What a lot of confrontation here... I find it a bit unnecessary, but here come my answers more adjusted to that tone:
I'm not an optical engineer but I don't think that this will have any meaning to them. Does it ?
I think it would, but it might be time for you to lift your sight and not limit yourself to what you can express by what you know about numbers and mathematics. Mathemathics is indeed very elegant, concise and beautiful way of capturing things; but also constrained, limited and not always intuitive as all/most other human constructs.
Don't misunderstand me here - I like mathematics and the quantitative, but limiting my view and reasoning to it would be foolish, I'm convinced. Moreover, photography is an art in its essence and the final impact of the images one produces is what is most important. All the operationalizations and definitions are merely tools to crisply understand how things work and how we can optimize them.
I also believe that an optical engineer dealing with photographic equipment will only benefit from developing his/her artistic vision and skill when it comes to photography. That way one can more efficiently do effective optimizations of photographic equipment without the need for hundreds of pages of scientific text, analysis, descriptions, data, etc. etc. to be produced and published.
Well start testing away then. We've heard a lot of claims about "3D pop" whatever over the years. Perhaps it's time to actually provide measurable test results or at least unequivocal visual evidence instead of claiming that "Grass is red. Don't you see how red grass is ? I'm sorry if you can't see it. Maybe you're just colour blind ?".
It's the job of those who claim these things to demonstrate them. Otherwise scientists would waste their time having to disprove every single bonkers opinion.
No argument against the direction which you suggest me to take here. I agree with it. However, this inquiry of mine and my drive to publish about it also has its limits and the level of rigor that you suggest exceed both that and the budgetary constraints I find defensible for it in my case. To get all the stuff (incl. lenses) for a piece of small research study like that, do the analysis and publish on it has requirements that fall beyond what I'm willing to give it at this point. Sorry for that if it disappoints you - I don't care enough to persuade those that are not themselves seeking what lies in and beyond these concepts. Perhaps more, perhaps less. I've seen enough to rule out that it is altogether bogus, though. It's not entirely my job do to what you say, as I haven't committed myself to carrying out a scientific research study on it.
If I was a paid optical scientist/engineer and had the time and possibility to carry out such research, I'd gladly commit myself to the task with the ambition to come up with results as true and waterproof as possible.
I don't know what "3D structure" means. So I don't know what to look for.
I'm not quite sure that a short video with a couple of zoomed in comparison shots is quite enough to ascertain anything.
If you have eyes to see and curiosity to drive you, you might indeed try. It's not my mission to convince you nor motivate you to understand; that is entirely up to your free will.
Those who are curious and willing to explore and understand what this 3D pop might be, will give it honest attempts, just as I do. Those that just want to disprove the concept or diminish it, will find their ways of doing so and there is pretty little I can do about it however hard I try.