Resolution limited by diffraction?

[William Mortensen]

I'm throwing this up as a new thread, even though it arises out of a concurrent thread on Quickloads. (I don't want to disrupt the flow of deep philosophy dominating that series of exchanges...)

On a side discussion of edge diffraction, Jorge noted, in part, "But.....when I was working with 4x5 I had some instances where difraction ruined my shots. For you and your printing method it might not be a consideration, but for others it might be. IMO it is good to be aware of the possibilities."

I'm familiar with edge diffraction in theory, and am trying to make it have a theoretical impact in my head. Mind you, I'm just doing the math off the top of my head, and I'm an ignorant fool besides... But, assuming an extremely small f/stop of 1mm (that's f/64 on a 65mm lens, or f/90 on a 90mm lens), and a wavelenght of light around 500 nanometers, (visible light is 400-700 nm), the area along the circumference that would affect light (pi x .oo05, where pi is the circumference in mm and 0.0005 is the mm value of 500 nm) is 0.oo157 square mm out of a total aperture area of 0.785 square mm. That comes out to 1/500 of the passing light possibly being affected by edge diffraction of the aperture.

I don't think 1/500 of the light being affected by diffraction would ruin an exposure. Anyone a bit more familiar with optics/physics/math care to clue me in where my logic is failing?

BTW,I think my high school students changed my posting name to "William Mortensen", and I've been trying to change it back. We'll see how it comes out this time...

[James E Galvin]

It takes some study of physical optics to derive diffraction equations. The results are:
the resolution of a diffraction limited lens is about 1600/f in lines per mm for visible light. That is an f/16 lens can resolve about 100 lines/mm, at f/64 you are down to about 25 lines/mm. If you want 10 lines/mm in the print, then 10x12 is the largest print you can make from 4x5 at f/64. I've used f/64 for a 12x16 print, its just fine at "normal" viewing distance, but a little softer than my usual f/22.5.

[robc]

diffraction limited is one of those terms which seems to be variable in that it depends on what you consider to be the acceptable size for the circle of confusion.

download the free rodenstock software here (http://www.winlens.de/en/predes_update.html) and play with it to see where diffraction kicks in depending on what you set CoC to.

[robc]

forgot to say that defraction limit is the point at which diffraction becomes more significant than other lens aberations in blurring the image. It doesn't mean image is ruined but rather that the required coc cannot be attained.

[John_4185]

The "bottom line", if you will, is that with LF diffraction won't make a damned bit of difference in your outcomes compared to the myriad of inevitable, real world human errors that screw up images. Put your attention to those rather than diffraction.

Now someone will jump in and say "Yeah, BUT if you enlarge to (some incredibly stupid size) AND (sniff grain) (and imposes stupidly irrelevant opitcal-bench-racing metrics) you will see the difference!

But YOU ain't THEM. Pitty the grain sniffers.

Are we okay now?

[Leonard Evens]

You seem to know a bit about the subject, but you also seem a bit off base. Read Jacobson's Lens Tutorial at www.photo.net. (You will find it under "Learn".) Diffraction theory says that the image of a point light source passing through a circular aperture is a central bright disc surrounded by concentric rings, with decreasing intensity from the center out. The rings are assumed to be too dark to affect everything, but the central Airy disc, not being a point, results in a blurry image of that point. The effect on the total image is to make it slightly blurry, uniformly over the whole image, indepdendent of other considerations. The formula for the radius of the Airy disc shows that its radius is dependent on the relative aperture (f-number) and the wavelength of light. It is usually calculated for a middle wavelength in the range where the eye is most sensitive.

The combined effect of diffraction and defocus is pretty complicated, and Jacobson has some discussion of that fact.

[paulr]

"with LF diffraction won't make a damned bit of difference in your outcomes compared to the myriad of inevitable, real world human errors that screw up images"

well, if you stop down real far, then it will make a difference everyone can see. it's hard to make a sharp looking enlargement from a neg made at f64 (all due respect to the f64 group). unless you consider stopping down too far to be a human error ;)

[John_4185]

well, if you stop down real far, then it will make a difference everyone can see. it's hard to make a sharp looking enlargement from a neg made at f64

On what format, what degree of enlargement? I call bullshit. Of course, this raises the opportunity for all the sofa-racers to claim their eyes are better than the norm without having to show evidence. Let the bullshit flow.

Spit the hook out of your mouth, paulr.

[Paddy Quinn]

I used to have a very clear explanation from a post on diffraction limits from here by one of our acknowledged maths wizzes that set it all out very clearly and basically said you don't need to worry your pretty little heads about it until you get beyond at least f45 in 4x5 and f64 in 8x10.

Always seemed pretty true in practice

[John Layton]

Despite what I've heard and studied about the effects of aperture related diffraction also being inversely proportional to focal length, as the actual, physical opening of a given f-stop increases as focal length increases, I've not really noticed this in practice. What I do notice is that yes - f/64 and smaller openings can be a little soft - but often advantageously so. To me, every aperture has its "ideal" use. If depth isn't an issue, I'll usually go to f/22 with F.L.'s longer than 120, or to f/16 with shorter lenses. One might argue for an even wider aperture, but I've never quite trusted the degree of flatness of L.F. film - in whatever holder. One to two stops down (f/22-32 to f/32-45, depending on F.L.) offer balances of compromise between sharpness and depth, while f/64 and smaller openings are used either when I need as much depth as possible and there's no other way to achieve this, or because there is some other compelling reason, like working with movement over time or wanting a different optical signature - which might feel right with a given subject.

[robc]

read the airy disc stuff and mtf stuff but can someone tell me where the theory discusses the light scatter and reflection from the aperture profile edge and its effect on the image quality/coc/resolution.

[Donald Qualls]

IMO only, of course...

...if you need to stop down to get DOF to cover what movements can't (either because you need more than a single plane in focus, or because you don't have the movements you need available for a particular scene), you have to think about which is worse: a little diffraction blur evenly applied to the entire image, or a progressive level of defocus blur applied to objects depending on their distance from the plane of focus?

As one who does pinhole photography on routine basis, where diffraction is a way of life (every image is a tradeoff between geometric projection of the pinhole and diffraction effects), I get more experience than most with situations where I have *too much* depth of field; that is, where everything in the scene has the same amount of blur. The art of pinholing is choosing the subject, the point of view, and exposure (controlled mainly by film speed) to make that a happy quality -- but when we pay lots of money for exceptionally sharp glass, we feel we need to use that sharpness, and then suddenly we want to have objects in focus that aren't all in or very close to a plane. Movements don't do the job in that case, we have to either stop down, or accept the defocus blur. Barring "throwing the focus" one could argue that every image in large format is a compromise between diffraction and defocus...

I don't have any shutters that will stop down beyond f/45, anyway, so it's almost moot for me...

[paulr]

"On what format, what degree of enlargement? I call bullshit"

have you looked yourself? i bet (all else being equal, looking at parts of the image that are in focus) you can see a significant difference between f22 and f64 on any decent lens ... in 4x5 i think it would be clear in an 11x14 print.

i think paddy's about right that f45 in 4x5 and f64 in 8x10 are reasonable cut offs for when it gets noticeable under most circumstances.

in real life situations, though, it isn't always obvious what to do with this info. when the diffraction is better or worse than the blur from lack of depth of field is a whole other conversation ... luckily it's one that gets repeated a lot in these pages.

[paulr]

"Spit the hook out of your mouth ..."

sorry, was that just a troll? if i'd cought that i would have answered with something more heated.

[John_4185]

I'm a fool. I've been on a network since 1977 and it still just friggin amazes me how the bullshit rolls on. Jeeze. So that's my problem. There's no end of the same old shit.

sorry, was that just a troll? if i'd cought that i would have answered with something more heated.

You think you can make some heat I haven't felt before? So do it. Amuse me.

[paulr]

i'm just trying to figure out if you're serious or not. i never suspected diffraction could be such a hot-button issue.

[Paul Fitzgerald]

Purely opinion,

I think there is a difference between an iris and a waterhouse stop with this. An iris has little jagged edges that make the problem worse.

I think the smallest waterhouse stop would be between 3 - 4mm, 1/8in.

Looking thru an aperture ring gun sight there is a bright ring around the edge, a darker ring next to it and a very sharp image in the center. I think this is the same at the circle-of-confussion at the focus point making it look fuzzy.

It doesn't matter because you still need the depth to carry the scene.

[William Mortensen]

Leonard- Thanks for the recommendation of Jaconson's lens tutorial. I spent half an hour digesting it... If anyone wants to wade though it, it's at: http://www.photo.net/learn/optics/lensTutorial

I think my problem is that I have a little knowledge of optics, and a little knowledge can be a dangerous thing... Somewhere I read that diffraction is caused by light passing by the edge of the aperture. That's what led to my above calculations, which presume only the light passing within a wavelength of the aperture could be affected by it. I guess that's not the case, but the last hour of net-surfing has failed to find the answer to "WHY does a smaller aperture diffract more?" Which is a trivial question, being that it does diffract more,but I'd like to have my tiny mind comprehend what's going on.

In the end, I suspect that for contact printing from 8x10 negatives, I don't have to worry too much about it; depth of field considerations will outweigh diffraction concerns. But now I have this rough concept of an "airy disc" portfolio kicking around the back of my mind. I like the terminology, and the formulae are quite eloquent, (see http://en.wikipedia.org/wiki/Diffraction). But with my luck, I'd just get hairy discs...

[Jack Flesher]

Another thread bites the dust! ,,,

And another thread gone and another thread gone and another thread bites the dust...

~~~

JezeLouise guys, take it easy. This used to be such a nice place to visit...

Happy F-ing New Year.

[William Mortensen]

"read the airy disc stuff and mtf stuff but can someone tell me where the theory discusses the light scatter and reflection from the aperture profile edge and its effect on the image quality/coc/resolution." --rob

That's what I'd like to see too. Lots of quantifying, but I can't find the physics of what's going on. Why is there more diffraction at a smaller aperture?

"Despite what I've heard and studied about the effects of aperture related diffraction also being inversely proportional to focal length, as the actual, physical opening of a given f-stop increases as focal length increases, I've not really noticed this in practice." --John Layton

John- the diffraction decreases with the increased aperture size of longer lenses, but due to the longer focal length, the light travels farther to the film, allowing it to diffract more. From what I've read, one cancels out the other, so diffraction from different focal length but otherwise equal lenses will be identical at a given f/stop.

BTW, I shot two identical views with my 480mm Apo Ronar, one at f/32, one at f/256, HP5 in HC110, dilution b. No great difference under a 4x loupe to my eyes... But I've long wondered, why would process lens manufacturers make such small f/stops for lenses made for high resolution of a flat-field subject?

[Aaron van de Sande]

You can start seeing some softness with f64 contact prints (8x10) when you go past a 1:1 enlargement.

[Oren Grad]

Mark, I've studied physical optics and can sling the math around. But the best practical insight has come from experience working in different formats and seeing what happens under different conditions.

I've seen diffraction effects have a visible impact on pictures under a wide range of circumstances. "Ruin" is a pretty strong word, though. For example, the performance of the 75mm lens for my Mamiya 6 gets distinctly worse at f/22, for example, and these days I'll generally stay away from anything beyond f/16 with that lens, but I have printed negatives exposed at f/22 and lived to tell about it. When I'm contact printing big negatives (e.g., 8x10) f/64 definitely loses just a hair of crispness compared with f/22, but the DOF advantages are almost always worth it. OTOH, f/90 starts to get a bit soft for my taste on the few lenses I've tested that far. In 4x5 negatives taken with a modern 135 and printed with modest enlargement, I can see some loss at f/45 with ultrasmooth films like TMX; it's a much closer call with a grittier film like HP5 Plus.

Just to see, I also did an experiment once with one of my enlarging lenses, where I printed the same negative using every aperture from wide open on down. The effect was gradual, but the loss of crispness at the smallest apertures was quite apparent.

And so on. The effects are real, but you just have to see for yourself what the practical tradeoffs are with the lenses and in the formats you use, and whether and when the effect gets large enough to be a problem for your purposes.

[Oren Grad]

Lots of quantifying, but I can't find the physics of what's going on.

Mark, the math that captures the Huygens-Fresnel formalism is the physics, at least the classical physics. But one good way to develop a qualitative intuition for what's going on is to play with an interactive wave tutorial. Here's an interesting and quite powerful one:

jlearn.mit.edu/simulations/waves/waves2d.htm (http://jlearn.mit.edu/simulations/waves/waves2d.htm)

It takes a few moments of fiddling to figure out how to use it, but stick with it - you can do a lot of nifty things with it.

[William Mortensen]

Thanks for the input, Oren! I agree, one just has to test the limits and see what's acceptable. Contact printing 8x10 with a fairly grainy film lets me get away with more than most, which is why I haven't bumped too hard into the diffraction limits, I suppose. Looking at some samples of pronounced airy discs, I've noticed that most of them still have a strong spike of defined illumination in the middle. I wonder if this, coupled with a grainier film and *perhaps* (big perhaps) adjacency effects from stand developing help mask the diffraction.

[William Mortensen]

jlearn.mit.edu/simulations/waves/waves2d.htm

That was definitely one of the coolest things I've seen on the web for quite a while! And after building a couple of different apertures with the walls, I think I can better understand (in theory) what's happening. It's just a matter of getting my tiny mind to comprehend electromagnetic radiation (light) acting as what *looks* like fluid dynamics.

[Struan Gray]

Mark, for me the easiest way to think of this is to use Huygens' original geometric conception of wave propagation. All points on the wavefront are regarded as little tiny emitters of new waves acting in time with each other. With a large aperture, light spread sideways from one such tiny emitter gets cancelled by the light from another elsewhere on the aperture. Near the edges you lose this cancellation and you get interference patterns as some of the light spills sideways. With a small aperture you cannot help but be near the edges, so light spills sideways even from the little emitter in the center of the stop.

To me, the amazing thing is not that light spreads out after passing through a hole, but rather that plane waves propagate as plane waves.

[N Dhananjay]

Like Struan, that is conceptually the way it makes the most sense to me. For the wavefront to continue to propogate smoothly, the different parts of the wavefront must be in sync with each other. Now think of what happens when you place an obstruction in the way such that it obstructs part of the beam. The part of the wavefront that just brushes past the aperture no longer is in balance because the parts that were doing the balancing on one side got cut off by the obstruction. Since this front is now out of sync, it also affects the wavefronts next to it to a smaller extent and so on. Therefore the spread.

In terms of why smaller apertures create more diffraction, based on the above, you can see that it is the ratio of the area of the aperture to the perimeter of the aperture that is important - that is, the area passes the light beam without much problem, the perimeter creates the edge and creates teh imbalance along the perimeter. As you reduce the radius of a circle, the area (pi *r*r) decreases much more rapidly than the perimeter (2*pi*r). In other words, as you reduce tha radius of the aperture, the perimeter is starting to contribute more and more to the image making light.

Diffraction is quite real - all you need to do is put a negative in your enlarger and examine the aeriel image as you stop down - you will see the grain turn to mush. However, I do agree with the previous posts in terms of the impact it has. If contact printing 8x10, you would be hard-pressed to ruin a photograph by diffraction (if by ruin one means unacceptably softness). Also, diffraction results in a gradual softening of image detail. That does not mean you cannot make a print from the negative - just that the degree of enlargment that is possible for a required CoC reduces. For many kinds of work, DOF trumps diffraction - the somewhat lower resolution is preferable to live with (at least all parts of the picture are equally out of focus, which if you think about it is pretty much what we always have - we never have perfect resolution) compared to having some parts of the picture being very obviously out of focus.

Cheers, DJ

[Tom Westbrook]

Here's an interesting page on diffraction:

www.cambridgeincolour.com/tutorials/diffraction-photography.htm (http://www.cambridgeincolour.com/tutorials/diffraction-photography.htm)

[John_4185]

Diffraction is quite real - all you need to do is put a negative in your enlarger and examine the aeriel image as you stop down - you will see the grain turn to mush.

Is that really an accurate measure?

Consider - is there a difference in the outcome of the enlarger's diffraction compared to using the same focal length lens at infinity in a camera?

[Leonard Evens]

Some further comments, agreements, etc.

1. At f/64, the diffraction limit should be about 1500/64 ~ 23 lp/mm. Few large format lenses have markings below f/64, and a contact print of an 8 x 10 would invovle no enlargement. I don't know that anyone claims to be able to see 23 lp/mm in near vision of a print. So you would seem pretty safe in any practical situation to ignore diffraction if you are contact printing 8 x 10 negatives.

2. The effect of diffraction is usually expressed in terms of the relative aperture or f-number, not the absolute size of the aperture. When you do that, there is no dependence on focal length. As noted previously, it depends just on the relative aperture and wavelength.

3. The intutitive explanation of diffraction given by Struan is as good as any. You might also note that the diffraction pattern from a single linear slit is a bright central band surrounded by less fainter bands in both directions. So it makes physical sense, to me at least, that the corresponding pattern for a circular aperture is a central spot surrounded by concentric rings. In the end, of course, you have to look at the mathematical theory in physical optics. This is even more true if you try to understand how diffraction and defocus combine to affect the image, which is the issue in photography.

[Emmanuel BIGLER]

There has been several other discussions about facts & figures related to diffraction, for example here :

largeformatphotography.info/lfforum/topic/500810.html (http://largeformatphotography.info/lfforum/topic/500810.html)

But it is a favourite subject, so let's play it again.

There is another way to look at the effect of diffraction, by looking at how the MTF of a given lens degrades when stopped down.

The Airy disk is a really tough guy and after one century he continues to resist the Fourier and MFT gang despite memorable efforts by, among others, French scientists (as early as WW-II) to definitely secure him forever in a scientific concept retirement home. But at any new discussion about diffraction on the 'net, the Airy disk comes back as strong and young as ever !! Long life to him ! Even if he does not help that much to understand how image quality is affected by diffraction !

Well if you want to visualize the effects of a small aperture in terms of MFT, you may have a look at those MTF charts hosted by Paul Butzi, computed for the apo-ronar.

The manufacturer has indicated physical diffraction limits, but the interesting thing is to notice that the MTF at the centre at f/22 reaches 70% @20lp/mm for distant objects, close to the physical limit, whereas at 1:1 ratio the MTF at the centre drops down to 40% simply because an effective aperture of f/22 at large distance becomes f/45 effective at 1:1 ratio. At 1:1 ratio the actual image circle is doubled but the image quality is not as good, due to diffraction.

www.butzi.net/rodenstock/apo-ronar/p12.htm (http://www.butzi.net/rodenstock/apo-ronar/p12.htm)

[Christopher Perez]

If a lens were perfect, the following would hold (from literature):

Resolving Power

This presents the theoretic resovling power of an ideal lens where the light's wavelenght is 589.3mu (green).

Tangential lines/mm
f-number Angular distance from axis (in degrees)
0 10 25
1 1391 1329 1035
2 695 665 518
4 348 332 259
5.6 246 235 183
8 174 166 130
11 123 117 92 <--- approx. limits of film resolution
16 87 83 65
22 61 59 46
32 43 41 32
45 31 29 23
64 22 21 16

Radial lines/mm
f-number Angular distance from axis (in degrees)
0 10 25
1 1391 1370 1260
2 695 685 630
4 348 343 315
5.6 246 243 223
8 174 171 158
11 123 121 111 <--- approx. limits of film resolution
16 87 86 79
22 61 61 56
32 43 43 39
45 31 30 28
64 22 21 20


Lenses are seldom "perfect", and these limits can be difficult to reach.

For example, a 90mm f/4.5 Super Angulon became visibly soft (loss of resolution and contrast) at f/32. I think the lens was designed for optimal use between f/11 and f/22. Or at least mine behaved that way.

With several four element air space "Artar"-like designs, I've seen where f/32 returns just about 42 l/mm - right at theoretic limits. The plasmat design lenses that I currently own can be nearly as good as the four element airspace designed lenses.

Additionally, I have a Mamiya 7 80mm L lens that performs quite admirably. Similarly, I have a brace of old Rolleiflex that are quite outstanding.

I guess what I'm trying to say is that there's theory, there's lens design, and then there's emperic evidence as to how an optical system will behave. We could probably wrangle over just about any aspect of this topic. For many of us, diffraction limiting comes into play only during extreme enlargements, and even then most people can't tell much difference.

It is far more common that people have sloppy work techniques. This will cause more problems than theory, physicals, or in many cases optical design. Which has led me to claim that the sharpest lens in any photographer's kit is a tripod. But that's perhaps unrelated to the original question here.

For me, the bottom line is: I shoot 4x5 between f/11 and f/22 and am happy with the results. I shoot 8x10 between f/16 and f/45 and, again, am happy with the results.

[paulr]

"1. At f/64, the diffraction limit should be about 1500/64 ~ 23 lp/mm. Few large format lenses have markings below f/64, and a contact print of an 8 x 10 would invovle no enlargement. I don't know that anyone claims to be able to see 23 lp/mm in near vision of a print."

it's true that no one's eyes can resolve anywhere near that. but resolution numbers (whether we look at yours or at Christophers) tell us nothing about how sharp the picture the looks. it makes no difference that 23 lp/mm of detail is theoretically resolvable ... what matters is how much contrast there is in the 1 to 5 lp/mm range (in a contact print). plenty of people have spent their careers contact printing 8x10 at f64, so i imagine this looks fine (although it may well be visibly softer than at f22)

with an 11x14 print from4x5, this would be the 3-14 lp/mm range on film. experience tells me that sharpness in this range is reduced in the final print when you stop down to f45 or so, presumeably from diffraction.

if someone can find an MTF chart that shows MTF50% (or some similar metric) graphed against aperture, the mechanism of the loss of sharpness will be pretty obvious (i've seen them before but couldn't find one in a quick google search).

[John O'Connell]

"is there a difference in the outcome of the enlarger's diffraction compared to using the same focal length lens at infinity in a camera?"

In an enlarger, you're passing an image through a lens. Diffraction works the same way as it does in a camera, and results in substantially sharper prints at wider apertures than small apertures. The "grain turing to mush" effect is obvious if you have a sufficiently high-power grain magnifier.

Additionally, in big enlargements from small formats, you're closer to infinity than you think. Rodenstock used to make a special enlarging lens for 20x enlargements which was reportedly excellent at in-camera distances, too.

[William Mortensen]

Thanks for a wonderful thread, guys! I'm getting a lot out of it, having always thought (in practical terms) of light behaving as rays rather than wavefronts. I sort of knew better in the back of my mind, but never applied it. Kinda like quantum mechanics, knowing a little of the theory but never using it for anything practical.

The difference with diffraction, of course, is that in some situations, it can make a difference. I'm lucky enough that my choice of format and materials make it less critical for my work.

Tom- thanks for the link to the Cambridge site! A nice piece of trivia there is that the Airy disc was named after its discoverer, George Airy. I'd previously thought it was some scientist's descriptive term!

Emmanuel- I'm running across lots of images of Airy discs, so I'm presuming they're a well-documented phenomenon, and they seems pretty fundamental to understanding the mechanics and effects of diffraction. Is there still some debate about there existance or importance?

[John_4185]

Additionally, in big enlargements from small formats, you're closer to infinity than you think.

I don't understand what you said, but I'm dense. FWIW, in the service, 'infinity' was something like 2000 * the focal length. I don't have a darkroom that big.

[Christopher Perez]

paulr writes:

... what matters is how much contrast there is in the 1 to 5 lp/mm range (in a contact print). plenty of people have spent their careers contact printing 8x10 at f64, so i imagine this looks fine (although it may well be visibly softer than at f22)

And this gets to the nub of the matter. Exactly. Contrast in B&W work is all important.

I can take a handheld Mamiya 7 image, shoot Tri-X, soup it in D76, knowing full well it's grainier than all get out, enlarge it to 11x14, use a #3.5 or #4 multigrade contrast filter and creat a print that people will swear to their dying breath that it's very very sharp. The human eye loves contrast.

What I can't work out is why contrast in the 1 to 5 l/mm range is more important than it is at other resolutions? Contrast is contrast, right? How does this relate to enlarged images? Does it take 20 l/mm on neg, enlarged 4x to get the 1 to 5 l/mm people talk about? I'd sure like to understand this from theory, math, and emperic observation.

[paulr]

"What I can't work out is why contrast in the 1 to 5 l/mm range is more important than it is at other resolutions?"

this information comes from research into the physiology of human vision. it's perception science, based on having a lot of people in clinical settings subjectively judge the optical qualities of images (that have known, measurable characteristics). i first learned about this from a schneider engineer; now there's research available all over the web.

it's been interesting seeing how well my personal experience echoes these findings. photoshop makes it easy to measure just how fine that fine detail really is, and to determine just how large an edge radius you apply when sharpening. sure enough, what looks best is usually right around what the research predicts. it's also interesting to see how completely invisible detail at 15 lp/mm is ... a bar or sinewave pattern at this frequency, printed with the contrast of normal photographic frequencies, just looks like flat gray. and my closeup vision is pretty good ... i can read the compact edition of the OED without the magnifying glass and without too much trouble.

"Does it take 20 l/mm on neg, enlarged 4x to get the 1 to 5 l/mm people talk about?"

yes, exactly.

but the science behind some of it gets strangely complicated. aparently detail at 1 lp/mm gives us a different set of visual cues than detail at 5 lp/mm. meanwhile, detail at 1/3 to 1/5 lp/mm we're strangely insensitive too ... we perceive less contrast at those frequencies than there really is. detail at 7 lp/mm is at the fringe of what most people can see under normal conditions, and makes very little difference (except maybe to jj's grain-sniffing enemies).

this all may be the product of evolution ... of the qualities our eyes needed to best serve us as hunter-gatherers. if we had the same eyes as cats, we'd probably design our lenses and films a lot differently.

new thread? lenses for cats?

[Christopher Perez]

... detail at 7 lp/mm is at the fringe of what most people can see under normal conditions...

OK. Last question. Maybe.

Are we saying similar things for similar reasons when you say that detail is somehow limited to these numbers and I say these are the limits of human eye resolution? Are we arriving at similar answers, perhaps from opposite sides of the discussion?

[paulr]

i think we're talking about different things (but for similar reasons ... ). resolution limits of lenses and film are usually determined by looking at test targets, sometimes with a microscope, and determining the highest frequency that has can be distinguished at all ... or else it's done a bit more scientifically, like the resolution at which MTF drops below 3%, or drops below the noise floor. i was under the impression you were talking about this phenomenon, in terms of the theoretical diffraction limits of lenses.

when i mentioned the 7lp/mm number i was talking about the resolution limits of the eye, under normal print viewing conditions.

for what it's worth, people can sometimes distinguish higher resolutions than that, if the contrast of the detail is high enough (like a well printed test target, which is contrastier and has cleaner edges than most detail in a photograph). and people with good eyes under ideal circumstances (a backlit test target, with enough but not too much contrast) can distinguish as many as 11 or 12 lp/mm. the theoretical limit of the human retina is about 14 lp/mm ... but most people have enough problems with aberrations (and even diffraction!) to make approaching this impossible.

by the way, this is all based on a 10" viewing distance, which is about as close as most people can focus.

and again, it's all much less important to how sharp a print looks than the contrast at lower frequencies.

[Craig Wactor]

A couple of reasons I think diffraction has more of an effect than it first seems it should:

1. Light enters the lens at more angles than just perpendicular to the diaphragm. Entering at an angle, your 1mm hole becomes a smaller slit -- the farther from perpendicular the angle, the smaller the slit becomes.

2. Light travels as a wave, which means light heading near the edge of the 1mm hole will be affected, not just the light headed directly at the edge.

www.craigwphoto.com (http://www.craigwphoto.com)

[Richard Ide]

Craig;

Interesting! I was thinking along the same lines and was wondering how a very thin waterhouse stop would work. This would minimize light entering from off axis from passing through a slit. I just checked my Melles Griot catalogue and they list precision pinholes up to 1 mm hole dia. Most are drilled in 13 micron stainless which is .0005 inch. The finest pinhole is 1 micron drilled in a .0025 mm disc. Many times thinner than a lens diaphragm. Worth further research at the very least. I will post any worthwhile findings at a later date.

Thanks

Richard

[Emmanuel BIGLER]

Emmanuel- I'm running across lots of images of Airy discs, so I'm presuming they're a well-documented phenomenon, and they seems pretty fundamental to understanding the mechanics and effects of diffraction. Is there still some debate about there existance or importance?



Non, Mark not at all, we all believe in Airy disks, but the concept is simply outdated in terms of modern photographic optics.

To support this, let me quickly go through some historical notes.

One of the first approach proposed to link the limitation of image quality to diffraction effects was Lord Rayleigh's. www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Rayleigh.html (http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Rayleigh.html)

The problem addressed by the famous physicist was related to the resolving power of prism or grating spectroscopes, but the problem of image resolution is similar, slightly more complex since being two-dimensional. Diffraction limits the width of the image of the entrance slit of any spectroscope to a minimum size diffraction image actually defining the limits of resolving power of the instrument.



The famous physicist proposed to define the limit of resolution for the spectroscope by comparing the distance centre-to-centre (He was British ;-) between two diffraction images ; the so-called Rayleigh's criterion states that the minimum distance between the two diffraction spots cannot be smaller than the full width at half maxium of a single spot. This can be applied to the resolving power of a telescope when you want to separate the images of double stars.

There is another Rayleigh's criterion for the quality assessment of telescope mirrors, this is another story, actually related to what we are considering here but more complex involving aberration theory and their influence on image quality.



In such a problem of diffraction-limited resolving power, either the image of a double star or the image of a fine spectroscope slit, what you actually see is the diffraction image of a single spot or a single line and not the image of an extended object.



Hence the sucess of the Airy disk, image delivered by any diffraction-limited optics for a point-size object like a distant star.. at least when the telescope is located in space, otherwise it might be limite by atmospherric turbulence !



But actually few of us take routinely images from stars, or image of point-source objects. We usually prefer ordinary scenes with extended objects any kind ;-), so the question is the assessment of image quality degraded by aberrations and diffraction is still unclear.



In the forties, electrical engineers developed the theory of electrical signal or image degradation due to the transmission through electrical instruments, say amplifiers. Some time later specialists in optics applied those so-called Fourier concepts to optical systems. In this approach it is considered equivalent to look at the output for a single point input signal, or to consider some filtering effects in the spectrum of the signal.



For optics this approach eventually yielded the MTF approach, and instead of considering an Airy disk, you can consider the spatial frequency filtering function corresponding to the Airy disk. It is a bit more complex in terms of maths (Fourier analysis), but more fruitful, since you can actually synthetise the blurred image when you know the original image and the filtering function, and even more, you can do the reverse, when you know the filtering function, under certain conditions, you can retrieve the un-blurred image.



Unfortunately nobody can retrieve completely an image blurred by diffraction, namely you cannot retrieve details smaller than about the size of the Airy disk. In terms of spatial filtering, every period of the object smaller than N x lambda where N is the effective f-number is definitely lost.



So there is actually no controversy about the Airy disk, simply models have greatly improved since the pioneer work by Lord Rayleigh. But Lord Rayleigh was such a giant in science, that many physicists were paralyzed, unable argue againts His Sacred Criterion.

Now modern computer software are able to compute the MTF of any lens design including diffraction effects with some reasonable assumptions of the wavelengths used. You can do it at home for free with demo-software like Oslo®-edu (limited to 10 surfaces).
You can simulate with a high degree of precision the effect of mixed defocusing and diffraction for the optics. You can choose to represent the image spot of a point source, or you can choose to represent the MTF. My understanding is that for photographic lenses, MTF charts are preferred to the image of a single spot, since it is known that some range of spatial frequencies are most important for a good image quality, e.g. 10, 20 and 40 lp/mm in medium format (see Zeiss charts) or most probably 5, 10 and 20 lp/mm for LF images.



So long life to the Airy disk, no offense against Him, but MTF simulations are mode modern and more efficient !!

[Emmanuel BIGLER]

Best with some curves. Temporary link valid for 21 days.
I have plotted the theoretical curves for an ideal diffraction-limited lens. Consider the values as realistic at the centre of a top-class lens used at its best f-number or stopped down beyond.
As a comparison I have plotted the theoretical MTF for a pure ideal, geometrical defocus without diffraction fo two circles of confusion, 100 microns and 200 microns.
The diffraction MTF curves have all the same hape and stop at the cut-off frequency of 1/(N*lambda) here I have taken lambda = 0.7 micron, a realistic values fitted to the published manufacturers MTF cruves (e.g. apo-componons at the centre at the best aperture). On the diagram the cut-off frequency is clearly shown.
In order to get a reasonable non-zero contrsta it makes sens to limit the usable part of the curve to 0.8 times the cut-off frequency, eventually we find the same criterion as Rayleigh's but re-visited in terms of a minimum readable period, .8/(N lambda) = 1.2 N lambda.

Defocus MTF curves have the same similar shape and exhibit a first zero at a frequency of 1.2/c where "c" is the coc diameter.

http://cjoint.com/?bgswWJ1NYB

In fact in all photographic situations our MTF is somewhere between the diffraction MTF and the defocus MFT. So we do not want too stop-down too much, since the defocused MTF curves can be considered as our absolute minimum. For me the rule of thumb in large format is that I am always allowed to stop down 1 stop beyond the best recommended f-stop, 2 stops beyond being the maximum. For example in 4x5", N=16 or 22 is often the recommended f-stop, so 32-45 are the absolute limit. In 8x10" those values are approximately shifted by 2 f-stops.

It can also be seen that depth-of-field models in the sense of pure geometrical blur are definitely questionable for example at f/64 in 8x10" where a coc of 200 microns is considered acceptable !!

The other conclusion, is that the Airy disc does not tell us much, whereas the comparison of those MTF curves shows us how the image is degraded and how much contrast we can reasonable expect at 5, 10 20 and 40 lp/mm, the important photographic values.

[Emmanuel BIGLER]

Well the temporary link is here :
cjoint.com/data/bgswWJ1NYB.htm (http://cjoint.com/data/bgswWJ1NYB.htm)

[William Mortensen]

Thanks, Emmanuel! This is far more information than is practical for my photography, but I do enjoy learning it, and while it may not always directly influence my shooting decisions, it gives me a better appreciation of the history and physics I'm taking advantage of. I think a fair number of others here are enjoying this too...

(Ansel Adam's story of shooting "Moonrise" would have been soooo much more impressive if, after telling how he calculated the exposure, he had gone on to say something like, "I then calculated the desired CoC resolution of 100 micons by recalling that the Optical Transfer Function can be determined by multiplying the Modulation Transfer Function by the Phase Transfer Function, then quickly plotting graphs of diffraction limitations in the dust on my car hood...")

[Jeff Conrad]

A very informative post! Note that the results are the same as those in
Jacobson's lens tutorial, except that Jacobson used c = 0.03 mm and N =
f/22 for 35 mm format. Maybe there really is some truth to this stuff ;-)

Although the results indicate that one cannot improve DoF by stopping down
forever, they do seem to suggest that, when you're outdoors, in most cases
the wind will get you before diffraction does. I think, in essence, that
Wheeler reached the same conclusion, though he didn't quite state it in
those terms. This would seem the sort of general conclusion that one,
whether technical or not, could take into the field.

[William Mortensen]

So why are process lenses like my Apo Ronar made to stop down to f/256? Considering they were made for high-resolution copying of a flat subject, it seems the manufacturers went to some trouble to include a feature that wouldn't be used.