Brain teaser for lab rats (and anyone else)

[MikeAurelius]

Rx: -1.75 -1.25 x 180
Index: 1.70
Base Curve 6.25
Lab tools in 1/8th increments

Which is the correct way to calculate the tool to use?

A: Differential

IRC: .530/.701 = .756

Base: 1.75 x .756 = 1.323 + 6.25 = 7.573 round to 7.62
Cross: 1.25 x .756 = .945 + 7.62 = 8.565 round to 8.62

B: Total Power

Base: 1.75 x .756 = 1.323 + 6.25 = 7.573 round to 7.62
Cross 3.00 x .756 = 2.268 + 6.25 = 8.518 round to 8.50

[HarryChiling]

B, total power. You could have included thickness and rounded to the nearest 1/10th diopter in another tool index to make the question truly applicable to todays labs rats.

[MikeAurelius]

Thickness comp on a minus power lens, even at high index (1.80) is negligible (at O.C.).

A would be a correct answer as well IF:

Cross: 1.25 x .756 = .945 + 7.573 = 8.518 round to 8.50 (note adding to non-rounded tool)

This is a "gotcha" I've used in the past when testing applicants for the surface lab. They get a pencil, calculator and paper, and have to hand calculate tools and thicknesses on 5 different Rx's (just in case the layout computer goes on the fritz).

We use 1/8th tooling here, but yes, it certainly could be modified for 1/10th. I'm not so sure about using different index tooling, how many labs use anything other than 1.530 tooling (out of curiosity)?

[JRS]

My personal opinion is, you should always include thickness in the math. Surprising sometimes how a subtle difference can alter rounding results.

Quite a few labs now use tooling other than 1.530 (1.600 in 1/10's). But being a glass lab, it would not change much for you.

[MikeAurelius]

My personal opinion is, you should always include thickness in the math. Surprising sometimes how a subtle difference can alter rounding results.

Quite a few labs now use tooling other than 1.530 (1.600 in 1/10's). But being a glass lab, it would not change much for you.

I've run a lot of calculations, and even on 1.80, at O.C., a 2.2 mm thick lens has roughly a 0.02 diopter power difference, which (IMHO) is meaningless.

[JRS]

And to a computer, that .02 (in raw data) could round up an 8th.... or down depending. A -6.055 would round (in 8ths) to -6.000, whereas a -6.070 would round to -6.125 (and that's only .015 diopters). And, depending on how your software works, it may make decisions based on which eye to round (and direction) first - then accomodate the other eye to move in a similar direction. That way the rounding "error" (for tooling selection) is in the same vein, on both eyes. Of course, in 10ths, both of those would round to -6.100

But it matters not, as you state, it's just a matter of opinion. I just happen to like as much accuracy as I can get. So we agree to disagree.

[MikeAurelius]

My software (like most, I presume) rounds at 0.0625 (0.063) D. I know for sure it doesn't round based on both eye directions, it rounds each curve, then back calculates total power and runs it again to optimize the tool curves.

[HarryChiling]

And to a computer, that .02 (in raw data) could round up an 8th.... or down depending. A -6.055 would round (in 8ths) to -6.000, whereas a -6.070 would round to -6.125 (and that's only .015 diopters). And, depending on how your software works, it may make decisions based on which eye to round (and direction) first - then accomodate the other eye to move in a similar direction. That way the rounding "error" (for tooling selection) is in the same vein, on both eyes. Of course, in 10ths, both of those would round to -6.100

But it matters not, as you state, it's just a matter of opinion. I just happen to like as much accuracy as I can get. So we agree to disagree.

+1, I like accuracy and even in a case where the computers went down I would use an excel sheet on my laptop or cell phone over pencil and paper and include thickness in the calculations. I use total power and would always use total power because it will make a difference in jobs with more disparity between the primary and secondary meridians. Also I convert the front curve to the material index and then calculate and then convert back to tooling index that way in the case where the tooling index varies which in a quality plastic processing lab I won't have discrepencies. The ideal behind any software is that the coding gets done once and then handles all the logic so it is easy to code more accuracy once and have all results run through the program be that much ore accurate. Their have been a few threads on this board that question the need for accuracy and in real life if a single job had ot be done on the fly the accuracy won't matter as much as the time wasted to attain that accuracy but in programming it is the opposite the the accuracy once will matter for the many lenses processed with the software.

It's crude but it would work in a situation where the computers went down from a cell phone:
http://onlineopticianry.com/wordpress/?p=111

[Darryl Meister]

My software (like most, I presume) rounds at 0.0625 (0.063) D

Are you guys using laboratory software that doesn't allow you to specify the increments of your lap tools? It might be in a settings or preferences menu somewhere.

The calculations are typically done out to the n-th decimal place in the progams that I am familiar with, and only later rounded to the nearest available tooling increment. And, to Harry's point, tenth-diopter tooling is quite popular.

Thickness comp on a minus power lens, even at high index (1.80) is negligible (at O.C.).

For you math buffs out there, you can show with a little bit of calculus that the variation in back vertex power F_V due to errors in lens thickness t is given by:


It is interesting to note that the power of a minus lens is less sensitive to changes in center thickness because of the flatter front curves associated with minus lenses, not just the thinner center.

The power varies as a function of 2*t*F₁/n when the thickness is held constant, and F₁^2/n when the front curve is held constant.

Best regards,
Darryl

[kcount]

Now, would all these be moot if one was using a new "Digital" production method?

[MikeAurelius]

Are you guys using laboratory software that doesn't allow you to specify the increments of your lap tools? It might be in a settings or preferences menu somewhere.

Written by me, and since all we do is glass, the 0.0625 break is quite sufficient.

I've looked at going to 1/10th tooling, but it would be a major pain in the butt to recut 80% of my tooling plus the expense of buying an additional 20% more tools and new lap racks...we don't do all that much 1.70/1.80 to really need it. Back in the day? Oh, yeah, would have made sense.

[MikeAurelius]

Now, would all these be moot if one was using a new "Digital" production method?

Yes, of course! I'd be doing it too if I didn't have to change cutters to go from cutting glass to cutting aluminium tools. If I can find enough parts for the Vector I've been using for spares, I'd turn that one into a dedicated lap cutter and go "fully digital" in a heartbeat (albeit for glass, which means no digital progressives lol).

[Darryl Meister]

Written by me

Well, if you're writing your own software, it should be pretty straightforward to swap out the rounding constant in the code, if you do ever change your tooling. For others, I believe that the most common lab software packages are customizable for your tooling nowadays.

and since all we do is glass, the 0.0625 break is quite sufficient.

Yeah, if you're primarily running crown glass, eighth-diopter tooling should be more than sufficient. If you cut the tools in 1.523 index, instead of 1.530, you could probably get away with quarter-diopter tooling for the cross curves as well.

Best regards,
Darryl

[MikeAurelius]

Yeah, if you're primarily running crown glass, eighth-diopter tooling should be more than sufficient. If you cut the tools in 1.523 index, instead of 1.530, you could probably get away with quarter-diopter tooling for the cross curves as well.

Best regards,
Darryl

Not when running high plus curves and using uncompensated progressive lenses! Get much beyond +3.50 and thickness compensation starts kicking in, and then using a 7 base progressive that has a true curve of 7.25 instead of 7.18...nope, need those 1/8th tools!!

We also run a lot of X-Ray glass, which is 1.806 index, so you see the problem.

[Darryl Meister]

Not when running high plus curves and using uncompensated progressive lenses! Get much beyond +3.50 and thickness compensation starts kicking in, and then using a 7 base progressive that has a true curve of 7.25 instead of 7.18...nope, need those 1/8th tools!!

Yeah, but none of those factors will affect the cross curve that you need to produce a given cylinder power, since the power compensation doesn't vary as a function of the back curve.

Once you get your toric back base curve as close as you can for the sphere power, the cylinder power will be exactly equal to the difference between the cross and back base curve, at least for lens materials close to the index of your tooling. Since cylinder powers are only ever prescribed in quarter-diopter increments, your cross curves never have to be any more precise than 0.25 D, if they have been cut in the index of the lens material.

If you do a lot of X-Ray glass, however, I'm surprised that you're able to get by with even eighth-diopter tooling. The rounding errors, alone, are almost +/-0.10 D, which eats up most of the ANSI Z80.1 power tolerance. I guess for your core prescription range, you could always cut a few extra tools in finer increments to be on the safe side, if you haven't already.

Not when running high plus curves and using uncompensated progressive lenses!

Gone are the days of figuring this stuff on the back of an envelope, I'm afraid. Manufacturers generally haven't relied on compensated base curves since lab surfacing programs became widely used. This is especially true for progressive lenses, since the center thickness can vary markedly, negating any predetermined base curve compensation.

Best regards,
Darryl

[MikeAurelius]

Oh, very true indeed! I was just commenting on the changes since I started (some 30+ years ago LOL)...my first layout program was on an old TRS-80 Model 1 (written in BASIC) and it took almost 15 seconds to calculate a pair of lenses. Now, I'm using a windows-based compiler and the calcs are finished as soon as I hit the 'Layout' button. Times, they are a-changing!!

I've got a full set of alum tools from +2.00 to +12.00 base, from 0.12 to 3.00 cylinder each all in 1/8 steps.

I get a lot closer than .10D on rounding errors, again that's why the 0.06125 break, plus the extra backwards calculation to double check the resultant power. I try to stay well within +/- 0.12 diopter of prescribed power on every X-Ray lens we send out, regardless of Z80.1. Logic is like this:

Calculate base and cross curves based on thickness and index. Anything over +1.00 is then double checked by calculating the resultant power of the tools, then if it is further than +/- 0.12 from prescribed power, it calculates the next higer or lower tool to see if it fits better. Before I started doing that, yeah, I was running quite close to the power tolerance, especially on the higher power rx's. There are times I wish I had a crate full of PVC tools to cut 'as needed' tools, maybe some day!

[Darryl Meister]

On a not-entirely-unrelated note, one of the first "big" programs that I ever wrote was an inventory management program for eyeglass frames at my father's practice on a Commodore 64, over twenty-plus years ago. Nowadays, that computer probably couldn't even run my microwave oven! Of course, that was back I had planned to become a computer programmer when I grew up, before I got sucked into the black hole that is Optical!

With eighth-diopter tooling, you'll get a break of 0.0625 D for lens materials with the same refractive index as your tooling. For higher index materials, however, your tooling increment will be significantly wider. Assuming your tools are cut to an index of 1.530, a lens material with a refractive index of 1.8 (like X-Ray glass) will provide an effective tooling increment of 0.0625 * (0.800/0.530) = 0.094 D. Unless I misunderstood what you meant.

Best regards,
Darryl

[Darryl Meister]

By the way, have you thought about just calculating the exact back that you need, and then rounding the value to your nearest tooling increment? It might increase your accuracy, while reducing the number of computations.

When I calculate lenses, I usually proceed as follows for an "uncut" shape:

1. Calculate approximate center thickness based on Rx power of lens using the R^2 / [2000*(n - 1)] approximation.
2. Iteratively determine a real center thickness and back curve combination that comes very close to the desired Rx.
3. Calculate final back curve based upon real center thickness from Step 2 (leaving only a small error in minimum thickness).
4. If necessary, calculate cross curve.
5. Round curve(s) to the nearest tooling increment.

A simple rounding function for eighth-diopter tools would look like Rounded = 0.125 * (INT(8 * Unrounded + 0.5)).

For shaped lenses, the thickness can be reduced significantly for plus prescriptions by considering the actual frame dimensions. "Many moon ago," I worked out a pretty accurate method of calculating the center and edge thickness of shaped plus lenses for a surfacing-like program that I had to develop for Lenscrafters to use with our Matrix equipment. I calculated the radius around the perimeter of the frame, determined the point of minimum edge thickness, and so on.

The program was actually surprisingly accurate, given that I had virtually no experience in writing laboratory calculation software at the time. In any case, the program definitely worked better than the Matrix concept!

Best regards,
Darryl

[MikeAurelius]

With eighth-diopter tooling, you'll get a break of 0.0625 D for lens materials with the same refractive index as your tooling. For higher index materials, however, your tooling increment will be significantly wider. Assuming your tools are cut to an index of 1.530, a lens material with a refractive index of 1.8 (like X-Ray glass) will provide an effective tooling increment of 0.0625 * (0.800/0.530) = 0.094 D. Unless I misunderstood what you meant.

Best regards,
Darryl

sort of, I think...(it's been a long day watching the blizzard outside LOL)...any error of 0.094 is going to be caught by the break at 0.06125, so the net error will be 0.094 minus 0.06125, call it 0.028something.

[MikeAurelius]

By the way, have you thought about just calculating the exact back that you need, and then rounding the value to your nearest tooling increment? It might increase your accuracy, while reducing the number of computations.

When I calculate lenses, I usually proceed as follows for an "uncut" shape:

1. Calculate approximate center thickness based on Rx power of lens using the R^2 / [2000*(n - 1)] approximation.
2. Iteratively determine a real center thickness and back curve combination that comes very close to the desired Rx.
3. Calculate final back curve based upon real center thickness from Step 2 (leaving only a small error in minimum thickness).
4. If necessary, calculate cross curve.
5. Round curve(s) to the nearest tooling increment.

A simple rounding function for eighth-diopter tools would look like Rounded = 0.125 * (INT(8 * Unrounded + 0.5)).

For shaped lenses, the thickness can be reduced significantly for plus prescriptions by considering the actual frame dimensions. "Many moon ago," I worked out a pretty accurate method of calculating the center and edge thickness of shaped plus lenses for a surfacing-like program that I had to develop for Lenscrafters to use with our Matrix equipment. I calculated the radius around the perimeter of the frame, determined the point of minimum edge thickness, and so on.

The program was actually surprisingly accurate, given that I had virtually no experience in writing laboratory calculation software at the time. In any case, the program definitely worked better than the Matrix concept!

Best regards,
Darryl

Over the years I've refined the program, and it is surprisingly close to what you've got there. For plano/minus Rx's, it defaults to a CT of 2.2/3.2 (although some of the materials I run have thicker CT's, for example the ACE glass for glassworkers is 2.5 as is X-Ray, some of the laser filters finish at 4.5 to 6.0 depending on the required optical density). For plus Rx's, I use A/B/ED measurements to calculate a rough approximation of the frame dimensions off axis to calculate the necessary strap thickness, in most cases, I'm within .2 to .4 mm of the desired 1.8 to 2.0 minimum edge thickness (or 3.0 for Z87).

I wish I had better data, but I don't want to mess with the WECO ZET 90 tracer to pull the actual radius information, but ideally that will most likely be the next step. Unfortunately, it's not too easy with the CL data interface (UGH). I've tried putting a data sniffer on it, but all I get is gibberish, just haven't had the time to mess with it.

[Darryl Meister]

sort of, I think...(it's been a long day watching the blizzard outside LOL)...any error of 0.094 is going to be caught by the break at 0.06125, so the net error will be 0.094 minus 0.06125, call it 0.028something.

The rounding error in the 1.530-based tooling is +/-0.0625 D, but these tools actually produce a much higher surface power on a higher-index material. Because of this, the effective tooling increment and, therefore, rounding error are also higher.

This might be easier to visualize with an example. Say, you have an X-Ray glass lens with a refractive index of 1.8 that requires a back curve of -5.00 D. This curve in a 1.530-based tooling index (F_T) is:



Now, the closest 1.530-based lap tool curves in eighth-diopter increments are then 3.25 D and 3.37 D. However, in the actual 1.8 refractive index of the lens material, these tool curves produce actual refractive surface powers (F₁ and F₂) of:




Now, this means that the errors (E₁ and E₂) from the required surface power of -5.00 D, in the actual refracive index of the lens material, are:




So either tool produces an actual rounding error of 0.094 D. Consequently, although the tool curves only have a rounding error of +/-0.0625 D in the 1.530-based tooling index, the error is actually significantly higher in the 1.8 refractive index of the actual lens material, which is ultimately what the power of the lens is based upon.

Best regards,
Darryl

[MikeAurelius]

thanks! that's what happens when I post mostly brain ded! now I need some coffee!!!!!!!!