# Hybrid Electrostatic-Atomic Accelerometer for Future Space Gravity Missions
## 3 Results and Discussions
### Proof-Mass Rotation
Note that the compensation of rotations with constant angular velocities has already been demonstrated with a reference mirror driven by PZT actuators [55; 57; 58; 60; 69]. Here, in our experiment, we consider additionally the impact of angular accelerations. The platform was excited around the \(Z\) axis with a sine function at a frequency of \(\approx\)5.435 Hz corresponding to \(1/\left(4T\right)\) where \(T=46\) ms. The CAI is therefore submitted to all types of acceleration coming from the effect of rotation, i.e., centrifugal, Coriolis, and angular accelerations. These accelerations induce a loss of contrast of the atomic signal as seen in the previous paragraphs. The gyroscope signal is  
Figure 18: EA’s PM rotation and impact on CAI’s contrast. (**a**) Proof-mass angle \(\Psi\) measurement during the interferometer phase delimited by the three laser pulse detected thanks to a photodiode (red signal). The rotation excitation is made at 10.87 Hz with an amplitude of 106 \(\upmu\)rad p-p. Two excitation phases are represented, 0 rad (black) and \(\pi/2\) rad (blue). The excitation phase is defined relative to the first Raman laser pulse of the CAI. The dashed yellow lines are sine-fitting functions. (**b**) Evolution of the atomic contrast according to the excitation phase for a 10.87 Hz sine excitation of amplitude 106 \(\upmu\)rad p-p. The experimental data are represented in black dots with \(\pm 2\sigma\) error bars. The red dashed line results from a calculation of contrast loss using as inputs the same experimental excitation parameters. The interrogation time of the CAI is \(T=46\) ms.  
integrated to drive the angular control of the proof-mass. After integration, a gain \(G_{comp}\) is applied to adapt the amplitude of the feedback, which is fed to the secondary entry of the EA controlling the \(\psi\) angle of the proof-mass. The first results on active rotation compensation were obtained for an excitation of the platform at 5.435 Hz, with an amplitude of angular velocities of 5 mrad/s p-p and angular accelerations of 170 mrad/s\({}^{2}\) p-p. The effect of the implemented compensation scheme on the atomic contrast is visible in Figure 20a. The variation of the atomic contrast was analyzed relative to the gain amplitude of the compensation signal. The offset signal of the CAI contrast was subtracted and then normalized by the atomic contrast value obtained with no rotation. We can see that if no compensation signal is applied (gain = 0), the CAI contrast drops by \(\approx\)93%. The CAI contrast does not fall completely due to the limited excitation amplitude of the platform. For higher excitation amplitudes, perturbations of the EA's proof-mass along the horizontal plan are too strong to allow precise control of the PM. Increasing the gain on the compensation signal allows recovering the CAI contrast. An optimum gain of \(\approx\) -2.6 (\(\times\)2000) enables up to 85 % of the CAI contrast to be recovered. Increasing the gain even further leads to an over-compensated regime where the contrast falls again. For gains higher than \(\approx\)\(-\)5.2 (\(\times\)2000), the contrast drops even more than the initial value with no compensation. The higher excitation amplitudes offered by PM control allow this time to decrease the contrast to zero for gains higher than \(\approx\)\(-\)7 (\(\times\)2000). Looking at the PM excitation amplitude (cf. Figure 20b), we can see that we were able to drive rotation amplitudes up to \(\approx\)16 mrad/s p-p, much higher than the platform excitation amplitudes, which explains that the CAI contrast drops efficiently to zero. As expected, the optimal contrast recovery was obtained for the same level of angular velocity that the platform was submitted to, i.e., \(\approx\)5 mrad/s p-p. In this configuration, the PM is motionless in the inertial frame.