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I recently wrote a white paper for the Lens Technical Committee of the Vision Council regarding the optical principles and practical implications associated with the position of wear of spectacle lenses, which some of you may find useful.
Memo on Understanding the Position of Wear
Best regards,
Darryl
i printed and will read later. Thanks for caring so much about what you do, you are rare.
Craig
Outstanding as usual, Darryl. I have long admired your development and appreciate all you do for Opticianry and the field at large. It is indeed a shame that the vast majority of Opticians now are so poorly trained that they will understand very liitle about the topic. I continue to work to alleviate that situation. I wish you the very best.
Warren
Glad you found the information useful, Warren.
Best regards,
Darryl
Great article, and by the way, will you be at SECO this year?
What a job. I just see all the hours and weeks of work that went into this master piece.
Congratulations Darryl
Do you have any reference to the "effective tilt" angle you discuss in the beginning. I have gone back and forth between the arctan and arcsin and eventually settled on the arcsin as you have outlined in your white paper but never really had a reference, just the geometry to look at. If you also have any reference to aspheric and as you discussed PAL's being hard to measure lens tilt that would be an interesting read as well. I too agree that the deviation from spherical to aspheric surfaces causes the formula to deviate from a more accurate estimation to a good guesstimation. I wonder if the apsheric radius can be subbed in to the equation to gain a more accurate measure?
I'll have to compare more in depth later when off work, but I have another question:
Past papers I have read have combined the tilt to create a combined effect that the dioptric matrix is rotated by, in this paper you outline a step by step process with the rotation matrix. How important is it to rotate around the x axis first and y axis second?
Also I wish there was a better discussion of hte merit functions with an example, I guess that would be divulging trade secrets or "secret sauce" as they call it.
If you are referring to the tilt due to meniscus decentration, Stimson acknowledges the effect in Ophthalmic Dispensing. I derived my own formula, however, many years ago for my old Rx compensation software, using the geometry of my figure and operating with the assumption that a modern, guided mini-bevel is generally positioned equidistant from the front surface of the lens.Quote:
Do you have any reference to the "effective tilt" angle you discuss in the beginning.
Also, you would use the arcsin function in this formula, not the arctan function, since you know the distance DEC and the length R1 to FP. It is difficult for me to explain without a drawing, but the arctan function would only apply if the distance DEC was measured in the plane of GC, with R1 extended past the surface, not in the plane of FP.
That said, for the small angles involved, the dfferences between the two are negligible and, in fact, you could drop the inverse function altogether and simply compute the angle in radians as the ratio, DEC/R1.
By "past papers," I assume that you are specifically referring to Keating's 1995 article, since he is one of the few who treats that particular subject in detail. His calculations actually assume the reverse of the Euler rotation order that I am describing. My order is more consistent with the orientation of the lens as established by electronic frame tracing though.Quote:
Past papers I have read have combined the tilt to create a combined effect that the dioptric matrix is rotated by, in this paper you outline a step by step process with the rotation matrix. How important is it to rotate around the x axis first and y axis second?
Nevertheless, I am certain that the differences between the two orders are small for the usual pantoscopic and face-form tilt angles involved. Neither way is necessarily superior to the other, although I feel that mine is more consistent with manufacturing practice. However, I haven't actually tried yet to work out numerical examples to see the actual differences, myself.
I mainly kept this section short and simple in the interest of length, since this particular topic wasn't really critical to the discussion. At the very least, astigmatism and mean add power are included as merit function terms, but I imagine that a lens designer may also include additional terms associated with quantities such as gradients of power, image swim, and so on. However, the more terms involved, the greater the computational burden.Quote:
Also I wish there was a better discussion of hte merit functions with an example, I guess that would be divulging trade secrets or "secret sauce" as they call it.
Best regards,
Darryl
I should add that Keating's is certainly not the only good paper on the topic. Harris (Optom Vis Sci 2002, Optom Vis Sci 2006), Blendowske (Optom Vis Sci 2002), and others have published some nice treatments on this subject, although I have spent more time personally digesting Keating's.Quote:
Originally Posted by Darryl
Best regards,
Darryl
That's interesting I ended up using the arcsin function I believe from past discussions that invloved your posts on this thread an even without images it makes sense that the tan function would have the hypotenuse extend beyond the front surface of the lens to a flat lens plane that would exist had the lens not been tilted, the sin function is definitely the more accurate. I'll have to look further into Stimsons book to see if I can find the inference.Quote:
Originally Posted by Darryl Meister
Yes for the small angles the ratio can be subbed out for the tilt altogether and tan and sin are very close in value at these small numbers but for the sake of accuracy and understanding I prefer to know which way is the most accurate.
I saw you mentioned that, so from a purist standpoint you are aligning your compensations to mimic the way in which the frame tracer is measuring the lens. I can see how that could eliminate or reduce inconsistencies in tilt measures.Quote:
By "past papers," I assume that you are specifically referring to Keating's 1995 article, since he is one of the few who treats that particular subject in detail. His calculations actually assume the reverse of the Euler rotation order that I am describing. My order is more consistent with the orientation of the lens as established by electronic frame tracing though.
I would have to say that if the compensation is more aligned with manufacturing methods then this is a more superior method. Conversions and rounding alone can cause loss in accuracy probably negligible given the accuracy required to dispense an average lens.Quote:
Nevertheless, I am certain that the differences between the two orders are probably small for the usual pantoscopic and face-form tilt angles involved. Neither way is necessarily superior to the other, although I feel that mine is more consistent with manufacturing practice. However, I haven't actually tried yet to work out numerical examples to see the actual differences, myself.
I would love to see more on the merit functions and specifically how each companies weighs their functions.Quote:
I mainly kept this section short and simple in the interest of length, since this particular topic wasn't really critical to the discussion. At the very least, astigmatism and mean add power are included as merit function terms, but I imagine that a lens designer may also include additional terms associated with quantities such as gradients of power, image swim, and so on. However, the more terms involved, the greater the computational burden.
Best regards,
Darryl
Yes, this is also the order of Euler rotations assumed by SOLA and ZEISS free-form lens designers.Quote:
I saw you mentioned that, so from a purist standpoint you are aligning your compensations to mimic the way in which the frame tracer is measuring the lens. I can see how that could eliminate or reduce inconsistencies in tilt measures
There are really two separate stages of lens design involved with progressive lenses that are customized for the position of wear: 1) the initial design of the original target lens and 2) the optical optimization of the prescription lens against the target lens.Quote:
I would love to see more on the merit functions and specifically how each companies weighs their functions
For the initial design of the target lens, more effort generally goes into determining the metrics associated with merit functions or arriving at other numerical and analytical solutions that achieve the desired distribution of optical performance, including defocus, unwanted astigmatism, image swim, high-order aberrations, binocularity, and so on. It is also not uncommon to begin with an analytical approach (using formulas) to generate a starting surface, and then to rely on a numerical approach (optimization) to refine the design of the surface.
For the free-form optical optimization process, on the other hand, we are only interested in replicating the ideal performance of the original target lens by minimizing the differences in optical power errors due to oblique astigmatism in the position of wear between the prescription lens and the target lens. So only mean power and astigmatism is important at this stage. It is assumed that the other performance metrics will be achieved if the power distribution of the lens is sufficiently replicated.
For the initial design of the target lens, the weightings are often determined manually, requiring the lens designer to tweak individual values at various points or areas over the lens design until he or she achieves the desired result. For free-form optical optimization, on the other hand, it may be more computationally economical just to specify a weighting function that varies with position over the lens, generally weighting the central regions more heavily.
Anyway, this is how the ZEISS and SOLA lens designers usually approach these problems. I'll leave it to the folks at the other lens manufacturers.
Best regards,
Darryl
I have heard this explanation before and appreciate it even though I would never be a situation to design it gives me great pleasure in knowing the process. So the 1st step is like a rough draft and further iterations refine. How many iterations of a design are customary when creating a new lens design or does it vary greatly?Quote:
Originally Posted by Darryl Meister
Also, to a give a weighing factor compared to defocus, oblique astigmatism would be worth 1/2 of a defocus error, (according to the spherical equivalent) is there a simple guesstimation that applies to other errors as well?
Thank you for all that you do for our profession Darryl!
Although most of the topic is way above my understanding and grasp, I am enjoying the discussion between PhiTrace and Darryl immensely!
Thanks guys!
I've been called crazy and I've been called brilliant, but only Darryl is crazy brilliant. Fezz, I really enjoy the posts and articles Darryl puts up, too bad he teases us with very little of his "optical crack" and with big gaps between.Quote:
Originally Posted by Fezz
This is a fairly complex question, because it will dependly greatly upon the particular approach of the lens designer. What you're referring to as an "iteration" is probably slightly different from how the term would be used in lens design. There are actually a number of stages at which an actual "iteration" of some sort may be performed; a few examples come to mind:Quote:
So the 1st step is like a rough draft and further iterations refine. How many iterations of a design are customary when creating a new lens design or does it vary greatly?
1. Prototype lens design iterations that each represent a specific combination of design parameters are utilized in wearer trials to evaluate the performance or satisfaction of one or more prototype lens designs under consideration.
2. Numerical optimization iterations are utilized during the lens design process to minimize merit functions, perform finite element analysis, or to otherwise seek a lens surface that satisfies some mathematical criteria as closely as posssible.
3. Design iterations are also performed for each base curve and add power combination, which often requires modifying the inset of the eyepath, fine-tuning the asphericity, or even varying the corridor and/or viewing zones for multi-design lenses.
4. Finally, mold iterations are performed to fine tune the lens design based upon measurements of lenses produced from the initial set of molds in order to ensure that the final lens surface matches the intended surface after shrinkage occurs.
But these iterations are actually distinct from the steps involved in developing a lens design using analytical and numerical tools. The "rough draft," as you put it, is often produced using an analytical or semi-analytical software tool that allows the lens designer to define the initial progressive lens surface by specifying various design parameters, such as the progressive corridor, size of the viewing zones, et cetera.
Multiple tools or stages may be involved to define the shape of the progressive power profile, design the periphery of the lens, improve binocularity, apply asphericity to the base curve, and so on.
This starting surface could then be fine-tuned using numerical optimization tools, such as finite element method, to improve certain optical measurements by minimizing a merit function, for instance. Bivariate splines are then frequently used to join smoothly the individually optimized sections or points of the lens. It is also possible to incorporate ray tracing for the position of wear into this optimization process.
I actually discuss the basic of a typical progressive lens design process in my Optics of Progressive Lenses article at OptiCampus.com.
Well, I appreciate the kind words but, in reality, I simply distill the work of men and women much smarter than I am into something that at least remotely resembles English.Quote:
but only Darryl is crazy brilliant
:wink:
Best regards,
Darryl
Is this proprietary software to Zeiss, or are we talking about available "over the counter" software such as ZEMAX or OSLO?Quote:
Originally Posted by Darryl Meister
So you translate engineerese to neaderthalese.Quote:
Originally Posted by Darryl Meister
I imagine that most of the major lens manufacturers probably develop their own lens design tools internally, but there are some private lens design firms out there that service a few lens suppliers and it is not uncommon for some of the major lens manufacturers to supply OEM designs to some lens suppliers.Quote:
Is this proprietary software to Zeiss, or are we talking about available "over the counter" software such as ZEMAX or OSLO?
I know that Carl Ziess, SOLA, and American Optical each have (well, "had" for AO, since they're all retired) their own lens design teams, typically comprising several different lens designers, mathematicians, vision scientists, and computer programmers as well as various ancillary personnel.
I don't know that popular commercial optical design packages like OSLO, Zemax, and Code V actually provide tools for designing progressive spectacle lenses though.
Best regards,
Darryl
I figured as much. I know that the ray tracing is pretty good with those packages and anlyzing lenses is great, but designing optics just seems a bit outside of the software's scope. Plus the parameters for the design I figure has got to come from scientists in the field applying the latest in geometric and physiological optics.Quote:
Originally Posted by Darryl Meister
In this day and age I would love to see the programmers, do you think they are aware of the science behind the optics or are these guys pure red bull drinking programming machines? I am guessing that free form software packages are the wave of the future and inputs have to be accepted from the various lab management systems in their respective formats and then feed to various machines in the the various formats that these newer CNC equipment requires. I have been boning up on my coding getting ready for the day and age that I am allowed to submit a file tot he lab and have them produce a design wholly my own. I don't think I would dable in the PAL market, yet anyway but I would love to cut my teeth on some free form SV lenses.
Do you get access to any equipment that you can tinker with? That would be optical nerd nirvana.
Honestly, with what appears to be so much derivative work in this industry, so it's hard to say.Quote:
In this day and age I would love to see the programmers, do you think they are aware of the science behind the optics or are these guys pure red bull drinking programming machines?
For Carl Zeiss Vision, at least, the computer programmers on our lens design teams are often mathematicians by education, so they often both develop and implement the algorithms and design tools, working closely with the lens designers. The lens designers are typically physicists who learn to specialize in optics or, particularly in Germany, optical engineers.
I work with our lens design software on a daily basis, but since I am no longer based at facility with an on-site laboratory, I don't do much tinkering with equipment anymore. Years ago, when SOLA still had manufacturing, the R&D department, and a test surfacing lab in Petaluma where I used to work, I did get to play around with a lot of neat stuff. <Insert Sigh>Quote:
Do you get access to any equipment that you can tinker with? That would be optical nerd nirvana
Best regards,
Darryl