I am a Computer Science student that has a personal project to do. I decided to try and take on a project for a company, and one of the things that I need to measure is how perpendicular a laser is to a surface. The surface is non-reflective, and I need to adjust it until it is perpendicular to a 5 degree error. The adjustment is not an issue, but I am having trouble figuring out how I could check for how perpendicular it is. The surface is spherical in nature, but it is not a perfect sphere. Any alternative methods of checking it without having equipment too close to the surface (due to the destructive nature of what happens later). I'm sorry if I'm not very accurate, I have never taken any engineering courses and I'm not sure of the terminology. Any help would be appreciated
There's some irregularities in the question that might make the answer easier or more difficult. With a non-spherical object, one can and must allow for discrepancies.
Consider the following: There exist measuring devices which use a laser beam "bounce" to determine distance. Mounting this laser aimed at the approximate center of the "sphere" will provide a reference distance. My DME reads to 0.1 mm but I'm not sure of the distance capacity, as I'm unable to locate the device.
Once the reference distance is determined, angling the measuring device to four cardinal directions by an equal amount will provide an indication of squareness.
The image above, created by myself, shows C as the centerline of the laser, with A and B as equal angular displacement from the centerline. Measuring distance A will return a value greater than that of distance C, while both will be values greater than B.
The view can be considered both a top/bottom and a front/back representation. When A and A' and B and B' are all as equal as possible (and within accepted tolerance), the spherical shape will be as close as possible to the desired perpendicular.
Even though the question presents as a non-reflective surface, one is not using a requirement of reflectivity for the laser. It need only provide a visible laser dot for the measuring device to function.
If the final distance exceeds the maximum distance of the measuring device, one could create a couple of intermediate points within the measuring distance and extend a line using other methods to reach the required station.
If, as you mention in a comment, you can apply a small reflective sticker, and the laser isn't too powerful (at least during this alignment procedure), and the radius of curvature of the surface isn't too small, then I think it should be doable. (You don't specify the range of possible radius-of-curvatures of the surface, but if they are comparable to or smaller than the laser beam diameter, "perpendicular" becomes ill defined.)
When aligning mirrors, I often put a transparent plastic ruler between the laser and the mirror so I can see a bright spot on the ruler where the laser passes through the plastic on the way to the mirror, and a fainter (but still very visible) spot where the beam reflected from the mirror hits the ruler. I adjust the mirror until the two spots are on top of each other, which tells me the mirror is perpendicular to the beam. With a camera observing the ruler, some image processing software to determine the position of the spots, and control over either the object or the laser position/angle, you should be able to automate this.
A possible method that does not require specular reflection is to use photometric stereo imaging to determine the normal to the surface, and then use that information to set the angle of the laser. There is a large research literature, public code (e.g. on github), and commercial photometric stereo systems are available.