even and odd aspherics

[d***@yahoo.com]

Most aspheric lens designs that I have seen contain even-order terms
(r^4, r^6, etc), but not odd-order terms (r^3, r^5, etc). The only
explanation I have found is on the Kreischer web site: "Avoid odd
polynomials (these can be processed, but require finding a best fit,
even polynomial for generating)." Is this true with state-of-the art
lens-generating equipment or only with older equipment? The reason I'm
asking is that my design gives very good performance (in Zemax) using
r^3 and r^4 terms. But when I get rid of the r^3 term, I can use
even-order terms up to r^12 and performance is still not as good. Will
a shop have trouble making an asphere that uses r^3 and r^4 terms?

[surfer]

odd power polinomials may produce shapes pointed at the center, unlike
even aspheres.

[Salmon Egg]

On 1/23/06 8:26 PM, in article

Post by d***@yahoo.com
Most aspheric lens designs that I have seen contain even-order terms
(r^4, r^6, etc), but not odd-order terms (r^3, r^5, etc). The only
explanation I have found is on the Kreischer web site: "Avoid odd
polynomials (these can be processed, but require finding a best fit,
even polynomial for generating)." Is this true with state-of-the art
lens-generating equipment or only with older equipment? The reason I'm
asking is that my design gives very good performance (in Zemax) using
r^3 and r^4 terms. But when I get rid of the r^3 term, I can use
even-order terms up to r^12 and performance is still not as good. Will
a shop have trouble making an asphere that uses r^3 and r^4 terms?

I do not fully understand this post. Even polynomials will give symmetric
performance for rays above and below the center line. That symmetry will not
be true for odd polynomial terms. I also believe that the best fit plane
would be tilted with odd polynomials thereby introducing an off center
response.

Bill

-- Ferme le Bush

[DonJan]

Post by d***@yahoo.com
Most aspheric lens designs that I have seen contain even-order terms
(r^4, r^6, etc), but not odd-order terms (r^3, r^5, etc). The only
explanation I have found is on the Kreischer web site: "Avoid odd
polynomials (these can be processed, but require finding a best fit,
even polynomial for generating)." Is this true with state-of-the art
lens-generating equipment or only with older equipment? The reason I'm
asking is that my design gives very good performance (in Zemax) using
r^3 and r^4 terms. But when I get rid of the r^3 term, I can use
even-order terms up to r^12 and performance is still not as good. Will
a shop have trouble making an asphere that uses r^3 and r^4 terms?

r^2 causes problems with the Radius of Curvature, r^4 causes problems
with the Conic Constant. That is the lens design, analysis and test
algorithums don't work well. r^3, r^5 are potato chips. That is the
surfaces are not rotationally sysmetric (very expensive and
questionable value).

[a***@earthlink.net]

Post by d***@yahoo.com
Most aspheric lens designs that I have seen contain even-order terms
(r^4, r^6, etc), but not odd-order terms (r^3, r^5, etc). The only
explanation I have found is on the Kreischer web site: "Avoid odd
polynomials (these can be processed, but require finding a best fit,
even polynomial for generating)." Is this true with state-of-the art
lens-generating equipment or only with older equipment? The reason I'm
asking is that my design gives very good performance (in Zemax) using
r^3 and r^4 terms. But when I get rid of the r^3 term, I can use
even-order terms up to r^12 and performance is still not as good. Will
a shop have trouble making an asphere that uses r^3 and r^4 terms?

The shop's we have used with CNC grinding and polishing machines should
have no problem with the odd terms. A couple of points to the other
responders: The standard odd terms in ZEMAX are rotationally symmetric
because they are in terms of r (which is always positive) and not x or
y. Also, if you don't use the term linear in r, then there will be no
sharp point on axis, so the surface is "well-behaved" with higher-order
odd terms.

Al Greynolds

[d***@yahoo.com]

Mr Greynolds, thank you for your answer. Just out of curiosity, is
there a simple explanation why non-CNC machines have trouble with
odd-order terms?

Because of inherent limitations of the machinery?

Or because there's hardly ever a use for odd-order terms (if this is
true, can somebody explain why?), and therefore the machines weren't
designed to handle them?

[a***@earthlink.net]

Post by d***@yahoo.com
Mr Greynolds, thank you for your answer. Just out of curiosity, is
there a simple explanation why non-CNC machines have trouble with
odd-order terms?
Because of inherent limitations of the machinery?
Or because there's hardly ever a use for odd-order terms (if this is
true, can somebody explain why?), and therefore the machines weren't
designed to handle them?

Its more of a problem with the support software, especially that used
for testing. One aspheric I designed on CodeV used a radial cubic
spline surface. Although splines are common in CAD software and have
been in optical design codes for decades, no optical manufacturer would
touch it (even those with CNC equipment). Because it was for an
illumination application that did not require anywhere near
fraction-of-a-wave accuracy, Kreischer eventually agreed to make the
part but I had to first best-fit it to a 15th-order ODD radial
poiynomial (including the linear term!). The machines could handle it
but I suspect their normal optical testing software (typically Zernike
based) couldn't and thats why we just agreed on a "best effort". The
part ended up being within a couple of microns of the desired surface,
good enough for our illumination application.

Al Greynolds
www.ruda.com

[surfer]

<<Also, if you don't use the term linear in r, then there will be no
sharp point on axis, so the surface is "well-behaved" with higher-order

odd terms>>

linear, 3-d power, and all other odd powers will produce a point on the
axis.

[Bob Knowlden]

Only the first order will produce a cusp.

(The third order and higher odd terms have zero slope at the origin.)

Post by surfer
<<Also, if you don't use the term linear in r, then there will be no
sharp point on axis, so the surface is "well-behaved" with higher-order
odd terms>>
linear, 3-d power, and all other odd powers will produce a point on the
axis.