Wow You are very educated about your vision. And yes, for esotropia, BO prism is appropriate. The question is, are you diplopic with the atropine? You should not be diplopic if your convergence is driven by your accomodation and you are cyclopleged.
It seems your docs are on top of your examinations and so I am assuming they have fully evaluated your diplopia for other causative conditions.
Please let me know this has been done. I know you have had a brain scan so that is reassuring.
Finally, here is a website to confirm you conclusions: http://www.revoptom.com/content/d/ophthalmic_lenses___and___dispensary/c/15234/
I don't know why they are correcting you with BI prism. If the cover/uncover test revealed exotropia they would correct with BI. But you have been overaccomodating which would create esotropia. So I am not certain why they are coming to this conclusion. Can you call and tell them exactly what you told me and ask why a BI prism?
Unfortunately every Dr. I've seen is ether incompetent or lazy, (or both). They have me sit through an exam, only to respond with statements like, "I'm not trained/experienced in your type of vision issue" ...or "your vision is just blurry because they are dry, some wetting drops will solve it" ... or "your eyes look fine, you're probably just imagining it", etc.
To answer your question, no they have not looked into the cause of my diplopia. None have been willing to do anything beyond prescribing a BI prism. BI felt like the wrong solution (and the glasses I bought with BI didn't help), so after a while I ended up not even mentioning it when going to a Dr. and instead focusing on the accommodative issue, hoping the convergence issue was a byproduct and would resolve once accommodation was working properly.
I've been under atropine for more than 24 hrs so far. It's not quite what I was expecting, but I may need to give it more time. I put in drops at night, and the next morning felt I was still accommodating, so put in more drops. Now things 2 feet or closer are blurry. The 1-2 foot range is made clear with +1.25 readers, and the 0-1 foot range with +2.5 readers. Anything beyond 2 feet is made blurry by readers.
I was not expecting to see things 3 feet away (like my monitor) while under atropine, but my vision seems to be unchanged beyond about 2 feet. (except for sensitivity to light of course). Maybe I'm not fully cyclopleged?
My vision is still double so far, and in fact it takes more effort/straining now to fuse the images, so I'm getting bad headache from it.
(sorry for coming across bitter, but you can imagine the frustration of more than 2 hours in the waiting room, plus a full exam done by an assistant, and then AFTER all that, being told something like "oh, you're here for double vision... I'm not the right kind of Dr. for that, you'll have to find someone else".) The only remaining option for me is to resolve this on my own utilizing reference sites like this one.
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Is my vision change in response to Atropine indicative of someone with hyper/spasm of accommodation, or indicative of someone with normal functioning accommodative system? Since my vision beyond 3 feet did not change, I'm wondering it it's the latter.
(oh, to answer your other question... yes, I made the apparent mistake once of politely asking why the BI if my issue seemed to be my lines of sight crossing pre-target, ... he abruptly snapped back "I'm the Doctor, if you don't like the prescription, go somewhere else!"... I conceded to his heavy hand, but thought it strange I couldn't ask a question or care about my vision and subsequent purchase of glasses. You could say I've had bad luck with Dr. visits.)
(the MRI I spoke of was done under my own accord when I made a self-referral appointment with a neurologist. It was not suggested by an ophthalmologist.)
I am very disappointed in my colleagues and unfortunately you are not the first patient I have heard complain of abrupt ophthalmologists or ones unwilling to listen. Time is money and some docs are not immune to greed.