
Goodbye Aberration: Physicist Solves 2,000-Year-Old Optical Problem - zafka
https://petapixel.com/2019/07/05/goodbye-aberration-physicist-solves-2000-year-old-optical-problem/
======
kragen
There are various people speculating on the _economic_ significance of this
solution, which, to me, is rather missing the point. It's like measuring the
significance of the excavation of Tutankhamen's† tomb by the tourist revenues
of museums. The point of economics is that it keeps us alive so we can do math
and also think in other ways; the point of consciousness is not to make money.

I don't think there is any economic significance. They found a closed-form
formula, not a manufacturing process. They verified that it produces
numerically correct results to 12 significant figures, but typical lens
grinding is only accurate to about 100 nm; if your lens is 10 mm thick, that's
an error in the 5th significant figure of any coordinate. Calculating a
_numerical_ solution to the Wasserman–Wolf problem to 5 significant figures is
straightforward, and you could probably do it by hand if you didn't have a
computer (although that _would_ involve significant economic cost). In fact,
it's not that hard to calculate it to 14 significant figures. The achievement
is finding a closed-form solution rather than an iterative numerical
approximation.

† Or Tutankhaten, as we used to call him.

~~~
VMG
> The point of economics is that it keeps us alive so we can do math

The most hacker news comment I read all year

~~~
kragen
I notice you don't seem to have dared to say you disagree — would you say that
the point of consciousness _is_ to make money?

~~~
kjeetgill
There's more to life than either math or money, haha. I think a lot of people
might fit something in there about friends, family, or community. Spiritual
growth maybe?

There's options.

~~~
kragen
I venture to say that spiritual growth is part of consciousness — that is,
it's "math and thinking in other ways", which is of course what I said above,
not "math".

As for friends, family, and community, what is it that gives friendship value,
if not your conscious experience of the friendship, and your friend's? Could
you coherently call something a good friendship if neither friend enjoys it or
improves their thinking from it? The same questions generalize to family and
community, though in more complex ways.

------
mykowebhn
> After months of working on solving the problem, Rafael González recalls, “I
> remember one morning I was making myself a slice of bread with Nutella, when
> suddenly, I said out loud: Mothers! It is there!”

> He then ran to his computer and started programming the idea. When he
> executed the solution and saw that it worked, he says he jumped all over the
> place. It is unclear whether he finished eating the Nutella bread.

This is my favorite quote from the article. Soon to be the most famous slice
of Nutella bread?

~~~
hyperpallium
This raises the perennial question of whether product placement is a
legitimate source of funding for fundamental scientific research.

 _After placing an ice-cube in my delicious glass of refreshing coca-cola
brand carbonated beverage, I yelled Eureka! and jumped out of the bath._

Is that _really_ how it happened? Is it not inconsistent with the pursuit of
truth?

~~~
soganess
It's really natural, on first mention, to refer to something using a member of
the degenerate set of its most unique identifier, right? From that point on,
to avoid repetition, mix in antecedents or generic names.

Brands exploit this mechanic in language so that any time a, thereto unknown,
good has to be addressed, that identification become advertising. It shifts
from being a unique identification of an object/item/thing to a conjuring of
the ethos/identity that contextualizes that good as being different from all
the others (un)like it.

I'm sure the dude was just having some hazelnut spread and that's how they
recalls it but us, like them, are getting hacked. Now if you'll excuse me, the
rey--, I mean tinfoil, is starting to get itchy, I need to switch it out.

~~~
jjeaff
Hazelnut spread is one of those things that is much more commonly referred to
as the brand name. No one says "Reynolds wrap" they say "aluminum foil".

No one says "hazelnut spread", they say Nutella.

No one says "resealable sandwich bags", they say ziploc bags.

~~~
nuxi
Nutella though is a sugar-and-palm/vegetable-oil spread, which - probably
accidentally - contains traces of hazelnuts, powdered milk and cocoa.

~~~
richardhod
I don't understand the downvoting of the parent here, which is factually
correct and worth noting. It's incredibly unhealthy and this is just down to
marketing that anybody eats it. You can make really nice chocolate spreads
with your own hazelnuts

~~~
mkl
The needlessly bad-faith "probably accidentally" is factually inaccurate.

~~~
nuxi
Just to clarify: it wasn't bad-faith, I was just (trying to be) sarcastic, as
most of the store-bought food nowadays "may contain traces of nuts and/or eggs
and/or celery" etc.

~~~
richardhod
Aha, do note that sarcasm mostly goes down badly on hn, because literal
people, and jokes historically frowned upon.

------
thechao
The paper is from Nov 2018, and is easy to find online. It’s a pretty amazing
result; the examples they give in the paper are for some reasonable shaped
primary surfaces and some really neat “exotic” stuff. The solution actually
admits aberrant free solutions for any geometry that doesn’t include self-
crossing rays. So, some of the ‘weird’ examples include a Bessel-function
cross section, negative index of refraction, and lenses that focus at negative
infinity.

The author’s have a paper from March 2019 (in arXiv) that uses the result to
build some novel telescope geometries.

~~~
jhncls
[0] [https://arxiv.org/abs/1811.03792](https://arxiv.org/abs/1811.03792)
"Rigorous analytical formula for freeform singlet lens design free of
spherical aberration"

[1] [https://arxiv.org/abs/1903.11129](https://arxiv.org/abs/1903.11129)
"Single lens telescope"

~~~
sdenton4
Hmmm..... I have a 1/3rd hand-ground telescope mirror lying around... maybe I
should see if I can apply some principles here...

------
readams
I'm not sure I really follow how this actually will result in better lenses.
Is the precision of the numerical solution really the problem, or is the
problem the actual precise manufacturing of the lens elements?

I have a strong suspicion that the numerical solution is as precise as needed
and the limiting factor is the manufacturing, but I would be interested to
hear how this results in something new.

~~~
Koshkin
Your suspicion is justified. The news here is the discovery of an analytical
formula - which is "precise," sure, but whether using it directly in an actual
computation could yield a more accurate and practically useful result is a
good question, due to the complexity of the formula.

------
joeberon
Slightly related: One thing I've learnt in Physics is that there are still a
huge number of practical and fundamental problems to be solved. You might
expect everything easy will already be done by now but that's just not true.
Hence we still manage to write so many papers! In fact many Physicists have
too many papers they want to write and not enough time to write them. This was
a huge surprise for me coming in to my PhD. I had naively assumed that
physicists were all scrounging for any morsel of content to publish!!

Of course it depends on the field. It's a requirement here in the UK to
publish a paper to get your PhD (at least I've been led to believe that), and
many particle physics students really struggle to manage to fulfill this. On
the other hand gravitational wave detectors have a huge amount of unexplored
science as there are so many things that we still do not fully understand
about the detectors themselves.

~~~
michelpp
I agree with this big time. One of my favorite Feynman quotes is that science
is an "expanding frontier of ignorance". There is always somewhere to go and
something on the other side, that may change everything and invalidate deeply
held convictions forever, all it takes is the guts to, again quoting Feynman,
"be willing to stick your neck out".

~~~
skybrian
Oh, I'm sure there are lots of things to discover, but I think this
underestimates what it takes to actually know enough to find the frontier and
decide on a good problem to solve.

------
rahimiali
To clarify: the innovation isn't that they design better lenses. It's that
given the first surface of a lens, they have an _analytical formula_ for the
lens's second surface so that the lens doesn't exhibit spherical aberration.
Traditionally, numerical methods are used to compute this second surface
instead of an analytical formula. Also, as a practical matter, designers often
use several spherical lenses instead of a few aspherics because the latter are
harder to manufacture/more expensive.

------
ChuckMcM
This is a seriously awesome piece of work. The mathematics in the paper are
pretty dense but if you're ok with vector calculus its not too bad.

The implication here is that you can build lenses that have a consistent focal
plane across their entire surface. A pair of glasses made this way would have
crystal clear vision regardless of your 'look' direction (as an example). It
also suggests that you could build lenses for lasers that were much more
consistent, so a laser projector could project an in focus image from edge to
edge rather than "fuzzing out" at the corners.

If there is a top prize in optics these guys clearly deserve it.

~~~
justinclift
Is this the kind of thing that will have an effect on optics in ray tracers?

"Real world" simulation optics I'm meaning (eg for material
design/prototyping), more than gamer oriented. ;)

~~~
andygreenwell
Expect to see an implementation included in subsequent releases of Code V and
Zemax.

------
gus_massa
It's an interesting mathematical result, but note that gives a solution for
the problem of the spherical aberration, but real lens have also chromatic
aberration. I.E. the speed of light for each color inside the glass is
slightly different, so the value n (refraction index) in the equation is
different, so in the equation you get a different surface for each color. In
the real lens you must pick one surface, so the effect is that one color is
perfectly focused and the other colors are not focused and you get some
rainbow-like effects.

The solution is to use combination of a few lens of different glasses, to
compensate the differences. It's not easy to design these kind of system,
because they must compensante also for other types of aberrations.

More details:

[https://en.wikipedia.org/wiki/Chromatic_aberration](https://en.wikipedia.org/wiki/Chromatic_aberration)

[https://kenrockwell.com/tech/lenstech.htm](https://kenrockwell.com/tech/lenstech.htm)

~~~
nomel
wouldn’t this be simply stacking SA free lenses, with the remaining
aberrations being alignment related?

~~~
gus_massa
It is SA free only for one color, not for every color.

------
jey
Fulltext:
[https://www.researchgate.net/publication/328536020_General_f...](https://www.researchgate.net/publication/328536020_General_formula_for_bi-
aspheric_singlet_lens_design_free_of_spherical_aberration/download)

~~~
TheRealPomax
And to anyone who is averse to reading dense, long papers: it's only 4 pages
long, and a quarter is pictures. It's heavy on the maths, because of course it
has to be, but there isn't a single integral in the entire thing. It's
remarkably accessible to anyone who took an introductory calculus course.

------
amluto
The article talks about the corners of an image being less sharp than the
center. That’s not spherical aberration; that’s off-axis aberration. Spherical
aberration causes the image to be less sharp at larger apertures.

I wouldn’t be terribly surprised if this result helps indirectly with off-axis
aberration, though — a closed-form solution to the spherical aberration
problem may make it easier to optimize for lens shapes that minimize other
aberrations.

~~~
ricardobeat
What’s your background? In the photography field this is known as spherical
aberration indeed:
[https://en.m.wikipedia.org/wiki/Spherical_aberration](https://en.m.wikipedia.org/wiki/Spherical_aberration)

~~~
amluto
Physics, but not optics. Also, I read and understood the paper. The Wikipedia
link seems to agree with me too. Look at the diagram there, and compare it to
the diagram for coma [0].

Spherical aberration causes the single point in the center of the object to
focus to a different place depending on where the ray hits the lens. This
means that the image _of that single point_ is not fully sharp. If you
restrict what parts of the lens can be hit by rays from that point (by closing
the iris, for example), you reduce the area in the focal plane that the rays
hit.

[0]
[https://en.m.wikipedia.org/wiki/Coma_(optics)](https://en.m.wikipedia.org/wiki/Coma_\(optics\))

------
tomrod
This was extremely well written. Not being a photographer myself, the
mathematical discussion and subsequent impact to optics/photography are very
accessible. Kudos to the author!

------
magicalhippo
> 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_ [...] (emphasis mine)

I didn't check out the paper in detail, sounds like the shape of the
correction surface depends on the distance to what you're imaging? Does it do
so in a non-trivial way? If so, this sounds a bit more like an academic
victory, no?

~~~
anonymfus
So it's useful if distance to your object changes predictably enough, like in
astronomy, satellite imaging and many other kinds of space missions.

~~~
magicalhippo
Well in astronomy you usually want your telescope to be able to observe
different targets. So it depends on the details of how the correction surface
has to change when the image-object distance.

If it's just a mild deformation and offset, then yeah I guess technology
similar to adaptive mirrors could work well.

~~~
oh_sigh
Distances are usually treated as infinity, at least in astrophotography. I'd
be surprised if this secondary lens was able to distinguish between light
coming from 1ly and 1000ly

~~~
magicalhippo
Doh, of course. Not sure what I was thinking.

------
bariswheel
Does this mean there’s hope for those of who had mild vertical diplopia
(double vision) before and after lasik surgery? [http://lee2see.com/double-
vision-vs-ghosty-image/](http://lee2see.com/double-vision-vs-ghosty-image/)

------
tambourine_man
I’m questioning my sense of humor because everyone here seemed to have enjoyed
the tone of the article, while I was quite put off by it.

~~~
adrianmonk
It's a good article if you enjoy jokes and references about photographers and
how they behave. It's not a good article if you want a minimum of fluff and
just want to understand what the discovery is and why it might be significant.

~~~
tambourine_man
I usually enjoy jokes intermingled with info, those didn’t hit the right note
for me, for some reason.

~~~
dentemple
Not every person finds every joke to be funny.

------
byebyetech
Hopefully this will increase the sweet spot in the VR headsets.

~~~
gfodor
VR headset lens already require software chromatic abberration correction --
I'm curious what constraints if any would limit the application of this new
result for VR spherical aberrations. Would love some thoughts from an optics
expert on this. I also wonder if this new knowledge could contribute to a
software corrector.

~~~
lux
Hopefully it leads to software-based spherical aberration correction too,
which may mean better perceived quality with the same lenses, or even
thinner/cheaper lenses over time.

Or maybe they'll find a way to apply it to make better lenses that need less
software-based corrections. They struggle a lot not just with clarity at the
edges but god rays and glare too.

~~~
lux
Not an optical expert, just also interested in optics for VR/AR :)

------
yagi
Doubtful that this paper is the first analytic solution. There's a light
artist who exhibited lenses like this at NYC's Museum of Math several years
ago. They turned flashlight beams into pictures. At the artist's talk he
passed around a wavy lens and mentioned that one of the surfaces was solved in
closed form. Looked like second-to-bottom lens on the page
[http://zintaglio.com/lens.html](http://zintaglio.com/lens.html)

~~~
djmips
I voted for your comment because it's interesting but I don't agree that the
example you linked is the same problem as solved in this post. But that is an
opinion because I'm not informed enough to know for sure. Meanwhile I did dig
up a paper related to mapping radiance with a shaped lens like the artist you
linked. It's a cool topic!
[https://arxiv.org/pdf/1701.03076.pdf](https://arxiv.org/pdf/1701.03076.pdf)

------
jonplackett
I wish there was a bit of insight into his mental process as he realised the
solution.

Like the description of Einstein sitting watching a clock and imagining what
it would be like to move towards it as a ray of light

------
chroem-
Will this have any implications for astronomy?

~~~
Quequau
From another comment in this thread:

"The author’s have a paper from March 2019 (in arXiv) that uses the result to
build some novel telescope geometries."

~~~
perlgeek
Note that "build" doesn't mean they built a physical telescope, they came up
with lense shapes.

There are some serious problems when building large telescope lenses; if they
get too heavy, they start to deform under their own weight, and non-spherical
shapes are hard and expensive to produce.

It would be awesome if this analytical solution inspired improvement in real
applications, but I'm cautions about that.

------
peter_d_sherman
Brilliant!

Two thoughts:

1) The size of the equation is rather large. Nature tends to like simple
equations, I wonder if this equation could be restated in a simpler format and
not lose its efficacy. I also wonder if there are still simpler versions that
trade off efficacy for degrees of error.

2) If the equation cannot be reduced, then this equation bears looking at from
an information preservation perspective, that is, to people who study how the
universe preserves information under various conditions, this is one of the
equations they should add to their list of equations to study...

But, overall a brilliant, laudable, commendable work with great applications
and benefit to society!

Well done!

------
MR4D
What wenT unsaid wasn’t anything about expensive camera gear, but that phone
thingy we hold in our pocket. THAT device will get much better at photography
in very quick order, and the price change will be largely immaterial.

I fully believe this will be the death of all but professional cameras in 5
years or less. (Yes, I know cameras are already in sharp decline, but I’m
talking true death - bankruptcies and firms leaving the market).

~~~
p1esk
_I fully believe_

Why? What makes you think this will be easier to implement than existing
methods?

~~~
MR4D
Gut feel. To me, photography is now a software game. If you can put a
reasonably cheap lens in front of a sensor and apply enough computing
horsepower, I believe that the old one lens and one sensor will be like the
mainframe of cameras. They will still be around, but smaller, modular ones put
together via software will dominate.

------
ur-whale
The fact that there is an analytical solution to the problem is a really nice
achievement, but I have to wonder: solving this problem numerically has surely
been within reach of computers for a long time, and should therefore have made
actually manufacturing such lenses somewhat straightforward.

What am i missing?

~~~
adammunich
CAD modeling is very slow when you need to use numerical simulation.

~~~
nullc
I don't follow.

I assume that if numerically solving for a correcting shape was burdensome you
would model an element using a first surface and a 'dummy' second surface that
your software just treats as magically correcting. ... then when you are happy
with your design, you go ahead and compute the actual shape for that second
surface... or similar.

I would expect a closed form solution to more useful for meta analysis of the
problem-- looking at its behaviors (and especially derivatives) in various
external cases may suggest interesting and novel optical system designs. Like,
"oh, foo changes cubically with with an infinite focal length that means if we
could make lenses with cherry flavored unobtanium we could bounce a
gravitation particle beam off the main deflector dish!".

------
mlevental
[https://petapixel.com/assets/uploads/2019/07/formula.gif](https://petapixel.com/assets/uploads/2019/07/formula.gif)

definitely generated by mathematica

------
TheRealPomax
"It is unclear whether he finished eating the Nutella bread."

This article is alright.

~~~
zaroth
Trying to figure out what voice you’re writing that in.

I hope you mean _alright_ alright, and not just _alright_ because I loved that
line!

~~~
dylan604
I read it as "This article is 'alright alright alright'".

------
visarga
Unrelated, but seems like optics use a different Arxiv format than ML papers,
which are always double column.

------
ernsheong
Nobel-price worthy, you think? But perhaps only if they manage to derive a
more beautiful formula...

------
cellular
Man, that is a long formula! Not something that would pop into my head while
spreading nutella.

------
p1mrx
Looking at the picture... does this mean we'll all be using mustache-shaped
lenses someday?

------
pizza
Awesome article, wild equation

~~~
smitty1e
Don't such things always seem a bit obvious in retrospect?

/joke

------
linuxlizard
I would love/hate to read the LaTex that generated that equation.

------
amelius
Does it solve chromatic aberration, or just spherical aberration?

~~~
perlgeek
Just spherical.

------
amelius
Is the resulting lens rotationally symmetric?

~~~
topspin
The formula computes ZbRa; z axis vs radius. So yes, I believe this is
symmetric around the center.

------
tsss
Hopefully video game makers will now finally stop putting that stupid
chromatic aberration effect in their games.

------
carlob
Proud to see it was solved using Mathematica :)

------
zaidukwahab
G Mga

------
dylan604
12 nines? Yawn. Let me know when they get to 15. j/k

That's some serious precision. I wonder if this would have been possible to
calculate on a Pentium?[0] After last week, cloud service providers would be
happy for 3 nines.

[0][https://en.wikipedia.org/wiki/Pentium_FDIV_bug](https://en.wikipedia.org/wiki/Pentium_FDIV_bug)

------
xondono
I have not checked the actual paper, but according to the article itself:

> Moreover, the solution involved _aspherical elements_ , which are harder to
> manufacture in a precise way and are thus more costly.

> Their findings were published in the article General Formula for _Bi-
> Aspheric Singlet Lens Design_ Free of Spherical Aberration, in the journal
> Applied Optics.

I’m no expert in optics, but that does not sound like the kind of advancement
that cheapens lenses, even if the math work is mathematically relevant

~~~
TheRealPomax
It also doesn't sound like the kind of advancement that makes camera lenses
play mp3 files, but then: neither of those two things are even remotely
relevant to the article?

These people solved optical abberation. Even if their work leads to lenses
that are twice as expensive as they are today, people whose research, or jobs,
rely on perfect optics will be more than happy to pay what it costs to work
with those.

Anyone else can wait until one or more companies figures out how to make the
manufacturing process cost effective at scale.

~~~
russdill
Currently abberation is dealt with by including multiple lenses. Even if the
lens costs twice as much, it's still a wine from a price point.

But yes, only for applications that care about abberation.

------
peterwwillis
I laughed when they tried to translate _" Madres!"_, but a pissed off Latina
mother running at you waving her sandal in the air like a medieval warrior
swinging a truncheon is definitely an _" Oh shit"_ moment.

~~~
david-gpu
My understanding is that centuries ago in Latin America "madre" became an
euphemism for "madame of a brothel", while actual moms are called "mamá". In
Spain it carries no such connotation.

~~~
peterwwillis
Mamá means mom, madre means mother. You use either depending on the context.
(I'm only talking about the Mexican use)

Madre is used more often in phrases, such as _" Madre de dios!"_, Or _" La
madre putria,"_ or _" Pinche tu madre"_, or it's used as a formal to refer to
one's mother. It's similar in English, such as _" On my mother's side"_, _"
Mother fucker"_, _" Mother of God!"_, etc.

In Mexico, _" tu madre"_ can be a general insult, probably shortened from _"
pinche tu madre"_, though in English we have a similar vulgar retort of _"
your mother"_. As a weird turn on the phrase, _" de puta madre"_ is slang for
a good thing.

I'm not aware of an association with brothels in Mexico, but certainly in some
Latin American country it could have.

~~~
manuelisimo
In México the word "Madrota" does carry that "madame of a brothel" connotation

