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

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

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.

Edit: 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.

For instance, if you are in the thin-lens approximation, the answer is easy: there is no distortion whatever its diameter or its focal length.

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.

What you want is ray tracing. If the shape is good enough, you can solve everything analytically and therefore derive an equation linking what you want.

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 one (used in ray-tracing setups) and there is little more to say about it.

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

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

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.

Edit: 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.

For instance, if you are in the thin-lens approximation, the answer is easy: there is no distortion whatever its diameter or its focal length.

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.

What you want is ray tracing. If the shape is good enough, you can solve everything analytically and therefore derive an equation linking what you want.

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 one (used in ray-tracing setups) and there is little more to say about it.

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

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

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.

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. 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 one (used in ray-tracing setups) and there is little more to say about it.

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.

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

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

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.

Edit: 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.

For instance, if you are in the thin-lens approximation, the answer is easy: there is no distortion whatever its diameter or its focal length.

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. 

What you want is ray tracing. If the shape is good enough, you can solve everything analytically and therefore derive an equation linking what you want.

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 one (used in ray-tracing setups) and there is little more to say about it.

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

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

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.

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

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

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.

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. 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 one (used in ray-tracing setups) and there is little more to say about it.

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.