I fully understand the vision issue.
I learned to fly in 1982 with uncorrected vision of 20/400 corrected to 20/10. At the time I still needed a demonstrated ability waiver and that 38 year old waiver still gets entered with each FAA medical. I ALWAYS schedule my annual eye exam a few weeks before my FAA medical. It lets me:
a) get documentation from my opthamologist that my distance, near and intermediate vision is corrected to 20/20 or better; and
b) it let's me show up for the medical with contacts and progressive readers that have my current prescription, in the event the AME still wants me to demonstrate it on his vision test. The distance correction in my contacts has been stable for decades, however, the progressive reader prescription changes every few years.
In my case, eye doctors have over the years tried to get me to:
1) switch to a contact in one eye for distance and a contact in the other eye for near vision; and/or
2) switch to contacts that correct for both distance and near vision; and/or
3) back off on the distance vision to 20/30 to improve the near and intermediate vision; and/or
4) Just wear glasses that correct for distance in addition to the progressive reader prescription (I do have a pair of glasses that does all this, but my acuity is just not quite as sharp, and peripheral vision suffers).
None of those approaches work for me when it comes to passing the FAA's vision requirements and/or going all day without eye strain. Numbers 1 and 2 are not allowed by the FAA (because they work poorly). Number 3 is a non starter as well as 20/20 distance vision plays a key role in traffic separation and the FAA is rather big on that for noise abatement purposes. Number 4 is just less optimal for me.
What works is what works. The eye doctor I have now is very good at listening to what I need and working with me to make it happen. You need to find an eye doctor willing to do the same for you.
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As noted by someone above, missing 1 or 2 letters on the 20/20 line should not be disqualifying. If your AME is disqualifying you on that basis, find a better/more amenable AME. Not all AMEs have the same attitude and it comes into play when the FAA has a "guideline" rather than a "standard". For example, I ride my bicycle 15 miles per day and at 55 I'm still in great cardiovascular health with no history of high blood pressure, high cholesterol, etc. EXCEPT, I've had a life long history of white coat syndrome. My BP will be 120/70 with a resting pulse of 67 the day before my FAA physical and then I'll have something like 145/90 with a 90 bpm pulse during the FAA physical. It's high stakes and my BP and pulse rise to the occasion. It becomes a self full filling prophecy as I start stressing about it this time, because it happened last time.
The FAA "guideline" is 155/95. That's really high and it would probably prompt a cardiologist to want to admit you to the hospital and put you on a boat load of meds, some of which might be disqualifying and most of which would require a couple months to show they resolve the issue, without resulting in periods of excessively low blood pressure.
However, a good AME will look at the total picture and if it's really a white coat issue, will pass you as fit for flight. However since it is a guideline and not a standard an AME doesn't have to pass someone tests 145/90 during the physical. He or she could require a cardiac workup and a whole bunch of hoops to jump through before you are able to be issued a medical certificate.
Some AMEs also look for things that are just not even requirements. For example, an ATP in the area went to one of the local AMEs for his first class medical and he was denied by the AME as one leg was 1/2" longer than the other. He would not issue a medical unless the pilot got corrective shoes to even out his leg length. This was an ATP with plenty of time who'd learned to fly, passed all his check rides and successfully flew for a major airline with the leg difference never being an issue. Apparently the AME felt it would impede his ability to use the rudder pedals or something similarly stupid. Basically it was a very picky AME going way out of his or her way for a reason to deny applicants. It took the ATP six months to get the decision overruled, and it almost cost him his job as it was 6 months of being unable to fly. Most of the pilots I know avoid that AME like the plague.
At the other extreme, 35 years ago a local AME (a rural doctor in a big flat state out west) would pretty much fill out the paperwork for a second class medical on the tail gate of his pickup truck while the applicant filled out the check. I suspect he kept some long in the tooth crop dusters in business a few years longer than they should have been. I'm not advocating that approach either, but there is a reasonable, happy medium. It's helps if you can find an AME who is both interested in your health and is just as interested in keeping you flying, rather than just denying an application.