Calibrating and Correcting Errors from the 45 degrees Mirror and Panning Motor

We have performed a simple experiment to estimate the error of both the panning motor and the 45 degrees mirror. It consists of taking 4 measurements in a large room as follows.

1.

Place the rangefinder in the approximate center of the room.

2.

Aim the laser horizontally at the center of one wall, and mark its position (called A).

3.

Rotate the mirror 180 degrees vertically, and mark its position on the opposite wall (called B).

4.

Rotate the panning unit 180 degrees horizontally, repeating the above markings (called C and D).

  

Figure: The measurement setup for determining error in the angle of the 45 degrees mirror and the panning motor. The angles are greatly exaggerated here. The gray areas designate the cone-shaped areas (rather than plane) swept by the laser as it reflects off the 45 degrees mirror. Measurements at A, B, C, and D were taken from which the spread distances could be measured. The angles $\alpha$ and $\beta$ were determined assuming right triangles.

The measurement results are shown (exaggerated for effect) in figure 8. The calibration result will define values for xand y, and are determined as follows.

If the mirror is at 45 degrees, then x will be 180 degrees. The value of x is determined by $360 = 2x + \alpha + \beta$. This yields x = 179.54 degrees. Thus the angle between the cone and the plane is (180 - x)/2 since the error is equal on both sides of the cone. It is $\epsilon = 0.23 degrees{}$. Knowing this value, we can recalculate the actual position of the laser.

The rotation of the panning motor is captured by the value for y. It is computed by $y = x + \alpha = 179.7$, since $\alpha$ is covered twice (note the rotation arrow in figure 8). This error is assumed to be linearly distributed over the span of the panning motor and is large enough that compensation is required. Fortunately, the compensation involves changing a single constant, the ratio of positions per degree, thus the correction is trivial.