standing waves in almabbutler/work/alma/calibration/hifi/abacmann.pdf · alma workshop - leiden,...
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ALMA workshop - Leiden, December 18-20th
ALMA Bandpass Calibration: Standing Waves
Aurore Bacmann (ESO)
Stéphane Guilloteau (IRAM)
Standing Waves: background
• Reflection of incident wave on feedsystem of standing waves between receiver and sub-reflector
• On single-dish telescopes: standing waves between receiver and calibration load
ALMA antenna
ALMA workshop - Leiden, December 18-20th
Frequency of standing waves
Dcn
n ⋅⋅=
2υ
Dc
ripple 2=υ
Where D is the distance between the feed and the secondary
Consequence: ripple of frequency
Example: spectrum at the IRAM 30m
D = 5 m υ = 30 MHz
ALMA workshop - Leiden, December 18-20th
Reducing standing waves
• Baseline ripple substantially degrades spectral observations– During observations: reflection receiver-secondary mirror
“high frequency ripple”– During calibration scans: reflection receiver - calibration
loadalso end up in observed spectrum
• reducing the amplitude of the ripple reducing the reflection coefficient– No control of the reflection on the feed– Need to reduce the reflection coefficient on the sub-
reflector
ALMA workshop - Leiden, December 18-20th
Reflection coefficient
∫ ⋅ΨΨ=subref
dS**)(γ
))(exp()( θθ jkrF −⋅=ΨF: gaussian illumination function
∫ −⋅=s
djkrFθ
θθθθπγ0
2 ))(2exp()sin()(2
ALMA workshop - Leiden, December 18-20th
Asymptotical expression
( )[( ) ]))(2exp(1)cos()(
))(2exp(1)cos()()1(2
2
22
02
002
sss jkreF
jkreFejkLe
θθθ
θθθπγ
−−−
−−×−
=
e: eccentricityL: distance to mirror vertex
Due to gaussian tapering, the second term can be neglected
λγ ∝⇒Standing waves are most disturbing at long wavelengths
If both terms are considered: γ will oscillate with λ around an increasing mean value
ALMA workshop - Leiden, December 18-20th
Representation of reflection coefficient in the complex plane
ALMA workshop - Leiden, December 18-20th
Considered Sub-reflector Geometries
Study of the effect of various sub-reflector geometries on the reflection coefficient
• Effect of an absorber on the blocage zone• Effect of a discontinuity (aperture in sub-
reflector)• Effect of a scattering cone
Mirror alone
Mirror with absorbing diskbetween 0 and θb
Mirror with tangent cone of semi-angle α
ALMA workshop - Leiden, December 18-20th
Sub-reflector with aperture Sub-reflector with aperture, cone within aperture
ALMA workshop - Leiden, December 18-20th
Possible design for sub-reflector
45° mirrordeflecting light towards - load (calibration measurements)- cone (observations)
Calibration: coupling of load to receiver ~ 1%
Avoids saturation of receiver
Aperture in sub-reflector
ALMA workshop - Leiden, December 18-20th
Simple sub-reflector
ALMA workshop - Leiden, December 18-20th
Tangent cone on Sub-reflector
α < 87°
3 mm
But if α is small, the cone covers much of the sub-reflector
ALMA workshop - Leiden, December 18-20th
Sub-reflector with discontinuityat 3 mm
γ ~ 0.009 with discontinuityγ ~ 0.0045 with absorbing disk
ALMA workshop - Leiden, December 18-20th
Aperture with coneat 3 mm
At angles < 85°, γ ~ same value as without aperture (0.005)
ALMA workshop - Leiden, December 18-20th
Standing Wave Ratio
• Incident amplitudeon the feed:
)2exp(1 ψjrrtab
ms
s
−−⋅
=
msrrbb ⋅+≈ 21
min
maxIn amplitude:
msrrPP ⋅+≈ 41
min
maxIn power:
ALMA workshop - Leiden, December 18-20th
Values for ALMApeak-to-peak ripple at 3mm
For rm ~ 0.4
0.8%Aperture with cone
1.3%Aperture without cone
0.08%Tangent cone
0.7%Absorbing disk
ALMA workshop - Leiden, December 18-20th
Summary
• At 3 mm, baseline ripple can reach ~1%
• Aperture in sub-reflector increases ripple by a factor of 2
• Can be reduced with cone within aperture
• Tangent cone is the best solution but choice of α = compromise