while manufacturing an aspheric lens, I wondered why Zemax has the second order term, i.e. the r^2 term, in the aspheric surfaces, which is also in the help pdf? Other definitions of aspheric surfaces leave out the r^2 term, which seems to make sense to me, as the r^2 term seems to closely interfere with the spherical radius. This becomes then a bit confusing also towards the manufacturers. Is there an advice when to use this 2nd order term in aspheric optimization? Also when to use a (or only a) conic term?
Also the tool Best Asphere does not use the 2nd order term.
Thanks you for the advice!
Markus
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The second order term is redundant if R and k are used, and you should use either (R, k) or a^2. It’s present so you can use a pure polynomial definition of the surface, which is useful when designing freeforms as distinct to aspheric deviations from a base sphere.
I think the r^2 term in the polynomial expansion is largely superfluous and can typically be ignored. Here is what Bentley and Olson say in The Field Guide to Lens Design:
Although as Mark noted, including the r^2 term and using only the polynomial expansion may be useful for some applications.
Yep. I think if the designer’s mindset is to produce a small deviation from a base conic asphere, a^2 should be ignored. That’s the typical case when trying to knock down the spherical etc. But if you’re designing a wilder asphere, where the curvature (power) at the vertex is not expected to be an approximate placeholder for the power elsewhere along the sag, then ignore R and k and just use the polynomial terms.
If the radius of curvature isn’t a good approximation to the best-fit sphere, or if there is no meaningful best-fit sphere, then ignore R and k and just use polynomials.
It’s interesting to note, though, that most smart phone camera lens patents disclose wild aspheres that are described by a base radius, conic, and polynomial terms starting with r^4. I don’t have enough experience in this space to know whether there is a fundamental reason for doing so, or if it’s just a matter of convention. In any event, here’s one example that I think may have been used in the iPhone 4S.
Although, in general, there appears to be varied opinions about when to set k=0. For example, attached are a few pages about aspheres from Lens Design: A Practical Guide by H. Sun.
I do agree, but the original question was why does OS have the r^2 term when it is redundant with R and k. The answer is: to give you the flexibility to use either approach. Just don’t use them both at the same time
Thanks to both of you! Great discussion and very helpful!
Markus
Yep. I think if the designer’s mindset is to produce a small deviation from a base conic asphere, a^2 should be ignored. That’s the typical case when trying to knock down the spherical etc. But if you’re designing a wilder asphere, where the curvature (power) at the vertex is not expected to be an approximate placeholder for the power elsewhere along the sag, then ignore R and k and just use the polynomial terms.
If the radius of curvature isn’t a good approximation to the best-fit sphere, or if there is no meaningful best-fit sphere, then ignore R and k and just use polynomials.
Small question on this, how would one just use the polynomials in Zemax? (ie: how do I start a design without putting in some radii)
Hi Rick,
You could just start with parallel plates and let the optimizer do the work. Or, think of the a^2 term as the curvature of a parabola. Depends on how much data you have at the start, of course. But it’s the same issue with any freeform surface or complex polynomial.
I wouldn’t make too much of this though. The original poster asked why the r^2 term was there, and this is why. The vast majority of people use R and k and omit a^2, especially when using an asphere for higher order aberration control.
