1. FFT study of the realistic Optics of LIGO I July 12th, 2004 Commissioning meeting Hiro Yamamoto, Biplab Bhawal, Xiao Xu (CIT-SURF)  LIGO I mirror phase map  FFT code modification  Thermal lensing  Beam splitter curvature  Things to do  Effect of optics aberration (Biplab)

2. FFT - commissioning mtg2 LIGO I Mirror phase map  R.Dodda - 2003 SURF from SLU »Phase map from raw data to FFT format »Effects of actual mirror phase maps in ARM CAVITIES  X.Xu - 2004 SURF from Caltech »Completed all conversion –Tilt removed (poor man’s ASC) –128x128 and 256x256 –Available from e2e home page »Studying effects of aberration, beam splitter curvature and ITM differential heating

3. FFT - commissioning mtg3 Beam splitter phase map WA4K BS WA4K BS - curvature subtracted x 10 -8 nm

4. FFT - commissioning mtg4 FFT code modification  Thermal lensing »Input beam specification –Input TEM00 base was indirectly specified by the base on ITMx HR »Separate refractive index for each mirror (poor man’s thermal lens)  Beam splitter curvature  LIGO I signals »POX, POY, POB  Better coding and interface »Use fftw »x10 faster (another x10 possible) »…

5. FFT - commissioning mtg5 Thermal lensing

6. FFT - commissioning mtg6 Beam splitter curvature    ref  tra  cur (cold) = -0.26  ref (x)= -0.027  ref (x)= -0.019

7. FFT - commissioning mtg7 SB dark port profile, asymmetry and BS curvature Flat BS 200k curved BS ITMX hot ITMY coldITMX cold ITMY hot SB- profile hot-cold SBP SBM enhancedreduced

8. FFT - commissioning mtg8 Thermal lensing and BS curvature

9. FFT - commissioning mtg9 What to do  Validation of results using e2e  Lock FFT using LIGO I LSC  C++ FFT »Easy customization »Time domain FFT