The Theory and Practice of Lens Design and Testing

This week's column by Ctein

For most photographers, lens designs are simply magic, and that's the way they should be. Knowing what goes into a lens design and what trade-offs have been made honestly won't do a single thing to improve your photographs. A side effect of this, though, is that some photographers become puzzled, even disturbed, by some of the choices lens designers make. Why isn't some new lens a stop faster, or smaller, or why did they "cheapen" the product by correcting some flaws in software instead of in glass?

A camera lens is a barrel of compromises. To appreciate this, think about the simplest lens—a cheap magnifying glass. It exhibits geometric distortion, spherical aberration, flare, astigmatism, coma, and lateral and longitudinal chromatic aberration up the wazoo. It's so bad that Newton was driven to reinvent the reflecting telescope, because he was convinced that lenses presented unsolvable optical problems.

Happily, he was wrong about that. You can combine single lenses to reduce aberrations. The groundbreaking two-element achromat proved that it was possible to reduce (but not eliminate) chromatic aberration. As a rule, you can't entirely erase an aberration, not over the entire field of view, over all apertures and working distances, and over the entire spectrum. Worse, reducing one aberration can increase another. Optimizing lens performance is a complicated balancing act.

Each time you add a new point of control to the lens design—a new optical glass, another lens element, an aspheric surface—you have another opportunity to improve the balancing act. Each time you add something new to the lens design, you increase its complexity, size, weight, and/or cost. "Optimize," though, is subjective; it depends on what you decide is most important. Also, if you don't test for the right things, you may not hit the optimal design. After all of that, you're still stuck with an imperfect compromise. Sometimes you just can't get there from here.

In practice...
That's what happened to me with one of the prescription lenses for my new SuperFocus glasses (which I last wrote about a few weeks back). Eyeglass lenses are optimized for acuity—how much fine detail you can see. Sometimes, in the real world, that's not, um, optimal.

In the doctor's office I could read text beautifully, but as soon as I got out of the office I noticed something odd. Bright lights, like stop lights or car's brake lights seemed slightly smeared. Ditto the LED lights on the various appliances at home. In the evening I stepped outside to look at the stars and distant city lights and there was very obviously a difference between the two eyes.

This is a sketch I made to show you what my left and right eyes saw when looking at pinpoint lights. The E is about the same size as the letters on the 20/20 line of an eye chart. The second illustration, below, shows what happens when looking at an extended bright object, where all those wispy comet tails get superimposed. It looks very much like what I saw looking at the LED and traffic lights.

Rotating the prescription lens rotated the tail about the light. OK, it's in that lens, not in the SuperFocus frame optics. When I put on my old glasses the lights were less sharp, but I didn't get the tail.

Back at the doctor's office, the refractometer showed that the lens matched the prescription. Dr. Kennedy ran me through a new eye exam and, in terms of visual acuity, a new prescription matched the original one. But, remember what I said about testing for the right things? I was now looking for something else. A normal eye chart, with dark letters on a white background, won't show this tailing; small dark objects on a light background will merely have a light wash of background light overlaying them. The contrast will be a bit lower, but there won't be any obvious artifacts.

I had modified an LED flashlight so it only emitted a half-millimeter beam. I rigged it up on top of the chest chart frame so that it was pointing at me. Now I could easily evaluate the tail. I also paid attention to the sharp edge of the white rectangle of the chart, to see how much it smeared out into the surrounding dark wall.

The problem I'd identified in the field was readily visible once I was running the right kind of tests. Dr. Kennedy adjusted the prescription to make the tail go away. Unexpectedly, the only way to make it disappear entirely drastically reduced visual acuity, to worse than 20/50 (my best left-eye acuity is 20/13). Fully correcting this one optical defect made others much worse.

How puzzling! My old glasses could eliminate the tailing with much less image degradation. So, Dr. Kennedy measured them on the refractometer and dialed that prescription into the phoropter.

It didn't work! The old glasses eliminated the tailing but the same prescription dialed into the phoropter didn't.

So, what was different? My old glasses had thick, low-refractive-index lenses. The new glasses require thin, very high-refractive-index lenses. Thick and thin lenses with the same surface curvatures don't behave the same way; there are different prismatic and second-order effects. It would appear that, by happy chance, the thickness of my old lenses just happened to correct the tailing well.

Unfortunately, that type of lens isn't an option within the physical constraints of the SuperFocus frames. I convinced Dr. Kennedy to let me look for a different optimum, one that didn't produce the highest visual acuity but was the best balance of acuity vs. the annoying tail. Eventually we settled on a prescription that was about a half diopter different from the original. It reduced the noticeability of the tailing by about two-thirds. It also degraded visual acuity in that eye by a third, taking it down to 20/20. I could live with that; it was a good compromise.

The new lens does work much better in the real world. The tailing is suppressed enough that I don't notice it unless I look for it. My overall vision is ever so slightly less sharp than it was prior to the re-optimization, but the overall image quality is so much better.

That's the way it is with lens design in the real world.

©2013 by Ctein, all rights reserved

Original contents copyright 2013 by Michael C. Johnston and/or the bylined author. All Rights Reserved. Links in this post may be to our affiliates; sales through affiliate links may benefit this site.

(To see all the comments, click on the "Comments" link below.)
Featured Comments from:

David Dyer-Bennet: "Don't forget price! I want camera lenses smaller, a couple of stops faster, twice the zoom range, and cheaper. But I'm a reasonable guy; I don't want a pony!"

Comments

[rnewman]

You are certainly correct about the need for trade-offs in lens design. Yet today, with the advantage of computer design programs, even the second and third tier lenses are generally much better corrected and consistent than in the "bad old days"v(~pre 1970s) of manual ray tracing, limited glass dopants, and the horror of trying to calculate an aspheric surface on a mechanical Marchant or Frieden calculator. Yes, the skill of the designer still counts, and sometimes back then they really got it right so that some old lenses are still worth using (I have a couple). But today the tools they have are SO much better. And in general, so are the results.

[Jim ullrich]

I have often wondered why lens manufactures and reviewers mentioned how many elements or what types of glass are used. It seems irrelevant from a users point of view, unless it is valuable for "bragging rights"

[Richard Green]

Your Optometrist is a saint! :)

[James Bullard]

I would observe that much of our "seeing" is in our brains and our brains tend to adjust over time, not a very long time either, just days or weeks. When I first started wearing glasses in my late 20s I saw the reflection of my eye on the inside of the lens (I was near sighted then) but my brain adjusted and after a week or so I never noticed it unless I looked for it.

About 10 years ago I had a viscous detachment that stirred up major "floaters" which initially appeared like small black pieces of torn paper in my field of vision. My opthalmologist said my brain would adjust and I wouldn't notice them so much after a while. He was correct. Unless they get stirred up I'm barely aware of them, like ticking of a clock that you don't notice until it stops. Even when I do see them they are now fuzzy light grey patches rather than dark black flakes.

In retrospect I suspect that even in my youth when I had good vision from about 4-5 inches to infinity a large part of that was my brain compensating for the limitations of my eye. All the same I wish I had my 18 year old vision today. Youth truly is wasted on the young.

[Peter]

Thanks for a great article. What a great application of lens design theories outside of designing camera lenses or telescopes. I wonder if optometrists (and opticians) get any of the basics of lens design.

[BigHank53]

When I switched to polycarbonate lenses in my prescription glasses, a ferocious chromatic error became apparent: yellow highway signs in direct sunlight would acquire a violet border.

The weight and thickness difference was enough of an improvement that I cheerfully lived with the color fringing--a different compromise.

[Bill Pierce]

I got into photography because I was so nearsighted as a child that the first time I ever saw a tree sharply, it was a photograph of a tree. Even when I first got glasses I couldn’t see that well. Not seeing what I was doing really helped my photography. Folks said it was an original vision. Eventually surgery restored my vision to 20/20, and the “originality” of my vision plummeted until I started shooting without holding the camera up to my eye. I’m worried because the photography that Ctein does really demands he look through the camera. I’m hoping that actually seeing what he is doing will not diminish the excellence of his images. But I’m worried.

[Stefan Mucha]

Dear Ctein,

I had colorful fringes around contrasty edges/objects with my glasses. Strongly pronounced towards the outer field of view and none at the centre (optical axis).
I even complained about it where I bought my glasses but left somehow frustrated.

What happend is that I learned to ignore it. The brain adjusts itself to the new situation. This happend rather fast and you shouldn't be too concerned.

Best regards
Stefan Mucha

[Christian]

Wow, what a clear example! Thanks for a great writeup, Ctein.

[John Haines]

Thanks for the update. So the SuperFocus contraption prevents you from using lower refractive-glass that are for you optically better. It will be interesting to hear how you like the compromise after prolonged use over time. I suspect you will get used to it, as we do with any other imperfect device, but there might come a situation where it just isn't good enough and you might want to keep your old lenses handy, just in case.

Speaking of compromises, for me, having to adjust the lenses by hand for various distances as opposed to moving my head a tad to choose another sector of my tri-focals, would, I think, drive me up the wall.

The last time I got new glasses the chart was sharp as a tack looking through the phoropter. The Dr. wrote out the RX, I had it filled at Pearle and the new glasses were horrible! (read, not as good as my old ones). I went back to the same Optometrist. He put me under the phoropter again and came up with a "tiny" (his word) adjustment to the Rx. New glasses were made (no charge, Pearle guarantees success) and they were fine.

I do await with keen interest the next installment, if there is one.

[zelph]

Any idea what happens to them when one goes outside in 40 below zero temperatures? Do they freeze? Does focus get worse?
Looks as if they sound nice but use is not measuring up to the hype and promises.

[roy]

I've worn specs for more than half a century and had no idea it was all so terrifically problematic. Up to now I've just periodically popped in to an opticians' (some might prefer an optometrist) got an eye test and ordered a new pair of glasses - which usually make me realise I should have done it sooner. I'd have said this procedure always worked pretty well, but reading this stuff makes me realise how poorly I've understood the whole process. I dread to think how bad my corrected eyesight must be, should I ever discover the truth. I'm happy to remain in ignorance, albeit with the illusion of decent vision through my bog-standard vari-focals.

[John Camp]

I was somewhat interested -- I wouldn't say "concerned" in any way -- by Ctein's use of the indefinite article "an" before "LED." Visually, "LED" would seem to require the use of "a" rather than "an." If one is writing by ear, rather than eye, then the "an" would be used if LED is pronounced "EL-EE-DEE." Recently, I had some new lights put in a house, and chose LEDs. The electrician who installed them called them "leds," to rhyme with "beds." If that's the pronunciation of choice, then "a" would be the correct article. I wonder if LED is becoming a word, rather than an abbreviation? It's sometimes hard to tell -- SD, as in SD cards, for example, is now (I would argue) a word -- few of the millions of people who buy SD cards would refer to them a "Secure Digital" cards. On the other hand, "CF" cards -- Compact Flash -- are hardly ever referred to as "CF" cards. It's almost always "Compact Flash." "CF" has not even become a recognizable abbreviation.

So, sometime in the future, I suspect, people will look at the TOP archives to see what kinds of things concern us in the opening years of the 21st Century, see that "an LED" of Ctein's, and laugh uproariously at the foolish error.

[ctein]

Dear zelph,

Thanks for the chuckle. I really appreciated it!

I would suspect these glasses will fail rather badly at minus 40. By the way, are we talking Fahrenheit or Celsius? **

But then, so will my Chevy HHR automobile, my iPad tablet computer, and my Olympus OMD camera.

Pretty clear proof that they don't live up to their hype and the promises either.

Come to think of it, I'll fail pretty badly at -40.

Presumably this means I don't live up to the hype, either.

But you all already knew that.

**(Alert to literal-minded readers––that's a joke)

~~~~

Dear Pierce,

I'm sorry, but looking THROUGH a camera is soooo last century.

Based on your theory, though, my photography should improve. My visual acuity is ever so slightly worse with the new glasses (20/20 - 20/15) than with my old style (20/13 - 20/15).

I'm looking forward to a palpable jump in the aesthetic merit of my photographs. I anticipate becoming the darling of the collectible set.

Fame and fortune, here I come. Woohoo!

~~~~

Dear Richard,

Dr. Kennedy is indeed very, very good. I gave a link to her practice in the previous columns.

I can also be quite persuasive. Doctors, whether or not they go into research, get a considerable amount of experimental training, and they recognize when someone knows that stuff. Walking in and being able to summarize in 30 seconds the tests I did that localized on exactly where the problem lay did not hurt my credibility.

Then there was the time my regular doctor was concerned about my consistently elevated PSA levels and wanted to schedule unpleasantly invasive tests every year. By the time I got done questioning him on the quantitative validity of the assays (I asked him for details on the precision , accuracy, random errors, and a very specific litany of systematic errors) he threw in the towel.

~~~~

Dear James,

Yes, accommodation is very important. A large part of why I don't notice the residual tailing unless I look for it is that my brain has learned to ignore it. In its original strength, though, it was impossible to ignore (I had the original prescription lenses for three weeks, which was plenty of time to find out).

The big accommodation I notice whenever I get a new prescription is for geometric distortions. Every change in the curvature of the lens surfaces creates a different mapping of the visual field. It takes me a while to see things properly squared off again. This time, I had the peculiar sensation that horizontal counters and table tops at the bottom of my field of view were strongly tilted towards me. For a day or so, I would (on occasion) reach for a pencil or pen to keep it from rolling onto the floor, which it was obviously going to do ... Not.

Now that's almost entirely gone away. Now and again there is just a twinge of it, but it's become less and less frequent and I'm sure it will disappear entirely.

pax \ Ctein
[ Please excuse any word-salad. MacSpeech in training! ]
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[ctein]

Dear Roy,

Truly, I think one of the amazing things about optometry is how well glasses do work! Partly it's a tribute to our adaptive brains, but even so. You've basically got a single-element lens with only 5 degrees of correction-- spherical curvature, cylindrical curvature and axis, and wedge strength and axis (this is before the recent advent of the wavefront aspherical lenses, which take things to a whole new level). This manages to work well over the entire range of viewing conditions (until presbyopia sets in). That's remarkably fortunate. We could be saddled with much, much worse visual prosthetics.

pax \ Ctein
[ Please excuse any word-salad. MacSpeech in training! ]
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-- Digital Restorations http://photo-repair.com 
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[James Sinks]

Jim Ullrich, you're correct that element counts and glass types are typically just impressive sounding padding for press releases. But element count does have its uses--I use it as a quick way to judge how badly a lens will flare.

My first thought when I read the press release for the Canon 40mm f2.8 was, "Six elements? I bet that puppy will never flare, even though it doesn't have a hood." Seems to be true.

My first thought when I read the Canon 24-70mm f2.8L II press release was "Eighteen elements and a terrible hood design? Flare will be a problem." Also seems to be true.

[Cmans]

What a relief! A previous poster mentioned seeing violet borders around yellow signs after switching to Polycarbonate lenses. I recently occasionally perceived seemingly random violet hues in my vision, which alarmed me because I recall reading or seeing on TV that someone bitten by a poisonous snake can experience color-tinged vision. I began to worry what toxins I had been ingesting to cause such a phenomena. I switched to Polycarbonate four years ago, but now that I ponder the circumstances, the effect happened as I was shifting my head either under fluorescent lights or sunlight and perhaps now that I am getting more "into" photography I might be slightly more aware of what I am "seeing". I find the lighter Polycarbonate eyeglasses to be much more comfortable than glass, plus I believe they are slightly more scratch-resistant because there is less weight pushing them against abrasives when I put them down wrong. I believe the earpiece hinges last longer due to the lighter weight. I wonder if Polycarbonate internal lenses in Photo lenses might make the bigger lenses lighter and be less stressful to the "internals" and the lens mounts, or are the lens makers already using Polycarbonate in their "Glass"?

[Kevin Purcell]

"I had modified an LED flashlight so it only emitted a half-millimeter beam."

Could you say a little more about the modification. This could be rather useful.

[MartSharm]

If I may respectfully correct an inaccuracy in this piece: the instrument an optometrist uses to check the power of a lens is called a focimeter. A refractometer is a much less common instrument used to check the refractive index of a material, not normally found in an optometrist's practice.

Aside from that, one curious aspect to this case is the report that the angle of the “tail” could be rotated by rotating the spectacle lens. This would suggest that the cause lies in either the astigmatic element of the prescription or some manufacturing defect of the spectacle lens itself. The fact that the same prescription, when dialled into the phoropter, gives the same “tailing” (that I would ordinarily be inclined to refer to as coma) would indicate it isn't a lens manufacturing problem. The fact that the previous spectacle prescription, which doesn't give the “tailing”, *does* give “tailing” when seen through the phoropter (which, by the way, more than likely uses crown glass elements – almost certainly nothing fancy and high-index) completely confounds the logic path.

In my opinion what is likely happening here is that your eyes (like everyone's, to a greater or lesser extent) are full of aberrations of first, second, third, and higher orders. The spectacle correction, which is rather a blunt instrument, correcting as it does only blur and astigmatism, cannot deal with higher order aberrations directly. Rather it seems you are more tolerant of blur rather than coma, so the coma “tail” of the focal cloud can be moved closer to the retina by adjusting the spectacle prescription, having the side effect of increasing blur. The optometrist will naturally prescribe the correction which gives the highest visual acuity, but as has been demonstrated, this is not the most tolerable correction in some cases. That's why refraction is considered as much art as science.

The way to truly measure this sort of thing is by using wavefront aberrometry, which measures the path of many points of light as they enter the eye and are reflected back from the retina having passed through the eye's entire refractive system. This system is most commonly used to customise a refractive laser surgery program to minimise post-operative symptoms of glare and haloing, but can also be used to manufacture custom-made aberration-controlled spectacle lenses - although this isn't commonplace in optometrist practices as yet. Perhaps you would be a good candidate for such a system?

Yours truly from a UK-registered optometrist.

[ctein]

Dear Mart,

I've been interested in wavefront aberrometry ever since I first read about it in the scientific journals. Unfortunately, it's not yet available in lenses that mount on SuperFocus frames. Someday, maybe. I'd love to give it a try.

Thanks for the correction on the nomenclature. Dunno how I got fixated on the word refractometer. I know what one of those is (I didn't know the word for the prescription measuring instrument, tho'; thanks!).

I don't think I'm more tolerant of blur-- the size of the coma tail was quite large! I'd never put up with blur anywhere near that large. Blur in the 20-20 range, that was acceptable to get a 2/3 reduction on the impact of the tail. But I wasn't willing to go beyond that.

pax / Ctein

[ctein]

Dear Kevin,

Black electrician's tape.

pax / Ctein

[Steve Jacob]

Modern camera lenses are pretty miraculous, but I can't help thinking that variable RI fluid lenses which are self-correcting (using sensor readout data) are the long term solution.

Evision Optics

Of course, the "shape" would have to be controlled over several points but such lenses would be fully corrected. A zoom version is also under development!

In theory you could even use LCDs to create an aperture and a shutter.... a complete solid state lens with very high flash sync..

[D. Hufford.]

I had the same problem as Stephan: colorful fringes around contrasty edges/objects that were most strongly pronounced towards the outer field of view and none at the centre. I was never able to learn to ignore it, though Lightroom helped to some degree. Ultimately, I just learned to avoid using the Panasonic Lumix 20mm 1.8 MFT lens in favor of the Panasonic "Leica" 25mm 1.4.

Oh, wait...Stephan meant his eyeglasses. Good lord, if I ever had eyeglasses as slow focusing as the 20mm Panasonic, I'd would have been run over by a turtle before I saw it. :)

Sorry. Cannot help myself.

[Joe]

I see I'm not the only one!

A few years ago I got a new eyeglasses prescription with thinner, lighter lenses, and a short time later I bought a new LCD monitor. But the monitor exhibited an annoying chromatic aberration that I couldn't figure out how to fix. Back it went, and I brought home a replacement. Same problem!

Then I started to notice that I could make the CA go away if I moved my head to just the right angle. That's when I discovered that it was my glasses producing the CA. The LCD monitor was the only thing in my daily experience with those bright, sharp, high-contrast lines, which is why I never noticed the CA before.

[Joe]

Oh, one more comment, off topic and yet...

Your signature says, "Please excuse any word-salad. MacSpeech in training!"

Hasn't it been years? How long does this training go on? Isn't it time to take off the training wheels? Can't MacSpeech finally move up from buck private to pfc or even corporal? Is it time to finally assert, "MacSpeech, trained though still imperfect!"?

[hugh crawford]

"I had modified an LED flashlight so it only emitted a half-millimeter beam."

"Black electrician's tape."

So black electricians tape passes deep infrared?

Yeah I know the LED flashlight probably does nor emit much IR, and you certainly can't see it, but if you are going to take that old -40 joke out of the fridge. Procedures that involve -40 degrees or modular arithmetic multiplying by nine always gets my shenanigans sense buzzing.

And of course black electricians tape passes deep infrared come to think of it based on some unintentional experimental results with Kodak HIE and black plastic tape in my childhood.

[hugh crawford]

David Dyer-Bennet:
Here's your Pony

cheaper and smaller, but not so fast and no zoom

[Bill Tyler]

John mentioned some interest in the correct article to use with LED. I'v been in high tech since before LEDs existed, and they've always been pronounced elleedee. It may be that electricians are now calling them 'leds', a single syllable rhyming with 'beds'. But that's not how most electronic engineers would pronounce it.

[James]

It's comforting to know someone is giving their eye doctor a harder time than I am.

When I asked about Lasic he said the other doctor he would refer me to would be delighted but that he wouldn't do it because I was too picky.

[Bruce Johnson]

So, Newton was right, after all.

[Bill Tyler]

Sidenote on Newton. The reason he didn't think lenses could be corrected was that he didn't know that different glasses have different amounts of dispersion, the variation of refractive index with wavelength. It's the use of different elements with different dispersions that allows for chromatic corrections.

[Patrick Perez]

I wonder how the glasses would perform at -40K?

Patrick

[Chuck Holst]

John Camp: I've always pronounced "LED" as "el-ee-dee," but maybe I'm old-school. To find out, I checked the OneLook Dictionary site, and all the dictionary pronunciation guides I looked at agree with me, so if there is a change in pronunciation underway, it hasn't reached the dictionaries yet. Maybe it's a dialect difference, the way my wife pronounces "vase" as "vahz." ;-)

[Nathan]

Going through my old photos lenses have really come a long way!

[Paul Whiting]

Hello Ctein,

I've had "comet tails" around bright lights for years... early on I was diagnosed with keratoconus, which I think means cone-shaped cornea. When the cornea is irregular like that, ie not spherical, the result is these comet tails. Are you seeing an opthamologist? Sorry if you said so and I missed it.

Sometimes contact lenses help, and sometimes a corneal transplant helps. Anyway, just wanted to pass that thought along.

Best wishes,

Paul