dropping oc for panto

[Rich R]

From the other post on pals, I've often heard about dropping oc 1mm for 2 degrees of pantoscopic tilt, I just don't understand the reason. Example if I have a 40 b dimension frame and spot oc 23 high, should be 3 mm up, however frame has 10 degrees panto, now oc should be moved 2 mm down? If this is a aspheric lens, won't patient be looking through wrong point when looking straight ahead.
I know the gurus here can enlighten me.
Thanks, Rich R

[David Wilson]

Rich,
The 2 mm down in your example is correct. The reason is so that the principal axis of the lens passes through the eye's center of rotation. So, if the person looks, say, 10 mm above the optical center they will look though the lens at a certain angle (say 70 degrees). If they look the same 10 mm below the optical center they will look through the lens at the same angle. The lens designers know these angles (they assume a distance from the center of rotation to the spectacle plane) and so they can choose the amount of asphericity (and the best type of conical section; hyperboloid, ellipse etc) required to eliminate oblique astigmatism.

There is a general belief in optics that we must look through the optical center of the lens. This is not actually true. Indeed, it is better if you are using aspherics for readers to set them at distance PD so that horizontally the principal axes will pass through the centers of rotation. True there will be prismatic effect induced but it will be similar to the prismatic effect created by bifocals or PALs at the reading position. We could even get into the issue of facial wrap (which I think Pete raised once before) but I won't.

Regards
David

[Jeff Trail]

Rich,

Here is some of the "math" that goes into what David was talking about.
If you want to really delve into this look up Martins formula for lens tilt. Changing the tilt of a lens induces oblique astigmatism
(sometimes called marginal astigmatism depending who is doing the
talking) Panto tilt changes the effective sphere power of the lens and
induces cylinder power on the 180 merridian. For plus spheres it plus
cyl and in a minus it's minus cyl.
Face form will also change the power of the lens but it induces cyl. in the 90 degree merridian...
the formula is:

S'={1+(sin a)^2/(2n)}
C'= S'(tana)2

Keys are S'= new spherical power
S= original sphere power
a= the degree of tilt
n= index of refrection of the lens material
C'= the induced cylinder on the axis of rotation

Hyperops are more of a problem than a myop when working in tilts and the effect on power, What it amounts to once you use this formula you can check to see the resultant power and how the amount of tilt in relation to the optical axes of rotation will neutrilize this unwanted power...(the one you mention oc 1 mm for every 2 degree of tilt
If you DO not lower and tilt than you induce power (get the answer with the formula on the amount) ....
Here is an example say we had a lens that is a +10, cr39 with 15
degree's of tilt .... the effective power if the oc was in front of the pupil and not lowered than the power at the oc would be...

S"= S{1+(sin a)2} = (+10.00)(1+{sin15}2/2(1.498})
=(10)(1+0.06699/2.996)=(10.22)(0.0718)=+10.22^
C'=S'(tan a)= (+10.22)(tan15)2= (+10.22)(0.0718)= +.73x180

The power if the oc was placed in front of the pupil and the frame did
have 15 degree of panto tilt when they looked through the lens the
effective power would be +10.22+.73x180 !!YIKES
That is why you lower the oc as you induce tilt


Most of this is from a posting I made a while back in this same area.. just went back found the thread and copy/pasted it into here...shoot all that text you think I want to type that twice? :-)
Darryl even was kind enough to check my math :-) in the other thread..between you and me he was probably wanting to get a chance to toss me against the mathmatical wall a few times..:-) For us "formula freaks", as my wife likes to call me, this is actually what we consider as a "fun hobby" :-)
Wish more people on here wanted to know this kind of stuff... does not come up very often and most people tend to know the 1 mm to 2 degree rule but do not want to know the reason "why" .. to bad, with all the math freaks on this site between all of us we probably could cover a lot of ground...

Jeff "2+2 is 4, right?" Trail