# Which figure provides the greatest change in angle per change in distance? (trigonometry)

I have been having a lively discussion with others about the following:

We (myself and others) are using triangulation to measure distance to an object with a linear image sensor (CCD) and a collimated light source. The light source forms a dot at the far distance that we are interested in reading. The dot "moves" with respect to the viewer (CCD) as the object moves closer or further away.

The following figure shows four combinations of light source and CCD. The light and CCD are shown at different angles to the datum.

While it is arguably easier to mount the two on a flat plate, it may be that we don't get enough change in pixels to make it as useful as the other designs.

-Assume that the base distance is the same between all the designs (e.g. 300 mm). -Assume any reasonable angle (e.g. 10 degrees) for the angle of the camera and/or light. More importantly, angle should be consistent between treatments. -Assume the same distance to the object for all treatments.

The question is, (1) what is the difference in performance between designs, and (2) will we have to throw away half of the linear array if the CCD is not placed at an angle to the base but less if it is placed at an angle?