Where Did the LSC Signals Come From?

1. Where Did the LSC Signals Come From? Fred Raab 27 June 02

2. Why We Use Sidebands • We want to work at the center of a dark fringe, because it provides immunity from imperfections carried by the light • Intensity noise on the light is a typical imperfection • In general experimental vernacular this is known as a “balanced” configuration • Problem is that a signal carried by light intensity is quadratic near the center of the fringe • Solution is to interfere the main light (“carrier”) with reference light (“sidebands”) that is modulated in a known way • Interference that affects the carrier and sidebands in different ways produces a signal upon demodulation of the light • This demodulation process is commonly used in FM radio receivers (music is broadcast as sidebands; carrier is station frequency) Raab - Where Did the LSC Signals Come From?

3. Example: Error Signal for a Single Fabry-Perot Cavity carrier + sidebands carrier altered by cavity Pure phase modulation input light (vector sum does not change over modulation cycle) Modulation phase 45o 90o 135o 180o Cavity shifts carrier if frequency not matched to cavity length, creating an amplitude modulation, whose peak amplitude is in phase with modulation (I.e., I-phase) Raab - Where Did the LSC Signals Come From?

4. Simple Michelson Antisymmetric Port Signals Equal-arm Michelson produces no signal at a dark antisymmetric port  Dr. L Schnupp suggested that an unequal-arm Michelson would give signals at a dark port Raab - Where Did the LSC Signals Come From?

5. Simple Michelson Antisymmetric Port Signals Explained Asymmetry  produces dispersion so only carrier has totally destructive interference at AS port, but a little bit of sidebands leak through. Sidebands at AS port when carrier matched to Michelson arms Sidebands at AS port when carrier mismatched to Michelson arms Modulation phase 45o 90o 135o 270o Signal appears in Q phase Raab - Where Did the LSC Signals Come From?

6. How This Applies to LIGO-1 IFO Raab - Where Did the LSC Signals Come From?

7. LIGO-1 Signal Recovery Configuration POB REFL AS Raab - Where Did the LSC Signals Come From?

8. A Possible LIGO-1 Length Control (LSC) Configuration PRC MICH DARM Common Mode Simple Matrix Raab - Where Did the LSC Signals Come From?

9. Now Look at LSC Screen Raab - Where Did the LSC Signals Come From?

10. AS, PO, REFL Inputs Raab - Where Did the LSC Signals Come From?

11. Input Matrix Decodes Input into DARM, CARM, MICH, PRC Raab - Where Did the LSC Signals Come From?

12. Separate Filtering and Gain Sections for Each Loop Raab - Where Did the LSC Signals Come From?

13. Output Matrix Translates Loop Feedback into Actuator Signals Raab - Where Did the LSC Signals Come From?

14. For Further Study • General signal analysis in Regehr’s thesis • Details of turning this into an “industrial” control system in LSC Final Design documentation • Regehr’s table-top demo locked easily with no smarts • A “smart” locking scheme was needed for the big IFO’s; analysis in Evans’ thesis; overview in recent Optics Letter • Still a work under way; progress will reduce introduction & propagation of noise through IFO; needs good servo modeling & simulations Raab - Where Did the LSC Signals Come From?