Ray-tracing of de-centered lenses
I am looking for formulas for ray tracing the oblique performance of a single vision lens (spherical and aspherical) that is de-centered in front of the eye.
Example: a spherical single vision lens has been decentered 2mm to reduce the prismatic effect on a pair of reading glasses.
How to calculate it's oblique characteristics (power, astigmatism, prism).
This has been bugging me for awhile so i am digging in the textbooks and would appreciate any help.
Best regards,
Nikolay Angelov
The oblique characteristics are less important that the vergence the lenses are being used for. CC theory if for infinity. Tscherning held that for a 40cm vergence, the Best fit CC needed to be reduced 2 diopters. After that, I would assume all other things are reasonably equal using these assumptions.
B
Interesting, B.
Do you mean that, since the converged eyes are looking though a lens somewhat obliquely, that the "best corrected curve" is different in that situation than in straight-ahead gaze? I never knew that.
What else?
Base curve error in near view will be taken in account as well.
I want to calculate the real lens performance thus i will use real base curves (from a lens blanks catalog) and not ideal ones (point-focal, Percival or other).
Decentration would make the oblique performance of the lens non rotationally symmetrical.
The optical axis will not pass through the eye's rotation center, which this would degrade oblique performance as well.
I am digging through Jalie's "The principles of ophthalmic lenses" to figure out the math :).
No. drk. The base curve reduction is to compsensate for the divergent rather than collimated rays.Originally Posted by drk
B
Let us know.
B
Nikolay,
Decentering a lens 2mm is different than a client looking through a lens 2mm from the optical center. I would assume that you need ray trace sequences, an older copy of Mo Jalie's Ophthalmic Dispensing had a sequence in the back that was a step by step ray trace that could be used for spherical ray traces. For aspherics I look to Conrady, I don't remember the book but it has many formulas and includes a ray trace through an aspherical lens surface. You could also look up Atchison (sp?) he has many great optics articles, with one or two I remember on ray tracing through aspherics.
If I get a chance I will see if I still have the text's but they may have been loaned out never to return again.
Thank you for the help.
On aspherics so far i have found "Ray tracing through a conicoid" in Chapter 21: Aspheric lenses (The principles of ophthalmic lenses).
Yup, that's the challenging partDecentering a lens 2mm is different than a client looking through a lens 2mm from the optical center..
All the ray tracing texts i have read so far assume a centered system (lens axis passing through the eye's rotation center).
Dag. Thanks.
This strictly only applies to a "centered" lens that has aligned with the line of sight. As some of the others have suggested, the situation is different for a decentered lens. If the lens has been decentered away from the line of sight to induce prism, corrected curve or best form theory, for either infinity or some finite reading distance, breaks down.The oblique characteristics are less important that the vergence the lenses are being used for.
Keep in mind that when the lens is decentered away from the line of sight for any particular angle of gaze, the vergence through the lens will no longer necessarily match the intended power, since the lens is effectively tilted with respect to the optical system of the eye, introducing oblique astigmatism.
Looking away from the center of a corrected curve or best form lens, however, will generally not introduce oblique astigmatism, since the purpose of the lens design is to compensate for this change in gaze angle. But, as you correctly noted, a different lens design or base curve would be required for near vision.
Practically speaking, lens tilt can be applied to offset some of the optical errors introduced by decentration in this case, by tilting the optical axis of the lens to intersect the center of rotation of the eye, as shown here.Example: a spherical single vision lens has been decentered 2mm to reduce the prismatic effect on a pair of reading glasses.
For horizontal decentration out from the lines of sight, you would have to apply 2 degrees of positive face-form (or wrap) tilt for every 1 mm of decentration to minimize the oblique astigmatism induced by the decentration. For horizontal decentration in, you would actually have to apply negative face-form tilt.
However, unless you've significantly decentered the lens, the optical effects involved will generally be negligible for most lens powers. In fact, virtually all SV reading lenses suffer from this effect to some extent, since the lenses are decentered to the desired Near PD.
Jalie covers spherical and aspheric lens ray tracing in Principles of Ophthalmic Lenses, but he still treats only the centered situation described above. I don't think that Jalie covers ray tracing in detail at all in his newer book though, Ophthalmic Lenses and Dispensing.I would assume that you need ray trace sequences, an older copy of Mo Jalie's Ophthalmic Dispensing had a sequence in the back that was a step by step ray trace that could be used for spherical ray traces
I've actually incorporated his ray-tracing sequence in one of the modules of my Spectacle Optics program. However, while you can adjust the reading distance and angle of view, my program still only ray traces centered lenses.
Best regards,
Darryl
Last edited by Darryl Meister; 03-09-2012 at 03:09 PM.
Darryl J. Meister, ABOM
Ray tracing is best explained in Geometic optics workbook by David Loshin . Even the problems have been explained well
There are currently 1 users browsing this thread. (0 members and 1 guests)
Posting Permissions
Reply With Quote
Bookmarks