# Optical Forums > Ophthalmic Optics >  High index single vision lenses

## 12345

Hi, is there any difference in vision when compared to essilor's crizal 1.67, zeiss clarity AS 1.67, hoya's 1.67 nulux as well as a standard 1.67 hmc lens. I do know that the multicoat applied to the lenses are different, but is there any difference in the vision seen by the px? Another qn will be is zeiss individual a single or double aspheric lens design?

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## drk

In reality, I think not.

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## essegn

All of them use their's own asphericity, so it could be a slighty difference among them. In this case i would no say that any of them is better than others (for particular lens power maybe). Probably the best way is to wear them all and compare :)
To lens material itself should be the same (mr7 or mr10) and all AR coatings have light transmission near to 99.9%.

Individual lenses have sense only when the pantoscopic tilt and wrap angle differ from average.

The using of single or double aspheric i would like to know as well.

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## Darryl Meister

Since it is optically optimized for the position of wear as well as the prescription requirements of the wearer, Individual Single Vision utilizes a "complex" surface on the back of the lens. Unlike simpler, symmetrical aspheric and atoric surfaces, the asphericity of Individual varies on a point-by-point basis over the lens.

There is no need for "double asphericity," since the design is also optically optimized for any cylinder power in addition to the sphere power before it is fabricated onto the back of the lens blank using a free-form generator.

In terms of design sophistication and potential visual benefit, you can think of it as follows:

1. Spherical design
2. Aspheric design
3. Atoric design
4. Complex free-form design

If the patient has no cylinder power, and selects a frame that has relatively little pantoscopic tilt and wrap, an aspheric design will often suffice. But keep in mind that even semi-finished aspheric designs still rely on base compromises, so many prescription powers will not achieve optimal visual performance.

Once significant cylinder power is incoporated into the prescription, an atoric design or better is required to achieve optimal vision. But, again, base curve compromises are often involved.

Once any frame tilt or prescribed prism is considered, a complex free-form design like Individual SV is required to achieve optimal vision. And these lenses do not suffer from base curve compromises either.

As for whether the patient will notice the difference, it will depend upon the patient's sensitivity to blur, the nature of the viewing tasks involved, and the deviation of the patient's prescription and position of wear from the values utilized to design traditional (semi-finished and finished) spherical, aspheric, and atoric lenses.

Best regards,
Darryl

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## Java99

I wear these lenses, and dispensed about 50 of them from various manufacturers last year.  The higher the power, the more people cared. The -2.00 sph wearer never commented much.  The -4.00 -1.25 @ 135 wearer was "wowed." The high wrap rx sunglass wearer was wowed as well.

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## Darryl Meister

> The higher the power, the more people cared


Yes, a good point to make. You can assume that the optical errors produced (and, therefore, potentially eliminated) will be proportional to lens power.

Best regards,
Darryl

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## Barry Santini

But, the -2.00 client wearing "flattened" poly stk lenses, fitted at mechanical center, in a frame where there is little pantoscopic angle and the pupil is 6-9mm above MC WILL MOST DEFINITELY see a difference when remade in FFSV with a 42-59 ABBE material, and with the base curve matched to the frame-bevel's curve.

B

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## Darryl Meister

The saddest part about this whole discussion is the fact that most eyeglass consumers have absolutely no idea that such factors exist or that an optician who understands optics is essential to making the most informed decisions that result in the best lens. Most consumers just seem to learn whether Lens A is cheaper than Lens B.

Best regards,
Darryl

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## EyeCare Rich

Totally agree with Darryl here.  All we can do at this point is try to keep plugging away with our communication to the patients we do see, and hope they tell their friends as well.  

Love the comment by Java99 above.  Love that WOW factor, or the initial "my vision is to clear" comment when the patient follows your recomendation to go freeform, either SV or Progressive.

Keep spreading the word folks!  Don't forget to ask your patient to spread the word as well.

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## Java99

> But, the -2.00 client wearing "flattened" poly stk lenses, fitted at mechanical center, in a frame where there is little pantoscopic angle and the pupil is 6-9mm above MC WILL MOST DEFINITELY see a difference when remade in FFSV with a 42-59 ABBE material, and with the base curve matched to the frame-bevel's curve.
> 
> B


Absolutely.  I didn't think about it because I can't recall the last time I didn't take an OC on someone.

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## MakeOptics

I think the design element is lost in this discussion, even the same manufacturing technique for achieving best form will not result in the same lens viewed through the patients eye's.  As mentioned their are a lot of variables when creating the most optimal lens, but their are also different philosophys as what constitutes the best lens design.  Even in SV lenses only so many aberrations can be corrected at one time, so the design has to weigh which aberrations to correct for more than others and balance the scales if I may.  Each manufacturer will have their own set of weights and scales so the visual outcome will be different.

If you don't believe me try putting a patient in 3 pairs:

1) OU - Essilor 360 SV
2) OU - Zeiss Individual SV
3) OD - Essilor 360 SV; OS - Zeiss Individual SV

I would suspect that the patient will be thrilled with both 1 and 2 (my preference would still be towards 2 though), and even be able to regularly switch between 1 and 2 with praises for both, but option 3 would be a horrible failure.  I have found this is also the case with aspheric stock lenses, I don't mix between manufacturers.

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## 12345

in terms of off axis performance regarding the following four options that are essilor's crizal 1.67, zeiss clarity AS 1.67, hoya's 1.67 nulux as well as a standard 1.67 hmc lens, is there going to be any difference? im guessing yes if each of the companies uses different mathematical calculations for their lenses right?

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## RKJ

I agree with you that we don't intentionally mix brands between the right and the left eye.  Having said that, I would not expect the Essilor 360 to be clinically equivalent to the Zeiss Individual.  I think the Essilor 360 is Free Form, meaning the topography is unique to each Rx and is mathematically calculated to decrease the aberrations of  1.Oblique Astigmatism, 2.Power Error, 3.Spherical Aberration, 4.Coma, and 5.Distortion.  Both brands would do this.  The Individual would go a step further as it can be customized for vertex, panto, and tilt.   The other way the lenses will be different, I think, is their default values for the position of wear measures.  Zeiss publishes their default values.  *I have not seen Essilor publish their default values.*  If we had them, we could predict when the lenses would be similar in optics.

*Essentially, all Free Form lens designers are using the same optical equations we learned in school to minimize the same aberrations.* * I imagine the industry would agree regarding those aberrations with greatest impact on visual clarity.*  In the identical index of refraction, I'd expect clinically equivalent lenses to be pretty much the same.  I have not experienced an argument otherwise for Single Vision Lenses.  I understand the design argument for Free Form progressives, that the progressive blend zone can be customized in a proprietary way, but I don't understand design differences for Free Form Single Vision Lenses.   I'd like other opinions about this, with optical arguments.

Free Form lenses have a different topography nasally than temporally, and the topography at the top of the lens will be different than the bottom of the lens.  Topography varies with angle between the eye and the lens and the distance between the eye and the lens.  Provided all of the same data, I would expect clinically equivalent Single Vison lenses (those that analyze the same parameters, and that are equally customizeable for vertex, panto, and wrap) to have very similar optics.

The additional advantage is computerized measuring techniques.  Some manufacturers are using new technologies to obtain better auto-refractions, sometimes better than the patient's ability to select a best quality subjective refraction - or perhaps better than the refractionist's ability to get a best quality subjective from the patient.  These leaders in our field are gathering lots and lots of data, fine tuning their automated measures against subjective refractions.  When they improve their technology until is succeeds the majority of the time, I think we'll see patients gain access to online refractions with their online eye wear orders, bypassing the doctor visit.  Time will tell.

I'd sure like to hear the thoughts of others on this topic.

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## Barry Santini

> Absolutely.  I didn't think about it because I can't recall the last time I didn't take an OC on someone.


Your post made me think of an excellent Q for the ABOM exam:

How would one ensure a BF/CC compliance in a bifoal/trifocal fitting?

B

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## Craig

> But, the -2.00 client wearing "flattened" poly stk lenses, fitted at mechanical center, in a frame where there is little pantoscopic angle and the pupil is 6-9mm above MC WILL MOST DEFINITELY see a difference when remade in FFSV with a 42-59 ABBE material, and with the base curve matched to the frame-bevel's curve.
> 
> B


Mr. B.,
Please keep the bevel stuff on the down low.  People are listening.
Craig

Do you take a ht on all orders?  We did but, the plus lenses started coming in too thick so we went back to the old lazy way.  I can do it on all but high plus as the still don't use aspheric blanks yet for the ones who need it.
Your thoughts.

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## Darryl Meister

> *Essentially, all Free Form lens designers are using the same optical equations we learned in school to minimize the same aberrations.* * I imagine the industry would agree regarding those aberrations with greatest impact on visual clarity.*  In the identical index of refraction, I'd expect clinically equivalent lenses to be pretty much the same.  I have not experienced an argument otherwise for Single Vision Lenses.  I understand the design argument for Free Form progressives, that the progressive blend zone can be customized in a proprietary way, but I don't understand design differences for Free Form Single Vision Lenses.   I'd like other opinions about this, with optical arguments.


Typically, aspheric, atoric, and free-form lens designs will differ from manufacturer to manufacturer. The wearer experience will also vary between lenses, although whether these wearers experience clinically significant differences will depend upon a number of factors related to the lens design, the Rx and fitting parameters, and the wearer.

Recall that years ago each lens manufacturer actually offered their own proprietary "corrected curve" or "best form" lens design. Some designs primarily corrected oblique astigmatism (e.g., Zeiss Punktal), some designs corrected tangential power error (e.g., AO Tillyer Masterpiece), and so on. Each design philosophy resulted in a slightly different base curve choice for each prescription. The number of available base curves was also an important parameter associated with each lens design.

The introduction of asphericity made possible more degrees of freedom, since the lens design could now be corrected for optical aberrations while the form of the lens was also manipulated. The use of weighting or merit functions could even allow the control of aberrations out to a certain diameter and then lens thickness beyond that point, resulting in unique aspheric designs that were considerably flatter and thinner than traditional corrected curve lenses.

The introduction of free-form surfaces makes possible even more degrees of freedom, since the lens design is no longer limited to a rotationally-symmetrical surface created by simply rotating a one-dimensional surface height function around the design center. Correcting optical aberrations due to the position of wear, prescribed prism, and other factors is now possible with sufficiently advanced optical design software, which allows lens designers to control the optics at points over the entire lens surface.

So, with free-form single vision lenses, lens manufacturers now actually have _more_ ways of differentiating their lens designs, not fewer ways. First, lens manufacturers can define their basic lens design to achieve a variety of goals, including the correction of specific optical aberrations, manipulation of lens form or thickness, control of mangification, and so on. Second, lens manufacturers can then offer different levels of customization for their lens design based upon factors such as the prescription, position of wear, frame shape, and/or ocular anatomy.

With both traditional and free-form progressive lenses, the overall optical layout or "fingerprint" of the basic progressive lens design is probably the single most important characteristic of the lens for most wearers. After all, even the best free-form optical customization strategy will simply preserve the intended performance of the lens for every wearer. Consequently, a fully customized free-form version of a mediocre lens design will just ensure the same mediocre performance for every wearer.

Because progressive lenses are obviously more complex designs than single-vision lenses, with many additional design parameters involved, optical customization using free-form technology offers even more avenues of product differentiation for lens manufacturers. Additionally, the choice of surface configuration becomes yet another degree of freedom with these lenses, whether the free-form lens design is located on the front surface, back surface, or split between the two.

Further, not all free-form lenses are created equally. The level of manufacturing quality and design sophistication may vary considerably from supplier to supplier. Unfortunately, these optical technicalities have been overlooked by many eyecare professionals today. This has resulted in many ECPS making the broad generalizations that "Free-Form" is inherently "Better" and that lenses are either "Free-Form" or "Not Free-Form," which are oversimplifications that may not accurately reflect differences between the various free-form products on the market.

Best regards,
Darryl

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## Darryl Meister

> I agree with you that we don't intentionally mix brands between the right and the left eye.  Having said that, I would not expect the Essilor 360 to be clinically equivalent to the Zeiss Individual... Time will tell.


By the way, I thought your post was well articulated and offered several insightful observations. Glad to have contributing to these forums.

Best regards,
Darryl

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## davidxuonline

> By the way, I thought your post was well articulated and offered several insightful observations. Glad to have contributing to these forums.
> 
> Best regards,
> Darryl


I agree with Darryl

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## RKJ

Darryl, when I set about re-learning optics to understand Free Form, your publications on OptiCampus and in published articles, and your content embedded in presentations at Vision Expo...well,no one helped me as much as you did.  Vendor reps have been great, but you make the optics _almost_ understandable.  I still have questions.
Recall that years ago each lens manufacturer actually offered their own proprietary "corrected curve" or "best form" lens design. Some designs primarily corrected oblique astigmatism (e.g., Zeiss Punktal), some designs corrected tangential power error (e.g., AO Tillyer Masterpiece), and so on. Each design philosophy resulted in a slightly different base curve choice for each prescription. The number of available base curves was also an important parameter associated with each lens design.

Before computers, great thinkers were using ray tracings and working from different philosophies.  I'm thinking that we now have the technology to help us analyze data and measure aberrations.  Best optics are best optics, an end point, and the base curves can be manipulated enough - while still providing best possible optics - so that brands can claim proprietary superiority.  I trust you will tell me if I'm oversimplifying, and I know you can explain it with optics and math.  I love that about you!
The introduction of free-form surfaces makes possible even more degrees of freedom, since the lens design is no longer limited to a rotationally-symmetrical surface created by simply rotating a one-dimensional surface height function around the design center. Correcting optical aberrations due to the position of wear, prescribed prism, and other factors is now possible with sufficiently advanced optical design software, which allows lens designers to control the optics at points over the entire lens surface.

So, with free-form single vision lenses, lens manufacturers now actually have _more_ ways of differentiating their lens designs, not fewer ways. 

First, lens manufacturers can define their basic lens design to achieve a variety of goals, including the correction of specific optical aberrations, manipulation of lens form or thickness, control of mangification, and so on. 

Here is the question:  assuming the ability to customize with vertex, panto, and tilt, wouldn't most lens designers use weighting and merit functions  to achieve pretty much the same objectives, for a Free Form Single Vision Lens?  More degrees of freedom means they have more ways to manipulate the front and back topographies to achieve the same results - agreed upon best possible optics for a given Rx.  Do new age thinkers with new age computer technologies hold differing philosophies regarding best possible optics for a given single vision Rx?
Further, not all free-form lenses are created equally. The level of manufacturing quality and design sophistication may vary considerably from supplier to supplier. Unfortunately, these optical technicalities have been overlooked by many eyecare professionals today.

Darryl, I hear what you are saying, however I've been trying to understand it and manufacturers are not forthright sharing contour maps.  Some are helpful; for example  Hoya's My Style images are very helpful - though I know the true contours will vary with each unique Rx.   Some manufacturers are just outright deceptive. 

*Now - please tollerate my soapbox issue:
*
Also, I think manufacturers benefit from sharing incomplete information.  I am of the opinion that Free Form optics have wider sweet spots than conventional progressives, and that one of the biggest reasons patient's don't get a Wow is because opticians order a fitting height, call it a seg height, and let the lab select a power profile that fits the frame.  Patients who enjoy short corridor lenses, and end up in long corridor free form lenses - will not be happy campers, regardless of the quality of free form optics.

Instead of teaching opticians to tailor the fixed segment height, or allowing opticians the freedom to manipulate the progressive blend zone,  manufacturers are instead telling opticians they need better measuring tools.  Manufacturers are selling high quality auto-refractors that have the side benefit of providing the manufacturer the opportunity to compare heaps of subjective refractions against autorefractor generated prescriptions, to continually improve the technologies that will eventually allow patients to by-pass the doctor and obtain online refractions.

I like that we can obtain better subjective refractions.  I believe, in the long run, this is best for the patient.  And I don't mind evolution in the optical marketplace and all the upcoming innovations that will make the internet more and more beneficial.  The global impact of great refractions in undeveloped countries has the potential to improve the world.  

Having said that, I really don't like manufacturers blaming doctors and opticians for not understanding the proprietary aspects of their lens designs.  Darryl, you have gone a long way to help us understand that the "good" "better" "best" model is not appropriately applied to Free Form.  I wish I could say the same industry wide.

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## MakeOptics

> *Essentially, all Free Form lens designers are using the same optical equations we learned in school to minimize the same aberrations.* * I imagine the industry would agree regarding those aberrations with greatest impact on visual clarity.*


This is where we must disagree, each manufacturer may have their own set of weights for the scales when it comes to which aberrations to correct for.  I'm sure you are aware by correcting for one aberration another may be exaggerated, each manufacturer is going to have a preferred method for how much of each aberration to correct given the sacrifices made to another aberration.  This set of preferences will differ between manufacturers and lead to some differences between even a SV design.  One manufacturer may prefer their lenses be point focal, which would eliminate oblique astigmatism, another manufacturer may prefer that their lenses be percival in design where the petzval surface is coincident with the far point sphere, these lenses will have no spherical error but the oblique astigmatism is still present, yet anothe rmanufacturer may decide to minimize the tangential error, so the far point sphere and the tangential error coincide, this design I prefer  because it's tscherning ellipse is roughly between the two other designs and has minimum amounts of oblique astigmatism.

A quick look at the tschernings ellipses for these various designs will show that they are not all equal, I personally don't like to mix the various design and I don't know which manufacturers designs are which, although I have a bit of intuition for each.

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## RKJ

> This is where we must disagree, each manufacturer may have their own set of weights for the scales when it comes to which aberrations to correct for.  ...
> A quick look at the tschernings ellipses for these various designs will show that they are not all equal, I personally don't like to mix the various design and I don't know which manufacturers designs are which, although I have a bit of intuition for each.


You understand this a lot better than I do.  You are saying that lens designers will not agree on "best possible optics" for a single vision lens.  

I agree with you, it is never a good idea to mix brands R and L eye same patient.  I anticipate subtle differences, in part because they have to be different for brands to hold their own design patents.  

I don't know how you decide which SV Free Form is best, except trial and error and patient experiences.  I'm leaning toward thinking some brands are clinically equivalent, and within a given tier I would select the one with lowest price point.  I don't know how to tell the difference except to trust vendor reps who are paid to have a bias, and they are educated by their employer who has a bias.

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## MakeOptics

> You understand this a lot better than I do.  You are saying that lens designers will not agree on "best possible optics" for a single vision lens.  
> 
> I agree with you, it is never a good idea to mix brands R and L eye same patient.  I anticipate subtle differences, in part because they have to be different for brands to hold their own design patents.  
> 
> I don't know how you decide which SV Free Form is best, except trial and error and patient experiences.  I'm leaning toward thinking some brands are clinically equivalent, and within a given tier I would select the one with lowest price point.  I don't know how to tell the difference except to trust vendor reps who are paid to have a bias, and they are educated by their employer who has a bias.


All reps, vendors, even independent labs will have their bias and no one seems to want to let anyone else know the corrections or philosophy that they use for "best form", so trial and error seems to be the only avenue of choice, until more sophisticated equipment becomes reasonable in cost.

I know Zeiss lenses incorporate a higher level of balance between the aberrations, I have gleaned this from their white papers over the years.

I know Essilor touts that their lenses have the least amount of spherical aberration so they weight heavily on correction towards spherical aberration.

I know that seiko talks about oblique astigmatism in their documents so they may lean more towards a oblique astigmatic correction.

I know HOYA likes to tout a more orthogonal lens design, always mentioning the aberration distortion.

I too wish the manufacturers were more straight forward but I can't blame them the lack of understanding in optics means that it would be a small market that would benefit from the information but their competitors would have a field day with it.  Basically big risk, small reward.

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## Barry Santini

But Zeiss as well as Hoya have FF designs that don't allow as much freedom to user-define base curve, which is in keeping within their design performance goals.  I think that, for most Rxs, the differences between SV designs are far less significant to the wearer than one might think. Darryl, I welcome your input herre.

Optimal lens recipes MUST include Abbe to be fully inclusive of all optical degradation factors.  This, of course, is left out of all this talk in the differences between lens design optimizations.  Also, as Rxs amplitudes climb, representative personalized measurements also become important.

B

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## RKJ

> Optimal lens recipes MUST include Abbe to be fully inclusive of all optical degradation factors.  This, of course, is left out of all this talk in the differences between lens design optimizations.  Also, as Rxs amplitudes climb, representative personalized measurements also become important.
> 
> B


Barry, I read your response and my first thought was "I wish I'd said that".  It takes me 3 paragraphs, or more, to say what you say in two sentences.  Amazing.  Just want you to know imitation is a form of flattery, because I intend to start using words like "optimal lens recipe" when I talk about lenses, and I probably won't give you credit - but I will know where it came from and think good thoughts your way :Wink: .

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## Darryl Meister

> Darryl, when I set about re-learning optics to understand Free Form, your publications on OptiCampus and in published articles, and your content embedded in presentations at Vision Expo...well,no one helped me as much as you did...


Well, I always appreciate the positive feedback! 
 :Biggrin: 




> Here is the question:  assuming the ability to customize with vertex, panto, and tilt, wouldn't most lens designers use weighting and merit functions  to achieve pretty much the same objectives, for a Free Form Single Vision Lens?  ...  Do new age thinkers with new age computer technologies hold differing philosophies regarding best possible optics for a given single vision Rx?


_If_ the lens designers are only optimizing for optics and _if_ the lens designers utilize the same forms of customization then it isn't unreasonable to expect similar patient-reported outcomes among customized single vision lenses, at least assuming that each lens was surfaced to the same level of quality.

Some lens designers may have more advanced software tools at their disposal, which may allow for more powerful optimization and tighter control of optics. But I won't argue a night-and-day difference. However, if you start factoring in clever ways to manipulate thickness or some other feature, you may see some meaningful differences, although not necessarily in terms of just vision quality.

And free-form surfacing quality can vary widely from lab to lab, depending upon their investments in quality control and process engineering. It is actually easier to produce a quality lens using traditional manufacturing methods, which rely on hard lap tools to fine and polish the surface. The kinematics of the soft lap polishing used in free-form surfacing have to be carefully controlled.

Free-form progressive lenses, on the other hand, can differ in more dramatic and visually significant ways. In addition to the obvious differences in the basic progressive lens design, itself, you are more likely to differences in the forms of customization available, methods used to control of optical aberrations, and so on.

In some cases, some manufacturers may also have to rely on less optimal or less efficient methods of designing free-form lenses due to various intellectual property constraints. A review of the relevant patent literature may be revealing in this case. Or, since optical design tools for ophthalmic lenses are often developed in-house, due to limitations in their software tools.




> Darryl, I hear what you are saying, however I've been trying to understand it and manufacturers are not forthright sharing contour maps


I can only speak for Carl Zeiss Vision, and we make contour plots of all of their free-form progressive lenses available to eyecare professionals; just download the white papers. We do not hide behind "smoke and mirrors," as they. I prefer not to get into product-specific discussions though, so I'll leave it at that. Other manufacturers are welcome to speak to their own approach to disclosing contour plots and numerical results.




> Manufacturers are selling high quality auto-refractors that have the side benefit of providing the manufacturer the opportunity to compare heaps of subjective refractions against autorefractor generated prescriptions, to continually improve the technologies that will eventually allow patients to by-pass the doctor and obtain online refractions.


I definitely agree that these new instruments can improve clinical outcomes for optometrists, although I doubt that they replace you guys anytime soon! Particularly when it comes to some of the more subtle "art" of optometry, like improving binocular vision function.

Best regards,
Darryl

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## Darryl Meister

> But Zeiss as well as Hoya have FF designs that don't allow as much freedom to user-define base curve, which is in keeping within their design performance goals.  I think that, for most Rxs, the differences between SV designs are far less significant to the wearer than one might think. Darryl, I welcome your input herre.


In my preceding post, above, I offered a qualified response to this. Unfortunately, many free-form lens manufacturers out there are not particularly forthcoming with the details of their lens design technology, so it may be difficult to say whether any two given free-form SV lenses should perform similarly or not.




> Optimal lens recipes MUST include Abbe to be fully inclusive of all optical degradation factors.  This, of course, is left out of all this talk in the differences between lens design optimizations.  Also, as Rxs amplitudes climb, representative personalized measurements also become important


Sure. Although, since chromatic aberration cannot really be significantly reduced by the lens design, you don't necessarily need to include a correction term for it directly in the calculations, as long as you choose a merit or optimization function that minimizes the monochromatic aberration that contributes most to the interaction between the monochromatic and chromatic aberrations.

For instance, while designing the Tillyer Masterpiece lens for American Optical, John Davis devised a merit function that included a lateral chromatic aberration term. He called this function a "blur index." However, you could get the same lens design result by simply minimizing the monochromatic tangential error of the lens.

Best regards,
Darryl

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## RKJ

> For instance, while designing the Tillyer Masterpiece lens for American Optical, John Davis devised a merit function that included a lateral chromatic aberration term. He called this function a "blur index." However, you could get the same lens design result by simply minimizing the monochromatic tangential error of the lens.
> 
> Best regards,
> Darryl


I'm learning from listening.  Darryl, I wonder if you would mind sharing a list of typical merit functions.  I'm trying to understand the scope of design considerations.

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## huashuo

HOYA 1.67 or 1.74 hi index is your best bet . all the multi coats are much the same and if i remember rightly polycarbonate lenses dont come with an AR coating . you maybe able to get them surfaced knife edged , just ask the dispenser if this is possible , it isnt always . If you do avoid supra frames and go for full frames . the finish will look better . hope this helps

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## Darryl Meister

> Darryl, I wonder if you would mind sharing a list of typical merit functions.  I'm trying to understand the scope of design considerations


I can describe a few of the more common optimization criterion terms used in single vision lens design, which are fairly simple:

Minimum Oblique Astigmatic Error (or "Point-Focal" design):



Minimum Mean Power Error (or "Percival" design):



Minimum Tangential Error:



John Davis's Blur Index, discussed earlier, where _C_ is the lateral chromatic aberration:



Minimum RMS Power Error (also known as the Dioptric Power Vector):



Note that these the terms rely primarily on the ray-traced tangential power error (_F_T) and sagittal power error (_F_S) from the desired prescription power at each point (x,y) on the lens.

Most commonly, the lens design process will manipulate the lens surface until a "least squares" merit function _M_ of the following form is minimized:



Where _E_i is one or more criterion terms, or the error result of the criterion term from the desired value, and _W_i is the weighting for each criterion term. These terms are assessed at (x,y) points over the lens.

A lens designer or software tool will then attempt to minimize the value of the chosen merit function for all points over the lens. A cosmetic term can also be added to the merit function, such as a term to minimize the lens volume _V_ out to the lens radius _r_:



So, for example, the weights associated with the optical criterion terms could get smaller at greater distances from the center of the lens, whereas the weight for the cosmetic term could get larger.

A good practical example of this stuff can be found, for instance, in US Patent 6,305,800, which describes a series of atoric lens designs and the various merit functions used to design them. You can download this from the USPTO website.

Modern progressive lens design relies on merit functions as well, although lens designers may incorporate a greater number of optimization criteria, considering factors such as gradients of surface astigmatism, skew distortion, and so on. Also, the process of minimizing the merit function becomes considerably more complex, requiring finite element method and similar mathematical techniques.

You might be interested in a slightly more advanced training presentation that I put together on ophthalmic lens design, which I presented to a class at the Pennsylvania College of Optometry several years ago. If so, just private message me with your e-mail address.

Best regards,
Darryl

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## RKJ

This is very cool.  Thank you!

I believe every single question I had has been answered as completely as possible.  Feels good.  Thank You!

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