Centre of Rotation - Tilt compensation

[eyeboy]

Hi,
The common diagram showing why tilt needs to be compensated does make some sense but could anyone answer a few questions I have regarding this.

1. The line of gaze doesn't change so by decentering the lens there will be induced oblique astigmatism so does this induced oblique astigmatism counteract the OA due to the tilt?

2.If not then it seems to me that the eye would have to rotate downwards in order to obtain the best vision which would seem impossible to view something properly directly in front of them!


3. Decentering the lens will induce prism. Assuming the eye rotates towards the apex then this would seem acceptable for a minus lens for question/statement (2), but worse for a plus lens.


4. At what point should Anisometropia be taken in to account? Taking a fairly common RX and frame combo... RE +7.00 LE +5.50, tilt of 12 deg. vertical decentration would be 6mm which would induce prism (using approx. prentices rule) of RE 4.2D LE 3.3D. Which would be beyond the theoretical limit of tolerated vertical prism (my books say between .5 to 0.75 D).

5. Jalie remarks that in Aspheric lenses it is even more important that the pole of the aspheric lens coincides with centre of rotation again if the axis of gaze doesn't change then how can this be so with a vertically decentred lens?

Thanks

[Darryl Meister]

The line of gaze doesn't change so by decentering the lens there will be induced oblique astigmatism so does this induced oblique astigmatism counteract the OA due to the tilt?... If not then it seems to me that the eye would have to rotate downwards in order to obtain the best vision

The familiar diagram, which inevitably shows the optical axis of the lens intercepting the center of rotation of the eye, assumes that the lens is a "best form" or "corrected curve" lens that minimizes oblique astigmatism during off-axis vision away from the optical center. Otherwise, you would be correct: The wearer would only enjoy astigmatism-free vision through the optical center after rotating his or her eye down from primary (straight-ahead) gaze.

Consider a +5.00 D sph Rx lens with 14 degrees of pantoscopic tilt, fitted with the optical center at pupil center. The prescription is effectively changed by oblique astigmatism due to lens tilt to +5.10 +0.32 x 180 when looking straight-ahead through the optical center. Now, assume that you lower the optical center roughly 7 mm (about 1 mm for every 2 degrees) in order to keep the optical axis passing through the center of rotation of the eye.

When looking through the optical center, which now requires about 14 degrees of ocular depression (an amount equal to the original lens tilt) below primary gaze, oblique astigmatism is eliminated, because your line of sight is now coincident with the optical axis of the lens. However, when looking straight-ahead in primary gaze, you are now effectively looking 14 degrees above the optical axis of the lens.

If the lens is not corrected properly for off-axis vision through choice of base curve or asphericity, the wearer will be exposed to oblique astigmatism when looking straight-ahead in primary gaze. If a 10.00 D front curve is used, oblique astigmatism is nearly zero when looking straight-head (14 degrees off-axis). If, however, the front curve is only 5.00 D, the prescription changes to +5.05 +0.22 x 180 when looking straight-ahead.

Decentering the lens will induce prism... At what point should Anisometropia be taken in to account?

When applied, in most cases, this compensation results in lowering the optical center only a few millimeters below the line of sight in primary gaze. Although this may result in a slight amount of prismatic effect during distance vision, it actually reduces the prismatic effect during near vision, which would be considerably higher, otherwise. For anisometropia, this would actually reduce vertical prism imbalance at near by introducing a small amount at distance.

Best regards,
Darryl

[eyeboy]

Thanks for the excellent reply I mostly get it now.

I suppose in a way by not decentering the lens then the Petzval surface and the far point sphere will not coincide compounding the issue?

" If, however, the front curve is only 5.00 D, the prescription changes to +5.05 +0.22 x 180 when looking straight-ahead."

So even in this case I guess it would still be worth decentering the lens? Will oblique astigmatism be worse in the periphery compared to an un-tilted lens?

Thanks

Tim.

[Darryl Meister]

I suppose in a way by not decentering the lens then the Petzval surface and the far point sphere will not coincide compounding the issue?

Just remember that you really only have a true Petzval surface if you have completely eliminated oblique astigmatism. And, with the exception of very high minus powers, the Petzval surface will generally not coincide with the far-point sphere of the eye, resulting in a residual spherical power error off-axis. In the presence of oblique astigmatism, the point focus at the Petzval surface breaks away into the separate tangential and sagittal focal lines.

If the lens produces oblique astigmatism for a given angle of gaze, you would generally calculate a spherical-like error by taking the average of the tangential and sagittal power errors from the far-point sphere. This spherical-like error is referred to as the mean power error or mean oblique power error. It is essentially represents the spherical equivalent or mean sphere of the power errors, just as the difference between the power errors represents the astigmatic error.

So even in this case I guess it would still be worth decentering the lens? Will oblique astigmatism be worse in the periphery compared to an un-tilted lens?

Either way, you will get the best optics by decentering the lens, if the lens is tilted. However, for lower Rx powers, it may or may not make a clinically significant difference to the wearer.

Further, if the lens utilizes a best-form base curve, you will minimize oblique astigmatism over the entire lens, if you decenter the lens to compensate for lens tilt. If the lens utilizes a flat, non-best-form base curve, on the other hand, vision will still be improved slightly when looking straight-ahead. However, in this case, truly clear will only be obtained when looking down through the (decentered) optical center. Away from this point, oblique astigmatism will increase.

Best regards,
Darryl