1. LIGO-G09xxxxx-v1 Form F0900043-v1 LIGO Laboratory1 Designing a frequency offset locking loop for the 40m prototype Arm Length Stabilization System Sai Akhil Reddy Indian Institute of Technology, Patna Mentors: Manasa T., Eric Quintero, Koji Arai

2. LIGO-G09xxxxx-v1 Form F0900043-v1 Outline of the Talk What is Arm Length Stabilization (ALS)? Issues in the ALS system. Solving the issue: Frequency Offset Locking (FOL) Loop. Building the FOL control loop. Challenges faced. Testing and Commissioning LIGO Laboratory2

3. LIGO-G09xxxxx-v1 Form F0900043-v1 Advanced LIGO Optical Configuration LIGO Laboratory3

4. LIGO-G09xxxxx-v1 Form F0900043-v1 Arm Length Stabilization (ALS) Precise length measurements ⇔ Lock acquisition of the interferometer. LIGO Laboratory4

5. LIGO-G09xxxxx-v1 Form F0900043-v1 Arm Length Stabilization (ALS) Precise length measurements ⇔ Lock acquisition of the interferometer. Problems: Higher degrees of freedom due to coupling of cavities, non-linearities in length measurement and noise. LIGO Laboratory5

6. LIGO-G09xxxxx-v1 Form F0900043-v1 Arm Length Stabilization (ALS) Precise length measurements ⇔ Lock acquisition of the interferometer. Problems: Higher degrees of freedom due to coupling of cavities, non-linearities in length measurement and noise. Multicolour laser interferometry technique LIGO Laboratory6

7. LIGO-G09xxxxx-v1 Form F0900043-v1 Arm Length Stabilization (ALS) Precise length measurements ⇔ Lock acquisition of the interferometer. Problems: Higher degrees of freedom due to coupling of cavities, non-linearities in length measurement and noise. Multicolour laser interferometry technique. Length information from Pound Drever Hall (PDH) scheme. LIGO Laboratory7

8. LIGO-G09xxxxx-v1 Form F0900043-v1 Pound Drever Hall (PDH) Scheme LIGO Laboratory8

9. LIGO-G09xxxxx-v1 Form F0900043-v1 Arm Length Stabilization (ALS) Precise length measurements ⇔ Lock acquisition of the interferometer. Problems: Higher degrees of freedom due to coupling of cavities, non-linearities in length measurement and noise. Multicolour laser interferometry technique Length information from Pound Drever Hall(PDH) scheme. Beat note between the Green Auxiliary(AUX) laser and the infrared Pre-Stabilised(PSL) used to stabilize the length of the cavity using a digital servo. LIGO Laboratory9

10. LIGO-G09xxxxx-v1 Form F0900043-v1 Arm Length Stabilization (ALS) LIGO Laboratory10

11. LIGO-G09xxxxx-v1 Form F0900043-v1 Issues in the ALS system Frequencies of two lasers hugely different (could vary by few GHz). LIGO Laboratory11

12. LIGO-G09xxxxx-v1 Form F0900043-v1 Issues in the ALS system Frequencies of two lasers hugely different (could vary by few GHz). The PDH control loop of the AUX laser allows its frequency to follow the motion of the cavity length. LIGO Laboratory12

13. LIGO-G09xxxxx-v1 Form F0900043-v1 Issues in the ALS system Frequencies of two lasers hugely different (could vary by few GHz). The PDH control loop of the AUX laser allows its frequency to follow the motion of the cavity length. The laser cavity Piezoelectric(PZT) actuator has a control range of a few hundred MHz and an actuator response of around 5 MHz/V. LIGO Laboratory13

14. LIGO-G09xxxxx-v1 Form F0900043-v1 Issues in the ALS system Frequencies of two lasers hugely different (could vary by few GHz). The PDH control loop of the AUX laser allows its frequency to follow the motion of the cavity length. The laser cavity Piezoelectric(PZT) actuator has a control range of a few hundred MHz and an actuator response of around 5 MHz/V. The PZT control becomes ineffective when the beat note between the lasers crosses the actuator range mainly due to green PD range. LIGO Laboratory14

15. LIGO-G09xxxxx-v1 Form F0900043-v1 Motivation of FOL Loop Slow control: Temperature Actuation -- larger response (1 GHz/K). LIGO Laboratory15

16. LIGO-G09xxxxx-v1 Form F0900043-v1 Motivation of FOL Loop Slow control: Temperature Actuation -- larger response (1 GHz/K). Tracks the infrared (PSL) beat note frequency and pushes it within the efficient working range of ALS (<100 MHz). LIGO Laboratory16

17. LIGO-G09xxxxx-v1 Form F0900043-v1 Motivation of FOL Loop Slow control: Temperature Actuation -- larger response (1 GHz/K). Tracks the infrared (PSL) beat note frequency and pushes it within the efficient working range of ALS (<100 MHz). So we build an automated Servo using a Proportional-Integral-Derivative controller (PID). LIGO Laboratory17

18. LIGO-G09xxxxx-v1 Form F0900043-v1 Motivation of FOL Loop Slow control: Temperature Actuation -- larger response (1 GHz/K). Tracks the infrared (PSL) beat note frequency and pushes it within the efficient working range of ALS (<100 MHz). So we build an automated Servo using a Proportional-Integral-Derivative controller (PID). FOL Works even when the green arm is not locked unlike the already existing temperature loop. LIGO Laboratory18

19. LIGO-G09xxxxx-v1 Form F0900043-v1 FOL Loop LIGO Laboratory19

20. LIGO-G09xxxxx-v1 Form F0900043-v1 Building the Digital Feedback System LIGO Laboratory20

21. LIGO-G09xxxxx-v1 Form F0900043-v1 ARM Processor LIGO Laboratory21

22. LIGO-G09xxxxx-v1 Form F0900043-v1 Control Sensor RF Frequency Counter- Mini-Circuits Model UFC-6000 RF Frequency Counter Frequency range of 1 MHz- 6000 MHz. LIGO Laboratory22

23. LIGO-G09xxxxx-v1 Form F0900043-v1 Resolving Timing Issues of R Pi and FC LIGO Laboratory23 Raspberry Pi: not an RTOS Issues in clock synchronization of R Pi and FC. Setup external clock to synchronously read data from the FC

24. LIGO-G09xxxxx-v1 Form F0900043-v1 Transfer Function of the Frequency Counter LIGO Laboratory24

25. LIGO-G09xxxxx-v1 Form F0900043-v1 Noise Characterization in FC LIGO Laboratory25

26. LIGO-G09xxxxx-v1 Form F0900043-v1 Transfer Function of the Plant: Thermal Actuator LIGO Laboratory26 Thermal Actuator- Slow control actuator : Actuates on the temperature of the NPRO

27. LIGO-G09xxxxx-v1 Form F0900043-v1 Interface with EPICS Channels Experimental Physics and Industrial Control System (EPICS): set of software components and tools used to create control systems. IOC: Input / Output Controller - Network and device interface LIGO Laboratory27

28. LIGO-G09xxxxx-v1 Form F0900043-v1 PID Controller Design P = I = D = LIGO Laboratory28

29. LIGO-G09xxxxx-v1 Form F0900043-v1 Installed FOL Box LIGO Laboratory29

30. LIGO-G09xxxxx-v1 Form F0900043-v1 Testing and Commissioning Setup tested with existing green laser beat note. To be tested with the infrared PSL after completion of optics installation. The FOL box will be permanently placed inside the 40m and the software issues can be remotely debugged. LIGO Laboratory30

31. LIGO-G09xxxxx-v1 Form F0900043-v1 Acknowledgements Mentors: Manasa T., Eric Q, Koji A. 40m folks: Rana A., Jamie, Jenne D., Steve V. Co-Interns: Harry, Nichin, Andres Organizations: Caltech and NSF LIGO Laboratory31

32. LIGO-G09xxxxx-v1 Form F0900043-v1 Thank You LIGO Laboratory32