# Optical Forums > Progressive Lens Discussion Forum >  Base curves of free-form PALs

## Sokoli

I have been reading a lot about the free form PALs, but what I dont understand is the issue about the base curve. It is clear to me that these base-curve-series are not needed anymore, as they were for the traditional PALs. Nowadays the companies write something like ... each Rx has its own ideal base curve..., which is true but then when you look closer to what some companies offer you see that they only have a restricted amount of base curves, so for me not a real difference to the semi-finished blanks from the past. I am aware that there are exceptions like Hoya Privilege and that not all lenses would look very nicely if they were produced according to their ideal base curve.

  So, why is the amount of base curves often restricted if there is the free form technology which actually could surface both surfaces? Is it because of the software? Or because the companies want to reduce costs, by continuing to use semi-finished lenses?

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## Barry Santini

Some design algorythms currently assume a default range of fitting values, and the software optimizes the design by selecting just from BCs that are "ideal" for a particular RX and companion BC.

If you depart too far from "ideal" BC for Rx/index/faceform/VD, the design may not perform as intended.


FWIW

B

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## Peter J Shaw OD

Base curves are as important as ever but have you ever thought why? Base curve affects binocularity, the industry has gone to as thin an flat as possible because it is easier to polish flat back curves. But flat lenses give very poor optical performance. Optimizing the base will reduce pincushioning, barrel, and vergence demand and also reduce effects of dynamic aniseikonia when properly specified. Digital lenses may in fact perform worse than traditional lenses because they are just too flat. there is a new digitally surfaced lens that manages binocular distortions. It is available only to optometrists (or opticians working with optometrists) due to additional binocular vision measurement requirements.

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## eyemanflying

> Base curves are as important as ever but have you ever thought why? Base curve affects binocularity, the industry has gone to as thin an flat as possible because it is easier to polish flat back curves. But flat lenses give very poor optical performance. Optimizing the base will reduce pincushioning, barrel, and vergence demand and also reduce effects of dynamic aniseikonia when properly specified. Digital lenses may in fact perform worse than traditional lenses because they are just too flat. there is a new digitally surfaced lens that manages binocular distortions. It is available only to optometrists (or opticians working with optometrists) due to additional binocular vision measurement requirements.


Way to hijack the thread - the topic is base curves.  Flatter BC's are better for cosmetics, frame compatibility and field of vision.  In my three decades of dispensing, I have never had a patient non-adapt due to a flatter BC, however the same can't be said for steeper BC's.

Polishing a flat or steep back curve, conventionally or digitally makes absolutely no difference in regards to effort.  Digital technology is proven and far superior to conventional methods, and now your claiming your new design (although you say above digital is inferior) if ordered through you is magically converted to be superior to digital?  My BS meter is pinging.

Are there any clinical trials (of say a min of 1000 people) you can provide details on vs. the other manufacturer's leading digital designs to back this claim?  

And only available to OD's through a single controlled distribution point?  Seems a bit controlling and sketchy to me.

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## Peter J Shaw OD

Without knowing with whom I am talking too I really can't be specific, We do have an internal  2000 patient clinical test group but not double blind. The technology is only available to optometrists as it requires an assessment and measurement of vergence facility,  Certainly I agree that with convex lenses flatter lenses provide less dynamic magnification individually at face form = 0 degrees and a wider field of view. 

In our method the higher plus lens is specified with a thin flat design but in the fellow lens the base curvature is steepened with an increase in the centre thickness  in order to reduce the dynamic and static magnification difference between fellow eyes. 

The technique is well published and supported by refereed journals in ophthalmology, optometry and vision science. Steeper base curves in general reduce the compensatory vergence in the binocular condition. It applies especially to minus power lenses with face form angles greater than about 5 degrees where significant base in prism is induced in lateral gaze due to the unequal angle of incident fellow rays.  Nothing sketchy, We use other manufacturers digital designs but modified to our own base curve schedule.

Our lens design calculations are based upon binocular conjugate rotations and measured vergence facility with lenses at the as worn position using a patent-pending method with strict linear production guidelines. We don't guess, our lens designs provide enhanced adaptation due to reduced prismatic effect in all positions of gaze with resorting to bi-centric grinding.

This thread brought about a discussion about Base Curves, and Free form designs did it not  that's  what we do, We exploit the power of free form in a novel way to provide a binocular correction rather than the monocular approach employed by conventional technology.

Optometrists have formalized training and unique expertise in binocular vision, the free app download is a useful tool in the diagnosis and treatment of binocular vision disorders such as aniseikonia, anisometropia, limited fusional vergence facility, myopia and merdional anisometropia.

And further: How does a -5.00D lens look with 0.50 base curve look in a 5 base frame anyway? Is that cosmetically better? Try and put even a 2 base into an Adidas 156 don't the temples flare out, And yes, digital polishing has limits and quality issues with short radius back curves (unless QA isn't important).

Our science is valid, we have been operating now for 3 weeks after 12 years R&D, we are in use in 7 schools of optometry, in 4 countries. Our consultants are all professors and/or PhD's in vision science (myself included), not engineers who never held a retinoscope or measured vergence facility.

Perhaps before condemning the science in a public forum a review of clinical facts or a private email would be more appropriate. 

Cheers,

If you want to find out more search (google) aniseikonia

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## Barry Santini

> Base curves are as important as ever but have you ever thought why? Base curve affects binocularity, the industry has gone to as thin an flat as possible because it is easier to polish flat back curves. But flat lenses give very poor optical performance. Optimizing the base will reduce pincushioning, barrel, and vergence demand and also reduce effects of dynamic aniseikonia when properly specified. Digital lenses may in fact perform worse than traditional lenses because they are just too flat. there is a new digitally surfaced lens that manages binocular distortions. It is available only to optometrists (or opticians working with optometrists) due to additional binocular vision measurement requirements.


Took a brochure on this very lens from VEE.  Very interesting.

B

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## jefe

> Base curves are as important as ever but have you ever thought why? Base curve affects binocularity, the industry has gone to as thin an flat as possible because it is easier to polish flat back curves. But flat lenses give very poor optical performance. Optimizing the base will reduce pincushioning, barrel, and vergence demand and also reduce effects of dynamic aniseikonia when properly specified. Digital lenses may in fact perform worse than traditional lenses because they are just too flat. there is a new digitally surfaced lens that manages binocular distortions. It is available only to optometrists (or opticians working with optometrists) due to additional binocular vision measurement requirements.


What additional measurements are necessary?

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## Darryl Meister

The choice of base curve influences a number of optical and mechanical factors, which are important in both traditional and free-form lens design.

*Optical Factors Associated with Base Curves:
*1. Off-center vision quality
2. Magnification
3. Geometric distortion

Flatter lenses generally compromise off-center vision quality in conventional lens designs using spherical base curves. Aspheric and optically optimized free-form lens designs are not subject to the same optical limitations, since the design can correct oblique astigmatism using local changes in curvature. However, as the base curve deviates farther and farther away from the "ideal" best form base curve, the asphericity or optical optimization required also increases. And the lens design then becomes more sensitive to factors such as lens tilt.

Flatter lenses generally produce less magnification through the center of the lens but more distortion (pin-cushion in plus powers, barrel in minus powers), which is caused by a change in magnification away from the center of the lens. Fortunately, the visual system will often "adapt" to these magnification effects within a week or so, since the brain essentially "remaps" the new visual input based upon the expected visual input and other sensory input. Aniseikonia can also become an issue in the presence of significant anisometropia.

*Mechanical Factors Associated with Base Curves:
*1. Lens thickness
2. Plate height (or bulge)
3. Frame shape and glazing ease

Flatter base curves result in thinner, cosmetically superior lenses (thinner centers in plus powers, thinner edges in minus powers), which are also lighter in weight. However, traditional eyeglass frames are commonly shaped for a nominal base curve of 6.00 diopters, which means that if the base curve of the lens is too flat or too steep, it may not fit securely in the frame (modern edgers have minimized this problem to some extent). Further, if the lens is too flat, eyelash clearance may become an issue or even contact between the lens and the cheeks or brow.

Extremely steep and extremely flat curves may also be difficult to fabricate using certain surfacing techniques. For instance, traditional, biaxial (diamond wheel) generators do not cut back curves below 3.00 diopters. And steep curves become difficult to fine and polish. Also, when fabricating a back-surface progressive lens using free-form surfacing, if the front base curve is too flat, the near zone on the back of the lens will become convex, resulting in a potato-chip-like shape that some lens designers prefer to avoid.

Consequently, even for free-form lenses that are optically optimized (and not necessarily all free-form lenses are), the choice of base curve is still important. You'll find that many free-form lens suppliers will generally use "pucks" (semi-finished lens blanks with spherical base curves) with base curves that are not entirely unlike the base curves of traditional lenses in order to produce finished lenses with a lens form or bend similar to traditional lenses. These lenses will often be somewhat flatter in order to improve cosmetics, like traditional aspheric lenses, but generally steep enough to avoid the optical and mechanical issues described above.

Best regards,
Darryl

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## Peter J Shaw OD

If you are working in association with an optometrist then we ask that vergence facility be assessed with loose or risley prisms at distance using standard optometric procedures. There is a short video on our website of how I prefer it is done.

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## Peter J Shaw OD

Thanks Darryl for the clear response, your input is always valuable.

Our iseikonic and isophoric design technology respects the limitations of frame base curve and manufacturing limitations but our lenses may be slightly (or sometimes) quite a lot thicker. Our goal in design is not to produce the thinnest most cosmetically pleasing lenses but rather to design a functional solution that facilitates single clear binocular vision across the majority of the visual field.

Cheers.

Peter

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## Peter J Shaw OD

Here's a question that Darryl brought up, that is the question of adaptation to pincushion and barrel distortion also what is significant anisekonia.

1. for an occasional spectacle lens wearer (contact lens wearer)  the barrel/pincushion distortion may never be adapted to due to the fact that the eyeglasses are only worn for brief periods of the day and he/she must constantly re-map.

2. Flatter  curves induce more  lateral prism in eccentric gaze with face form angles. Our predictive model uses the measured negative and positive lateral fusional reserves to map out whether adaptation would be an issue. This is especially problematic with esophoric myopes. So rather than relying on the patient adapting (or not) we can accurately predict adaptation and enhance binocularity with our patent pending method.

3. What is significant aniseikonia? I have many cases where 0.50D of anisometropia has resulted in poor adaptation, this is not due to the static aniseikonia (sensory) but rather the dynamic (motor, induced prism). If the vertical vergence reserve is low (easily measured by the optometrist) then an isophoric design is warranted as vertical vergences are resistant to vision therapy.   Providing a treatment for aniseikonia is no longer complex, our iseikonic/isophoric  designs are usually better and never worse because the optometrist determines the adaptability of the patient prior to lens design.

Check out the shawlens website for our real case summaries, selected from over 2000 successful cases over a 10 year period.

Peter

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## Darryl Meister

Peter, If your website addresses something relevant to this topic, I would encourage you to include an actual link to it in your post in order to help interested readers navigate to it more easily (you're not really trying to "peddle" your product if it's topical to this thread).

You mention "dynamic aniseikonia"... I'm reminded of some articles on rotational/dynamic magnification by Remole. As I recall, he had proposed some very extreme lens geometries in order to produce what I guess you could describe as "isophoric" lenses. Is this concept also related to your product?

Best regards,
Darryl

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## Peter J Shaw OD

Thanks Darryl
http://shawlens.com/
Prof Arnulf Remole was in fact my professor in the 70's and it was his research subsequent to my graduation that inspired my development of this design method. He invented a clinically effective paraxial equation for dynamic aniseikonia that put the nail into the Prentice's approximation's coffin. It was essentially the standard magnification equation but with the vertex distance replaced by the stop distance. 

I have taken it one step further by employing ray path analysis using the power of modern computing.  Ray path tracing brings about the possibility of an entirely new method to predict the interocular prismatic effect and allows exploitation of the inherent non-linearity effect of constant radius base curvatures at the  'as worn' position'.  It is very complex, yet simplified through the power of today's powerful computers. The software determines the optimum base, index, centre thickness and corridor design at the position of wear to provide a  clinically effective design without bi-centric designs.  

When the 53 page patent is successfully prosecuted I can be more precise in the method.

We also look at the rate of change in vergence demand in lateral gaze, (prism dioptres/degree/degree)  the method adjusts the base curve to "linearize" this rate of change to provide a more predictable vergence adjustment, this is especially useful when consumers switch between pairs of eyeglasses or contact lenses. (vergence is the requirement for the eyes to diverge or converge prior or subsequent to fixation, vergences are slower that saccades)

Anyway the website has a much more friendly explanation (the marketing department wrote it) 

Cheers, thanks for the discussion

Peter

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## Darryl Meister

Sounds intriguing, Peter. I can't say that I've gone through Remole's work in detail, although I had a brief look over it when Cliff Brooks brought it to my attention several years ago, while he was revising one of his textbooks.

It seemed to me at the time that Remole's proposed lens forms resulted in some pretty thick, bulbous lenses (for the +4.00 D versus +2.00 D comparison that I computed back then, the +2.00 lens had to be three times as thick with a 6.00 D steeper base curve than the +4.00 lens). Of course, from an optical standpoint, the oblique astigmatism would be very severe in both lenses, but it sounds as though you are addressing this issue, which is good. I suspect that lens cosmetics will now be your biggest challenge.

The other issue I brought up was the fact that while the "dynamic" or rotational magnification may have become equalized, the _paraxial_ magnification was not equalized; it was essentially over-compensated compared to a conventional iseikonic lens correction for aniseikonia. It was unclear to me whether this would actually cause more or less issue for the wearer than the spectacle-induced anisophoria. I'm assuming that you've done some wearer trials of some sort that have obtained positive results though?

Also, I argued that Prentice's rule really still holds true for a thick lens, although strictly speaking the decentration would need to be determined at the principal plane, not at the plane of the back (or front) surface, which is the traditional assumption. At least if we assume primary gaze for an infinitely distant object and ignore third-order aberrations; with shorter object distances or field-dependent optical aberrations, things become more complicated. Of course, this doesn't really matter, Remole's calculations obstensibly preclude the need to worry about Prenctice's rule in the first place.

Best regards,
Darryl

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## wmcdonald

This is, indeed, a very entertaining thread. I fear most here will have very little understanding of the material, but it is refreshing. I appreciate the dialogue, and will take a look at Remole's work. I must admit that I am not familiar, and it sounds fascinating. Thank you, gentlemen, for the depth of this discussion.

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## Peter J Shaw OD

Its cold and rainy here in Toronto, listening to opera. 

For those interested ref: Optometry and Vision Science 1989 
Anisophoria and Aniseikonia, Part 1 Vol 66 1-10, PP 659-670, Part 2   Arnulf Remole
Part 2 Vol 66, No 11 pp 736-746


You are right, equalizing the dynamic will over-correct the static which will present some adaptation problems. 

Our method has built in AI that uses experience from 12 years applied optometry and corrects the dynamic to a level that satisfies the measured tolerance to prism without over compensating the static. That is why we ask the optometrist to supply vergence measurements in the desktop application. The optometrist has full control over the final design and can prescribe to a desired endpoint iseikonic correction using the iseikonic design tool, the iterative algorithm then will choose the best lens pair that reduces prismatic effect also to be within the measured vergence. 

Prentic'e approximation is just that, it fails to predict the prism inluenced by index, base and curvature, it works reasonably with lenses of flat base curves and thin centres (minus lenses). The influence of base curve is non-linear (hence pincushion/barrel) so that disproves Prentice right there. But it wasn't bad for 100 years ago.  Clinically though it is an effective tool to predict when the prismatic effect might be a problem but it fails to explain why our lenses work (which they do :) ) . Ray tracing is the only way to go, that's what we do.

Last year we won the American Optometric Foundation grant for implementation at U Waterloo. Our technloogy (Optometrica tm) is part of both formal  academic and clinical curriculae in 3 schools of Optometry in 3 countries and in use in 4 more, as soon as I can, I foresee it being in every school because its just good science. 

As for the third order issue, we need to determine what the frame of reference is, I would be happy to argue that in a private forum. When I started this enterprise it was with conventional progressive lenses from Rodenstock, (life 2 and XS), I started to use Impression custom modified by myself and approved by Munich. The advantage being that we could customise inset and corridor length to match the adjusted base curvature. (with conventional  uncuts the inset is preset in the mold). Unfortunately, Rodenstock were unable to commit to an expanded market presence in North America due to fiscal constraints. We use position of wear surface designs that address the third order aberrations created in eccentric viewing at the position of wear.

So to recap, Prentice's Rule is OK to predict prism but not to design a correcting lens. Spectacle induced 3rd order aberrations are reduced (but never eliminated)by the Tscherning ellipse and free form designs.

Certainly object distance and plays a role in manifest aniseikonia, that too is considered as part of the target correction. Rather than taking an engineers perspective, our technology is based upon clinical observations and patient response. 

Always a pleasure to talk to an intelligent audience,

Peter

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## Darryl Meister

> Prentic'e approximation is just that, it fails to predict the prism inluenced by index, base and curvature, it works reasonably with lenses of flat base curves and thin centres (minus lenses). The influence of base curve is non-linear (hence pincushion/barrel) so that disproves Prentice right there


Yes, the influence of distortion gets into those field-dependent third-order aberrations that I referred to earlier. But, as far as I remember, Remole's proposed calculation doesn't actually consider the effect of third-order aberrations either, does it? My impression was that it also relied on paraxial-like assumptions, although the intersection of the chief ray is calculated for the center of rotation instead of the entrance pupil. (Not that you're necessarily using only his calculations.)

I agree that Prentice's rule isn't accurate once third-order errors become significant or for oblique angles of view, but it is still no less accurate than the conjugate foci, lens maker's, and vertex power equations used to determine lens power, since these all rely on the very same small-angle approximations. I also agree that Prentice's rule is not ideal for designing a correcting lens, just as the vertex equation does not predict the presence of off-axis aberrations such as oblique astigmatism.

In any case, I am glad to hear of your work. Nowadays, aniseikonia seems to be all but ignored in most clinical settings. After firms such as AO stopped supporting instruments like the space eikonometer, interest seemed to wane. I suspect that a lot of patients with spectacle-induced aniseikonia have simply had to deal with the symptoms one way or another.

Best regards,
Darryl

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## Darryl Meister

> it sounds fascinating.


That's why all the cool kids hang out in the Ophthalmic Optics Forum, Warren.  :Smile: 

Best regards,
Darryl

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## wmcdonald

Darryl,
I have been away from the study of optics for too many years, but still do my best to keep up. I am enjoying it.

Thanks!

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## Peter J Shaw OD

Hey Darryl isn't this fun (in a weird geeky way) (my inner Sheldon Cooper seems to have woken up :)))





I will send you graphs of how the 

So the above 2 graphs show the relationship between Prentice/Remoles/Ray Tracing in prismatic effect of the standard design case (equal base curves, minimum thickness and the corrected situation that does not cause a reversal in static aniseikonia. not how Prentice doesn't vary (because its a rule not a Law), ray tracing uses Snell's law, thats the only equation you can trust because its a law. 

Both graphs are for a real patient OD +0.s5, OS + 3.00, Constant radii front and back  surfaces . 

The left one is the standard design, all 3 methods are close, but the graph on the right is after isophoric design, Same Rx, optimized base index and CT note the dramatic reduction in induced prism.

Note how in real life (ray tracing (the perpendicular case of wave front) is non-linear. 

On another note! how do I make this text box bigger? I write code, design lenses and am pretty good at applied mathamatics, physics and optometry but I HATE COMPUTERS.

Peter

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## Darryl Meister

Interesting comparisons, Peter. Good stuff.

Back when I discussing this issue with Cliff, I performed a similar analysis comparing the ray-traced prism introduced at equal points below the optical center of a lens for different lens designs (standard lenses and iseikonic lenses designed using conventional and Remole's calculations). See attached PDF.

Of course, this is only somewhat meaningful, since the rays traced through the right and left lenses will generally not intersect the same point on the front lens surface. Nevertheless, you can see that Remole's method does indeed minimize ray-traced differences in prism between equal points for very different powers. (Of course, you can also see the lens forms that are required to accomplish a strict adherence to his proposed method.)

When you say "textbox," what specifically are you referring to?

Best regards,
Darryl

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## Peter J Shaw OD

The tiny space that this blog provides to write! I am a full page guy!

RE: eikonometers, currently there is no commercial production model of a space eikonometer  (although I might commercialize the one I have in development using a 3D TV) . This issue is that just because we can't measure aniseikonia accurately does not mean that we should ignore it and assume that the patient will adapt (in reality they adapt by popping tylenol and taking off their glasses or complaining to me). Its the dynamic effects that are the most problematic in most adult cases, the vergence accommodation system is now firmly developed and not wanting to change, by measuring the vergence facility we can predict issues with potential non-adaptation without a space eikonometer.

A space eikonometer is useful when patients suffer from axial length changes due to scleral buckle or maculopathy. Cases due to congenital or refractive change without axial implications do well with a dynamic approach. Prof Kenneth Robertson (now at Aukland University in NZ) developed a method for evaluation of dynamic aniseikonia using size lenses and a maddox rod. The Robertson eikonometer accurately measures dynamic aniseikonia, Atnulf Remole developed a better Static apace eikonometer that measured the horopter and the effect of aniseikonia. 

We have had enormous success with straight eye anisometropic amblyopia without patching, there is conclusive evidence shortly to be published Plus seems that amblyopes recover faster and better  when isogonal (static = 0%) lenses are prescribed. We are currently  undertaking a 50 patient study in the UK with adolescent amblyopes.


Essentially I have taken over where AO left off, Computers have made the process simple for the primary care optometrist so that he/she can focus on the patient and not be concerned with the complex mathematics.

Thanks for your comments

Peter

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## Darryl Meister

> The tiny space that this blog provides to write! I am a full page guy!


Ah, I see. Beneath the "textbox" is a few option buttons; click on the "Go Advanced" button to open up a bigger text editor (not much bigger, but bigger).




> Essentially I have taken over where AO left off, Computers have made the process simple for the primary care optometrist so that he/she can focus on the patient and not be concerned with the complex mathematics.


Well, I think you will be servicing a very real need in the industry, assuming that you attract enough clients. Certainly, the less time-consuming and complex your solution is, the greater chance your company will have at success. I suspect that relying on careful measurements by a separate instrument (the space eikonometer) was ultimately what turned many optometrists away from AO's product.

And please keep us posted!

Best regards,
Darryl

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## Peter J Shaw OD

Thanks for the encouragement, I built the technology around conventional test methods because the last thing an optometrists wants to do is to buy another device to collect dust (myself included).  Now that I have stopped practicing (last month) treating aniseikonia will become as routine and easy as prescribing cylinder. The public will have a whole new concept of the potential of eyeglasses.  If unavoidable thickness of lenses is an issues then the consumer will decide whether to ignore treatment, wear contact lenses or have refractive surgery. Eyeglasses are incredibly complicated medical devices, our goal is to neutralize the commodity approach from the Big Box retailers and internet suppliers. I believ that on that front we are in total agreement.

The better educated consumer will get better eyecare, that's our next goal.

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## Darryl Meister

Well put.

Best regards,
Darryl

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## Robert Martellaro

> I suspect that a lot of patients with spectacle-induced aniseikonia have simply had to deal with the symptoms one way or another.


I see about two to three a year, and virtually all had to travel the long road to find a solution for their visual distress. 

The 3rd edition of 'System for Ophthalmic Dispensing' discusses and gives examples of Remole's equations for bicentric grinding (slab-offs).

http://journals.lww.com/optvissci/Fu..._Ocular.9.aspx
http://journals.lww.com/optvissci/Fu...ies__a.13.aspx

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## Peter J Shaw OD

You can avoid slab off 99% of the time  with application of the dynamic aniseikonia concept , in my practiceIi had 18% of patients with clinically significant anisometropia 2000 isophoric Rx's out of 10,000 supplied in 8 years 2 bicentrics used zero non-adapts.

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## LENNY

I am lost, but if you convince Darryl you have the best lens out there. Even though Darryl is not an Optometrist....

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