1. LIGO-G020277-00-W Where Did the LSC Signals Come From? Fred Raab 27 June 02

2. LIGO-G020277-00-W Raab - Where Did the LSC Signals Come From?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)

3. LIGO-G020277-00-W 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) 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) 45 o 90 o 135 o 180 o Modulation phase

4. LIGO-G020277-00-W 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 

5. LIGO-G020277-00-W 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 45 o 90 o 135 o Modulation phase Sidebands at AS port when carrier mismatched to Michelson arms 270 o Signal appears in Q phase

6. LIGO-G020277-00-W Raab - Where Did the LSC Signals Come From?6 How This Applies to LIGO-1 IFO

7. LIGO-G020277-00-W Raab - Where Did the LSC Signals Come From?7 LIGO-1 Signal Recovery Configuration AS REFL POB

8. LIGO-G020277-00-W Raab - Where Did the LSC Signals Come From?8 A Possible LIGO-1 Length Control (LSC) Configuration DARM PRC MICH Common Mode Simple Matrix

9. LIGO-G020277-00-W Raab - Where Did the LSC Signals Come From?9 Now Look at LSC Screen

10. LIGO-G020277-00-W Raab - Where Did the LSC Signals Come From?10 AS, PO, REFL Inputs

11. LIGO-G020277-00-W Raab - Where Did the LSC Signals Come From?11 Input Matrix Decodes Input into DARM, CARM, MICH, PRC

12. LIGO-G020277-00-W Raab - Where Did the LSC Signals Come From?12 Separate Filtering and Gain Sections for Each Loop

13. LIGO-G020277-00-W Raab - Where Did the LSC Signals Come From?13 Output Matrix Translates Loop Feedback into Actuator Signals

14. LIGO-G020277-00-W 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