1. ST7 Interferometer LIGO-G040043-00-Z1 The ST7 Interferometer Andreas Kuhnert Robert Spero Jet Propulsion Laboratory California Institute of Technology

2. ST7 Interferometer LIGO-G040043-00-Z2 ST7 Concept Measure suspended masses within spacecraft Test thruster performance in drag-free control Hitch ride on LISA Pathfinder Optical bench TM1 TM2 Interferometer optical bench fixed to spacecraft x 1 and x 2 measured separately; x 1 + x 2 is low-noise x1x1 x2x2

3. ST7 Interferometer LIGO-G040043-00-Z3 Optical Bench Beam-splitter Collimator Insensitive path Sensitive path Intensity Monitor Optical Fiber Quadrant photodiode 20 cm TM1 TM2

4. ST7 Interferometer LIGO-G040043-00-Z4 Interferometer Features Beam diameter 1 mm, Rayleigh range 70 cm, sensitive path lengths 10 cm. No modulators, phasemeters, intensity stabilization, or frequency stabilization. Requires test mass to be positioned near mid-fringe. Intensity monitored, noise removed in data analysis. Separate measurements of both bench/test-mass distances. Quadrant photodiodes monitor total fringe signal, and two axes of alignment. Automatic alignment, autonomous operation.

5. ST7 Interferometer LIGO-G040043-00-Z5 Manual Alignment Thermal Expansion Homodyne Signal A B A B Optical Bench 

6. ST7 Interferometer LIGO-G040043-00-Z6 Contacted Optics in Vacuum Chamber

7. ST7 Interferometer LIGO-G040043-00-Z7 Testbed Drift

8. ST7 Interferometer LIGO-G040043-00-Z8 60 pm rms optical bench modulation Testbed Noise 1000 100 10 1 mHz pm/rtHz 1 100 Allocated noise Measured noise

9. ST7 Interferometer LIGO-G040043-00-Z9 Measurements Demonstrate: 1.Analog electronics and ADC noise adequately low 2.Thermal sensitivity probably adequately low 3.Bench motion suppression typically x200, without calibration (x1000 needed) 4.Frequency stabilization not needed 5.Intensity noise can be suppressed in data analysis

10. ST7 Interferometer LIGO-G040043-00-Z10 Alignment Sensitivity 1: Geometric error  x S = s 1   s1s1 p  x c = p     x S = s 1 sin  x c = p cos  Errors are correlated, and of same order: s 1 ~ p   s 1 = 40  ; p = 10 cm;   = 400  rad

11. ST7 Interferometer LIGO-G040043-00-Z11 Alignment Sensitivity 2: Fringe position error  x x =  x     (  w  2 =  x 10 6, w=beam radius p + x  

12. ST7 Interferometer LIGO-G040043-00-Z12 Total angle-jitter noise Test mass jitter, 1  rad/rthz Displacement noise, 30 pm/rthz Transverse error, 40  m Misalignment, 400  rad Fringe center error, 30 nm

13. ST7 Interferometer LIGO-G040043-00-Z13 Initialization 1. Starting state 2. IFO finds bright fringe 3. GRS moves to quarter fringe 4. IFO Aligns 5. GRS to half fringe Position Intensity

14. ST7 Interferometer LIGO-G040043-00-Z14 Dithered alignment -- concept

15. ST7 Interferometer LIGO-G040043-00-Z15 Dithered alignment -- Simulink model

16. ST7 Interferometer LIGO-G040043-00-Z16 Dithered alignment -- Simulink run

17. ST7 Interferometer LIGO-G040043-00-Z17 Bright fringe finder -- Simulink model

18. ST7 Interferometer LIGO-G040043-00-Z18 Bright fringe finder -- Simulink run

19. ST7 Interferometer LIGO-G040043-00-Z19 QPD difference alignment -- Simulink model

20. ST7 Interferometer LIGO-G040043-00-Z20 QPD difference alignment -- Experiment

21. ST7 Interferometer LIGO-G040043-00-Z21 QPD difference signal alignment sensitivity

22. ST7 Interferometer LIGO-G040043-00-Z22 Sum vs. difference signals at half-fringe

23. ST7 Interferometer LIGO-G040043-00-Z23 Backups

24. ST7 Interferometer LIGO-G040043-00-Z24 Intensity Pattern with Misalignment Horizontal misalignment shown. Pattern insensitive to fringe offset near mid-fringe. Sample with 4 pixels (quadrant photodiode). Difference/sum response: dQ/d  = sqrt(8kw/  3 )

25. ST7 Interferometer LIGO-G040043-00-Z25 Static Misalignment and Static Longitudinal Error Fringe Visibility Error Sensitivity w=0.5 mm w=1.0 mm w=2.0 mm 0 1 Misalignment (  rad) Bright Mid Dark Electronic noise Alignment noise