Camera calibration and extrinsic parameters for perspective transformation
For your application, here are the steps I would follow:


Calibrate the camera and obtain the intrinsics - You have obviously done that and corrected for the distortion already. initUndistortRectifyMap only lets you to precompute the projection. Otherwise, you might as well use projectPoints each time. This is a detail and I would not care about that initially. But it's a good practice anyways.)
The main idea is to find the laser plane (with extrinsic calibration to the camera). To find the extrinsics:

a. Place a checkerboard in front of the camera and leave enough space on the board for the laser line to be projected. 

b. Image the laser line projections together with the checkerboard.

c. Now we can compute two planes with respect to the camera: The plane joining the laser line with the camera center, and the plane that checkerboard lies in (we now the checkerboard). 

d. Intersect the two planes to find the line in 3D space. 

e. Collect all such lines from multiple images and fit a plane to all of them. This is the equation of the laser plane.
To make measurements in 3D, simply shoot lines through the observed laser points in 2D image and intersect the rays with the laser plane. Each intersection will give a single point in 3D space.


This way we also do not explicitly need $(R,t)$. Our extrinsics are rather the equation of the laser plane. 

In case we use a point-laser, the equation also remains the same, as instead of lines, we can collect sets of points and still do the plane fit.

By the way, here is a toolbox and a recent further read.