# X and Y profile of a round object using a 45degree mirror (why is the Y profile smaller)

I'm trying to measure the X and Y profiles of a round object using a single camera. The camera has a direct view of the object in the X profile but sees the Y profile of the object as a reflection on a mirror mounted at 45 degrees. The problem is that the Y profile seen by the camera is smaller than the X profile of the object. Although the object is round. See the attached diagram, photo of the setup and a photo from the camera.

I would think that the reflection of the Y profile will be the same distance from the camera as the X profile and therefore have the same size. But it does not.

Why is the Y profile smaller than the X profile? Or why is the Y profile (reflection) further away from the camera?

I did get the mirror from my wife's makeup so it could be that the reflective coating is at a radius. But the glass itself seems flat.

## 1 Answer

The way you have drawn your diagram suggests the mirror reflecting the y-profile is at the same distance from the camera as the object is. But the 'effective' distance to the y-profile image also needs to include the distance from the object to the mirror. See my adaption of your original sketch,

• I should have asked my question to myself. "Or why is the Y profile (reflection) further away from the camera?" I'm going to have to play with the optics an placement of the object. Nov 25, 2020 at 21:03
• @bluscape If there is sufficient space to do so, then the simplest solution is to put the mirror very close to the object, so Dx ~= Dy, and Dxy << Dx Nov 25, 2020 at 21:08
• I intentionally introduced the distance between the mirror and the object to simplify the measurements or detection between the two profiles. My setup is not very controlled and have to allow tolerance if the object moves. But I will see by how much I can reduce it. Both does not HAVE to be the same size, I can compensate for that but it would be nice if they were the same. Nov 25, 2020 at 21:14
• Ok. I just moved the camera horizontally towards the mirror such that Dx ~= Dy + Dxy. The placement does distort the X profile a little bit though. Nov 26, 2020 at 6:37