Lens Design & Aspherics

**eyeboy** · 06-23-2006, 08:44 AM

When choosing the best base curve/p-value for an astigmatic patient is it better to choose the mean RX i.e. Sphere + (cyl/2), the highest meridian or the lowest meridian.:hammer:

**Darryl Meister** · 06-23-2006, 11:42 AM

Usually you would consider the spherical equivalent or rhe strongest meridian.

**eyeboy** · 06-23-2006, 11:51 AM

Originally Posted by Darryl Meister

Usually you would consider the spherical equivalent or rhe strongest meridian.

Spherical equivalent? Is that the mean Rx as i described above.

**OPTIDONN** · 06-23-2006, 12:09 PM

It's 1/2 cyl. power + sphere power.

**Darryl Meister** · 06-23-2006, 01:13 PM

Yes, they are the same. Though, when referring to a prescription, "spherical equivalent" is usually the preferred usage.

**HarryChiling** · 06-23-2006, 01:43 PM

If you are designing an atoric lens then you would consider each meridian independantly for base and p-value. :D

**Jim Stone** · 06-23-2006, 04:38 PM

Originally Posted by HarryChiling

If you are designing an atoric lens then you would consider each meridian independantly for base and p-value. :D

Aint to many people can manufacture those Harry.

**OPTIDONN** · 06-23-2006, 05:08 PM

Will lens companies provide the P value of thier aspherics?

**Darryl Meister** · 06-23-2006, 05:14 PM

I imagine that most companies (certainly Zeiss and SOLA) use higher order polynomial aspherics, not conic p-values.

**eyeboy** · 06-26-2006, 06:45 AM

What's the difference?

**HarryChiling** · 06-26-2006, 08:08 AM

The p-value describes how much the lens changes and remains constant throughout the entire lens surface. When Darryl talks about higher order polynomial aspherics the difference is their is no constant p-value. The polynomial aspherics may take the center 20mm and optimize for the best vision possible with least amount of abberations, then take the 20-30mm area and slowly start adjusting the lens for better aesthetics instead of optimal vision, and then take the 30-whatever and use this area purely for making the lens thinner. The numbers are not accurate, but the theory should be.

Originally Posted by Jim Stone

Aint to many people can manufacture those Harry.

I know, but thought I would throw it in their for knowledge sake.

**eyeboy** · 06-27-2006, 07:49 AM

Can you still get semi-finished in these types of aspheric? Also could you describe the centre 20mm using a p-value so that the best design could be given for the prescription, the remainder of the surface taken up with aestetics?

**Darryl Meister** · 06-27-2006, 01:26 PM

Can you still get semi-finished in these types of aspheric?

You'd have to check with the individual manufacturer to find out how their aspheric lenses are designed. However, most continuous surface cataract aspherics (like AO's old Ful-vue lens and Silor's Super Modular) use a blending polynomial like this.

Also could you describe the centre 20mm using a p-value so that the best design could be given for the prescription, the remainder of the surface taken up with aestetics?

While it would be somewhat cumbersome to use a conic expression for the central 20 mm and a separate polynomial expression for the remainder of the lens (you'd have to use two piece-wise functions), you can actually employ a deformed conicoid equation, which essentially uses as the first term a conic section and then higher order terms for the remainder of the polynomial.

**eyeboy** · 06-30-2006, 02:03 PM

I'm a little confused. Are polynomal surfaces used for cataract/high plus lenses. After a bit of reading I thought the low plus aspherics were hyperbolic and could be described with a p-value?????

**Darryl Meister** · 06-30-2006, 02:15 PM

You may consider reading this article on lens design.

**rolandclaur** · 07-03-2006, 11:57 PM

Wow.. a lot of what you guys are saying is scratching my head. I understand the very basics of asphericity, but do you guys know where I would go besides the fantastic link Darryl provided where I can learn in depth about aspheric lenses, their design, etc etc?? I WANT TO KNOW!!!

**66Lenses** · 07-04-2006, 01:19 AM

This is good information resource and many threads here are informative to the extent that it helps newbies and beginners as well. Keep up with good work guys and gals.

**eyeboy** · 07-08-2006, 11:12 AM

Here's what Jalie had to say about aspherics used for low plus.

'Needless to say. any higher order aspherical surface could be used but,in practice, it would not depart significantly from a hyperboloid since the curve regulates the astigmatism at the correct rate'
Opthalmic Lenses and Dispensing, Mo Jalie.

So can these 'low-plus' aspherics be described using a p-value???

**Darryl Meister** · 07-08-2006, 11:23 AM

A hyperboloid can certainly be described using a p-value.

**HarryChiling** · 07-09-2006, 05:34 PM

http://www.optometry.co.uk/files/737...ie20050325.pdf

Here is an article by Mo Jalie describing aspheric lenses, I think that it would be useful for understanding aspherics. As for a hyperboloid being described with a p-value yes it can.

a list of conics

Circle
Hyperbola
Porabola
Ellipse

Any of these curves are sections of a conic, imagine taking an ice cream cone (your conic) and taking a stright cut through it then looking down into it. This would describe a circle. Imagine taking that same cone and slicing it at a slight angle. This would describe an ellipse. Imagine slicing it parralell up one side of the cone. This would be a parabola. Now imagine slicing it at an angle greater than parallel to one of the sides. This would describe a hyperbola. This is probably a horrible explanation of the differences in the surfaes, but it is the only conic I could think of that would relate. I think a picture would probably best describe it.

**eyeboy** · 07-10-2006, 02:02 PM

I understand that p-value describes its degree of flattening and the diagram in Jalie shows different p-values for curves i.e prolate ellipse etc. Is there any way of showing p in a diagram, how is it calculated. Jalie just seems to present it in formula and then, well thats kinda of it???

**HarryChiling** · 07-10-2006, 02:37 PM

Check out thread 11579 post #17 This should give you an idea of how to determine what the radius and base curve at any specific point on a aspheric lens (excluding polynomials).

**Darryl Meister** · 07-10-2006, 03:15 PM

The "p-value" is basically a mathematical transformation of the eccentricity value of a conic (often denoted in formulas using an 'e'). This is the ratio of the distance from the conic curve to its focus to the distance from the conic curve to its directrix. You can learn all about conics and eccentricity at this Wikipedia article, as well as at many math sites on the Internet.

However, I wonder if you don't really mean to ask how you would determine what the value of 'p' should be for a given lens? This would require a great deal of optical ray tracing. While it might be possible to do this analytically strictly by "doing the math," it would generally be done numerically using a computer program. I actually have an Optical Analysis program available for download in the File Archives, which you could use to determine the p-value for a given prescription and Base curve.

**eyeboy** · 07-12-2006, 08:23 AM

Originally Posted by I actually have an [url="http://www.optiboard.com/forums/showthread.php?t=14881"

Optical Analysis program[/url] available for download in the File Archives, which you could use to determine the p-value for a given prescription and Base curve.

On your program do you mean for a given base and rx what the best p-value would be to minimse oblique astigmatism etc?

**Darryl Meister** · 07-12-2006, 11:20 AM

Yes. You can change the p-value until you've minimized whatever aberrations you'd like for a given prescription, Base curve, lens material, vertex distance, angle of view, etcetera.