Frist of all ,
Nice idea to work with , but I have some concerns
1) You are planning to use IR radiation....but As per as my knowledge IR radiation most of the time is spherical wave it is not propagate like a coherent beam as you are shown in the picture...when you try to use the transmitter available in the market....
2) One can focus the spherical waves into the plane wave using lens but in that case you need to design the lens for the frequency of your radiation other wise it will generate either diverging of converging beam based on the distance
3) The traditional method of optical triangulation uses the laser beam most of the time with focused diameter, one of the key aspect in your approach is how you are making the beam fall every time on the lens bcz the angle of incidence of the beam will change based on the target position and as it will results in the change in angle of reflection....
4) The present IR system uses two different method for such linear position estimation using single IR detection method ( in which the magnitude of the IR radiation is key signal, however this is most of the time empirical calculation [Experimental ]) , the second one is use of multiple IR detector ( in which the magnitude at every position of IR sensor acts as a signal , the method that is similar to your idea)
Now coming back to the detection of object position using optical triangulation is based on the magnitude of the Radiation receiver ....but in case you are planning to use laser of optical radiation I will suggest you to go for position sensitive detector or array of the detectors....
One need to do some mathematical model for the idea ...In my view you should start writing the optical triangulation formalism with out lens initially ...
Good Luck