If someone say honestly that they receive the photons coming from the moon, then they must get a number of photons that is bigger than the error margin, preferably a few times bigger than the error margin. If it is smaller they can't be sure that it is not some noise.
There are three sets of three graphs. They are very similar, so let's see only the first one.
In the first graph there is a dark line in the center that shows that there are more photons coming at the expected time, than before or after that time. The signal is easy to see, but it is difficult to get any numerical values from this graph.
From the second graph it is possible to read some numerical values. Each bar shows the number of photons that arrive in a 100 ps interval. They have probably a Poisson distribution, but for simplicity let's approximate that by a Normal distribution.
Before the peak, there are approximately 10 +/- 10 photons coming every 100 ps. (These values are estimated from the graph with a lot of zoom, I can't be very sure about them. The values seem to be scattered between 0 an 20, so I assume that the average is ~10 and the standard deviation is ~10.) These are the photons that come from others sources. So if no mirror is present in the moon, or the laser dos not have enough power, then this is the expected value during all the experiment.
At the peak, there are approximately 400 photons in the same time interval. The difference between this value and the average of the first values is like 40 times the standard deviation. So it is almost impossible that they get these peaks by a random chance. For example, the probability to get a value that is bigger than 5 standard deviation is less than 1E-6, for 10 standard deviation it is less than 1E-23, and for 40 standard deviation it is almost almost 0. And they get not only one, but 8 intervals with more than 100 photons.
After the peak, they get more photons than before the peak for technical problems. I see something like 20 +/- 20. Whit these numbers, the chance of a 400 photons peak is bigger, but still almost 0, but I think that the correct way to do the estimations is using the first values.
The third graph is an auxiliary measure with an earth based mirror to get the dispersion caused by the system.
The analysis in the web page is more elaborated. They estimate the shape of the mirror and use the data from the third graph to explain the shape of the peak.
The data about these measures is hard to find. But after some googling the best data I could find are in http://physics.ucsd.edu/~tmurphy/apollo/highlights.html . It it possible to make some estimations from the graphs.
There are three sets of three graphs. They are very similar, so let's see only the first one.
In the first graph there is a dark line in the center that shows that there are more photons coming at the expected time, than before or after that time. The signal is easy to see, but it is difficult to get any numerical values from this graph.
From the second graph it is possible to read some numerical values. Each bar shows the number of photons that arrive in a 100 ps interval. They have probably a Poisson distribution, but for simplicity let's approximate that by a Normal distribution.
Before the peak, there are approximately 10 +/- 10 photons coming every 100 ps. (These values are estimated from the graph with a lot of zoom, I can't be very sure about them. The values seem to be scattered between 0 an 20, so I assume that the average is ~10 and the standard deviation is ~10.) These are the photons that come from others sources. So if no mirror is present in the moon, or the laser dos not have enough power, then this is the expected value during all the experiment.
At the peak, there are approximately 400 photons in the same time interval. The difference between this value and the average of the first values is like 40 times the standard deviation. So it is almost impossible that they get these peaks by a random chance. For example, the probability to get a value that is bigger than 5 standard deviation is less than 1E-6, for 10 standard deviation it is less than 1E-23, and for 40 standard deviation it is almost almost 0. And they get not only one, but 8 intervals with more than 100 photons.
After the peak, they get more photons than before the peak for technical problems. I see something like 20 +/- 20. Whit these numbers, the chance of a 400 photons peak is bigger, but still almost 0, but I think that the correct way to do the estimations is using the first values.
The third graph is an auxiliary measure with an earth based mirror to get the dispersion caused by the system.
The analysis in the web page is more elaborated. They estimate the shape of the mirror and use the data from the third graph to explain the shape of the peak.