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Wednesday, May 21, 2003

Focus on Infinity

I picked up some reading glasses today. Since I don't need them, it took me a minute to figure out a strategy for selecting the strength. Normally one would just select the pair that lets you focus easily at reading distance, but I can already do that without them. I should have researched it ahead of time, but I hadn't gotten around to it yet, and it proved convenient to buy them today...

So, I held some text up at computer-monitor distance, and then held the glasses so they split my view with the glasses covering the near text, and leaving a large sign in the distance un-obscured. The goal: to find the lens that allowed me to keep both objects in focus at the same time, thus implying that the lens is defocusing the near text from arms reach to infinity (where the eyes are most relaxed).

I settled on the +150s and crossed my fingers that I wouldn't kick myself when I got home and researched my choice. It proved a good choice! Here are the simple principles nobody bothers to tell you (derived from a number of different sources):

First off, 150 is really just marketing speak for a diopter of 1.5. Reading glasses are typically available between 1 and 2.5 or so, in increments of 0.25 (100, 125, etc..). The diopter is most easily understood in terms of what distance (the "focal length", in meters) it re-focuses to infinity, which is expressed by the simple relation:

distance = 1/diopter

So, for instance, the 150s I bought will make an object 2/3rds (=1/1.5) of a meter away focus as if it were off at the horizon. (Note that since your eyes aren't made to focus further than infinity, these glasses are going to make anything more than 2/3rds of a meter away fuzzy to most people.) Quite simple!

So, conversely, if you want to select reading glasses for your computer work (or reading or whatever), measure the furthest distance you're likely to work at regularly, invert, and that's the prescription you want. In my case, 2/3rds of a meter is about right.

Here is a more general formula:

focus_distance = 1 / ( 1/actual_distance - diopter )

This tells us where, in terms of how our eyes have to focus, an object will appear (focus_distance) relative to where it actually is (actual_distance). For instance, if I move just a few inches closer to the screen, the focus goes quite rapidly from infinity down to just a few feet. Note that if we are aiming for a focus_distance of infinity, the second equation just resolves to the simpler first one.

Now, why bother will all this? It turns out that the astigmatism I have, based on its orientation (axis between 61 and 119 degrees), is called an "against the rule" astigmatism (only about one in twenty are) and is likely caused by too much near-focusing (surprise surprise!). ATR astigmatism appears (the research is still vague, but this is the emerging hypothesis) to be the eye's attempt to keep things in focus under the strains of up-close work, which would explain why my astigmatism is most noticeable at distance (because my eyes have reconfigured themselves for up-close work). The glasses the optometrist prescribed me make my distance vision great, but don't do nearly as much for my up-close work. In fact, they're likely just setting me back, forcing my eyes to compensate even more, which is just going to accelerate the decline of my vision (assuming I don't become a rancher). Indeed, I found a few references to ATR astigmatisms being a common source of "conflict" between patients and optometrists because the prescriptions given typically just lead to increased eye strain. Their recommendation? Plus lenses! Exactly what I asked the optometrist for in the first place, which she refused to prescribe.

So, now I've made my own--double-decker glasses for the do-it-yourselfer. My hope is that eventually I'll be able to chuck the prescription ones, but I don't know if this astigmatism is reversible. Time will tell.

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Simon Funk / simonfunk@gmail.com