microK (peak-to-peak) and 1.3 microK (rms)
73
Far beam at 44 GHz
Co− and cross− polar components of the 4pi beam at 44 GHz (feed horn #24 Y polarised)
The maximum level of the main spillover is about −5.4 dBi at φ ~ 0° and θ ~ 85° for the co−
polar component, and the cross− polar component is down to −15 dBi everywhere.
GSC ⇒ 3.1 microK (peak-to-peak) and 0.31 microK (rms)
74
Far beam at 70 GHz
Co− and cross− polar components of the 4pi beam at 70 GHz (feed horn #23 Y polarised)
The maximum level of the main spillover is about −7.0 dBi at φ ~ 10° and θ ~ 85° for the co−
polar component, and the cross− polar component is, in the main spillover region, at about
−11 dBi.
GSC ⇒ 2.8 microK (peak-to-peak) and 0.29 microK (rms)
75
76
BEAMS AND POLARIZATION
Each MB has been computed in its own coordinate system defined w.r.t the LOS, in which:
 the power peak of the co- polar component lies in the center of the UV- grid
 a minimum in the cross- polar component appears in the same point (i.e. the major axis of the polarization ellipse is along the U- axis)
 the main beam polarization directions of the t wo symmetrically located feed horns in the focal plane unit are at 45° in angle when they
observe the same direction in the sky
Scan Direction
45°
77
Main beam #23
Main beam #23 X- polarized
computed with the QM telescope (copolar component is on the left side
and cross- polar component is on the
right side).
Main beam #23 Y- polarized
computed with the QM telescope (copolar component is on the left side
and cross- polar component is on the
right side).
78
Polarization Angle
Polarization Angle of LFI21
Polarization Angle of LFI24
Very close to the beam pointing direction, the main beam can be assumed linearly polarized and the X- axis of
the beam frame can be assumed as the main beam polarization direction.
79
Gaussian Vs Dual Profiled
Directivity ⇒ 53.79 dBi
Directivity ⇒ 54.09 dBi
% DEP ⇒ 0.23
% DEP ⇒ 0.29
FWHM ⇒ 23.77 arcmin
FWHM ⇒ 23.09 arcmin
e ⇒ 1.39
e ⇒ 1.41
Spill-over ⇒ 0.05%
Spill-over ⇒ 0.16%
80
Bandwidth effects
Because of
–
different response of feed horns with frequency
–
different telescope diameter with frequency (normalized to wavelength)
the main beam shape is expected to be frequency dependent within the bandwidth of each detector
(20% for LFI).
Directivity ⇒ 54.10 dBi
% DEP ⇒ 0.35
FWHM ⇒ 22.95 arcmin
e ⇒ 1.30
Spill-over ⇒ 0.68%
Directivity ⇒ 54.09 dBi
% DEP ⇒ 0.29
FWHM ⇒ 23.09 arcmin
e ⇒ 1.38
Spill-over ⇒ 0.16%
Directivity ⇒ 53.82 dBi
% DEP ⇒ 0.51
FWHM ⇒ 24.16 arcmin
e ⇒ 1.52
Spill-over ⇒ 0.17%
81
30 GHz channel
27 GHz
33 GHz
AVERAGE
82
30 GHz channel
blue rays
pink rays
Main reflector
Sub reflector
83
30 GHz channel
84
OTTICA GEOMETRICA (GO)

Legge di Snell
 Angolo di incidenza = angolo di riflessione

Principio di Fermat
 Se un raggio propaga tra due punti A e B, attraverso C su un
riflettore, la lunghezza di cammino ABC e’ stazionaria rispetto
allo spostamento di C
85
TEORIA GEOMETRICA DELLA DIFFRAZIONE (GTD)

Estensione della GO (Keller, 1962)
 Calcolo della diffrazione dovuta ai bordi dei riflettori
I raggi diffratti sono linearmente dipendenti
dall’onda incidente.
La dipendenza e’ espressa mediante una
matrice di COEFFICIENTI DI DIFFRAZIONE
86
OTTICA FISICA (PO)
Il campo elettromagnetico
incidente induce delle correnti sul
riflettore che a sua volta re –
irradia un campo
elettromagnetico.

Il
singolo elemento del riflettore e’
approssimato da una superficie
piana e si considera l’onda
incidente come localmente piana
87
PO IN DETTAGLIO
  
J= n × H tot =



= n × H inc + H rifl =


Approssimazione
= 2 n × H rifl =
Dell’Ottica Fisica


= 2 n × H inc
(
)
88
TEORIA FISICA DELLA DIFFRAZIONE (PTD)
Estensione della PO

Calcolo della diffrazione dovuta ai bordi dei
riflettori
Integrazione delle correnti equivalenti degli spigoli
… formulazione complicata …
89
G
O
PO
/G
/P
TD
TD
+
PO
METODI DI SIMULAZIONE
Up => -0.00002 Vp => 0.00001
Up => -0.00002 Vp => 0.00002
COMP1 MAX => 32.99 dBi
COMP1 MAX => 33.01 dBi
COMP2 MAX => 60.68 dBi
COMP2 MAX => 60.69 dBi
% DEP => 0.44
% DEP => 0.44
FWHM X => 9.33 arcmin
FWHM X => 9.31 arcmin
FWHM Y => 11.80 arcmin
FWHM Y => 11.81 arcmin
FWHM AVE => 10.56 arcmin
FWHM AVE => 10.56 arcmin
e => 1.27
e => 1.27
90