3 Experiment description

The experiment, as performed at OCA, is shown in Fig. 1.

  

Figure 1: OCA Lunar Laser Ranging facility

The YAG laser emits four short pulses at a rate of 10 Hz. The time intervals between the first and the second pulse, the third and the last one, are respectively: 1.6 ns, 4.1 ns and 5.7 ns. This temporal code, imagined by Jean-François Mangin, permits to deduce, without any ambiguity, the pulse position in the echo diagram. A telescope of 1.5 meter aperture collimates the laser beam in the lunar direction. A fraction of the photons coming from the laser output is sent onto a PIN photodiode. This detector is connected to a start timer giving the start time $t_{\rm Start}$ of the laser pulse. The photons coming from the Moon impinge a return detector. This return detector is connected to a return timer, similar to the start timer, giving $t_{\rm Return}$. The time base of the timers is a caesium atomic clock. A corner cube, at the telescope output, returns a fraction of the emitted photons onto the return detector (Mangin 1982). This permits to calibrate the instrumentation. The arrival time of the calibration pulse on the return detector is $t_{\rm Calib}$. This calibration information allows us to know accurately the transit time of the light pulse between the corner cube on the Moon and the calibration corner cube. The spatial reference of the LLR station is the crossing of the telescope mount axes. Finally, the distance between this spatial reference and the target will be known if the distance between the cross axis and the calibration corner cube distance $d_{\rm Calib}$is known (see Fig. 1). This distance is measured geometrically. The round trip travel time $T_{\rm Obs}$ of the light pulse between the spatial reference and the Moon corner cubes is

$$\begin{eqnarray} T_{\rm Obs}(t_{\rm Start}) &=&\left( t_{\rm Return}-t_{\rm Star... ...}\right\rangle \nonumber \\ &&+\frac{2d_{\rm Calib}n_{\rm Air}}{c}\end{eqnarray}$$ (1)

where $\left\langle t_{\rm Calib}-t_{\rm Start}\right\rangle$ is the calibration mean value integrated over a period $\tau _{\rm Calib}$, $n_{\rm Air}$ is the air refraction index, and c is the light velocity. The mean value of the photon number coming from the Moon and detected per pulse by the return detector is of the order of 0.01. Thus, the return detector works in a single photon mode. Since the transit time of the return detection device depends on the number of received photons, the calibration will be valid if it is also performed in a single photon mode.