One of the important information in astrophotography is a scale (arcsec) per pixel. Usually, the lowest angular diameter per pixel you can achieve is amateur astrophotography is 0.5 arcsec/pixel, while 1-2 arcsec/pixel is considered comfortable to work with.
How to calculate it? On the internet you can find the following formula for it:
If you are like me, you would like to know what is 206.265 constant and why result of dividing \( \mu m \) by \( mm \) is \( arcsec/pixel \).
So let's start from the beginning and try to figure out how to calculate scale per pixel; after all, it is a simple geometry.
As we focus in infinity (see hyperfocal distance), we can assume that the image plane is exactly at focal length \( f \) from the lens. Of course, \( \alpha \) is on both sides, so we end up with the following formula to calculate it:
As a reward for reading so far, here is an online calculator. It doesn't simplify the equation and uses \( \arctan \) so can be used for bigger angles (like to calculate FOV of the whole matrix). Enjoy!