I scanned a picture from a Moore & Wright micrometer handbook and measured the angle by importing the picture into Autocad. I got 57.16 degrees.
When you measured the angle, did you measure the enlarged view or the main picture? Try both and see if they differ.
Before you measure the angle, you might have to scale the scan in X and Y to make sure it is proportionally correct (to compensate for distortion in the scanning process).
This may not be as simple as it first looks. In the X-direction, you need 40 crests per unit (inch). In the Y-direction I think you would need to measure across the crests of an existing micrometer, use that value and scale Y to suit.
We know that all the bodies use 40 tpi. What I do not know is if all bodies are the same diameter.
If the ratio of the X and Y scale factors you eventually use is significantly different from unity, something has gone wrong - scanners are not too bad.