Academia Sinica Yuki Inoue On behalf of KAGRA collaboration Supported by Wang-Yau Cheng, Rick Savage, Tomotada Akutsu… 1 Development of photon calibrator system in KAGRA
Outline 2 • Introduction • KAGRA photon calibrator • Systematic error • Summary
Introduction The reconstruction of h(t) is one of the most important for the gravitational wave experiment h(t) Gravitational waveforms 3 • Direction • Mass • Distance
Reconstruction of h(t) measurement accuracy of gravitational waveforms. 4 • The uncertainties of A and C determine the
Photon calibrator S.Karki et al.(2016) function Transfer force Absolute 5 Rotation Photon pressure establish the low uncertainty calibration method. the powerful tools to calibrate the parameters directly. • R. Savage team in LIGO achieve to ! ! ⎛ ⎞ δ x = Δ P c cos θ s ( f ) 1 + M a b ⋅ ⎜ ⎟ • The photon calibrator (Pcal) is one of ⎝ I ⎠
Uncertainty of photon calibrator in LIGO another methods. 6 LHO LLO LIGO-P1500248 • They try the crosscheck between Pcal and • The photon calibrator looks small uncertainty.
KAGRA photon calibrator 7
5 phases of study 8 Design phase Development phase Characterization phase Install phase Observation phase
KAGRA Pcal 36m Beam waist Transmitter module Receiver module Periscope Camera system Baffle Oplev 9 EYA
Instruments summary 10 advanced LIGO KAGRA Mirror material Silica Sapphire Mirror mass 40 kg 22.8 kg Mirror diameter 340 mm 220 mm laser Power of calibrator 2W->10W 10W Laser frequency 1047 nm 1047 nm Incident angle 8.75 deg 0.72 deg
Current status of Lab. in KEK Class 4 laser room Digital system Telecamera Control PC Receiver module Transmitter module Readout tower 11
Transmitter module Transmitter module 12 AOM IS Detector Laser SolidWorks 教育版(実習にのみ使用可) • placed the mirror and lenses on the optical table • mount the aluminum cover for safety
Goals of KAGRA Pcal -Beam position control (Pico-motor) -High power (~10W) -WAOM (Independently control) Development items (1st phase bKAGRA) 13 (2nd phase bKAGRA) (3rd phase bKAGRA) • Calibration of interferometer output • Hardware signal injection
Systematic errors 14
Uncertainty of laser power 15 function Transfer force Absolute Rotation with integrating sphere Parameter uncertainty Laser power 0.57% Angle 0.007% Mass of test 0.005% RotaLon 0.40% Total 0.75% ! • Monitor the power ! ⎛ ⎞ δ x = Δ P c cos θ s ( f ) 1 + M a b ⋅ ⎜ ⎟ ⎝ I ⎠
Calibration standard 16 • The uncertainty of the PCAL is limited by the power standard in NIST. • Calibrate the GS in NIST. • Each observatory makes the WSs which are calibrated by GS.
Uncertainty of Rotation 17 function Transfer force Absolute Rotation geometrical factor. generate the systematic error Parameter uncertainty Laser power 0.57% Angle 0.007% Mass of test 0.005% RotaLon 0.40% Total 0.75% • Rotation effect corresponds to ! ! ⎛ ⎞ δ x = Δ P c cos θ s ( f ) 1 + M a b ⋅ ⎜ ⎟ ⎝ I ⎠ • Uncertainty of beam position
Telecamera 18 KAGRA Telecamera D810(36million pixel ) SolidWorks 教育版(実習にのみ使用可) • In order to monitor the beam position, we employ the telecamera. • Requirement: less than 1mm.
Telecamera test 36m We place the target maker 36m away from telecamera. Result Zoom in The resolution of telecamera meets our requirement. 19 24mm 24mm D810(36million pixel )
Estimation of beam position LIGO LIGO estimate the origin of mirror surface by fitting mirror edge We try and demonstrate the estimation of the mirror origin with outer circle. We use the openCV for analysis. Trimming data Estimate this point Outer circle 20
Analysis and result 6.9±0.1 Threshold Masking ーfitting Resolution: 0.1 mm Fitting[mm] Design[mm] Radius 7.0 Trimming X center 11.9±0.1 12.0 Y center 11.9±0.1 12.0 Established image analysis method for estimation of beam position Gray scale 21 1 Y 180 0.9 160 0.8 140 0.7 120 0.6 100 0.5 80 0.4 60 0.3 40 0.2 20 0.1 0 0 0 20 40 60 80 100 120 140 160 180 X 24 22 20 18 16 14 Y[mm] 12 10 8 6 4 2 0 0 2 4 6 8 10 12 14 16 18 20 22 24 X[mm]
5 phases of study 22 Design phase Development phase Characterization phase Install phase Observation phase
Summary important technologies for the accurate measurement of gravitational waves. calibration technology, photon calibrator. install the Pcal at 2018 April. 23 • The calibration is one of the most essential and • LIGO achieve to make the low uncertainty • KAGRA is making the Pcal calibrator. • Design of KAGRA Pcal have already done. We will
Schedule characterize of the camera system characterization of the Transmitter module and Receiver module (WAOM…) 24 • 2016 Nov.-2017 Mar.: Development and • 2017 Apr. - May.: Installation of the Camera system • 2017 June - 2018 Mar.: Development and • 2018 June: Development of new technologies
Modal simulation with COMSOL 15,914Hz COMSOL COMSOL 15915Hz 23,661Hz Ansys Ansys 23,659Hz Drum head mode Butterfly mode and ANSYS 12 25 • Density: • 4.00g/cm3 • Young’s module • 400Gpa • Poison ratio • 0.3
Elastic deformation positions. 26 Elastic deformation Free mass motion Total motion Elastic deformation Free mass Motion • Total motion can decompose the elastic deformation and free mass motion. • The amplitude of the elastic deformation strongly depend on the beam • require to reduce the elastic deformation with choosing optimal beam positions
Drumhead and butterfly mode Drumhead mode Drumhead 23,659Hz 8,153Hz LIGO KAGRA 27 Butterfly mode 15,914Hz 15,914Hz 23,659Hz 5,946Hz 8,153Hz Optimal beam position are corresponding to 5,946Hz Butterfly KAGRA 2.20g/cm3 advLIGO Material Sapphire Silica Density 4.00g/cm3 Young’s 0.1631 modulus 400Gpa 72.6GPa Poisson ratio 0.3 drumhead node point.
Elastic deformation of LIGO 28 • Optimal points is 111.6mm • The free mass motion corresponds to unity.
Elastic deformation of KAGRA 29 LIGO 3mm point 1.04 - 3.0mm( 79.8mm) ± - 1.0mm( 81.8mm) ± optimal positions( 82.8mm) 1.03 ± + 1.0mm( 83.8mm) ± + 3.0mm( 85.8mm) ± 1.02 Displacement ratio 1.01 1 0.99 0.98 0.97 0.96 0 2000 4000 6000 8000 10000 12000 Frequency [Hz] • Optimal position is 82.8 mm • Sapphire have an advantage of the elastic deformation.
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