koji murakawa (astron) b. tubbs, r. mather, r. le poole, j. meisner, e. bakker (leiden), f....
TRANSCRIPT
![Page 1: Koji Murakawa (ASTRON) B. Tubbs, R. Mather, R. Le Poole, J. Meisner, E. Bakker (Leiden), F. Delplancke, K. Scale (ESO) Conceptual Design Review for PRIMA](https://reader036.vdocuments.site/reader036/viewer/2022062422/56649ede5503460f94beeaa6/html5/thumbnails/1.jpg)
Koji Murakawa (ASTRON)B. Tubbs, R. Mather, R. Le Poole, J. Meisner,
E. Bakker (Leiden), F. Delplancke, K. Scale (ESO)
Conceptual Design Review for PRIMA
@Lorentz Center, Leiden on 29 Sep., 2004
PRIMA Astrometric ObservationsPolarization effectsTechnical Report
AS-TRE-AOS-15753-0011
Frosty Leo CW Leo
![Page 2: Koji Murakawa (ASTRON) B. Tubbs, R. Mather, R. Le Poole, J. Meisner, E. Bakker (Leiden), F. Delplancke, K. Scale (ESO) Conceptual Design Review for PRIMA](https://reader036.vdocuments.site/reader036/viewer/2022062422/56649ede5503460f94beeaa6/html5/thumbnails/2.jpg)
- OUTLINE -1. Introduction Why instrumental polarization analysis?2. Effects of phase error on astrometry Operation principle of the FSU3. Polarization properties of PRIMA optics Basic concepts of polarization model
![Page 3: Koji Murakawa (ASTRON) B. Tubbs, R. Mather, R. Le Poole, J. Meisner, E. Bakker (Leiden), F. Delplancke, K. Scale (ESO) Conceptual Design Review for PRIMA](https://reader036.vdocuments.site/reader036/viewer/2022062422/56649ede5503460f94beeaa6/html5/thumbnails/3.jpg)
Introduction
Why instrumental polarization analysis? changes phase and amplitude VLT telescope, StS, base line, etc (telescope pointing, separation, station…) the fringe sensor unit detects a wrong phase delay. provide an error in astrometry what kind of error? (</100?)
![Page 4: Koji Murakawa (ASTRON) B. Tubbs, R. Mather, R. Le Poole, J. Meisner, E. Bakker (Leiden), F. Delplancke, K. Scale (ESO) Conceptual Design Review for PRIMA](https://reader036.vdocuments.site/reader036/viewer/2022062422/56649ede5503460f94beeaa6/html5/thumbnails/4.jpg)
What we have to do?
Establish a strategy of analysis Study the operation principle of FSU Make a polarization model of VLTI opticsAnalysis Fringe detection by FSU polarization model analysis of VLTI optics
telescope, StS, base line optics time evolution (as a function of hour angle) difference between the ref. and the obj.
![Page 5: Koji Murakawa (ASTRON) B. Tubbs, R. Mather, R. Le Poole, J. Meisner, E. Bakker (Leiden), F. Delplancke, K. Scale (ESO) Conceptual Design Review for PRIMA](https://reader036.vdocuments.site/reader036/viewer/2022062422/56649ede5503460f94beeaa6/html5/thumbnails/5.jpg)
The Operation Principleof the Fringe Sensor Unit
achromaticλ/4
compensator light
from T1
light from T2
BC
p1 & s1
p2 & s2τp1 + ρp2 τs1 + ρs 2
|ϕp2 - ϕs2| = 90°
PBS
τp1 + ρp2
PBS
τs1 + ρs 2
ρp1 + τp2
ρs1 + τs 2
ρp1 + τp2 ρs1 + τs 2
Φ0
Φ2 = Φ
0 +
A
C
Φ1 = Φ
0 + /2
Φ
Ck
ΦΦ
3 = Φ
0 + 3/2
D
B
Alenia Co., VLT-TRE-ALS-15740-0004
![Page 6: Koji Murakawa (ASTRON) B. Tubbs, R. Mather, R. Le Poole, J. Meisner, E. Bakker (Leiden), F. Delplancke, K. Scale (ESO) Conceptual Design Review for PRIMA](https://reader036.vdocuments.site/reader036/viewer/2022062422/56649ede5503460f94beeaa6/html5/thumbnails/6.jpg)
The original ABCD Algorithm
Complex AmplitudeEA = -(P1-P2)EB = (S1+S2)EC = (P1+P2)ED = -(S1-S2)
Identical polarizationS1 = expi(kLopl,1)S2 = expi(kLopl,2)P1 = expi(kLopl,1) P2 = expi(kLopl,2 +/2)
k: wave number (k=2/λ)Lopl,i: optical path length at the station i
![Page 7: Koji Murakawa (ASTRON) B. Tubbs, R. Mather, R. Le Poole, J. Meisner, E. Bakker (Leiden), F. Delplancke, K. Scale (ESO) Conceptual Design Review for PRIMA](https://reader036.vdocuments.site/reader036/viewer/2022062422/56649ede5503460f94beeaa6/html5/thumbnails/7.jpg)
The original ABCD Algorithm
ABCD signalsIA = 2||2{1+sin(kLopd)}IB = 2||2{1+cos(kLopd)}IC = 2||2{1-sin(kLopd)}ID = 2||2{1-cos(kLopd)}
VisibilityV = 1/2(IA+IB+IC+ID)=4||2
Phase delay ϕ = kLopd
= arctan(IA-IC/IB-ID)
Lopd: optical path difference Lopd = Lopl,1 - Lopl,2
The phase delay can be measured with a simple way.
![Page 8: Koji Murakawa (ASTRON) B. Tubbs, R. Mather, R. Le Poole, J. Meisner, E. Bakker (Leiden), F. Delplancke, K. Scale (ESO) Conceptual Design Review for PRIMA](https://reader036.vdocuments.site/reader036/viewer/2022062422/56649ede5503460f94beeaa6/html5/thumbnails/8.jpg)
The original ABCD Algorithm
Complex AmplitudeEA = -(P1-P2)EB = (S1+S2)EC = (P1+P2)ED = -(S1-S2)
Different polarizationS1 = S1expi(kLopl,1)S2 = S1expi(kLopl,2)P1 = P1expi(kLopl,1) P2 = P1expi(kLopl,2+/2)
k: wave number (k=2/λ)Lopl,i: optical path length at the station i
![Page 9: Koji Murakawa (ASTRON) B. Tubbs, R. Mather, R. Le Poole, J. Meisner, E. Bakker (Leiden), F. Delplancke, K. Scale (ESO) Conceptual Design Review for PRIMA](https://reader036.vdocuments.site/reader036/viewer/2022062422/56649ede5503460f94beeaa6/html5/thumbnails/9.jpg)
The original ABCD AlgorithmABCD signalsIA = 2|P1|2{1+sin(kLopd)}IB = 2|S1|2{1+cos(kLopd)}IC = 2|P1|2{1-sin(kLopd)}ID = 2|S1|2{1-cos(kLopd)}
VisibilityV = 1/2(IA+IB+IC+ID) = 2||2(|P1|2+|S1|2)Phase delay ϕ = kLopd
= arctan(IA-IC/IA+IC * IB+ID/IB-ID)
Lopd: optical path difference Lopd = Lopl,1 - Lopl,2
The phase delay can be measured not affectedby different polarization status between S and P.
![Page 10: Koji Murakawa (ASTRON) B. Tubbs, R. Mather, R. Le Poole, J. Meisner, E. Bakker (Leiden), F. Delplancke, K. Scale (ESO) Conceptual Design Review for PRIMA](https://reader036.vdocuments.site/reader036/viewer/2022062422/56649ede5503460f94beeaa6/html5/thumbnails/10.jpg)
A Modified ABCD Algorithm
Complex AmplitudeEA = -(P1-P2)EB = (S1+S2)EC = (P1+P2)ED = -(S1-S2)
Different polarizationS1 = S1expi(kLopl,1)S2 = S2expi(kLopl,2)P1 = P1expi(kLopl,1+ϕS) P2 = P2expi(kLopl,2+ϕP+/2)
Different polarization between beam 1 and 2• phase ϕS = ϕS,2-ϕS,1, and ϕP = ϕP,2-ϕP,1 • amplitude S2≠S1, P2≠P1
![Page 11: Koji Murakawa (ASTRON) B. Tubbs, R. Mather, R. Le Poole, J. Meisner, E. Bakker (Leiden), F. Delplancke, K. Scale (ESO) Conceptual Design Review for PRIMA](https://reader036.vdocuments.site/reader036/viewer/2022062422/56649ede5503460f94beeaa6/html5/thumbnails/11.jpg)
A Problem on the ABCD Algorithm
ABCD signalsIA = ||2{P1
2+P22+2P1P2sin(kLopd+ϕP)}
IB = ||2{S12+S2
2+2S1S2cos(kLopd+ϕS)}IC = ||2{P1
2+P22-2P1P2sin(kLopd+ϕP)}
ID = ||2{S12+S2
2-2S1S2cos(kLopd+ϕS)}
The ABCD algorithm tells a wrong phase delay.
![Page 12: Koji Murakawa (ASTRON) B. Tubbs, R. Mather, R. Le Poole, J. Meisner, E. Bakker (Leiden), F. Delplancke, K. Scale (ESO) Conceptual Design Review for PRIMA](https://reader036.vdocuments.site/reader036/viewer/2022062422/56649ede5503460f94beeaa6/html5/thumbnails/12.jpg)
A Modified ABCD Algorithm
Get another sampling with a /2(=λ/4) stepIA0 = ||2{P1
2+P22+2P1P2sin(kLopd+ϕP)}
IA1 = ||2{P12+P2
2+2P1P2cos(kLopd+ϕP)}IC0 = ||2{P1
2+P22-2P1P2sin(kLopd+ϕP)}
IC1 = ||2{P12+P2
2-2P1P2cos(kLopd+ϕP)}
• only P-polarization is described above.• assume fixed P1 and P2
![Page 13: Koji Murakawa (ASTRON) B. Tubbs, R. Mather, R. Le Poole, J. Meisner, E. Bakker (Leiden), F. Delplancke, K. Scale (ESO) Conceptual Design Review for PRIMA](https://reader036.vdocuments.site/reader036/viewer/2022062422/56649ede5503460f94beeaa6/html5/thumbnails/13.jpg)
A Modified ABCD Algorithm& Polarization Effects
Phase delay ΦP = kLopd + ϕP = arctan(IA0-IC0/IA1+IC1) ΦS = kLopd + ϕS = arctan(IB0-ID0/IB1+ID1)The FSU may correct (detect) 1/2(ΦP+ΦS) = kLopd+1/2(ϕP+ϕS)
• Instrumental polarization between two beams cannot be principally corrected.• a phase delay of |ϕS-ϕP| still remains.
![Page 14: Koji Murakawa (ASTRON) B. Tubbs, R. Mather, R. Le Poole, J. Meisner, E. Bakker (Leiden), F. Delplancke, K. Scale (ESO) Conceptual Design Review for PRIMA](https://reader036.vdocuments.site/reader036/viewer/2022062422/56649ede5503460f94beeaa6/html5/thumbnails/14.jpg)
Impact on Astrometry- Polarization Effects on Object -
Visibility of the object V = <|ES,1+ES,2+EP,1+EP,2|2> = <|ES,1|2>+<|ES,2|2>+<|EP,1|2>+<|EP,2|2> +<ES,1ES,2
*>+<ES,1*ES,2>
+<ES,1EP,1*>+<ES,1
*EP,1> +<ES,1EP,2
*>+<ES,1*EP,2>
+<ES,2EP,1*>+<ES,2
*EP,1> +<ES,2EP,2
*>+<ES,2*EP,2>
+<EP,1EP,2*>+<EP,1
*EP,2>
ES,1 = S1expi(kLopl,1’)ES,2 = S2expi(kLopl,2’+ϕS’)EP,1 = P1expi(kLopl,1’+ϕSP’)EP,2 = P2expi(kLopl,2’+ϕSP’+ϕP’)
![Page 15: Koji Murakawa (ASTRON) B. Tubbs, R. Mather, R. Le Poole, J. Meisner, E. Bakker (Leiden), F. Delplancke, K. Scale (ESO) Conceptual Design Review for PRIMA](https://reader036.vdocuments.site/reader036/viewer/2022062422/56649ede5503460f94beeaa6/html5/thumbnails/15.jpg)
Impact on Astrometry- Polarization Effects on Object -
Cross correlation <ES,1ES,2
*>+<ES,1*ES,2> = 2S1S2<cos(klopd’-ϕS’)>
<ES,1EP,1*>+<ES,1
*EP,1> = 2S1P1<cos(ϕSP’)><ES,1EP,2
*>+<ES,1*EP,2> = 2S1P2<cos(klopd’-ϕSP’-ϕP’)>
<ES,2EP,1*>+<ES,2
*EP,1> = 2S2P1<cos(klopd’+ϕSP’-ϕS’)><ES,2EP,2
*>+<ES,2*EP,2> = 2S2P2<cos(ϕSP’+ϕP’-ϕS’)>
<EP,1EP,2*>+<EP,1
*EP,2> = 2P1P2<cos(klopd’-ϕP’)>
![Page 16: Koji Murakawa (ASTRON) B. Tubbs, R. Mather, R. Le Poole, J. Meisner, E. Bakker (Leiden), F. Delplancke, K. Scale (ESO) Conceptual Design Review for PRIMA](https://reader036.vdocuments.site/reader036/viewer/2022062422/56649ede5503460f94beeaa6/html5/thumbnails/16.jpg)
Impact on Astrometry- Polarization Effects on Object -
Visibility of the unpolarized object V = <|ES,1+ES,2+EP,1+EP,2|2> = <|ES,1|2>+<|ES,2|2>+<|EP,1|2>+<|EP,2|2> +2<S1S2cos(klopd’-ϕS’)>+2<P1P2cos(klopd’-ϕP’)>Because of <cos(ϕSP’)>=0….unpolarized lightAstrometry of the unpolarized object k(Lopd-Lopd’)+{(ϕS-ϕP)-(ϕS’-ϕP’)}= kLBLsin+{(ϕS-ϕP)-(ϕS’-ϕP’)} … : astrometry
![Page 17: Koji Murakawa (ASTRON) B. Tubbs, R. Mather, R. Le Poole, J. Meisner, E. Bakker (Leiden), F. Delplancke, K. Scale (ESO) Conceptual Design Review for PRIMA](https://reader036.vdocuments.site/reader036/viewer/2022062422/56649ede5503460f94beeaa6/html5/thumbnails/17.jpg)
Impact on Astrometry- Summary -
1. Operation principle of FSU Phase delay measurement not affected by polarization status of the reference. A modified ABCD algorithm to calibrate instrumental polarization
2. Impact on astrometry {(ϕS-ϕP)-(ϕS’-ϕP’)} gives error in astrometry Similar beam combiner to the FSU is
encouraged to science instrument
![Page 18: Koji Murakawa (ASTRON) B. Tubbs, R. Mather, R. Le Poole, J. Meisner, E. Bakker (Leiden), F. Delplancke, K. Scale (ESO) Conceptual Design Review for PRIMA](https://reader036.vdocuments.site/reader036/viewer/2022062422/56649ede5503460f94beeaa6/html5/thumbnails/18.jpg)
Polarization Model
Optics can work as a phase retarder or a polarizer So = J Si … S: Stokes parm, J: Jones matrix Sf = JNJN-1…J1 S*
Grouping Jtel(Az(h), El(h), r, , λ, St): telescope optics JStS(r, , λ): star separator optics JBL(λ, St): base line opticsModel Sf = JBL JStS Jtel S*
![Page 19: Koji Murakawa (ASTRON) B. Tubbs, R. Mather, R. Le Poole, J. Meisner, E. Bakker (Leiden), F. Delplancke, K. Scale (ESO) Conceptual Design Review for PRIMA](https://reader036.vdocuments.site/reader036/viewer/2022062422/56649ede5503460f94beeaa6/html5/thumbnails/19.jpg)
Future Activities
1. Telescope optics (Jtel) time evolution: |ϕS-ϕP|(h, Dec, r, )2. Star separator optics (JStS) |ϕS-ϕP|(r)3. Base line optics (JBL) |ϕS-ϕP|(St)4. Color dependence ϕopd(λ), Ix(λ)@FSU, group delay