1. Calibration and the status of the photon calibrators Evan Goetz University of Michigan with Peter Kalmus (Columbia U.) & Rick Savage (LHO) 17 October 2006

2. 2 Outline DARM servo loop Calibration model Obtaining the calibration factor Discrepancy The way forward

3. 3 Calibration of LIGO Strain signal = Response * Detector output Need to relate detector output to gravitational wave parameters » Amplitude » Frequency » Phase Inject a well-known signal into the interferometer and study the detector output

4. 4 Calibration preliminaries: DARM loop + - Sensing  (t)C Q (f) s(t,f) AS_Q Digital filters D D (f) + + Actuation A(f) DARM_CTRL_EXC (calibration lines) DARM_CTRL 0  (t) DARM_ERR Noise or GWs!

5. 5 Calibration preliminaries: DARM loop Sensing = the interferometer and photodiode and electronics Digital filters = variety of filters used to maintain DARM loop stability Actuation = the pendulum of the test masses and associated electronics » Coil actuation: magnets and voice coils Front Side Magnets

6. 6 Calibration preliminaries: DARM loop Open loop gain Error points (gravitational-wave channels)

7. 7 Response function Example DARM_ERR response:

8. 8 Calibration methods Use a model to understand the DARM loop » Includes all electronic, mechanical and optical components Model gives the shape of the interferometer response, the calibration gives the scaling factor Fit the model to the measurement to fully understand the loop Methods to obtain calibration scaling factor: » Near-DC calibration » In-band calibration » Photon calibration

9. 9 Near-DC calibration Fringe fitting procedure (unlocked Michelson) » Drive an ITM through multiple bright-to-dark fringes recording both the AS_DC signal and the ITM read-back » Fit the AS_DC and ITM read-back signals to equations to find the calibration value of the drive to the ITM Uses the laser wavelength to calibrate the ITM Propagate the ITM calibration to the ETM via transfer function measurements with the locked cavities Worry about propagation of the calibration to the gravitational wave frequency band (40 Hz to 2 kHz)

10. 10 Fringe fitting data Time (sec)

11. 11 Fringe fitting results

12. 12 In-band calibration This method is done in the gravitational wave band Uses the laser wavelength to calibrate the ITM drive Procedure: » With an unlocked Michelson drive AS_Q to a maximum and minimum by allowing the ITMs to swing through fringes. This calibrates AS_Q to a change in length from an ITM using the laser wavelength (amplitude peak-to-peak = /4) Propagate the ITM calibration to the ETM via transfer function measurements with the locked cavities

13. 13 In-band calibration details

14. 14 Photon calibration Use a power modulated laser to exert an external force on the ETMs By knowing the power of the laser we can know the external strain injected into the interferometer Assume the mirror acts as a free mass Relatively simple:

15. 15 Interferometer status during a run We need to track how sensitive the instrument is while we take data Periodic calibration measurements (described previously) Auto-calibration: swept sine » Uses knowledge from calibration measurements Calibration lines » Real and imaginary components in Fourier spectrum give status of optical alignment » Computers track changes in digital filters

16. 16 Discrepancy Peter Kalmus looked at long-term photon calibrator calculated response function from single lines injected by the photon calibrator at ~1.6 kHz Did not agree with official calibration response function We started doing swept sine measurements to map out the frequency dependence of the photon calibrator response function Continued to find discrepancy Discrepancy below 1kHz varies on each IFO » ~20-40 percent for H1, ~20 percent for H2, ~10 percent for L1 Past 1kHz, the discrepancy grows!

17. 17 A first look at the response function discrepancy The good: Correct trend The bad: Ratio doesn't agree

18. 18 Calibration factor discrepancy We decided to compare apples-to-apples and look at the calibration factor for both measurements Calibration factor obtained from near-DC, in-band techniques or photon calibrator Drive the photon calibrator and the coil actuators Scale the photon calibrator drive to DC using our knowledge of the photon calibrator Take the ratio of transfer functions to DARM_ERR to obtain the calibration factor Consistent discrepancy with the official methods » 15-20 percent on all LHO ETMs

19. 19 H1 calibration factor discrepancy Official cal: 0.812e-9 m/ct Photon cal: 0.963e-9 m/ct Official cal: 0.831e-9 m/ct Photon cal: 0.982e-9 m/ct

20. 20 H2 calibration factor discrepancy Official cal: 0.860e-9 m/ct Photon cal: 0.900e-9 m/ct Official cal: 0.896e-9 m/ct Photon cal: 1.062e-9 m/ct

21. 21 H1 response using coils and derived calibration factor from photon calibrator

22. 22 Resolutions What has been solved or confirmed? » Reflecting power from H2 ETMX is what we expect. This gives the photon calibrator a more solid argument » Photon calibrators are in good agreement on LHO interferometer » Rotation induced effects by non-centered photon calibrator beams can be accounted for in the photon calibration procedure » Variability in the comparison of response function on H1 probably solved. Attributed to changes in gain of the DARM loop » Initial in-band calibration equations are proportionally correct (just a confirmation of the official calibration)

23. 23 What remains? Calibration factor discrepancy (15-20 percent on H1 and H2) Response function discrepancy (~40 percent on H1, but now probably ~20 percent. ~20 percent on H2) Thermal effects driving discrepancy higher past 1kHz

24. 24 Future work Similar measurements to be made at LLO 2-beam photon calibrator » Send 2 beams from the photon calibrator » Virtually eliminates rotational effects » Only thermal effect is the “radiometer effect” Thermal modeling and high frequency sweeps Scrutinize all calibration factor procedures in official method and photon calibrator method Can we get phase information? Timing? High power photon calibrator?

25. 25 The end.