Find the equations (for instance in [here][1]). And solve them.

If this is good enough for you, you can make use of the usual [quadratic formulae][2].

In parallel to this I've heard of the actual use of ray tracing as a Monte-Carlo-typed method to get the same information.

However, I guess that even with that, a few effects are not taken into account. But again, it depends on the precision you need.

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**Edit:** I guess I understand now, intrinsics such as the lens actual curvature, shape and composition?

It is perfectly possible: that's what's called [geometrical optics](https://en.wikipedia.org/wiki/Geometrical_optics). What you want is ray tracing (if the shape is good enough, you can solve everything analytically). 

This is basically the "ray tracing" stuff I was already talking about.

However, in contrast with a real calibration, with real images, this technique does not take a few effects into account (like diffraction, interferences, non-linearities or the errors in the specifications compared to the actual lens).

The main equation is the [refraction][3] one (used in ray-tracing setups) and there is little more to say about it.

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AFAIK, diameter and focal length is not enough: the full shape is important. With the diameter and the focal length alone, you need to make extra assumptions.


  [1]: http://www.researchgate.net/publication/220436724_Rational_Radial_Distortion_Models_of_Camera_Lenses_with_Analytical_Solution_for_Distortion_Correction
  [2]: http://math.stackexchange.com/questions/302093/how-to-calculate-the-lens-distortion-coefficients-with-a-known-displacement-vect
  [3]: https://en.wikipedia.org/wiki/Refraction