Somewhat lengthy, but worth the time...
rjl2001:
While I am not a doctor, here's the "skinny" on depth perception, FAR 67.103 (f), the test with the lines that cross, and the requirements to hold a first class medical certificate... based on my opinion and experiences.
First of all, I'll impart some of my personal history with this issue. That way you know that I've, "Been there, done that." I was born with strabismus (congenital esotrophia or crossed eyes), and it was so bad that the doctors told my parents that I'd likely lose most of my vision in the eye that was less favored (we all favor one eye over the other.) They were also told that I'd never see very well and will likely need an eye-patch and glasses all my life. This prognosis was provided by the Air Force doctors at the AFB where my father was stationed. Not willing to accept these findings, my parents went to a local pediatric eye doctor at a civilian regional hospital. He was Dr. Sherwood Maddux of Macon, GA. (I remember him becaue I owe my career to this guy.) His solution was to use corrective surgery to reconnect the connective tissues that align the eyes. That was in the early 1970s and the procedure had been around for about 20 years or so.
After three surgeries (1972 to 1973), I no longer have strabismus and my vision is perfectly fine in both eyes... no corrective lenses. However, in the early 1990s I was disqualified from military flying simply because I had the surgery in the first place, and they gave me the same silly stereo-vision test with the housefly wings and sets of dots. Remember it's the military flight surgeon's job to say, "No." They don't want to spend all that money training someone only for that person to have a medical problem... if you're a senator's son, then that might be different. So before I spent a lot of my own money on flight training, I got a comprehensive eye exam from a civilian doc. He spent a good hour or so giving me all kinds of different tests to check for depth perception, stereo-vision, and peripheral visual fields in addition to acuity and color tests. He basically said my vision, depth perception and stereopsis was fine and didn't see any reason why the FAA wouldn't issue a medical certificate (he wasn't an FAA doc, but was familiar with what was required by the FAA.) However, he did note that I have a few (2 or 3) "prism diopters" of esophoria (eyes cross inward), but he didn't think it would be disqualifying. In fact, the FAA allows up to 6 prism diopters of esophoria (eyes cross inward) or exophoria (eyes diverge outward) and 1 prism diopter of hyperphoria (eyes deviate vertically.)
When I first applied for a First class medical, I disclosed my history to the FAA, passes the physcial, and have yet to hear a word from anyone in Oklahoma City regarding the issue. I have held a first class medical for over 10 years and have never encountered a problem with the FAA or the tests given by the AMEs I've gone to. Most AMEs are interested when they see item "d" checked on the application and they'll ask about it, but that's about it. None of the airlines I've worked for considered it an issue either. In fact, when I did the UAL medical in 2000, they saw it on my paperwork, gave me the standard stereo-vision test, and never said another word about it. I passed the medical and worked at United for 8 months, but that's another story.
Now about FAR 67: The key here is in 67.103 paragraph "f." The requirement is that you have adequate stereo-vision and that you don't see double (that's the "breaks in fusion" part of the paragraph) when performing normal airman duties. The assumption is that if you have adequate stereo-vision, then you should have adequate depth-perception. Your brain works wonders and does a lot to compensate for any problems you might have with not possessing 100% depth perception. Motion of objects plays a big role in the compensation done by the brain. Most tests given for depth perception consist of static objects on a flat screen or paper. Your brain is perfectly capable of determining depth simply by observing the motion of objects in front of you (real or relative motion.) If you're walking down a path in the woods, you'll notice the trees that are closer appear to move by more quickly than the trees in the distance... there's your depth perception. Or try this, close one eye and rock your head back and forth... does the relative motion of objects in the room provide depth clues? The point is, the test administered by the AMEs have limitations. There are many other factors which provide for depth perception.
The test with the lines (usually in the form of a musical note and a series of numbers) is checking for esophoria, exophoria, and hyperphoria. The vertical line is checking for the first two and the horizontal line is checking for hyperphoria. I covered these earlier, but unless you have more than the values described in 67.103 (f) you won't need further testing. If you exceed those values, then the FAA will likely require further testing by an eye specialist. To get a first class medical certificate you may have to get corrective lenses to adjust any deviations. Then you have to show your vision is normal with no "breaks in fusion" or double vision, and the FAA will likely issue you a certificate with a limitation requiring you to wear your glasses while flying (not a big deal.) This late in your life, the surgical procedure that I described is probably not advised. That procedure works best for children under age two. Adults typically get best results with corrective lenses.
The bottom line is: don't let anyone tell you that you cannot have a flying career because of this. If I'd stopped after listening to the USAF docs, then I wouldn't be flying for a major air carrier today. You may not become "Mav" or "Iceman" or "Buck Rogers" or whatever

but you can still have a very rewarding career flying airplanes or helicopters. Definitely look into Army flying. Just because one service says "no" doesn't mean the other will. I have flown with several guys at the airlines who flew helos in the Army after being told no by the AF and Navy. They ended up flying both rotary and fixed wing aircraft in the Army and had a great time doing it. (The Army has C-12s aka Beech King Airs)
Anyway, here are some interesting links to look at and good luck with your career!!
http://www.children-special-needs.org/
http://www.strabismus.org/
http://www.vision3d.com/stereo.html