Conceptual Design Review for PRIMA

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Conceptual Design Review for PRIMA
Frosty Leo
CW Leo
PRIMA Astrometric Observations Polarization
effects Technical Report AS-TRE-AOS-15753-0011
Koji Murakawa (ASTRON) B. Tubbs, R. Mather, R. Le
Poole, J. Meisner, E. Bakker (Leiden), F.
Delplancke, K. Scale (ESO)
_at_Lorentz Center, Leiden on 29 Sep., 2004
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• - OUTLINE -
• 1. Introduction
• Why instrumental polarization analysis?
• 2. Effects of phase error on astrometry
• Operation principle of the FSU
• 3. Polarization properties of PRIMA optics
• Basic concepts of polarization model

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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? (ltp/100?)

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What we have to do?

• Establish a strategy of analysis
• Study the operation principle of FSU
• Make a polarization model of VLTI optics
• Analysis
• 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.

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The Operation Principleof the Fringe Sensor Unit
Alenia Co., VLT-TRE-ALS-15740-0004
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The original ABCD Algorithm
Complex Amplitude EA -b(P1-P2) EB
b(S1S2) EC b(P1P2) ED -b(S1-S2)
Identical polarization S1 expi(kLopl,1) S2
expi(kLopl,2) P1 expi(kLopl,1) P2
expi(kLopl,2 p/2)
k wave number (k2p/l) Lopl,i optical path
length at the station i
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The original ABCD Algorithm
ABCD signals IA 2b21sin(kLopd) IB
2b21cos(kLopd) IC 2b21-sin(kLopd) ID
2b21-cos(kLopd)
Visibility V 1/2(IAIBICID)4b2 Phase delay
f 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.
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The original ABCD Algorithm
Complex Amplitude EA -b(P1-P2) EB
b(S1S2) EC b(P1P2) ED -b(S1-S2)
Different polarization S1 S1expi(kLopl,1) S2
S1expi(kLopl,2) P1 P1expi(kLopl,1) P2
P1expi(kLopl,2p/2)
k wave number (k2p/l) Lopl,i optical path
length at the station i
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The original ABCD Algorithm
ABCD signals IA 2bP121sin(kLopd) IB
2bS121cos(kLopd) IC 2bP121-sin(kLopd) I
D 2bS121-cos(kLopd)
Visibility V 1/2(IAIBICID)
2b2(P12S12) Phase delay f kLopd
arctan(IA-IC/IAIC IBID/IB-ID)
Lopd optical path difference Lopd
Lopl,1 - Lopl,2
The phase delay can be measured not affected by
different polarization status between S and P.
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A Modified ABCD Algorithm
Complex Amplitude EA -b(P1-P2) EB
b(S1S2) EC b(P1P2) ED -b(S1-S2)
Different polarization S1 S1expi(kLopl,1) S2
S2expi(kLopl,2) P1 P1expi(kLopl,1fS) P2
P2expi(kLopl,2fPp/2)

• Different polarization between beam 1 and 2
• phase fS fS,2-fS,1, and fP fP,2-fP,1
• amplitude S2?S1, P2?P1

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A Problem on the ABCD Algorithm
ABCD signals IA b2P12P222P1P2sin(kLopdfP)
IB b2S12S222S1S2cos(kLopdfS) IC
b2P12P22-2P1P2sin(kLopdfP) ID
b2S12S22-2S1S2cos(kLopdfS)
The ABCD algorithm tells a wrong phase delay.
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A Modified ABCD Algorithm
Get another sampling with a p/2(l/4) step IA0
b2P12P222P1P2sin(kLopdfP) IA1
b2P12P222P1P2cos(kLopdfP) IC0
b2P12P22-2P1P2sin(kLopdfP) IC1
b2P12P22-2P1P2cos(kLopdfP)

• only P-polarization is described above.
• assume fixed P1 and P2

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A Modified ABCD Algorithm Polarization Effects
Phase delay FP kLopd fP
arctan(IA0-IC0/IA1IC1) FS kLopd fS
arctan(IB0-ID0/IB1ID1) The FSU may correct
(detect) 1/2(FPFS) kLopd1/2(fPfS)

• Instrumental polarization between two beams
• cannot be principally corrected.
• a phase delay of fS-fP still remains.

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Impact on Astrometry- Polarization Effects on
Object -

• Visibility of the object
• V ltES,1ES,2EP,1EP,22gt
• ltES,12gtltES,22gtltEP,12gtltEP,22gt
• ltES,1ES,2gtltES,1ES,2gt
• ltES,1EP,1gtltES,1EP,1gt
• ltES,1EP,2gtltES,1EP,2gt
• ltES,2EP,1gtltES,2EP,1gt
• ltES,2EP,2gtltES,2EP,2gt
• ltEP,1EP,2gtltEP,1EP,2gt

• ES,1 S1expi(kLopl,1)
• ES,2 S2expi(kLopl,2fS)
• EP,1 P1expi(kLopl,1fSP)
• EP,2 P2expi(kLopl,2fSPfP)

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Impact on Astrometry- Polarization Effects on
Object -

• Cross correlation
• ltES,1ES,2gtltES,1ES,2gt 2S1S2ltcos(klopd-fS)gt
• ltES,1EP,1gtltES,1EP,1gt 2S1P1ltcos(fSP)gt
• ltES,1EP,2gtltES,1EP,2gt 2S1P2ltcos(klopd-fSP-fP
  )gt
• ltES,2EP,1gtltES,2EP,1gt 2S2P1ltcos(klopdfSP-fS
  )gt
• ltES,2EP,2gtltES,2EP,2gt 2S2P2ltcos(fSPfP-fS)gt
  
• ltEP,1EP,2gtltEP,1EP,2gt 2P1P2ltcos(klopd-fP)gt

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Impact on Astrometry- Polarization Effects on
Object -

• Visibility of the unpolarized object
• V ltES,1ES,2EP,1EP,22gt
• ltES,12gtltES,22gtltEP,12gtltEP,22gt
• 2ltS1S2cos(klopd-fS)gt2ltP1P2cos(klopd-fP)
  gt
• Because of ltcos(fSP)gt0.unpolarized light
• Astrometry of the unpolarized object
• k(Lopd-Lopd)(fS-fP)-(fS-fP)
• kLBLsinq(fS-fP)-(fS-fP) q astrometry

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Impact on Astrometry- Summary -

• 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
• (fS-fP)-(fS-fP) gives error in astrometry
• Similar beam combiner to the FSU is
• encouraged to science instrument

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Polarization Model
Optics can work as a phase retarder or a
polarizer So J Si S Stokes parm, J Jones
matrix Sf JNJN-1J1 S Grouping
Jtel(Az(h), El(h), r, q, l, St) telescope
optics JStS(r, q, l) star separator optics
JBL(l, St) base line optics Model Sf JBL
JStS Jtel S
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Future Activities
1. Telescope optics (Jtel) time evolution
fS-fP(h, Dec, r, q) 2. Star separator optics
(JStS) fS-fP(r) 3. Base line optics (JBL)
fS-fP(St) 4. Color dependence fopd(l),
Ix(l)_at_FSU, group delay