It's time for me to get cataract surgery. I think I'll go for the fixed-focal-length lenses, maybe with astig correction.
I've always been nearsighted, which suits me fine, since I read a lot, compute a lot, and work with tiny parts on PC boards. I can wear glasses to drive or ski or whatever.
So, what should the focal lengths be? I've noticed that two eyes have a lot better resolution than one, even if one isn't well focussed. Brains integrate the images somehow. Some people go for one eye close-focussed, and one at distance, so they don't use glasses at all, but I have another idea:
Focus one eye really close, like 10" maybe, and the other at computer distance, 20" maybe. Ideally, that will give me good resolution from, say, 8 to 24 inches.
Something like this:
There would be a box that defines a minimum resolution over some range of distances. This is starting to look a lot like a Chebychev bandpass filter, and I guess the math is similar. I could also get a flat Butterworth looking curve if I moved the peaks closer together, but that would reduce the working range.
The complications are:
Pupil size changes with illumination, so the two peaks get narrower in dim light.
I don't know how well a brain combines two inputs; probably better than just summing amplitudes. So the peaks could be farther apart than simple math suggests.
And, of course, I have to convince the doctor that I'm not crazy.