1. Laser Interferometry for a future GRACE follow-on mission
Marina Dehne, Felipe Guzmán Cervantes, Gerhard Heinzel and Karsten Danzmann

2. Introduction
1670 Isaac Newton with his Law of Gravitation questioned the pure spheric geometry of Earth:
Flattening of the poles and enlargement of the Equator due to rotation
→ Spheroid
Today:
→ Equatorial radius approx. 21 km larger than radius at the poles

3. Spheroid (reference ellipsoid)
Gravitational acceleration g=9,81 ms-²
Increase of 0,02 ms-² at poles
Gravity at Equator g-ω2r=9,78 ms-²
Gravity depends on latitude
Units of gravity:
Gal = ms-2 or mGal = 10-5 ms-2

4. Geoid undulations
Geoid: undulating equipotential surface that closely matches Mean Sea Level
Geoid undulation: deviation between geoid and ellipsoid
→ ± 100 meters
Geoid
Ellipsoid
Ocean
topographic surface

5. Geoid undulations
Geoid: undulating equipotential surface that closely matches Mean Sea Level
Geoid undulation: deviation between geoid and ellipsoid
→ ± 100 meters
mGal

6. Gravity anomalies
Irregular mass distributions with different density distribution
Effective gravity field differs from nominal gravity field:
→ Gravity anomalies: ± 500 mGal

7. Temporal changes of gravity field
Gravity field changes in time
→ Possible explanations:
Changes in distribution of
Atmospheric masses
Oceanic water masses
Continental water masses (ground water)
Ice masses in Antarctica and Greenland
Solid earth (postglacial rebound)

8. Temporal changes of gravity field
Effect on relevant climatic phenomena
Investigations of Earth system dynamics
Effects are small and hard to disentangle
→ High temporal and spatial resolution necessary, (long time span)
CHAMP (2000),
GRACE (2002)
and GOCE (2008)

9. GRACE (Gravity Recovery And Climate Experiment)
Satellite to satellite tracking (SST):
Separation: 220 km
Altitude: ~500 km (decline orbit)
Measurement: microwaves in K-band
Relative range
Relative velocity (range rate)

10. GRACE (Gravity Recovery And Climate Experiment)
Mission concept:
Approaching a mass anomaly: satellite 1 accelerates
Passing across a mass anomaly: satellite 1 slows down, satellite 2 accelerates
By moving away from mass anomaly: satellite 2 slows down

11. Comparison between obtained accuracies

12. Challenges for future gravity satellite missions
We‘re at the very beginning!
Sneeuw et al., 2005

13. Aim of GRACE follow-on mission
Aim: temporal and spatial resolution enhancement,
(long time scales)
Improvement of measurement system
→ Laser interferometry
→ SSI (Satellite-to-Satellite-Interferometry)
Lower altitude
Improvement of „drag-free“ control systems
Improvement of the data post-processing

14. GRACE follow-on mission
Short separation between two satellites: e.g. 10 km
Laser interferometer (SSI)
→ Benefit from LISA and LISA Pathfinder (LTP)
Low Earth Orbit
Significant drag
→ „drag-free“ technology of LISA Pathfinder

15. Interferometer concept
Large dynamic range (several wavelengths)
Baseline: heterodyne interferometer
absolute heterodyne frequency larger than maximal Doppler shift
→ fhet= 500 kHz

16. Requirement I Distance fluctuations:
Sensitivity with LTP better than 3 orders of magnitude (pm/√Hz)
SSI requirements achievable!

17. Requirement II Already achieved at our labs! Laser frequency noise:
Interferometer with unequal arms
Pathlength difference corresponds to the armlength → ΔL = L = 10 km
Laser frequency noise translates to interferometric phase noise
For resolution of δL < 1 nm/√Hz between 10mHz and 100mHz
(measured by M. Tröbs)
Already achieved at our labs!

18. Interferometer with polarising optics
Two possible ways to separate incoming and outgoing beams:
non-polarising optics
polarising optics
Advantage of pol. optics:
Freedom to choose LO-Level
Utilization of all light for interference
Possible disadvantages:
Thermal stability of polarising optics

19. Polarising interferometer breadboarding
Modulation bench: laser + 2 approx. 80 MHz
fhet = 1,6 kHz
Fiber coupling to optical bench
Optical bench: 3 Mach-Zehnder interferometers (2 non-pol +1 pol)

20. Sensitivity limited by mechanical stability of current setup
First results
Sensitivity limited by mechanical stability of current setup
Next step: bonding!

21. Bonded optical bench 4 interferometers:
(3 non-polarising + 1 polarising)

22. Bonded optical bench 4 interferometers:
(3 non-polarising polarising)
Reference Interferometer

23. Bonded optical bench 4 interferometers:
(3 non-polarising polarising)
Non-polarising Interferometer

24. Bonded optical bench 4 interferometers:
(3 non-polarising polarising)
Polarising Interferometer

25. Bonded optical bench 4 interferometers:
(3 non-polarising polarising)
Interferometer for frequency stabilisation

26. Outlook: heterodyne interferometry 500 kHz/phasemeter
Operate bonded optical bench with fhet = 500 kHz
Phasemeter has been adapted already
Phasemeter for variable frequencies
Include Doppler shift in phasemeter processing (LISA-like PM)

27. Summary
Measure the Earth’s gravitational field with much higher resolution
Constellation of 2 satellites separated by 10 km in a Low-Earth-Orbit
Measurement technique is heterodyne laser interferometry (benefit from LISA and LPF experience!).
Breadboarding on possible optical configurations has started
Investigations on interferometry with polarising components at mHz (also relevant for LISA)

28. Thank you for your attention!
Albert Einstein Institute
Hannover
Max Planck Institute
for
Gravitational Physics
Thank you for your attention!

29. Resolution of gravity anomalies
CHAMP
GRACE
Gravity anomalies (mgal) derived from the EIGEN-CHAMP03S (left) and EIGEN-GRACE02S (right) models.