The Vertical Interferometer
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By adding the PRO Tower to your existing interferometer, you can take advantage of many benefits that not only makes it faster and easier to use, but safer and more reliable. Upgrade Your Horizontal Interferometer If you measure spherical optics or aspheres with a Fizeau interferometer that is horizontally configured, you could be sacrificing precision, productivity, and safety.
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Interferometric optical path difference scanners and FT spectrophotometers incorporating them. CNC en. CNA en. JPA en. The platform is stabilized using an integrated inertial measurement system and maintains the sensor head aligned with the gravity acceleration with a precision of 0. The lasers needed for the sensor are obtained using a compact frequency doubled telecom fiber bench 36 which is compatible with onboard environment.
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The gravimeter has been first characterized in static conditions. The measurement uncertainty has been estimated to 0. These uncertainties have been evaluated by analyzing the systematic effects affecting the sensor see Methods section. The estimation of the uncertainties has been confirmed by the comparison with an absolute A10 gravimeter. The difference between the two gravimeters has been measured equal to 0. The measurement sensitivity of our gravimeter in static is equal to 0. The gravimeter was subjected to vertical accelerations of frequency around 0.
The data processing which allows to calculate the gravity anomaly from the acceleration measurement is described in Methods section.
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Map of the location of the gravity survey. Blue line: course of the ship during October survey. Red line: course of the ship during January survey. First, we measured the gravity along a profile crossing the continental slope where there is an important gravity signal. This is the calibration profile where all spring gravimeters of Shom are tested and we have, therefore, a very good knowledge of the gravity anomaly along the profile.
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The round trip measurements on this profile are shown in Fig. A very good reproducibility is obtained between forward and backward measurements with a standard deviation on the difference equal to 0.
The measurements are also in good agreement with the reference data of Shom. The differences between the forward and backward measurements and the reference data have a standard deviation of 0. Absolute gravity measurements along the calibration profile. Then, we measured the gravity along a grid on the Meriadzec terrace at the edge of the continental margin. The measurement error of this survey has been estimated to 0.
A gravity model of the area has been established using the GMT software The extrapolation of the data was achieved using adjustable tension continuous curvature splines This model is compared to the one obtained by satellite altimetry 1 see Fig. The two models are similar but with a higher spatial resolution for the ship-borne model. The difference between the ship-borne measurements and the satellite model has a mean of 1. Gravity anomaly model of Meriadzec terrace. The red lines are the profiles on which the gravity was measured. The important differences on the left and right border are due to the extrapolation procedure of the ship-borne gravity measurements.
The measurements along the circular profile were done in order to investigate the precision of gravity measurements during the turning of the ship. For straight profiles, the difference between forward and backward has a mean value of 0. From the differences at the crossing points, we estimate an error of 0.
The precision in circular profile has been estimated by using the difference at the crossing points with the linear profiles. With the gravity measurements along straight and circular lines, we established a gravity model of the area see Fig. This model is compared to the model obtained by satellite altimetry 1. We see clearly here that the satellite model does not reproduce the gravity signal deduced from the ship-borne measurement.
The satellite model has an offset of 7. This highlights the fact that satellite altimetry gravity model is not precise in coastal areas and that ship-borne or airborne measurements are essential for gravity measurements in these areas. Gravity anomaly model of Douarnenez bay. The blue lines are the profiles on which the gravity was measured.
The two gravimeters were placed next to each other in the ship see Fig. Systematically better precision is obtained for the atom gravimeter with an improvement factor up to 5.
This improved precision can be attributed to the removal of calibration error for the absolute atom gravimeter, to the intrinsic better precision of the cold atom sensor, and to the good quality of the gyro-stabilized platform. The last point is clearly visible with the measurements in circular profile in which the platform of the relative gravimeter is responsible of performance degradations.
In conclusion, we demonstrated sub-mGal ship-borne gravity measurements with a matter-wave sensor. This technology has allowed us to obtain absolute gravity measurements from a ship and to improve the precision compared to a conventional spring gravimeter. The atom gravimeter could address other carrier like aircraft or underwater vehicle and thus offers a development in onboard gravimetry.
Our results support also the development of matter-wave sensor for measuring the Earth gravity field from space Finally, the demonstration of absolute acceleration measurements in dynamic opens the way to the next generation of inertial sensors accelerometer and gyroscope able to make absolute measurement in a dynamic environment. We can therefore imagine in the future absolute Inertial Measurement Units which do not drift and do not need to be calibrated.
An additional laser pulse of 1. The acceleration is deduced from the atom sensor signal P by using the following equation:. The value of P m and C are estimated continuously by assuming that the phase of the interferometer is randomly distributed and by measuring the mean value and the standard deviation of the atom sensor signal. The continuous acceleration measurement is obtained by filling the dead time of the atom accelerometer with the measurement of the force balanced accelerometer:.
This protocol allows having a continuous and absolute measurement of the acceleration with a dynamical range compatible with onboard applications. The main sources of this error are the different localization of the measurement points, the misalignment between the accelerometers, the bias of the classical accelerometer and the uncertainty of the scale factor, and the transfer function of the classical accelerometer.
To overcome this limitation, an automatic determination of the optimum interrogation time is implemented. The algorithm chooses between the following values of T : 2. The biases caused by the non-homogeneity of the magnetic field and by the first-order light shift are not reported in this table because they are canceled with our protocol of changing the sign of k eff and thus the sign of k eff at each measurement cycle.
The second-order light shift 41 , 42 has been calibrated by measuring gravity vs. The generation of the Raman laser by modulation produces additional laser lines which are responsible of a bias. This effect was calibrated by using the method described in ref.
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The uncertainty caused by the wavefront curvature of the Raman laser beams 43 , 44 has been evaluated, thanks to the estimation of the wavefront deformation induced by our optics. Due to the limited bandwidth of the laser frequency lock, the Raman laser frequency is not perfectly the same for the three laser pulses and causes a bias equal to. This bias has been estimated by measuring the laser frequency for each pulse.
The gravimeter is measuring the acceleration along the gravity acceleration with the ship as a reference frame. To deduce the gravity anomaly from the measurements, we apply the following data processing see Fig. Since the ship remains on average at the same elevation, the vertical acceleration of the boat a ship can be filtered by applying a low-pass filter Bessel 4th order. The choice of the filter time constant depends on the sea conditions and is a trade off between the spatial resolution and the filtering of vertical acceleration of the ship.
The data are corrected from this effect by using navigation data coming from the inertial navigation system of the ship. Finally, the gravity anomaly is obtained by subtracting to the data the normal gravity model 45 g norm. Illustration of data processing during the gravimetric survey of October and January The data used in this manuscript are available from the corresponding author upon reasonable request.
Sandwell, D. New global marine gravity model from CryoSat-2 and Jason-1 reveals buried tectonic structure. Science , 65—67 Carbone, D. Balancing bulk gas accumulation and gas output before and during lava fountaining episodes at Mt.