Cylinder Power in the 180-degree meridian

[Bob Price]

Bob, Did you ever get your formulas sorted out?

Things have been really hectic at work and at home, however, I still work on it every chance I get. I don't have it figured out yet and still plan on purchasing some more books to help me out. This will be an ongoing process that I will have to stay committed to. I tend to get going in too many directions and need to focus on one task at a time.

By trying to use the formulas, that are in the books I have, to surface a lens in the lab, seems to be where the challenges are. I want to be able to put all of this to practice and believe me, I know how over my head I am right now. It seems that the formulas the lab software uses are more detailed and accurate and I just need some help in gathering that type of information. Although I am looking for the answers, I don't expect to have them given to me.

Thanks for the follow up.

[Bob Price]

I am seeking some more advice, as I seem to be stalled in my search. Even though I would like to be able to duplicate our workticket, I realize it helps to know how to walk before you try and run, so that will have to come later.

This thread started with me wanting to know how to figure the prism axis on a SV, with an oblique axis, when I was moving the OC for decentration, and has gone in a little different direction, for which I'm glad. In trying to take things one step at a time, I'm going to focus on grinding prism in a lens (SV or Multifocal, but mainly Bi's & Tri's) to move the OC to a desired location. Using the formulas that Darryl provided -
Ph = y * Fc * sin A * cos A + x (Fs + Fc * sin^2 A)
Pv = y (Fs + Fc * cos^2 A) + x * Fc * sin A * cos A -
I feel I have been able to accomplish this, but know that the index of the lens affects prism and should be figured into these formulas somehow or the formulas in the Whitney article need to be used somehow. I did run some tests from our system, in different indexes with the same power, and saw that the prism amount changed for each index. I thought that the Whitney article was the answer, but remember Darryl saying that this didn't pertain to what I was trying to accomplish. Even if it did, I haven't been successful in figuring out either formula in the article. I think my problem was in the difference between the Front Surface Power (1.53), which I thought was n-1/ti-1*true curve, and the True Front Surface Power. I also tried taking the prism result, from the above equation, and multiplying by ti-1/n-1, but that didn't seem to be the answer.

Am I going down the right road or on a complete dead end? Any advice would be much appreciated.

P.S. Someone did give an example on the Whitney formula and I will find it and look it over.

[Darryl Meister]

I feel I have been able to accomplish this, but know that the index of the lens affects prism and should be figured into these formulas... I did run some tests from our system, in different indexes with the same power, and saw that the prism amount changed for each index.

As JR noted earlier, the difference might very well be due to a "prism index" setting (though, unless you're blocking prism into the lens, I'm not entirely sure why this setting would matter). You could probably check this quite easily by running a sample work ticket with a significant amount of prescribed prism (e.g., 4.0 PD), and then adjusting the prism index from its highest to lowest setting in order to see whether it changes the values significantly. If you are blocking for prism, you might also check to see whether the software rounds the calculations to match your prism ring steps.

I thought that the Whitney article was the answer, but remember Darryl saying that this didn't pertain to what I was trying to accomplish.

Whitney's article deals with something akin to ray traced prism. Prentice's rule is indeed valid for any power, at least until the effects of spherical aberration kick in. The difference is that Prentice's rule applies to a perfect horizontal translation of the lens. A focimeter, on the other hand, does not translate a lens across a flat horizontal plane when it is moved across the lens stop, but rather it translates the lens across an arc equivalent to the back surface of the lens (since the lens stop is always perpendicular to the back surface).

But I don't know that your computer software is even getting into this level of detail, though it could be. And, even if it were, the differences would be marginal in most prescriptions (while the linear distance may seem large in Whitney's examples, the prism is very small and would not fail ANSI tolerances). If it is getting into this level of detail, it may be doing these calculations at a level of sophistication or complexity that you will have a hard time reproducing.

Nevertheless, once you have eliminated the prism index as a potential culprit, you could verify the accuracy of your calculations by running a sample work ticket using a relatively flat, high-powered plus lens (e.g., a +3.00 sphere on a 4.00 Base). If the prism results are closer for this job than for a -0.25 sphere on a 6.00 Base, it could be due to calculating ray traced prism versus Prentice's prism.

Also, ensure that the software you're comparing your results against is producing dead-on accurate results for these prism calculations in the first place, or you may be spending a lot of time trying to reproduce small systematic errors.

[Bob Price]

[QUOTE = As JR noted earlier, the difference might very well be due to a "prism index" setting QUOTE]

I know that the software has a Prism Index setting listed for each material, but am not sure how or if it figures it into the equation. I will try and find this out. If the Prism Index is taken into account when figuring prism, then is it possible to factor it into your formulas to get similar results? All of this still baffles me, because there should only be one correct amount of prism and prism axis that correctly moves the OC to the proper location.


[QUOTE = Whitney's article deals with something akin to ray traced prism[/QUOTE]

This is totally new to me and have only heard of it since joining this site. From what I am gathering, it takes into account the power (and whatever else) at every position of the lens. Is Ray Tracing something that is found thru calculations or measuring? Don't worry, I won't go diving into this until I'm more seasoned.

[QUOTE = Also, ensure that the software you're comparing your results against is producing dead-on accurate results for these prism calculations in the first place, or you may be spending a lot of time trying to reproduce small systematic errors.[/QUOTE]

Our OC's spot really good, so this is all I have to go on to determine that the software produces spot on results. Of course, when we calibrate our generator, a lot of time goes into making sure there is as little prism as possible in a plano lens.

[Darryl Meister]

I know that the software has a Prism Index setting listed for each material, but am not sure how or if it figures it into the equation.

It doesn't. The prism calculated by the equation tells you how much prism you need. The prism index setting tells you how much prism you need to surface into your n1 index material using an n2 index prism ring in order to produce the desired results. This will adjust the prism by an amount equal to (n2 - 1) / (n1 - 1).

If the Prism Index is taken into account when figuring prism, then is it possible to factor it into your formulas to get similar results?

You would just reverse the process described above.

All of this still baffles me, because there should only be one correct amount of prism and prism axis that correctly moves the OC to the proper location.

For a given lens configuration, There Can Be Only One. (Cue the Queen theme music from Highlander.)

Is Ray Tracing something that is found thru calculations or measuring?

It is done through analytical calculations. Ray tracing in the traditional sense of the term is generally used in lens design, though good surfacing software should account for various optical effects, like the astigmatism induced by prism, the change in prism produced tilt angle in low powers, and so on, which can only be determined using certain ray tracing calculations. (I know that SOLARx -- SOLA's surface software -- does, since it is written by the same guys who write our ray tracing programs, but someone like Shanbaum or JR would have to speak to whether or not this is typically the case with commercial surfacing software.)

[Bob Price]

It doesn't. The prism calculated by the equation tells you how much prism you need. The prism index setting tells you how much prism you need to surface into your n1 index material using an n2 index prism ring in order to produce the desired results. This will adjust the prism by an amount equal to (n2 - 1) / (n1 - 1).

In the information that you and J.R. have provided, I am finally seeing that I already have the correct amount of prism needed for any given RX, using the formulas that you provided. Now, it is a matter of knowing the equipment settings in the software and converting it to the amount on the workticket.

I'm not totally following your example above. From my previous example where I had a poly ST28, and I came up with a prism value of 1.36D and the workticket called for 1.24D. n1 would be the index of refraction of the lens and n2 would be the prism ring index. Is the prism ring index a value like 1.523 or is it the depth or diameter of the ring?

So, is this similar to what happens for laps cut in different indexes? A radius of curve is the same in 1.53 or 1.60, but is expressed differently depending on what index the lap is cut in.

Am I getting hotter or colder?

[JRS]

Bob, in your LMS System, the prism index - per material, may be the same indice, or may equal material index. You should look at the settings within the software.

If you take 3 materials and create 3 equal Rx's (plano powered SV with 3 diopters BI prescribed) and print tickets... you will likely see 3 different amounts printed for "grind this prism at generator", yet all 3 will produce 3 diopters of BI prism when viewed through an inspection device.

[Bob Price]

Bob, in your LMS System, the prism index - per material, may be the same indice, or may equal material index. You should look at the settings within the software.

If you take 3 materials and create 3 equal Rx's (plano powered SV with 3 diopters BI prescribed) and print tickets... you will likely see 3 different amounts printed for "grind this prism at generator", yet all 3 will produce 3 diopters of BI prism when viewed through an inspection device.

J.R.,

Yes, the prism indexes are different. As is the ring depth and Prism ring diameter. I did run tests with a plano with 3 diopters base in and the prism amount required at the generator was different for each material. The higher the index the less prism required.

[Darryl Meister]

I did run tests with a plano with 3 diopters base in and the prism amount required at the generator was different for each material. The higher the index the less prism required.

Assuming your prism index (n2) is set to 1.530 and you are using polycarbonate (n1 = 1.586), you should be seeing this much prism relative to your prescribed prism:

(n2 - 1) / (n1 - 1) = (1.530 - 1) / (1.586 - 1) = 0.904

Or, roughly 1 - 0.904 = 9.6% less prism. This would change 3.0 prism diopters to 2.7 prism diopters.

[Darryl Meister]

To clarify, you need a weaker prism ring in a higher index lens material since the actual strength of the prism ring increases as the refractive index of the material increases. A 3.0 prism ring calibrated for a tooling index of 1.530 will produce exactly 3.0 prism diopters in a lens material with a refractive index of 1.530, but 3.31 prism diopters in a lens material with a refractive index of 1.586 -- and only 2.82 prism diopters in a lens material with a refractive index of 1.499.

While each lens material will need the same amount of prism, the actual amount of prism produced by the wedge angle of the prism ring will vary from material to material. Consequently, a single prism ring will not produce a consistent amount of prism across different lens materials. Though you can convert back and forth using that expression, (n1 - 1) / (n2 - 1) or (n2 - 1) / (n1 - 1), depending on which way you need to go.

[Bob Price]

Darryl,

I brought a couple worktickets home tonight, to work on you're latest post, and stummbled across something I never realized (or maybe still don't). The Rx is a CR-39 ST35 +2.00 -100 Ax 70 OU. The OC needs to be moved in 3.5mm and down 2mm. Right eye calls for prism of .45 @322, the left eye .68 @ 226. If I use the formulas that we have been discussing in this thread, I would come up with the same result. In examining the workticket you can plainly see that the OC is traveling differently thru the cylinder of the right lens compared to the left lens. If the left eye axis was 110, I would imagine that the prism amount would be the same.

Sorry to bring up something else when I don't even have a handle on our main topic, but I wanted to get yours and everyone elses opinion.

[Bob Price]

I must have blown it and you guys are scratching your heads thinking, "This guy is an idiot." In regards to my last post, does the formula I'm using take this into account and I'm not seeing it? Also, I think that as the OC height changes a different angle is created in relation to the cylinder and needs to be taken into account.

Maybe this is what your saying about learning the basics first, because I don't know the inner workings of the formula yet, to know everything it is figuring.

[Darryl Meister]

Hi Bob, I won't have time to go through the math for a bit, but you are flipping the sign of the decentration between the right and left lenses, right?

[Bob Price]

I will be now. Thanks.

[Bob Price]

I spent some time yesterday going over my inconsistent results. It all boiled down to not having the formula plugged into my calculator correctly. I went thru the formulas piece by piece and got much better results. Another missing piece was the prism index, which I'm pretty sure is set to 1.498.

I did notice more inconsistencies in the higher powers and am wondering if this is because of a possible "prism rounding" in the software? Also, when dealing with a plano, my calculations call for no prism when there should be around .05. Any suggestions would be greatly appreciated.

Darryl mentioned using the proper sign convention for the decentration between the right and left eyes. Is this just for the vertical? For instance, if the bifocal is 6mm down and the difference between the seg ht and OC is 3mm, I would use a -.3 for the left eye but not for the right? A more in depth explanation of this would also be greatly appreciated.

Thanks.

[Darryl Meister]

Darryl mentioned using the proper sign convention for the decentration between the right and left eyes. Is this just for the vertical?

No, it's just for horizontal.

[lensgrinder]

Darryl mentioned using the proper sign convention for the decentration between the right and left eyes. Is this just for the vertical? For instance, if the bifocal is 6mm down and the difference between the seg ht and OC is 3mm, I would use a -.3 for the left eye but not for the right? A more in depth explanation of this would also be greatly appreciated.

Bob,
If you think of a coordinate system with 0 degrees to the right 180 degrees to the left 90 degrees at top and 270 degrees at the bottom. Now think of two of them side by side like you were looking at the person. On the left you have your right eye and on the right you have your left eye. When you move the OC in or towards 0 for the right eye you are moving in the positive direction. When you move out or towards 180 you are moving in the negative direction. The opposite applies to the left lens, except when you move toward 90 or up then you are moving in the positive direction and the same applies to the right eye. When you move a left lens in and down (towards 180 and towars 270) you are moving both in the negative direction. I hope this helps.

[Bob Price]

Also, when dealing with a plano, my calculations call for no prism when there should be around .05.

I'm thinking that if I were to figure the power, in these formulas, using the radius of the front and back curves (combined with thickness and index of refraction), then when figuring for prism it would take into account that it is not a true plano and that prism needs to be ground for decentration.

I've been messing around a little bit with this tonight, but would like to be shut down, if I'm way off base again, before I waste a bunch of time.

[lensgrinder]

No, it's just for horizontal.

Why do you not use negative numbers in the vertical?

[Darryl Meister]

Why do you not use negative numbers in the vertical?

You do use positive and negative numbers for the vertical meridian, but this convention doesn't change between the right and left eyes (as you noted in your earlier post). For horizontal decentration, on the other hand, the sign convention is flipped between the two eyes.

[lensgrinder]

You do use positive and negative numbers for the vertical meridian,

OK, good. I just wanted to make sure I was not loosing my mind. I misunderstood when you said it is just for horizontal. Thanks for clearing that up.

[Aarlan]

This is on the ABO, right?


AA

[Darryl Meister]

This is on the ABO, right?

Not this kind of stuff. You may need to know that a lens with cylinder power has no cylinder power along its axis and maximum cylinder power at 90 degrees away from its axis, but that's about it.