Agreed about the complexity.  A few people in the field have told me that the orthogonality is pretty handy, though, especially for polishing, and I do like that the RMS and slopes just fall out of the coefficients.

Hi Erin!

Can you tell me more about “I do like that the RMS and slopes just fall out of the coefficients”?

• M

I know exactly what you mean. Will do. 

I have huge respect for Greg Forbes, and his insights in applying Gaussian Quadrature to optical design alone is enough to induct him into the Optical Design Hall of Fame. But I have never grasped the utility of his aspheric formalism. Nobody has ever given me a clear, simple explanation as to why the things the Q-coefficients do matter. 

It’s true that when you optimize, the particular polynomial form you use for the surfaces affects the route the optimizer takes in coming to a minimum. But it’s far from clear to me that the Qs are inherently superior. If you set up a cell phone design with even aspheres and optimize, then with extended evens and optimize, then with Zernikes and then optimize, or with Qs and then optimize, or with Jose Sasian’s pedal surface and optimize, you can’t predict which one will come to a better solution.

By all means give them a try, but in all my tests the only conclusion I have come to is that the Qs are slow and cumbersome, but get to the same point within some +/-.

Change my mind 😀

Seriously, I’d really like to have a discussion with people who have used it and obtained results they would not have gotten otherwise. I just don’t understand the hype.

• Mark

Hi Mark,

The Qbfs are quite complex but the Qcon are actually very simple, and you can convert them to usual polynomial form very easily, e.g. in Excel (or with a few lines of Matlab). Also, Qcon asphere is really compatible with the even/odd asphere formula.

I have used Qcon in surface fitting as the orthonormality makes a huge difference in convergence for fitting algorithms. At the end, I converted back to usual form.

Hey Michael,

The Ma et al paper is really good, but I don’t think it’s doing what I’m referring to. In section 2.2 they say:

The purpose of this optical design study was to compare solutions developed using Q-type aspheric departure surfaces optimized without slope constraints and Q-type surfaces optimized with aspheric slope constraints.

In other words, they are optimizing the Q surfaces with and without the slope constraints. With slope constraints is better for manufacturability, and I totally get that. BUT, you don’t need the Qs for that. Slope constraints can be added to any surface type: even asphere, Zernike, superconic, whatever. In section 3, they say

An optimization based in a Q-type was found to take similar time, with and without the slope constraints. However in the case of the slope constraint solution, the impact on the time to assemble a specification compliant system is reduced, potentially substantially.

In other words, the benefit comes from the slope constraint, not the surface type. Now Ma et al used Code V, so they are coy about revealing exactly how the slope constraint was implemented, but in OS one would use operands like BFSD

That would seem to me to do everything you ask for when you say:

With all that said, I still use Even Aspheres just due to legacy designs and workflows but if a Q-Type operand could be developed which would minimize the RMS slope of the asphere (for sensitivity) and  another operand for peak spherical departure (for metrology), Q-Types could be really cool in OpticStudio.

Am I missing something?

I’m sorry to bang on about this, and there’s probably only Ken Moore and me in the world who care about this, but it still seems to me that the ‘benefits’ of Q-types are really not related to the surface at all, but to the optimization operands used to control the resulting shape. Or, again, am I missing something?

• Mark

Can you do that with Zernikes too, as they’re also orthonormal?

Also, is that (polishing method) intended for high budget things like telescope primaries, or for high-volume optics? I can’t quite visualize how that works, are there any references to it?

And yes, there are lots of ways to constrain surface sag, slope and curvature in the merit function. I just never could see how that was the product of the surface description. The exact same surface profile can be defined using even aspheres, Zernike's, extended aspheres, Q-types etc. If A=B, then B=A after all.

At least with Chebyshev polynomials there is a clear, singular benefit: as you extend the aperture out from the clear semi-diameter, the surface doesn’t fly away like all the other surface types do. That’s the kind of thing I can really get behind. That’s what’s always been missing for me with the Qs: a single, clear, explicable benefit that doesn’t rely on hearsay. The Qs have always been a bit Emperor’s New Clothes for me 😀

Hi Ray,

The problem is that when you look at the Q-terms, you see exactly those alternating sign high order aspheres:

You aren’t getting rid of them, you’re just representing them via a different polynomial. But it’s the same underlying polynomial. Remember that Qs and even aspheres (and extended aspheres) all optimize to the same solution within some small delta, and there is no characteristic benefit. This is why, despite all the hand-waving about polynomial coefficients competing, that no-one can produce a test case that actually shows a benefit to using Q-types. It’s all hat and no cattle, as the Texans say.

I remember an episode of Penn and Teller’s great Bullshit show, where they took a banana, cut it in half, and told people that one half was organic and the other half was a (presumably) conventional banana. Everyone said the organic half tasted better. But it was the same banana!

So take an aspheric lens, cut it in half and call one half the Q-asphere and the other the even asphere. Which one optimizes better? Which one tolerances better? How could you tell the difference? It’s the same sag!

Hi Brian,

Any new representation will take time to trickle to all software in the chain.

Regarding point 2, Zemax has had this implemented for quite a while

For point 1, there is a non rotation-symmetric extension of Forbes polynomials (if your shape has a symmetry, it’s not truly a freeform). I am not sure what they bring compared to the other  methods to represent freeforms (XY polynomials, Zernike polynomials, Chebyshev polynomials, NURBS, ...). Note that none of these, can create arbitrary shapes in practice (because they would require way too many parameters). It’s just that their capabilities differ. The composite surface allows to play on each base’s strength.

For point 3, again, Forbes polynomials do not differ from the others. Having perhaps more specialized optimization operands in that field could help.

[edit: 2 typos, 1 missing word]

I’ve always thought that the term ‘freeform’ should not be used when the surface is described by a known function, as the surfaces are never really freeform: they can only take some set of shapes. I think the current usage of ‘freeform’ is that there is no vertex-based reference that can be used as a proxy for a quick-n-dirty first approximation.

I greatly prefer OpticStudio’s TrueFreeForm as an approach that is genuinely capable of providing surfaces that cannot be described analytically at all. That of course raises its own set of issues, as we all want to be able to describe our freeforms with a small set of data.

Further, I think we should distinguish the surface description from constraints on the surface. SCUR for example can be used to provide constraints on many manufacturability issues. The smallest radius of curvature that a tool can make is the upper limit of the curvature of that surface, for example.

• Mark

Rather than use SCUR, which provides that absolute value of the curvature, I use SDRV which provides a signed value where I can determine if it is concave or convex.

However, at present, I still need to:

1. Define the sampling across the clear aperture with individual entries for each evaluation
2. Include a separate Merit Function entry for OPGT or OPLT to evaluate the curvature

If OpticStudio is looking to add features that distinguish itself from the competition and simultaneously drive value that reduces effort in workflow, I advocate for optimization that is related to manufacturing.

In my efforts, I can’t see how to use PanDao to select a vendor and make a more practical design.  Can you?

BTW, I asked on this forum if anyone was using PanDao and what they thought of it, but it got deleted by the site admins. I’m personally a bit underwhelmed by PanDao, despite the glowing reviews they post on their website about it. 

I’ve not yet heard from anyone who has bought and paid for it, as to what they think. I’d really like to hear what paying customers say.

• Mark