0:Title
Horn on Dish method
∼A part of master thesis(Kagoshima univ.)∼
The Graduate University for Advanced Studies
SOKENDAI
Department of Astronomical Science
Doctor course first grade
Masachika Kijima
•
•
•
•
•
version
2006/02/16 master thesis presentationin Kagoshima univ.
2006/04/18 VERAscienceWG
2006/04/29 Kawaguchi seminnar
2006/06/07 VLBIseminar (new model)
2006/09/08 SOKENDAI colloquium
0:contens
contens
•
Introduction “radio astronomy”
– Single Dish observation and Interferometry
– 1beam Interferometry and Phase Referencing
•
Introduction “horn on dish method”
–
–
–
–
•
Role of “horn on dish method”
Phase of “horn on dish method” ~RPLD and contribution of deformation etc~
Redisual of “horn on dish method” calibration
Purpose of this research
Compare PCDmeasurement with Simulation~result-A~
– Simulation ~response function and deformation measurement~
– PCD
~measurement and analysis~
– Compare PCD with simulation (and deformation measurement)
subtitle
Introduction “radio astronomy”
1-1:Radio astronomy
SignleDish observation and Interferometery
•
Single Dish
– You gatta a Power and/or Spectroscopy and/or Mapping.
– The Physical limitation of angular resolution, θb ~ λ/D
VERA, water maser(2005)
NRO, CO(1-0),Yonezawa et.al (1998)
IRAS10248-1158
[Jy]
90
70
50
30
10
-10
0
50
100
[km/s]
•
Interferometer
– You gatta a Power, Spectroscopy, Mapping and high anguler resolution.
VERA,water maser, honma et.al (2005)
1-2:Interferometry
Interferometry~It’s a D○nald masic!!~
•
Overview
I(l,m):Intentity
2-dimensional
FT
V(u,v):Visibility
C(τ):cross correlation
function
FT
•
equality
S(ν):cross power spectrum
Visibility
φobs =φg +φatm +φinst
1-3:VREAproject
VERA project ∼VLBI Exploration of Radio Astrometry ∼
•
•
•
•
VERA measure the distances using trigonometric parallaxes with high
angular accuracy 10 micro arcsec.(10%error@10kpc)
High accuracy is carried out by 2beam Phase Referencing.
Targets are 1000 water and SiO maser sources in our galaxy
Distances,proper motions reveal galactic rotation curve,distribution of
dark matter, 3-D kinetic ,etcetc
＃Ａ
＃Ｂ
1-4:Phase Referencing
Phase Referencing
•
1beam interferometry
– Solve φg using intensity(unknown position),so Lost the absolute position.
φobs =φg + (φatm1 −φatm 2 ) + (φinst1 −φinst 2 )
•
Phase Referencing
– Observe two sources(target and QSO),
obtain relative position
– Observed two source(A,B),1th and2nd station baseline
A
B
A
B
φobs
−φobs
=φgA −φBg + (φatm
−
φ
1
atm1 )
Relative position
A
B
A
B
A
B
− (φatm
−
φ
)
+
(
φ
−
φ
)
−
(
φ
−
φ
2
atm 2
inst 1
inst 1
inst 2
inst 2 )
subtitle
Introduction “horn on dish method”
2:Phase Referencing
Phase Referencing
•
Baseline between station 1 and station 2
A
B
A
B
A
B
φobs
−φobs
=φgA −φBg + (φatm
−
φ
)
−
(
φ
−
φ
1
atm1
atm 2
atm 2 )
Relative
position
Atomoshere’s Excess path delay. VERA’s purpose of
calibration is less than 0.05 mm
A
B
A
B
+ (φinst
−
φ
)
−
(
φ
−
φ
1
inst1
inst 2
inst 2 )
Instrumental phase difference.VERA’s purpose of
calibration is 0.05 mm
D×Δθ≒ｃΔτ
D=2300[km](Mizusawa-Ishigakijima baseline)
Δθ=10[μarcsec]
ｃΔτ <0.1[mm]
3:instrumental delay
~What is φinst~
(optical path difference between A and B-beam)
A
B
A
B
A
B
(φinst
−
φ
)
=
(
φ
−
φ
)
+
(
φ
−
φ
inst1
ant
ant
rx
rx )
1
=φant +φrx ≡ ΦS
•
•
•
•
•
Φant：antenna modification between 2beam
(main dish,sub-reflector,2beam jack etcetc)
Φrx：electrical path variation of receiving sysytem
between 2beam
(cable modification,local oscillater etcetc)
1beam antenna system, calibrate excess path delay between Source
A and B by observing continuum source periodically.
Unfortunately,2beam antenna cannot observe one source at the
same time.
Antenna deformation model forecast($5) or Measurement($6)
4-1:horn on dish method :nice figure
Abstract of Horn on dish method
2beam excess path difference
Add source
signal
Φsource =φant +φrx
Add noise
source’s signal
ΦNS =φ'ant +φrx +φref
+φant
It has a little difference
Because φant is combine all wave
+φ’anｔ
+φref
noise source
+φRX
same
4-2:φns
~What is φns~
φiNS =φiant ' +φRX +φiref
•
•
•
•
Φant’：path length difference between 2beam from
NS to Receiver due to antenna modification
(main dish,sub-reflector,2beam jack etcetc)
Φrx：electrical path variation between 2beam of
receiving sysytem
(cable,local oscillater etcetc)
Φref ：Reference path length difference(RPLD)
i:NS number(i=1-4) in VERA.(NS1,NS2,etc)
4
i
φ
∑ NS =φant ' +φRX ≡φPCD
i =1
4-3:φant’
~What is φant’~
-180
ΔXha(Source)
-90
[mm]
φant’
-180
0.25
0.2
0.15
0.1
0.05
0
-0.05 0
-0.1
-0.15
-0.2
-0.25
FR[deg]
•
90
180
Simulation:
Many Noise Sources which is
symmetry with mirror axis, averaged
φant’ approach φant.
The residual φant and averagedφant’
ΔXha(NS)
-90
0.25
0.2
0.15
0.1
0.05
0
-0.05 0
-0.1
-0.15
-0.2
-0.25
FR[deg]
ΔXha(Source-NSaverage)
90
180
NS1
NS2
NS3
NS4
[mm]
[mm]
φant
-180
-90
0.008
0.006
0.004
0.002
0
-0.002 0
-0.004
-0.006
-0.008
FR[deg]
90
180
4-4:RPLD nice figure
~What is φref：Reference Path Length Difference~
•
ABC#A = A’B’C’#A
•
BC’#B + ΔL = BC#A
AB +ΔL =A’B’
BC#A = B’C’#A + ΔL
C
C’ C
C’
A’
A
B’
B
#B
#A
B(=B’)
(Noise source) #B
#A
4-5:RPLD
~What is φref：Reference Path Length Difference~
Averaged RPLD(φref) approach zero.
RPLD(model)
150
100
•
•
•
[mm]
50
0
-180
-90
0
-50
Simulation
90
180
NS3
NS4
0
-180
-90
90
-150
FR[deg]
-150
FR[deg]
NSes isn’t symmetry with mirror axis
0.10
0.05
0.05
0.00
-0.05
average
90
180
+ antenna modification at EL=90[deg]
0.15
0.10
0
180
NS1
NS2
NS3
NS4
RPLDaverage(measure)
[mm]
[mm]
0
-100
0.15
-90
-50
-100
RPLDaverage(model)
-180
Measurement at EL=90[deg]
RPLD(measure)
RPLD is a bias with FR dependency
150
RPLD can be estimated
100
鏡軸対称に設置したNoiseSourceのφNSを平均す
NS1
50
れば相殺される。
NS2
[mm]
•
0.00
-180
-90
-0.05
average
0
-0.10
-0.10
-0.15
FR[deg]
-0.15
FR[deg]
90
180
4-6equipment
VERA equipment
NoiseSource
(NS)
Antenna system
#A
#A
#B
Phase Cal Detector (PCD)
#B
Phase Cal Detector (PCD)
correlator
A
B
A
B
A
B
φobs
−φobs
=φgA −φBg + (φatm
−
φ
)
−
(
φ
−
φ
1
atm1
atm 2
atm 2 )
A
B
A
B
+ (φinst
−
φ
−
φ
)
−
(
φ
−
φ
1
inst 1
PCD1
inst 2
inst 2 −φPCD 2 )
Residual calibration <0.05[mm]
4-7:calibration and residual
Residual of Calibration
The purpose Limit of calibration residual is less than 0.05[mm]
• Calibration by “horn on dish method” only
A
B
A
B
(φinst
−
φ
−
Φ
)
−
(
φ
−
φ
1
inst 1
PCD1
inst 2
inst 2 −ΦPCD 2 )
= (φant1 −φ'ant1 ) − (φant 2 −φ'ant 2 )
:The residual
The problem is only contribution of antenna modification
(modification of main dish, sub reflector and 2beam jack)
• Calibration by “horn on dish method” and Modification forecast
(φant1 −φ'ant1 ) − (φant1 ( x) −φ'ant1 ( x)) = (φant1 (∆x) −φ'ant1 (∆x))
Calibration by NS
Modification forecast
− (φant 2 (∆x) −φ'ant 2 (∆x))
The residual: (φant1 (∆x) −φ'ant1 (∆x)) subtitle
•
Compare
PCDmeasurement with Simulation
~result-A~
Compare PCDmeasurement with Simulation (result-A)
– Accuracy of PCDmeasurement at ELdepend
– EL=5,30,60,90[deg]
deformation
•
•
We can estimate by simulation and
deformation measurement.
(mitsubishi.co)
We can measure by PCD.
(VERA team)
Masurement
byＰＣＤ
Response function φ’ant(a)
Simularion results
PCD results
compare（result-A）
5-1-1:definition of modification and FR angle
Definition of modification and FR angle
1:Definition of modification
Ｘ
Ｚ：mirror axis
Sub-reflector
1. ΔＸs
Ｙ：EL axis
2. ΔZs
2beam jack
3. Δθys
1. ΔＸha
2. ΔYha
3. ΔZha
2:Definition of FR(field rotator) angle
5. ΔYhb
Ｘ
#A
θFR
Y
Z
#B
4. ΔＸhb
6. ΔZhb
Ｚ：mirror axis
Quantity of modification
(Mitsubishi.co.)
1.00
0.01
[mm]
3.00
0.00
0.00
-0.01
-1.00
-0.01
-2.00
-0.02
-0.02
-3.00
-4.00
0
20
40
60
EL[deg]
•
80
-0.03
100
Ｙ：EL axis
ジャッキ変位(EL=0[deg])
2
1
ΔXha
ΔXhb
ΔYha
ΔYhb
ΔZha
ΔZhb
0
[mm]
2.00
ΔZs
ΔXs
Δθys 0.02
0.01
[deg]
副鏡変位
5-1-2:Quantity Ｘ
of modification
-1
-2
-3
-4
-5
-200
-100
0
FR[deg]
2beam jack’s modification depend on FR angle
100
200
5-2-1:response function NS1
Response function at NS1 (mitsubishi.co.)
•
Defferent FR depence with each antenna modification.
NS1微係数(1[mm]変位)
NS1微係数（1[mm]変位）
1
0.3
[mm]
0.1
0
-200
-100
-0.1
0
100
200
-0.2
delta_xs
delta_ys
delta_zs
delta_xha
delta_yha
delta_xhb
delta_yhb
0.995
0.99
[mm]
0.2
⊿Zha
0.985
0.98
0.975
-0.3
FR[deg]
-200
-100
NS1微係数（1[deg]変位）
0
100
200
⊿θxs
⊿θys
[mm]
[deg]
2
-4
-100
0
200
-0.985
⊿Zhb
-0.99
-0.995
-6
-8
FR[deg]
100
-0.98
4
-2 0
200
-0.975
-200
6
-100
100
NS1微係数(1[mm]変位)
8
-200
0
FR[deg]
-1
FR[deg]
5-2-2:response fuction allNS
Response functions all NSes (mitsubishi.co.)
•
exsample
NS微係数⊿Xs
NS微係数⊿Zha（1[mm]変位）
0.998
0.996
0.994
0.992
0.99
0.988
0.986
0.984
0.982
0.98
0.978
0.976
0.3
[mm]
0.1
0
-200
-100
-0.1
0
100
200
NS1
NS2
NS3
NS4
[mm]
0.2
-0.2
-0.3
FR[deg]
same FR dependency about all NS
-200
-100
0
FR[deg]
NS1
NS2
NS3
NS4
100
200
FR dependency Depends on NS
5-3:simulation results
simulation
EL
φ'ant
= (∑φ'ant ( xiEL )) − ∑φ'ant ( xiEL =90 )
i =1
i =1
NS3
0.8
0.6
0.4
0.2
0
-0.2-180
0.8
0.6
-90
0
90
180
EL0
EL30
EL60
[mm]
[mm]
NS1
0.4
0.2
0
-0.2-180
-90
180
180
EL0
EL30
EL60
-0.6
-0.8
FR[deg]
FR[deg]
NS4
NS2
0.8
0.6
0.8
0.6
0.4
0.2
0.4
0.2
-90
0
90
180
EL0
EL30
EL60
[mm]
[mm]
90
-0.4
-0.4
-0.6
-0.8
0
-0.2-180
0
EL0
EL30
EL60
0
-0.2-180
-0.4
-0.4
-0.6
-0.8
-0.6
-0.8
FR[deg]
-90
0
FR[deg]
90
6-1:PCDmeasurement
PCDmeasurement
•
•
•
•
•
(Where)
(When)
(Who)
(Why)
(How)
MIZUSAWA Station
2004/04
Honma,Suda,Kijima
research φNS EL dependency
”rot_FR technique”~Honma~
– Only one NS be operated. Rotating Field Rotator(FR) from –
180 to 180[deg],steps 15[deg],stop 30[sec] each FRangle
– Averaging the data about 20[sec] (about 5[sec] to 25[sec]) in
30[sec].Solve the 2pi ambiguity by Cosine fitting.
– EL=90,60,30,5[deg]
– So, there are 4(NS)*4(EL)=16 data.
6-2:PCDanalysis
PCDmeasurement analysis~Suda software
PCD output in 1[sec]
←group delay(raw)
↓phase delay(raw)
Group Delay
Group Delay
Group Delay
Group Delay
Phase Delay
Phase Delay
Phase Delay
Phase Delay
calc：φ22G = GroupDelay ×ν+ PhaseDelay
After fitting
φ22G = a × cos( FR − b) + c
Fitting residual
Solve ambiguity
with fitting
Calced phase difference
6-3:PCDresults
PCDmeasurement~result
~Honma,Suda,Kijima
•
“bias” is ignored
PCDresult_NS3
PCDresult_NS1
1.5
1.5
1
1
0
-180
-0.5
-90
0
90
180
EL0
EL30
EL60
0.5
[mm]
[mm]
0.5
0
-180
-0.5
-1
-1
-1.5
-1.5
-90
1.5
1.5
1
1
-1
90
180
EL0
EL30
EL60
0
-180
-0.5
-90
0
-1
-1.5
-1.5
FR[deg]
180
EL0
EL30
EL60
0.5
[mm]
[mm]
0.5
0
180
PCDresult_NS4
PCDresult_NS2
-90
90
FR[deg]
FR[deg]
0
-180
-0.5
0
EL0
EL30
EL60
FR[deg]
90
6-4:PCDresults matome
PCDmeasurement~ELdependence
~Honma,Suda,Kijima
•
•
EL dependence (Φ=amp×cos(FR-phase)+bias)
Symmetric(with mirror axis) NS pair has Symmetric tendency.
PCDmeasurement(amp)
PCDmeasurement(phase)
1.50
1.00
0.00
-0.50
0
30
60
-1.00
-1.50
EL[deg]
90
[deg]
[mm]
0.50
0.8
0.6
0.4
NS1
0.2
NS2
0.0
NS3
-0.2 0
NS4
-0.4
-0.6
-0.8
30
60
EL[deg]
90
NS1
NS2
NS3
NS4
7:result-A
Result-A:Compare PCDresult with Simulation
•
•
Φ=PCDresult − SimulationResult
PCDresult is consistent with Simulation About 0.5[mm]
•
NS3 has different EL tendency. Mistake of response function? or PCDmeasurement?
NS1
NS3
0.6
0.6
0.4
0.4
0
-0.2-180
-90
0
90
180
EL0
EL30
EL60
0.2
[mm]
[mm]
0.2
-0.4
0
-180
-0.2
-0.6
-0.4
-0.8
-0.6
-90
FR[deg]
0
0.6
0.4
0.4
EL0
EL30
EL60
-0.4
0
-180
-0.2
-0.6
-0.4
-0.8
90
180
-90
0
-0.6
FR[deg]
180
0.2
[mm]
[mm]
0.2
0
EL0
EL30
EL60
NS4
0.6
-90
180
FR[deg]
NS2
0
-0.2-180
90
EL0
EL30
EL60
FR[deg]
90
8-1:end
Horn on Dish method
∼A part of master thesis(Kagoshima univ.)∼
~Fin~
Thank you.
8-2:Title
Horn on Dish method
∼B part of master thesis(Kagoshima univ.)∼
9:subtitle
Estimate
Residual of “horn on dish” calibration
•
The residual of “horn on dish” calibration about one station
real
real
φant −φ'ant = (∑φreal
)) − ∑φ'real
)
ant ( xi
ant ( xi
i =1
i =1
PCDmeasurement
•
IF PCDresult has contribution of real response function and real deformation
quantity, dark deformation(Δｘ) be estimated by gap in PCD and simulation The
residual is follow formula
Simulation :φ'ant = ∑φ'ant ( xi )
Estimate the Δx
i =1
PCDmeasurement :φ'ant = ∑φ'ant ( xi + ∆xi )
φant −φ'ant = (∑φant ( xi + ∆ix=1i )) − ∑φ'ant ( xi + ∆xi )
Result-C
i =1
•
i =1
“horn on dish” calibration and deformation forecast calibration. The residual is
following formula
φant −φ'ant −[(∑φant ( xi )) − ∑φ'ant ( xi )] = (∑φant (∆xi )) − ∑φ'ant (∆xi )
i =1
“Horn on dish method”
i =1
i =1
Deformation forecast calibration
i =1
Result-D
9-1:Estimate delta deformation
~judgment~
Estimate delta deformation
•
Estimate only one deformation respectively
–
–
–
–
•
ΔXs = arcφant’(result-A)
Δθys= arcφant’(result-A)
・・・
And so on.
Judgment
– EL tendency is same in all Noise Sources
Siutable sample
Unsiutable sample
⊿Zs
⊿Xs
15.0
2.50
10.0
NS1
NS2
NS3
NS4
1.50
1.00
0.50
5.0
[mm]
[mm]
2.00
0.0
-5.0
0
30
60
-10.0
0.00
-15.0
0
30
60
EL[deg]
90
-20.0
EL[deg]
90
NS1
NS2
NS3
NS4
9-2:Estimete delta deformation
~result~
Estimate delta deformation
⊿Xs
⊿θys
2.50
0.10
NS1
NS2
NS3
NS4
1.50
1.00
0.50
0.08
[deg]
[mm]
2.00
NS1
NS2
NS3
NS4
0.06
0.04
0.02
0.00
0.00
0
30
60
90
0
30
EL[deg]
60
90
⊿Xhb
0.00
0.00
60
90
-0.50 0
NS1
NS2
NS3
NS4
-1.50
-2.00
-2.50
NS1
NS2
NS3
NS4
-1.50
-2.00
-2.50
-3.00
-3.00
-3.50
-3.50
EL[deg]
30
-1.00
[mm]
30
-1.00
[mm]
90
EL[deg]
⊿Xha
-0.50 0
60
EL[deg]
9-3:Result-C
Result-C
φant −φ'ant = (∑φant ( xi + ∆xi )) − ∑φ'ant ( xi + ∆xi )
i =1
i =1
ΔXs
Δθys
0.1
0
-180
-90
0
90
180
EL0
EL30
EL60
[mm]
[mm]
0.05
-0.05
0.2
0.15
0.1
0.05
0
-0.05-180
-90
FR[deg]
180
180
EL0
EL30
EL60
FR[deg]
ΔXha
ΔXhb
0.1
0.1
0.05
0.05
-90
0
90
180
EL0
EL30
EL60
[mm]
[mm]
90
-0.1
-0.15
-0.2
-0.1
0
-180
-0.05
0
EL0
EL30
EL60
0
-180
-90
0
-0.05
-0.1
-0.15
-0.1
FR[deg]
FR[deg]
90
9-4:Result-D
Result-D
φant −φ'ant −[(∑φant ( xi )) − ∑φ'ant ( xi )] = (∑φant (∆xi )) − ∑φ'ant (∆xi )
i =1
i =1
i =1
i =1
Δθys
ΔXs
0.06
0.06
0.04
0.04
0
-180
-0.02
-90
0
90
180
EL0
EL30
EL60
0.02
[mm]
[mm]
0.02
0
-180
-0.02
-0.04
-0.04
-0.06
-0.06
-90
ΔXha
0.06
0.04
0.04
90
180
⊿Xha
EL30
EL60
0.02
[mm]
[mm]
0.02
0
0
-180
-0.02
-0.04
-0.04
-0.06
-0.06
FR[deg]
180
ΔXhb
0.06
-90
90
FR[deg]
FR[deg]
0
-180
-0.02
0
EL0
EL30
EL60
-90
0
FR[deg]
90
180
⊿Xhb
EL30
EL60
10-1:Conclusions
conclusions
•
•
I introduce the role and basis of “horn on dish method”
Compare PCDmeasurement with simulation(and deformation
measurement):result-A
– Max 0.5[mm] defferent
•
•
Estimate delta deformation By result-A and simulation
Estimate residual of [“horn on dish” calibration]
– Less than 0.1[mm] (except the case of delta theta ys) at one station
– It has possiblle to be less than 0.05[mm] at one baseline
•
Estimate residual of [“horn on dish” calibration and deformation forecast]
– Less than 0.05[mm] at one station
– It is clear to be less than 0.05[mm] at one baseline
10-2:end
Horn on Dish method
∼”true” a part (A and B part) of master thesis(Kagoshima univ.)∼
~Fin~
Thank you.
10-3:end
Horn on Dish method
∼C part of master thesis(Kagoshima univ.)∼
~joke~
Thank you.