Two aspects of how cylindrical distortion: how do they work?!
Question: Two aspects of how cylindrical distortion: how do they work?
If I were to have drawn a vector field to model the prism distortion on such a lens I would have thought that every vector would have pointed to the center of the "cylinder", such that instead of having a focal POINT the lens would have something like a focal LINE parallel to the axis. Because the cylindrical has a minus power, the horizontal component of every single vector in that field would be *toward* the focal point, not away from it. Something else is going on there, but I don't know what. Any idea how I'd calculate it, at the very least what the variables are?
The second thing is: along the lenses of the prescriptions I've had over the years the axis on the lens seems "shift" along the surface of the lens as though the cylinder were a kind of right-side up U drawn across it. That is to say, if a lens is x170 nearest the focal point, at the rightmost edge the axis feels as though it's tending toward x165 or so, and the leftmost edge tends toward x175. This is true whether there is spherical correction on the lens or not. What causes that?
I'm frankly not sure whether these lenses are spheric or apsheric, or exactly what kind of difference it would make.
Answers:
OK, I've had to read your question twice to [try to] understand what you're experiencing.... so here goes.
1. The focus of a cylinder is a LINE parallel to the axis, like you said...
The axis of the cylinder is perpendicular to power of the cylinder... so if your axis is 180, then the power direction is 90... so when you say the 'horizontal component' your really mean the vertical component?....
Now as the power is a minus, and the axis is 180, then along the vertical, the cylinder will have a MINIFYING effect. Meaning that the Vertical Component of every vector would point towards the Focal line that is horizontal (180). If you view a circle.. it will appear to be squashed in the vertical direction.
As there is NO sphere power, then there is NO power along the 180 axis.. and so there is no magnification or minification along the HORIZONTAL component.
NOW this is the CRUNCH... if you look through the lens, and you see a minification in the Vertical direction... and none in the HORIZONTAL direction, the the horizontal appears to be BIGGER than the vertical measurements/distances... giving you the FALSE impression that things pull OUTWARDS.
Your 2nd point....
Most lenses... the front surface has a Positive Sphere Curve (ie, it bulges forwards)... usually +4 or +6 curves... 'wrap-around' sunnies have +8.00 curves...
If your glasses have no spherical power.. then the back surface must also have a MINUS sphere to counter-act the front surface sphere... Let's say your lens has a +4.00D front curve... then your lens back surface will have a power of -4.00D sphere as well as - (cyl power) x axis.
Now this is a combined power grind, and so when you vectorally sum up the sphere vector (radially poining towards the optical centre (point) of the lens, as well as the cylinder vector, which points vertically down (to the 180 axis focal line).. then the resultant vector will NOT always have an equivalent axis of 180.. but it will shift relative to where you're measuring.
I hope you don't have to read my answer more than twice to understand what I'm saying.. and that I've answered your querries.
"on the horizontal meridian parts of the image seem to pull OUTWARDS as you get further from the focal point, as though there were some positive sphere on the lens. Why is that?"
distortion...probably pincushion or barrel:
http://en.wikipedia.org/wiki/Distortion_…
http://www.dpreview.com/learn/?/Glossary…
" the axis on the lens seems "shift" along the surface of the lens as though the cylinder were a kind of right-side up U drawn across it. That is to say, if a lens is x170 nearest the focal point, at the rightmost edge the axis feels as though it's tending toward x165 or so, and the leftmost edge tends toward x175. This is true whether there is spherical correction on the lens or not. What causes that?"
likely PRISMATIC effect
optometrist
http://myeyepod.blogspot.com/