Improving Interferometric Null Depth Measurement with statistics : theory and first results with the Palomar Fiber Nuller

Transcription

1 Improving Interferometric Null Depth Measurement with statistics : theory and first results with the Palomar Fiber Nuller Charles Hanot AEOS, University of Liège, Belgium hanot@astro.ulg.ac.be TMT, ESO, June

2 If you sometimes wonder: Why do we spend so much time on calib.? or Why is this data reduction so tricky? Please, have a seat!

3 What is the Null Depth? N = I min I Bkg I max I Bkg

4 What is the Null Depth? N = I min I Bkg I max I Bkg

5 What is the Null Depth? N = I min I Bkg I max I Bkg

6 What is the Null Depth? N = I min I Bkg I max I Bkg

7 What is the Null Depth? N = I min I Bkg I max I Bkg

8 What is the Null Depth? N = I min I Bkg I max I Bkg

9 Problem : How to measure Null Depths? N = I min I Bkg I max I Bkg

10 Problem : How to measure Null Depths?

11 Problem : How to measure Null Depths? Mean?

12 Problem : How to measure Null Depths? Median??

13 Problem : How to measure Null Depths? How??

14 Classical method Non-calibrated ND N(t 1 ) = N a + N Ins (t 1 ) Science target Sci.

15 Classical method Non-calibrated ND N(t 1 ) = N a + N Ins (t 1 ) N cal (t 2 ) = N a, cal + N Ins, cal (t 2 ) Science target Calibrator star Sci. Cal.

16 Classical method Non-calibrated ND N(t 1 ) = N a + N Ins (t 1 ) N cal (t 2 ) = N a, cal + N Ins, cal (t 2 ) Science target Calibrator star Calibrated ND N a = N a, cal + N(t 1 ) N cal (t 2 ) Sci. Cal.

17 Classical method Advantages Drawbacks + Easy to process + Used for centuries - Duty cycle - Require lots of observations - Limited by fluctuations - Na,cal dependent

18 Statistical Method N(t) Ir(t)(δI(t) 2 +Δϕ(t) 2 +αrot 2 +Na)+NBkg(t)

19 Statistical Method N(t) Ir(t)(δI(t) 2 +Δϕ(t) 2 +αrot 2 +Na)+NBkg(t) Normalized intensity

20 Statistical Method N(t) Ir(t)(δI(t) 2 +Δϕ(t) 2 +αrot 2 +Na)+NBkg(t) Normalized intensity Intensity mismatch

21 Statistical Method N(t) Ir(t)(δI(t) 2 +Δϕ(t) 2 +αrot 2 +Na)+NBkg(t) Normalized intensity Intensity mismatch Phase error

22 Statistical Method N(t) Ir(t)(δI(t) 2 +Δϕ(t) 2 +αrot 2 +Na)+NBkg(t) Normalized intensity Polarization Intensity mismatch Phase error

23 Statistical Method N(t) Ir(t)(δI(t) 2 +Δϕ(t) 2 +αrot 2 +Na)+NBkg(t) Normalized intensity Polarization Intensity mismatch Phase error Astrophysical leakage

24 Statistical Method N(t) Ir(t)(δI(t) 2 +Δϕ(t) 2 +αrot 2 +Na)+NBkg(t) Background Normalized intensity Polarization Intensity mismatch Phase error Astrophysical leakage

25 Statistical Method N(t) Ir(t)(δI(t) 2 +Δϕ(t) 2 +αrot 2 +Na)+NBkg(t) Background Normalized intensity Polarization Intensity mismatch Phase error Astrophysical leakage

26 Statistical Method N(t) Ir(t)(δI(t) 2 +Δϕ(t) 2 +αrot 2 +Na)+NBkg(t) Background Normalized intensity Polarization Intensity mismatch Phase error Astrophysical leakage

27 Statistical Method N(t) Ir(t)(δI(t) 2 +Δϕ(t) 2 +αrot 2 +Na)+NBkg(t) Background Normalized intensity Polarization Intensity mismatch Phase error Astrophysical leakage

28 Statistical Method N(t) Ir(t)(δI(t) 2 +Δϕ(t) 2 +αrot 2 +Na)+NBkg(t) Background Normalized intensity Polarization Intensity mismatch Phase error Astrophysical leakage

29 Statistical Method N(t) Ir(t)(δI(t) 2 +Δϕ(t) 2 +αrot 2 +Na)+NBkg(t) Stat. ND Median Mean

30 Statistical Method N(t) Ir(t)(δI(t) 2 +Δϕ(t) 2 +αrot 2 +Na)+NBkg(t) N astro = /! µ " # = 0.35 rad $ " # = 0.41 rad µ! I =!6.54% $! I = 12.15% µ IN = 1 $ IN = 5.8% Nulling histogram! I 2 / Occurence Null Depth

31 Statistical Method N(t) Ir(t)(δI(t) 2 +Δϕ(t) 2 +αrot 2 +Na)+NBkg(t) N astro = /! µ! " = 0.35 rad $! " = 0.41 rad µ # I =!6.54% $ # I = 12.15% µ IN = 1 $ IN = 5.8% Nulling histogram!" 2 /4 # I 2 / Occurence Null Depth

32 Statistical Method N(t) Ir(t)(δI(t) 2 +Δϕ(t) 2 +αrot 2 +Na)+NBkg(t) N astro = /! µ! " = 0.35 rad $! " = 0.41 rad µ # I =!6.54% $ # I = 12.15% µ IN = 1 $ IN = 5.8% Nulling histogram!" 2 /4 # I 2 /16!" 2 /4 + # I 2 /16 N a Occurence Null Depth

33 Statistical Method N(t) Ir(t)(δI(t) 2 +Δϕ(t) 2 +αrot 2 +Na)+NBkg(t) N astro = /! µ! " = 0.35 rad $! " = 0.41 rad µ # I =!6.54% $ # I = 12.15% µ IN = 1 $ IN = 5.8% Nulling histogram!" 2 /4 # I 2 /16!" 2 /4 + # I 2 /16!" 2 /4 + # I 2 /16 + N a N a Occurence Null Depth

34 Statistical Method N(t) Ir(t)(δI(t) 2 +Δϕ(t) 2 +αrot 2 +Na)+NBkg(t) N astro = /! µ! " = 0.35 rad $! " = 0.41 rad µ # I =!6.54% $ # I = 12.15% µ IN = 1 $ IN = 5.8% Nulling histogram Model histogram!" 2 /4 # I 2 /16!" 2 /4 + # I 2 /16!" 2 /4 + # I 2 /16 + N a N a 1400 Occurence Null Depth

35 Is the solution unique? N(t) Ir(t)(δI(t) 2 +Δϕ(t) 2 +αrot 2 +Na)+NBkg(t) Case #1 : No fluctuation Δϕ(t) 2 Δϕ 2 Infinite num. of solutions )!!! #(!! 78,+1986-:' 78,+1986-:# ANSWER: NO!!! 344+5/64/ #!!! '(!! '!!! Na = 0.06 μϕ = 0 rad σϕ = 0 rad Na = 0.02 μϕ = 0.4 rad σϕ = 0 rad (!!!!!"!#!"!$!"!%!"!&!"'!"'# *+,,-./012

36 Is the solution unique? N(t) Ir(t)(δI(t) 2 +Δϕ(t) 2 +αrot 2 +Na)+NBkg(t) Case #2 : Fluctuations Can be small fluctuations Only one solution )!!! #(!! 78,+1986-:' 78,+1986-:#! ANSWER: YES!!! 344+5/64/ #!!! '(!! '!!! Na = 0.06 μϕ = 0 rad σϕ = 0 rad Na = 0.02 μϕ = 0.4 rad σϕ = 0.05 rad (!!!!!"!#!"!$!"!%!"!&!"'!"'# *+,,-./012

37 Classical method Advantages + Easy to use + Fast + No calibration! + Better accuracy + Better sensitivity

38 Application #1 The Palomar Fiber Nuller (PFN)

39 Palomar Fiber Nuller!="!=0

40 Palomar Fiber Nuller!"#$%&'()*&%+,+-.)/+ 01/",&()%2%)( 3/+(%1(+&* "6#,+7*)8+&'"9+(

41 Palomar Fiber Nuller

42 Comparison classical vs statistical Alpha Boo Alpha Boo LBI: Na = 1.35% ± 0.01% Class. : Na = 1.23% ± 0.4% Stat. : Na = 1.35% ± 0.004% Null Depth Classical ND Averaged classical ND Statistical ND Averaged statistical ND!0.01!0.02! Time [min]

43 Comparison classical vs statistical Alpha Her Alpha Her LBI: Na = 3.25% ± 0.15% Class. : Na = 3.24% ± 0.4% Stat. : Na = 3.12% ± 0.04% Null Depth Class. ND Averaged class. ND Stat. ND Averaged stat. ND Time [min]

44 Comparison classical vs statistical Vega Alpha Her Excess = 0.11% ± 0.05% Class. : bad calibration 89,,/:+;2< #&#$% #&#$ #&##% #!#&##%!#&#$!#&#$% A,)**->),/8: BC+1)6+5/>,)**->),/8: =2)2-*2->),/8: BC+1)6+5/*2)2-*2->),/8:?+6)@*/;<323*;<+1+/8:!!#&#"!#&#"%!#&#'!!"#!$%!$#!% # % $# $% "# ()*+,-.+/01-+.2)2-3./45+67

45 Reaching High contrasts Eta Peg ND excess : 4.7 x 10-4 Theo. excess : 3.5 x 10-4 Bias : 1.2 x 10-4 Occurence Model Null histogram N Astro =!0.047% +/! 0.028% RMS Phase = 0.25! Mean Phase = 0.03! RMS " I = Mean " I =! RMS I = Mean I = ! Null Depth

46 Application #2 Measurement of stellar diameters

47 Measurement of stellar diameters Method: Combining coronagraphy and interferometry a b c d e f T1 L1 L2 D1 Densified L3 D2 Interferometer Recombination! " T2 din Bin Monomode Fibers Fizeau Mode Coronagraphic Lyot Stop 2nd Pupil device in the focal plane (FQPM / AGPM) Fizeau Mode Plane # i " # i r i dout Bout $ I = 1! r i $ I Coronagraphic image > 1! " Source Input pupil Output pupil for coronagraphic mode Image plane 1 Output pupil for final imaging mode Image plane 2

48 Measurement of stellar diameters Stel. Diam. (µas) µ φ in wave σ φ in wave rms µ di in % σ di in % rms σ I in % rms Retreived Diam. (µas)

49 Conclusion A new data reduction method for interferometry Better stability and accuracy of the measurements Better sensitivity Best ND ever achieved on the sky Not restricted to a particular instrument