New formula for eliminating spherical aberration

[alanrockwood]

The hyperbole is not in the scientific papers, but in the hysterical musings of journalists and news reporters........universally disliked by scientists.

The cold fusion lot were not scientists...they were frauds.

Actually, I knew Stanley Pons and Martin Fleischmann personally. They were not frauds. They were legitimate scientists. However, their work on cold fusion did bring them into disrepute.

By the way, Martin passed away a few years ago, and Stan is said to be continuing his work on cold fusion in secret somewhere in France.

 

[David A. Goldfarb]

Lots of off topic posting in this thread. Politics deleted. Title updated.

Please use an informative title when creating a new thread.

 

[AgX]

The physicist worked out a mathematical solution — which is great — for a problem that is solved via other methods every day by lens designers. That’s a great way to earn his doctorate.

Good point. Academics are called so for talking academic... However a new approach for an already solved problem may be benefitial in the future.


Furthermore, freeform optical elements are applied even in commercial products. Even most of use have already used it long ago in their photographic practise: in the Polaroid SX-70 SLR one such lens element was employed in the taking lens, another in the finder.

These were amongst the most early consumer applications. Today we find these much more spread.
And for sure you can give a much better overview of current freeform optics applications.

Here a glimpse into the issue given by a belgian university:
https://fhi.nl/app/uploads/sites/32/2016/06/0.2016Tailoredlighting.pdf

And here the term "revolutionize" is used (for lighting applications)...

 

[Nodda Duma]

There are technical limits to what is possible with freeform optics and of course the conversation between a designer and the optical shop is almost entirely removed from discussions at a University or in a thesis dissertation. Those details are far beyond the scope of an internet forum, and I'd be hesitant anyways to crush the dreams of photographers looking for that perfect image by exploring the limitations.

While this topic cannot be fully appreciated without a deep understanding into optical fabrication, there's nothing wrong with wishful thinking. So sure, anything's possible.

 

[alanrockwood]

Putting another twist on thoughts already presented in this thread, I gather that what this scientist has done is to work out an equation in closed form that makes spherical aberration zero. The words "closed form" are key here. Solving the problem by some sort of successive approximation approach to bring spherical aberration down to limits below any detectable practical level is not too hard, but that is not the same thing as solving a problem in closed form, i.e. writing an equation that provides the solution.

Actually, I have done it myself, and I am not an optical designer. When I say "done it myself" I mean that I have fired up the Winlens program (which is an optical design program that you can download for free, at least the basic version of the it is free), and played with aspheric lens profiles until spherical aberration was essentially zero, as evident in dot plots for the lens. This is essentially a successive approximation approach, which is not the same thing as solving the problem in closed form

One thing to note is that this does not necessarily improve the off-axis aberrations, nor does it solve the problem of chromatic aberration. Chromatic aberration is particularly difficult because one is limited in the glass types that can be used, and completely eliminating residual chromatic aberration is very diffucult (probably impossible) using existing glass types.

By the way, it would go a long way toward reducing both spherical aberration and chromatic aberration if it were practical to use sapphire lenses extensively. The beauty of sapphire is that it has both a high refractive index and low dispersion. That would allow building lenses with more gentle curvatures, which makes it easier to control spherical aberration, and the low dispersion should make it easier to correct for chromatic aberration. However, sapphire is very expensive. It is also very hard, which makes it difficult to grind the surfaces. In addition, it is birefringent, which would introduce another form of aberration into the system.

It might be possible to add elements made of crystaline quartz to correct for the birefringence of sapphire because quartz is birefringent of opposite sign compared to sapphire. Most likely such a correction (if possible) would only work at a specific conjugate ratio because birefringence depends on the angle that the light makes with repect to a crystaline axis, and the angles in the various lens elements will change when the conjugate ratio changes.

 

[Nodda Duma]

Careful... that line of thinking leads to "over design" of optical systems. The best designs are just good enough, with tolerances that make them easy to fabricate and assemble. Too much performance unnecessarily drives up cost, complexity, and risk. Too little performance and obviously that's not a solution.

In the lens design world, meeting requirements with an elegant solution is considered the best. Creating the absolutely highest most perfect performance is not where the challenge is.

The closed form solution to spherical aberration has been inferred ever since Sir Isaac Newton deduced that the paraboloidal surface corrects on-axis aberrations entirely, confirmed when Seidel derived the aberration coefficients in the 19th century. So obviously the reporting and/or interpretation of his dissertation has missed the mark. Lens designers don't just play around in software by trial and error. Customers don't have that kind of budget.

Sapphire has issues beyond what you point out ... including the fact there exist significantly lower cost and easier-to-work optical glass with index / dispersion values near enough sapphire to replicate its optical properties. There are also lower cost glasstypes with even higher indices and even lower dispersion. Sapphire has its place in the lens designer's toolbox, but not as a lens with optical power.

 

[alanrockwood]

The closed form solution to spherical aberration has been inferred ever since Sir Isaac Newton deduced that the paraboloidal surface corrects on-axis aberrations entirely, confirmed when Seidel derived the aberration coefficients in the 19th century...

Thanks for the comments.

I think that using the paraboloid surface to correct spherical aberration only applies to mirrors, not lenses. For mirrors the correction for spherical is, of course, perfect. Off-axis perfomance is, however, not great, which is the reason that Schmidt optical designs are often used for wide angle telescopes.

Regarding sapphire, I am posting an image of the glass map supplied with Winlens. Sapphire is labeled and circled. I don't see any glass type that is even remotely close to sapphire in the glass map, so I don't think there is a nearly-drop-in-replacement that could substitute for sapphire in a hypothetical lens design. This of course does not mean that one should use sapphire for a number of reason, and it does not preclude getting good results using other means. However, I am pretty sure that if there was a conventional glass that was a good approximation to sapphire's optical properties (reasonably high refractive index and reasonably low dispersion) while being easily worked and economical in price it would likely dominate lens designs.

 

[wiltw]

I read once in a paper about Bokeh that spherical aberration is often not fully corrected in the lens design in order to make for better Bokeh. So what does a lens of this new type do, relative to the Bokeh quality?

 

[alanrockwood]

I read once in a paper about Bokeh that spherical aberration is often not fully corrected in the lens design in order to make for better Bokeh. So what does a lens of this new type do, relative to the Bokeh quality?

Good question.

 

[Helge]

It is often said that maximum center sharpness comes at the cost of among other things bokeh, colours and corner sharpness.
The precise explanation why that is, I have never been able to find though.

 

[Sirius Glass]

It is often said that maximum center sharpness comes at the cost of among other things bokeh, colours and corner sharpness.
The precise explanation why that is, I have never been able to find though.

Optics designs always involve trade off. Which tradeoff are done depend on the designer not automatic results.

 

[RalphLambrecht]

So a Mexican physicist has apparently developed a new formula that completely eliminates spherical aberration. This could be the final days of large complicated lenses and the begining of cheap, fast, and sharp lenses.

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

I'm sure it won't reduce everything to single elements because there are other aberrations to worry about, as well as focusing and zoom issues. But we'll soon say goodbye to soft corners!

just take pinhole camera.

 

[mshchem]

This sounds a bit like cold fusion

Even if it's true all the big camera companies will buy the formula and destroy it

Like ExxonMobil did with the carburetor that allowed you to get 84 miles per gallon with an Oldsmobile Rocket 88!

 

[Helge]

Optics designs always involve trade off. Which tradeoff are done depend on the designer not automatic results.

That is almost a truism.
I’d be interested in an actual explanation.

 

[ced]

This will likely help in face recognition photography which is rapidly coming to your nearest high street. Beware!

 

[alanrockwood]

It is often said that maximum center sharpness comes at the cost of among other things bokeh, colours and corner sharpness.
The precise explanation why that is, I have never been able to find though.

The basic reason is that different aberrations react to changes in the optical formula in different ways. Consequently, roughly speaking, it would only be by luck that one could get all of the aberrations to go to zero at the same time. (That's not quite true, because there is more than luck involved, but it is a reasonable way to look at it.)

Some aberrations are relatively easy to correct. For example, there is a simple formula that governs how field curvature depends on the curvature of the optical surfaces and the refractive indexes of the lenses. You don't even need to do ray tracing to do that one. It's just a fairly simple algebraic calculation. Unfortunately, correcting curvature of field does not automatically correct for the closely related aberration of astigmatism.

There is a simple way to give a simultaneous correction for spherical aberration and comma (perfect correction mind you), but it only works at a specific conjugate ratio, and it only works when the image is a virtual image, not as a real image, so it can only be use as part of a larger optical system, and it doesn't correct for the other aberrations.

There is a simple way to correct for comma (a symmetrical optical system) but it only works at unit magnification.

There is a fairly simple way to correct for chromatic aberration using just algeraic equations, but it can only correct for two colors, and it doesn't correct for other aberrations. Fortunately one can often combine this approach with bending of the optical components to correct for sperical aberration, but it leaves some residual higher order spherical aberration, and it doesn't correct for other aberrations.

It's possible to correct for all of the third order (seidel) aberrations without getting too fancy. For example a cook triplet does it, but it still leaves higher order aberrations, and as a practical matter sometimes they will leave some of the third order (Seidel) aberrations partially uncorrected (or possibly over-corrected) in order to reduce some of the higher order aberrations.

There is a concept in optimization theory which says that (unless you get lucky) you have to have at least as many degrees of freedeom (i.e. parameters in a design that you can vary) as there are are properties that need to be optimized, and sometimes even that isn't enough degrees of freedom.

 

[MattKing]

Alan,
Am I correct in assuming you meant to type "coma" in the preceding post, and not "comma"?
Thanks for the informative analysis.

 

[Helge]

Thank you for the kind and insightful reply.
Most optimization processes is a game of rock, paper and scissors, often with many more parameters to set though.
You can have two or more set to your liking, but once you try to correct them all at once you run into trouble, or your design gets unreasonably expensive and complex by trying to brute force things.
For a simple example, with speaker design, there is Hoffman’s Iron Law where you can set cabinet size, sensitivity and bass extension.
You can have two of them as you like, but the third will always have to be compromised or “set free”.
Is this somewhat the same thing? Or have I misunderstood?

The basic reason is that different aberrations react to changes in the optical formula in different ways. Consequently, roughly speaking, it would only be by luck that one could get all of the aberrations to go to zero at the same time. (That's not quite true, because there is more than luck involved, but it is a reasonable way to look at it.)

Some aberrations are relatively easy to correct. For example, there is a simple formula that governs how field curvature depends on the curvature of the optical surfaces and the refractive indexes of the lenses. You don't even need to do ray tracing to do that one. It's just a fairly simple algebraic calculation. Unfortunately, correcting curvature of field does not automatically correct for the closely related aberration of astigmatism.

There is a simple way to give a simultaneous correction for spherical aberration and comma (perfect correction mind you), but it only works at a specific conjugate ratio, and it only works when the image is a virtual image, not as a real image, so it can only be use as part of a larger optical system, and it doesn't correct for the other aberrations.

There is a simple way to correct for comma (a symmetrical optical system) but it only works at unit magnification.

There is a fairly simple way to correct for chromatic aberration using just algeraic equations, but it can only correct for two colors, and it doesn't correct for other aberrations. Fortunately one can often combine this approach with bending of the optical components to correct for sperical aberration, but it leaves some residual higher order spherical aberration, and it doesn't correct for other aberrations.

It's possible to correct for all of the third order (seidel) aberrations without getting too fancy. For example a cook triplet does it, but it still leaves higher order aberrations, and as a practical matter sometimes they will leave some of the third order (Seidel) aberrations partially uncorrected (or possibly over-corrected) in order to reduce some of the higher order aberrations.

There is a concept in optimization theory which says that (unless you get lucky) you have to have at least as many degrees of freedeom (i.e. parameters in a design that you can vary) as there are are properties that need to be optimized, and sometimes even that isn't enough degrees of freedom.

 

[Nodda Duma]

Alan’s analysis sounds good, but the details are all wrong.

For the discussion we should assume we’re talking about the basic third order Seidel aberrations.

The Cooke triplet has just enough variables to correct all the third order aberrations. Sph Ab, Coma, Astigmatism, Field Curvature, Distortion, and the two chromatic aberrations. In a well-designed Cooke, all that remains are higher order stuff.

The odd aberrations - distortion, coma, lateral color - are easy to correct with symmetry.

Field curvature contributes more than any other to design complexity.

There’s more to it, of course, much more. A university or two library’s worth.

 

[alanrockwood]

Alan’s analysis sounds good, but the details are all wrong.

I wonder what specific details are wrong.

 

[jsmoove]

I have heard of Snake Oil before - perhaps they have found a way to 3D digital print these new lens designs. I have now switched on my cynicism module to full volume.

http://glassomer.com/index.php/technology.html
https://www.femtoprint.ch/

 

[alanrockwood]

...The Cooke triplet has just enough variables to correct all the third order aberrations. Sph Ab, Coma, Astigmatism, Field Curvature, Distortion, and the two chromatic aberrations. In a well-designed Cooke, all that remains are higher order stuff...

Yes, I agree that a Cooke triplet has enough degrees of freedom to correct for all third order aberrations. In fact, I mentioned that in my post. However, I believe it is seldom done in practice because most designers consider it a better compromise is to balance the third order aberrations against higher order aberrations to get a better overall image quality.

The WinLens program includes a bunch of design examples in their free lens library. There are 9 triplet, 8 conventional tessars, one aspheric tessar, and 14 double Gauss designs in the library. Not one of them corrects for all Seidel aberrations.

I would like to see a practical triplet design that corrects for all aberrations. I would put the lens geometry and glasses into WinLens and have WinLens calculate the Seidel aberrations to confirm that they are all zero. I am sure that such designs are possible on paper, but seldom used in practice because other designs that balance the third order aberrations against the higher order aberrations turn out to give better overall practical image quality.

 

[alanrockwood]

...Field curvature contributes more than any other to design complexity...

Well, that all depends. If all one wants to do is correct for curvature of field, then it is exceedingly easy to correct for field curvature. Here is an example that one can write down without doing any calculations.

Lens element 1: a plano convex lens made of any type of glass (let us say BK7 for example)
Lens element 2: a double Concave lens with the same radii of curvature as the curved surface in lens element 1 and made of the same glass as lens element 1
Lens element 3: a plano convex lens identical to element 1. Might as well reverse it to get some symmetry in the system.

Space the elements symmetrically.

The petzvel sum of this design will be zero, so the field curvature is non-existent. Of course, most of the other aberrations will be non-zero. However, if the magnification is 1 (actually, -1) then several of the aberrations in this symmetrical design will be zero by symmetry, notably Coma, distortion lateral color. (Actually, they might not be perfectly zero, depending on where the stop is placed, but we won't worry about that little detail right now.)

On the other hand, if you want to zero out the field curvature as well as minimizing the other aberrations, then I will not disagree with you that field curvature may be very troublesome. I have read that sometimes designers will leave a little field curvature in the design because it often helps them minimize astigmatism.

 

[alanrockwood]

Thank you for the kind and insightful reply.
Most optimization processes is a game of rock, paper and scissors, often with many more parameters to set though.
You can have two or more set to your liking, but once you try to correct them all at once you run into trouble, or your design gets unreasonably expensive and complex by trying to brute force things.
For a simple example, with speaker design, there is Hoffman’s Iron Law where you can set cabinet size, sensitivity and bass extension.
You can have two of them as you like, but the third will always have to be compromised or “set free”.
Is this somewhat the same thing? Or have I misunderstood?

Yes, I would say it is somewhat the same thing.

Engineers often face problems where they need to optimize three parameters, such as fast, good, and inexpensive. Then they say "you can have any two of the three. Which two do you want?"

 

[alanrockwood]

Yes, I agree that a Cooke triplet has enough degrees of freedom to correct for all third order aberrations. In fact, I mentioned that in my post. However, I believe it is seldom done in practice because most designers consider it a better compromise is to balance the third order aberrations against higher order aberrations to get a better overall image quality.

Here's a quote from a textbook on optics that reinforces the point I made.

"Although it is possible in a Cooke Triplet to correct all seven first- and third-order aberrations exactly to zero, in practice this is never done. Controlled amounts of third-order aberrations are always deliberately left in to balance the fifth- and higher-orders."

Here's a link to the chapter that contians the quote: https://www.willbell.com/tm/ChapterB.3.pdf