What is an Aspheric???

[HarryChiling]

Darryl,

If I understand it correctly your program is in a sense a lens design tool. This is a great program for designing lenses. My interest was peaked a while ago when someone posted a question involving an aspheric lens and the true power. Someone posed a question about the aspheric surface and off my mind went. I used Keplers Law of Planetary motion to come up with my answers. I have only so far looked at the ellipse, I don't really see a need for the hyperbola or the parabola, its the only one that I would think would be used for the design of a lens. I have an do enjoy your opticslite program it's genius. I have a hard time looking at the answer if I have not had any research or understanding into how it was derived. YOU CAN CALL ME HARD HEADED. It's just the way I was raised. My equation is usefull in determining properties of a lens when you have the parameters and you just need to know the power of the curve at a given point. I would take and figure the base at the ED and use this to calculate my thickness. It is not completely accurate due to the fact that most lenses are not aspheric all the way through, but it works. I have some experience with visual basic if you need to farm out some of the code work let me know I would be more than willing to give you a hand.

[Darryl Meister]

If I understand it correctly your program is in a sense a lens design tool

More or less.

I used Keplers Law of Planetary motion to come up with my answers.

Kepler's laws do make much use of conic calculus, since orbits are generally elliptical with the sun at one focus, but that does seem like a roundabout way to figure this out. ;)

I have only so far looked at the ellipse, I don't really see a need for the hyperbola or the parabola, its the only one that I would think would be used for the design of a lens.

As it turns out, an aspheric lens can use a variety of conic sections, including hyperbolic, parabolic, oblate elliptical, and prolate elliptical curves, depending upon how flat the lens is, whether the aspheric surface is on the front or back, and so on. That's the advantage to using the p value, which manipulates the curve through the entire conic family (p = 1 is a circle).

I have some experience with visual basic if you need to farm out some of the code work let me know I would be more than willing to give you a hand.

At some point, I'll probably convert the entire spreadsheet into a Visual Basic program. But I'll have to burn through many a vacation day to do it.

[HarryChiling]

Yes I made mistakes in my calculations above again I used the eccentricity as .8 instead of .5 but you get the drift. I am working on a calculator for this equation as well. Post it soon

[QDO1]

I can guarenty that it would be an helpfull information because i want to produce aspherical lenses from spherical blanks wich are realy cheaper.... if it is "just" a formula I just have to put in in a FreeForm Generator and the work is done...

why not employ the sevices of a optical scientist when you buy your free-form machine, that (in proportion) will be small fish. If you dont know anything about Aspheric lenses, why are you trying to make them. All the coeficents, in the equations are there for a purpose, get one wrong, and yes you will make an aspheric lens, but unfortunatally they will be of no use to a patient

[HarryChiling]

I have the calculator online at

www.harrychiling.com/equations/index.html

[Payman]

Here is an article I wrote on the subject many years ago:

Aspherics Lenses: Optics and Applications

You cannot produce aspheric lenses using conventional toric surfacers (cylinder machines), since they are designed for fining and polishing lenses with circular cross-sections and aspheric surfaces use non-circular cross-sections.

Aspheric lenses also require "optimization" of some form in order to calculate the surface, which generally requires a ray tracing program and a basic knowledge of polynomial and/or conicoid optical surfaces.

Best regards,
Darryl

Dear Darry,
Would you please send me a copy of the article you introduced in your message by email? it seems the link does not exist or has error to download.
my email address is paymanrajai@gmail.com

Regards
Payman

[lensgrinder]

Here is the link

It is found in the Optiboard file directory.

[EyeFitWell]

No, I'm not confusing the two, but I do not think that peripheral asphericity improves visual acuity if the patient happens to move their line of sight and looks through a point off the optical center.

I thought that was exactly the point of aspheric lenses.
I found this site a while back looking for a picture of aspheric vs. nonaspheric lenses (B/C our VSP pts want to know why there is a specific charge on their reciept for aspheric when they upgrade from CR-39). According to this the benefits are:
1. thinner, lighter.
2. reduced image minification/magnification visible when looking at the eye of the wearer
3. better vision on the periphery of the lenses. (in other words, away from the OC)
4. lenses fit better in the frame when working with strong plus
http://www.allaboutvision.com/lenses...ric-lenses.htm

[Darryl Meister]

I thought that was exactly the point of aspheric lenses.

The point of an aspheric lens for low to moderate powers is to allow the use of flatter, non-standard Base curves to improve cosmetics and weight. Aspheric lenses cannot really "improve" optical performance compared to a standard or "best form" lens using spherical curves. They just allow similar optical performance to be obtained with thinner, flatter lenses.

However, for cataract lens designs above +8.00 D, which represents the mathematical limit of the prescription range of "best form" lenses, aspheric lenses can improve optical performance compared to spherical lenses.

[Payman]

Dear Fred,
Your question does not have an straight answer. It was a part of my M.Sc.Thesis 5 years ago. I can introduce you some crucial references as follow:
1- Bennett 1988, Aspheric and continuous curve contact lenses, optometry Today; 2 jan. pp 11-14, 27 Feb. pp 140-142; 23 April pp 238-242; 30 July pp 433-444; 5 Nov.pp 630-632
2- Bennett 1968, Aspherical Contact Lens Surfaces, The ophthalmic optician, part one ?, part two:30 Nov. pp 1297-1311; part three: 8:1037-1040 or 1969:9:222-224 & 229-230
3- Baker, Ray tracing through non-sphercial surfaces. Proc.Phys.Soc (Lond) or Proc.R.Soc. 1943:55:361-4
4- Hopkins, the wave theory of abberations, Clarendon Oxford 1950.

Payman

[LxGoodies]

Hello @Darryl Meister,

Thanks for your your sagitta formula for R-P. For a programmer (not an optometrist) like me, some terminology is difficult to grasp intuitively. Maybe I can add something usefull to this thread.. your remark..

Nor could you use the Pythagorean theorem to determine the radius at any point using the X and Y coordinates (you actually use calculus).

Indeed, I use the following Pascal procedure for that.. It takes three subsequent x,y points from the result polynome, it yields the midpoint (xc,yc), maybe forum members can use this too.

function SOLVE_2r(a,b,c,d,e,f: real; var x,y: real) : boolean;
var t: real;
begin
 t:= (b*d - e*a);
 if ((t>-1e-14) and (t<1e-14)) then begin SOLVE_2r:=false; exit; end;
 x:= (b*f - e*c)/t;
 y:= (a*f - d*c)/(-t);
 SOLVE_2r:=true;
end;
 
function find_arc_center(x1,y1,x2,y2,x3,y3: real; var xc,yc: double): boolean;
//  Given three points (x1,y1) (x2,y2) (x3,y3) determine arc center (xc,yc)
var a,b,c,d,e,f,x,y: real;
begin
 find_arc_center:=false;
 a := x3 - x1; b := y3 - y1; c := (x3*x3 + y3*y3 - x1*x1 - y1*y1)/2.0;
 d := x3 - x2; e := y3 - y2; f := (x3*x3 + y3*y3 - x2*x2 - y2*y2)/2.0;
 if SOLVE_2r(a,b,c,d,e,f,x,y) then
 begin
   xc:=x; yc:=y;
   find_arc_center:=true
 end;
end; 

Kind regards,

:)
Lex

[Darryl Meister]

Looks interesting. I might have to experiment with it a bit...

[LxGoodies]

Looks interesting. I might have to experiment with it a bit...

It is always needed for visualisation things, in 3d it can also be done. By the way, above version is speed optimized, to support graphics. Double precision calculation (and slower) must be done by changing the code to

function SOLVE_2r(a,b,c,d,e,f: extended; var x,y: extended) : boolean;
var t: extended;
begin
 t:= (b*d - e*a);
 if ((t>-1e-14) and (t<1e-14)) then begin SOLVE_2r:=false; exit; end;
 x:= (b*f - e*c)/t;
 y:= (a*f - d*c)/(-t);
 SOLVE_2r:=true;
end;
 
function find_arc_center(x1,y1,x2,y2,x3,y3: double; var xc,yc: double): boolean;
//  Given three points (x1,y1) (x2,y2) (x3,y3) determine arc center (xc,yc)
var a,b,c,d,e,f,x,y: extended;
begin
 find_arc_center:=false;
 a := x3 - x1; b := y3 - y1; c := (x3*x3 + y3*y3 - x1*x1 - y1*y1)/2.0;
 d := x3 - x2; e := y3 - y2; f := (x3*x3 + y3*y3 - x2*x2 - y2*y2)/2.0;
 if SOLVE_2r(a,b,c,d,e,f,x,y) then
 begin
   xc:=x; yc:=y;
   find_arc_center:=true
 end;
end; 

Lx

[Darryl Meister]

Double precision calculation (and slower) must be done by changing the code to

I'll have to convert it all into either Visual Basic or C++ before I can do anything with it anyway. ;)