Anisometropic Base Curves

[go_hercules]

Okay, assuming that anisokeonia, differing image sizes, etc. is NOT an issue and we are only interested in best distortion free vision, then here is the question>>> If each eye has a different prescription, say +1.0 L and +4.0 right, is it best to use the optimum front base curve on each eye individually or is there some aspect of matching one eye to the other that is important? In other words, if one eye calls for a 4BC and the other calls for a 10BC, should we just go with that, or is there some maximum difference eye to eye we should be aware of when selectin base curves? Again, this is assuming no other issues such as magnification or anything else. Thanks everybody.

[HarryChiling]

Different BC's IMO.

[xiaowei]

Okay, assuming that anisokeonia, differing image sizes, etc. is NOT an issue and we are only interested in best distortion free vision......
Again, this is assuming no other issues such as magnification or anything else. Thanks everybody.

If there is **no need to match** both eyes in any regard, the overall best should be what is best for both *individually*. If you go for similar base curves with a different prescription, the amount of distortion will not be minimum in at least one of the eyes and even differ from left to right what´s probably even more distracting, I´d say!;)

(However, in the real case, there would be anisokonia, causing left-right mismatch too)

XW

[Del]

I was just reading up about this in my course and i will quote it.

"In cases where two lenses in a given prescription require different base curves owing to differing powers it is usual to match the base curves by chosing the more convex curve for each lens"

Now silly question time, how do companies come up with Nominal Base selection tables for semi finished blanks? I have learned how to figure out the nominal powers using the bc from one of these tables but just wondering how they come up with the tables to begin with?





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[xiaowei]

I was just reading up about this in my course and i will quote it.

"In cases where two lenses in a given prescription require different base curves owing to differing powers it is usual to match the base curves by chosing the more convex curve for each lens"

Now silly question time, how do companies come up with Nominal Base selection tables for semi finished blanks? I have learned how to figure out the nominal powers using the bc from one of these tables but just wondering how they come up with the tables to begin with?

Hi,

I´m not sureif I understand what exactly your question is, as I think the answer should be in your course material too: "Cosmetic" reasons aside (i.e. flat lenses), base curves are selected to minimize cylinder and/or power error for off-axis viewing. What is considered the best compromise depends on the manufacturer. The necessary calculations are probably based on approximations or - more likely today - on explicit ray tracing from an assumed eye position through the lens. The basic theory behind it is pretty old already, early product using such an approach were Zeiss "Punktal" glasses or AO "Tillyer/Masterpiece" lenses besides other products I surely forgot to mention.

Hope this helps

小卫

[HarryChiling]

Now silly question time, how do companies come up with Nominal Base selection tables for semi finished blanks? I have learned how to figure out the nominal powers using the bc from one of these tables but just wondering how they come up with the tables to begin

First they decide which design they will be using.

Point Focal - example was given the Punktal, which is accomplished by reduceing or eliminateing the oblique astigmatic error.

Percival - which again I belive was mentioned with the AO lens, the idea here is to place the disk of least confusion on the retina, or eliminate or reduce mean oblique error.

Minimum Tangential Error - again and older AO design, since the tangetial plane is the one that runs through the optical center fo the lens and the point off axis reduceing the tangential error can help create a more comfortable off axis view.

Then they pick the base curves that accomplish this, when choosing semi finished curves the idea is to have a limit for the amount of error that is acceptable to the company. This way the designs can be used for the power that is fully optimized and plus or minus that acceptable error so that more powers can fit on the same base curve. This would mean less inventory to stock.

[xiaowei]

Percival - which again I belive was mentioned with the AO lens, the idea here is to place the disk of least confusion on the retina, or eliminate or reduce mean oblique error.

Harry,

very interesting, I did not yet know about the "Percival" design. Looking it up on the web I found a pretty good looking article (did not yet read it throughly) that may be of interest to others:

http://www.optometry.co.uk/articles/...ie20050225.pdf

[HarryChiling]

Harry,

very interesting, I did not yet know about the "Percival" design. Looking it up on the web I found a pretty good looking article (did not yet read it throughly) that may be of interest to others:

http://www.optometry.co.uk/articles/...ie20050225.pdf

I absolutely love Jalies stuff he has a way of explaining tyhe concepts that are easy to comprehed. I have been reading the articles on that site for quite some time now, but forgot the address, thanks for posting it I am book marking it now.

[xiaowei]

I absolutely love Jalies stuff he has a way of explaining tyhe concepts that are easy to comprehed. I have been reading the articles on that site for quite some time now, but forgot the address, thanks for posting it I am book marking it now.

Hi,

just another point.;) I noted that the article (and similar ones I found) claim that the "Percival condition" is actually the condition where the "Petzval surface" is maximally flat. This leaves the impression, that both names are even actually the same and it all is likely the result of a fancy misspelling that somebody started.

HOWEVER, it´s not!

1) It´s seems the was a Dr. A. Percival who came up with this the first time. The other guy was a Hungarian mathematican and physicist called J. Petzval.

2) Technically, the best surface between both astigmatic surfaces (T and S) is NOT the Petzval surface P, this *IS* an error in the papers I read. The petzval surface, in technical optics, for mathematical reasons, is always *outside* both T and S surfaces (only in the case both coincide, they also coincide with P). See here, for example

http://www.vanwalree.com/optics/astigmatism.html

Cheers

[HarryChiling]

If memory serves me correctly the idea of getting the disk of least confusion on the petzval surface doesn't necessarily create the least amount of off axis power, the purpose here is to create a more orthoscopic lens. Again don't quote me on that I will have to look through my texts at some poitn to get you a more detailed explanation, but if the poitns viewed off axis fall on the petzval surface then the object looks more flat to the wearer, I would venture to say this would be more important in progressives.

[Darryl Meister]

The Percival condition in ophthalmic lens design refers to minimizing the mean oblique power error of the lens at off-axis points. In traditional Rx terms, this is equal to an error in the "spherical equivalent" (i.e., sphere + 1/2 cylinder). Since the ideal image plane of spectacle lenses is inevitably curved, corresponding to the locus of points formed by the far-point sphere as it revolves around the center of rotation of the eye, minimizing the mean oblique power error will not result in a "flat" full-field image plane.

At Carl Zeiss Vision, we often seek to minimize the "RMS" (root-mean-square or standard deviation) power error of the lens during the optical design process, which is also equivalent to the optometric power vector used frequently in vision science.

[xiaowei]

The Percival condition in ophthalmic lens design refers to minimizing the mean oblique power error of the lens at off-axis points. In traditional Rx terms, this is equal to an error in the "spherical equivalent" (i.e., sphere + 1/2 cylinder). Since the ideal image plane of spectacle lenses is inevitably curved, corresponding to the locus of points formed by the far-point sphere as it revolves around the center of rotation of the eye, minimizing the mean oblique power error will not result in a "flat" full-field image plane.

As always, very detailed answer! Totally agree!

The point that I wanted to make is that the Petzval surface (if properly "redefined" for the moving eye, because it´s normally defined over the image plane of a fixed lens) is not the surface that minimizes the "spherical equivalent" as implied in the papers I noted, but usually lies even more far away from both astigmatic image planes.

Cheers

[HarryChiling]

Thanks for the explanation Darryl and xiaowei. So which design is the current lenses based on?

Which designs are outdated?

[Darryl Meister]

The point that I wanted to make is that the Petzval surface (if properly "redefined" for the moving eye, because it´s normally defined over the image plane of a fixed lens) is not the surface that minimizes the "spherical equivalent" as implied in the papers I noted, but usually lies even more far away from both astigmatic image planes

Just so we're all on the same page here, Petzval's surface (after Joseph Petzval, Hungarian engineer) is an image surface produced in the absence of oblique astigmatism; it is important in optical design, in general, including the design of spectacle lenses.

On the hand, Percival's condition (after Archibald Percival, English ophthalmologist) refers to eliminating the mean oblique error of the lens; this occurs when circle of least confusion of the obliquely refracted astigmatic pencil falls upon the far-point sphere of the lens and eye.

When oblique astigmatism has been eliminated in a lens or system, the focus falls upon Petzval's surface. The curvature of Petzval's surface from a flat plane produces an aberration known as curvature of the field. Although this aberration is unwanted when the ideal image plane is flat, such as the film in a camera, this aberration is actually desired in ophthalmic lens design, since the ideal image plane of the lens is also curved as the eye rotates behind the lens. Unfortunately, the curvature of Petzval's surface is generally not curved enough to match the curvature of the far-point sphere of a typical eye.

The radius of Petzval's surface is given by n * f, where n is the refractive index and f is the focal length of the lens. The radius of the far-point sphere, on the other hand, is given by f - s, where s is the stop distance (around 27 mm). In most cases, except for very high minus lenses, these two curves will differ. The difference between Petzval's surface and the far-point sphere for a given angle of view is referred to as power error.

If you introduce oblique astigmatism, you can increase the curvature of Petzval's surface, although each focus splits into a tagential focal line and a sagittal focal line. The average distance between the two focal lines -- which is also the location of the circle of least confusion -- and the far-point sphere is referred to as mean oblique error, although you're just as likely to see this referred to as power error, too. If you introduce enough mean oblique error, you can cause the average error to approach zero as the circle of least confusion is moved to the far-point sphere. This is what Percival proposed to do with ophthalmic lenses.

Thanks for the explanation Darryl and xiaowei. So which design is the current lenses based on? Which designs are outdated?

I don't know that any of them will ever be "outdated," since they are simply examples of the various "cases" involved. In some ways, Percival forms represent one extreme, while point-focal forms with zero oblique astigmatism represent the other. Most modern lens designs probably try to reach a compromise between the two extremes; Davis's minimum tangential error form is a good example. For progressive lenses, on the other hand, more complex merit functions are often utilized; the lens designer can specify an arbitrary "weighting factor" for each lens aberration or criterion.

[xiaowei]

Thanks for the explanation Darryl and xiaowei. So which design is the current lenses based on? Which designs are outdated?

I don't know that any of them will ever be "outdated," since they are simply examples of the various "cases" involved. In some ways, Percival forms represent one extreme, while point-focal forms with zero oblique astigmatism represent the other. Most modern lens designs probably try to reach a compromise between the two extremes; Davis's minimum tangential error form is a good example.

One reason that there is no "optimum" design is also that in "real life" (as often.....) the situation is not that easy as in the article, as the image surfaces may be curved in a more complicated way (mixed exponents involved). This means it will probably start to slightly bend in one way for small off-axis angles and later bend backwards ond "overshoot" for larger off-axis angles. In this case it is obvious that you only can reach a compromise and the "best" compromise will depend on a "weighting" how important gazing vs. head turning is considered. (A factor much more important in PAL design because of the way more complicated image surfaces due to the progression). I seem to remember that some designs had a certain "standard" gaze angle in the order of 30° (??) where the error was minimized

That´s only one example what generally makes life hard for optical designers, if ophthalmic or not....

[HarryChiling]

I don't know that any of them will ever be "outdated," since they are simply examples of the various "cases" involved. In some ways, Percival forms represent one extreme, while point-focal forms with zero oblique astigmatism represent the other. Most modern lens designs probably try to reach a compromise between the two extremes; Davis's minimum tangential error form is a good example. For progressive lenses, on the other hand, more complex merit functions are often utilized; the lens designer can specify an arbitrary "weighting factor" for each lens aberration or criterion.

One reason that there is no "optimum" design is also that in "real life" (as often.....) the situation is not that easy as in the article, as the image surfaces may be curved in a more complicated way (mixed exponents involved). This means it will probably start to slightly bend in one way for small off-axis angles and later bend backwards ond "overshoot" for larger off-axis angles. In this case it is obvious that you only can reach a compromise and the "best" compromise will depend on a "weighting" how important gazing vs. head turning is considered. (A factor much more important in PAL design because of the way more complicated image surfaces due to the progression). I seem to remember that some designs had a certain "standard" gaze angle in the order of 30° (??) where the error was minimized

That´s only one example what generally makes life hard for optical designers, if ophthalmic or not....

Thanks for those responses, it feels like Christmas in stereo with the two of you giving such great responses. The reason I aksed is that a question comes to mind:

Since various companies can be using different desings for their lenses, does this mean it's a bad idea to mix and match finished lenses between manufacturer's so that the design between both eye's is the same? Or is the differences between the designs minimal enough it probably won't make a difference? Do companies pick one design and stick to it fro all the brands they offer? Or is it more likely that a company can have various designs available at one time on the market?

[Darryl Meister]

I seem to remember that some designs had a certain "standard" gaze angle in the order of 30° (??) where the error was minimized

A 30° viewing angle was the standard reference angle utilized by lens designers at American Optical. It was thought that ocular rotation seldom exceeded this value before a compensatory head movement was executed. Later, this standard reference angle was used in the first ANSI Z80.1 standard for setting tolerances on off-axis optical performance.

Since various companies can be using different desings for their lenses, does this mean it's a bad idea to mix and match finished lenses between manufacturer's so that the design between both eye's is the same?

For spherical lens designs, as long as the front curves are reasonably close, you should be fine; magnification differences will probably be more noticeable to the patient at first than the off-axis performance when there is a significant difference in base curves. For aspheric lens designs, however, you should not mix and match lens designs.

[HarryChiling]

For aspheric lens designs, however, you should not mix and match lens designs.

That's a good piece of information to know. I don't now anyway, but have never actually sit there and thought of it. If the situation presented itself where a lens was BO for one reason or another I might have grabbed and mixed and matched and not thought one iota about it. Thanks Darryl.