Hi,

The Return Number is the pulse return number for a given output pulse. A given output laser pulse can have many returns, and they must be marked in sequence of return.

The first return will have a Return Number of on e, the second a Return Number of two, and so on up to five returns.

The Number of Returns is the total number of returns for a given pulse. For example, a laser data point may be return two (Return Number) within a total number of five returns.

As it is written in your tex file, there are three labeled returns (1,2 and 3). These three returns can correspond to the same obstacle but perceived at a different altitude (the Z-coordinate is rather different for the three returns). That's why you do not have the same X-Y coordinate for the diffferent returns. The number of returns can be explained by the number of received echoes at the reception stage (for example).

Thank you Benoît for your answer. But again I do not understand why the returns do not have the same X-Y coordinate. Indeed, I think when the LiDAR is at position Xlidar-Ylidar , it emits a pulse then receives the different returns (in my case three returns) corresponding to the different elements of a given obstacle (in my case, it is a tree). So the LiDAR will measure the altitudes Zi for the returns {1,2,3}. For me, I must have in "las" file: Xlidar-Ylidar-Z1, then Xlidar-Ylidar-Z2, then Xlidar-Ylidar-Z3.  

If it is not the case, do you think that LiDAR can measure the exact  Xi-Yi coordinate for each return i ?

Indeed, in the las file the X-Y coordinates are not the coordinates of the LIDAR. They are the coordinates of the obstacle. So the three X-Y coordinates are disturbed by the measurement noise, and so we do not have X1=X2=X3 and Y1=Y2=Y3.

To answer to your last question, a LIDAR can indeed measures the Xi Yi coordinates (not fully exact but disturbed by the range measurement noise, given by the manufacturer). These coordinates are provided by a polar to cartesian conversion, which can also explain the approximations.

Ok I understand thank you.

Hi Abdelaziz!

The sounding angle is off-nadir. Then the returns at different heights have different x-y coordinates.

Thank you Andres and Philipp

I think that you are right, the observation are off-nadir: 34o