Abberation free lenses? (1 Viewer)

https://gizmodo.com/a-mexican-physicist-solved-a-2-000-year-old-problem-tha-1837031984

The above just showed up on the tech side of my Google news feed. The physics are leagues over my head, but will surely have interest for some. So here it is B

Hi,

while fully understanding the maths of it is certainly nice, making designs with aspheric elements could be done by simulating their effect with raytracing software and the main problem with them has been manufacturing them, especially if plastic is not good enough.
They have been in use for many years, usually with a master optician hand-aspherizing some element at the end of the polishing process.
Lately you get a lot of cheaper bins with aspheric elements made from plastic - they work well enough. But automatically making them in reproducible manner from glass is still tricky.

Joachim

The Gizmodo article linked to by Steve was referencing a scientific paper: General formula for bi-aspheric singlet lens design free of spherical aberration

There is some interesting comment about it on Mike Johnston's blog, The Online Photographer, at: https://theonlinephotographer.typepad.com/the_online_photographer/blog_index.html

See the post for the 9th August, especially the first of the Featured Comments. I'd expect further useful comment over time (on Mike's blog comments are mediated, preventing a lot of dross)

And for those with the mathematical wherewithal, it also includes a link to the full paper by González-Acuña and Chaparro-Romo at: https://www.osapublishing.org/ao/fulltext.cfm?uri=ao-57-31-9341&id=399640


John

Having done some additional Googling around:

1) The Featured Comment by GK Froehlich in Mike Johnston’s blog referred to in my previous post, puts the significance of the formula into a scientific context
The formula provides a ‘closed-form’ solution to eliminate lens aberrations i.e. plug in the numbers and get a precise result, instead of doing a series of 'best guess' approximations
- see especially the last paragraph


2) The intention of the formula
A) As stated in the abstract to the scientific article:
“. . . we present a rigorous analytical solution for the bi-aspheric singlet lens design problem.
The input of the general formula presented here is the first surface of the singlet lens; this surface must be continuous and such that the rays inside the lens do not cross each other.
The output is the correcting second surface of the singlet; the second surface is such that the singlet is free of spherical aberration.”

B) As stated somewhat differently by Rafael González-Acuña in an interview posted by PetaPixel:
“In this equation we describe how the shape of the second aspherical surface of the given lens should be given a first surface, which is provided by the user, as well as the object-image distance.
The second surface is such that it corrects all the aberration generated by the first surface, and the spherical aberration is eliminated.”
see: https://petapixel.com/2019/07/05/goodbye-aberration-physicist-solves-2000-year-old-optical-problem/


However, I'm still unclear as to how the above can be put into practice - especially when one considers the examples of spherical aberration free lenses from the scientific article
e.g. How could such shapes be achieved in mass production? And how durable would they be in use (especially in binocular size or 35mm format camera size)? How would they be mounted?

AND as noted by Froehlich in 1) above: the solution supplied by the formula is likely to only apply to either a single wavelength of light, or at best a narrow wave band!

At this point, I’m reminded of the observation “In theory, there’s not much difference between theory and practice. However, in practice that’s often not the case.”



John

John, et all.
Don't get me wrong here, I'm no where close to being an optics expert but a few questions do occur.

Would this solution for those single or narrow wave lengths necessarily make matters worse outside of those wavelengths for any given design? Or would it net out to zero? That might might mean a little something is better than a big nothing.
Also what narrow band of wavelengths are we talking about here, useful ones or ones we might not notice?

The interesting thing to me is how will this equation change the iteration process everyone is familiar with now?

By the way Mike's blog is one of the best things going on the interweb these days.

Cheers,
Bryan

jring said:

Hi,

...the main problem with them has been manufacturing them, especially if plastic is not good enough.

They have been in use for many years, usually with a master optician hand-aspherizing some element at the end of the polishing process.

Lately you get a lot of cheaper bins with aspheric elements made from plastic - they work well enough. But automatically making them in reproducible manner from glass is still tricky.

Joachim

Click to expand...

let's hope that the increasing demand for quality smartphone cameras will result in improvements to plastics that (after the usual delay) filter down into binoculars. Maybe 10 years down the line most binoculars will offer edge performance similar to today's Swarovski ELs.

Having thought about things over night . . .

As indicated by Froehlich, the paper of González-Acuña and Chaparro-Romo is an important contribution to theoretical optics
- it provides a formula that solves what’s known as the Wasserman Wolf Problem - that of designing a single lens with 2 aspheric surfaces that is free of spherical aberration


However, this does not mean that the formula has immediate application to practical lens design
e.g. the ‘sizzle’ in the Gizmodo headline: A Mexican Physicist Solved A 2,000-Year Old Problem That Will Lead To Cheaper, Sharper Lenses

As with much theoretical work:
- the formula will pave the way for further theoretical advances
- and whatever practical applications it has, may be far from the obvious


Also, the formula expressly addresses only the first of the 5 classic monochromatic Seidel aberrations: spherical aberration; coma; astigmatism; field curvature, and; distortion
(see the image from this quick introduction: http://www.quadibloc.com/science/opt0505.htm )

And additionally, there are also 2 chromatic aberrations: axial/ longitudinal, and; transverse/ lateral (see the 2 images from: https://photographylife.com/what-is-chromatic-aberration )

It’s minimising and trading-off the effects of these 7 aberrations that occupy the days of optical designers, and in turn underlie much of the discussion on this forum about optical performance


John

John A Roberts said:

.....
.....
.....
It’s minimising and trading-off the effects of these 7 aberrations that occupy the days of optical designers, and in turn underlie much of the discussion on this forum about optical performance

....

Click to expand...

Very well said , John :t::t::t: