5 Perspectives and conclusions

Some recent instrumental developments will allow us to improve both the stability and the accuracy of the distance measurements. The terms $E_{\rm Calibration\ Detector}$ and $\sigma _{\rm Calibration\ Detector}$ could be reduced by improving the Geiger voltage stability applied on the photodiode and by reducing the spot size of the light beam. We designed a device able to apply the Geiger voltage with a delay of the order of 10 ns having a voltage stability of 1 Vpp. The spot reduction could be achieved by increasing the optical magnification. Some optical components having adapted the equivalent focal and a sufficient aperture are today capable to obtain a spot size for both the calibration and the lunar echoes in the range of 100 $\mu$m. With these improvements, $E_{\rm Calibration\ Detector}$ would be reduced to 10 ps, and $\sigma _{\rm Calibration\ Detector}$ to 37 ps. These minor modifications will permit to obtain a residual precision $\sigma _{\rm Residual}$ = 50 ps as compared to the present 60 ps, and an accuracy on the normal point $E_{\rm Normal}$ = 105 ps (16 mm) as compared to 160 ps (24 mm). An improvement of the electronic devices used to shape the photodiode signals for the timer, and the utilisation of some high performance wire will permit to obtain a better time stability of the measurements. Figure 9

  

Figure 9: LLR time stability as compared to the improved experiment in single photon and multi-photons modes. The best time stability curve is imposed by the laser width stability

shows a workbench calibration time stability obtained when taking into account all the remarks listed above. The first plot is performed in a single photon mode, and the second in a multi-photons mode (about 1500 photons per pulse). The third plot represents the LLR calibration time stability as it is working today. The LLR calibration drift is of the order of 40 ps over three hours and less than 4 ps over the same time amount for the workbench experiment. The time stability of this workbench experiment obtained in multi-photons mode, is in the range of the laser width time stability (see Fig. 2). This means that, in this experiment, the main limitation comes from the laser. A temperature control improvement of the laser cavity or a reduction of the laser width would probably improve the limit. The performances obtained in multi-photons are interesting for the satellite laser ranging but not for the LLR, since the return photon number is in the 0.01 range for the Moon. Converted into distance, this limit would permit to obtain some normal points integrated over $\tau$ = 300 s with a precision of 0.1 mm. Of course, some other noises coming from the clock, the satellite corner cubes and the atmosphere, which are not taken into account here, will degrade this precision and it is difficult today to envisage the real precision that one would really observe. These stability improvement developments are first led at OCA for the Time Transfer by Laser Link (T2L2) experiment (Fridelance et al. 1997). The experiment will permit to transfer the temporal information of the new clock generation (Lea et al. 1994); (Salomon et al. 1996) without degrading the performances. In this context, the time stability of the laser station has to be better than the clock stability.

The main cause for dispersion on the Earth-Moon distance measurement comes from the orientation of the corner cubes array. The uncertainty added by this phenomenon in the measurement depends on the size of the retroreflector and the lunar libration. Statistically, since 1995, only 4.3% of the lunar echoes precision have been obtained with the intrinsic precision of the OCA LLR station. Due to the bad link budget, 88% of the normal point are obtained on the largest Apollo XV reflector, 5% and 6% on Apollo XI and XIV and only 1% on Lunakhod 2 which is the smallest one. As the average precision is proportional to the panel size, the improvement of the global precision will be obtained by increasing the number of echoes on the small panels. This could be obtained by increasing the photon number per pulse sent in the lunar direction, by increasing the laser shoot rate, by using adapted optics in order the decrease the spot size of the laser beam on the Moon, or by changing the laser wavelength to improve the quantum efficiency of the return detector. As long as almost all the echoes are obtained only on the largest Apollo XV retroreflectors, a major improvement of the LLR station precision is not useful.

An important term is added by the atmosphere in the accuracy error budget. A preliminary work is led today by Nicolas Pelloquin to envisage a correction of the atmospheric delay deduced from some parameters directly measured by the retro-diffusion of the laser pulse sent to the Moon (Hauchecorne et al. 1992); (Argall & Jacka 1996). Another correction method, would be the two colours laser ranging (Lucchini 1996). In this method, the atmospheric delay information is extracted from the difference between the time propagation of light pulses having different wavelengths. Probably this information could not be extracted from the lunar echoes because the link budget is too bad, but from a satellite target located roughly in the direction of the Moon. The success of this method will depend on the spatial homogeneity of the atmosphere. The study of the two colour laser ranging is supported at OCA by Jean Gaignebet.

A continuous set of quality measurements is necessary to maintain and improve the ephemeris, the Earth's precession and nutation determination. The increased data density with an improved precision and accuracy will allow a better understanding of the Moon, the Earth, and the Earth-Moon system, and will also improve tests of gravitational physics and relativity.

Acknowledgements

The lunar libration ephemeris used in the computation of the residual precision has been provided by the NASA.