Insight into/about/on/to

Hi everyone!

I'd appreciate if someone could answer my question.

Can I use give insights about in this kind of sentence:

Not only do measurements provide important information on the structure of the nucleus...bla-bla-bla, but they also give insights about the degree of excitation..bla-bla-bla.

I need to somehow find a synonym for provide information phrase but can't think of anything except for give insights about/give insight to/give insight into/give insight on. Are these correct and can I use them intercomplementary? Perhaps you can suggest a better synonym?

I know that there's a basic rule for using give/provide insight into, but I've just searched and found some articles written by native speakers where they use other phrases - the ones I listed here.

Thanks!