Diffraction and f stops

peterm1

peterm1

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Warning semi-scientific content.

Well if I got this right I mean.

Someone once asked a question on one of these forums (it may have been this one) about why some lenses exhibit diffraction effects more readily at others - why some can be stopped down to f16 or smaller and produce OK images whilst others begin to show evidence of deterioration at (say) f 11 or even wider (e.g. most digital pocket compacts seldom have f stops smaller than f8 partly for this reason - as well as not needing it for depth of field purposes of course. In this size camera f8 would actually be tiny!) A good exemplar of this at the other end of the scale (and this was the specific exmple used in the fore mentioned prior post) is that Ansell Adams often used f stops of f64 or smaller in his cameras.

The question and the thread that resulted produced much heat and little light as such technical issues often do in these forums. I was never satisfied with the outcome so here I am at pandora's box once more.

For me the answer is simple. Diffraction is not a function of the f stop in use per se. Diffraction is a function of the absolute / physical size of the "hole" / aperture in use. Whilst this has a general relationship to the f stop its not totally directly related - especially in these days of retro focus lenses and other fancy exotic zoom lenses designs.

Why do I say this. Well an f stop is a relative measure in the sense that the actual size of an f8 - f stop is not the same physical size in all lenses. An f stop measures the amount of light reaching the film plane not the actual size of the aperture. If the iris / aperture is closer to the film plane as it can be in some lens designs (and certainly is in wider lenses - in a given format camera) then the size of the "hole" for a given f stop can be - actually must be, smaller than it would be if the iris /aperture were located further away from the film plane.

To prove this to yourself if you need to, grab a 35mm lens and a 135mm lens. Set both to f5.6 and peer down the front. You will see that f5.6 is physically much smaller in the wider lens as being closer to the film plane it will still allow the correct amount of light to reach the film plane even though it is smaller.

Ansell Adams used large format lenses which are "all scaled up." In these, any given aperture should be larger than it would be in a 35mm format camera. So the physical size of f 64 in a large format lens might only be the same as perhaps f8 in a 35mm camera. Hence llittle or no diffraction effects.

Why do I say diffraction is related to the physical size of the aperture - well because in this case aperture is caused when light waves encounter the physical barrier of the metal iris which controls the aperture size. This is located at the diameter of the circular aperture. As the aperture / hole gets bigger, proportionaltely more undiffracted light passes thru the central part of the hole compared with the amount of diffracted light hitting the edge of the iris.

How do I know this - because the area of a circle is proportionate to the square of its diameter (actually pi multiplied by radius both squared) while the circumference is not (it is calculated by two pi multiplied by the radius). In other words if you double the physical size of the aperture you will get 2 times as much light affected by diffraction BUT you will also get 4 times as much light that is not diffracted because its passed unaffected throught the central parts of the aperture. The "good" undiffracted light begins to "outnumber " the "bad" diffracted light more and the image quality improves - other things being equal (wow glad I got that bit in - its always the ultimate disclaimer used by economists and scientists.)

If this did not occur - all lenses at all f sstops would be affected by the same amount of diffraction irregardless and we know this is not true.

I reckon thats about as good a lay persons explanation as I can come up with. Does it make sense? Does it ring true?
 
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That's my understanding from High School Physics class- Diffraction has to do with light passing around an edge. The diameter of the opening compared to the wavelength of the light passing through it is the important factor. So a lens that expands its light bundle, places its aperture at the maximum of the expanse, then brings it into focus would minimize diffraction. The formula of the lens is a factor in determining effects of diffraction.
 
Note: I am not a physicist. Well, not really.

That said, you got the gist of the thing, with regard to the effect of diffraction being controlled by the size of the aperture. The wavelength of the radiation (in this case, light) also plays a part, too. It's also important to consider the object one if trying to image, as well.

Every lens will produce diffractive effects due to the nature of the optical system; in so-called "diffraction limited" systems, given the lack of other aberrations, there is still an inherent limit to angular resolving power. Only very small apertures relative to the wavelength of light will cause gross effects. In practice, the effect is difficult to see, since film grain/pixel size may also conspire against you.

In my opinion, those lenses that produce images seemingly marred by diffractive phenomena are likely to have optical glass that is prone to coma and chromatic aberration in the first place. Just my opinion, though.

However, it seems that not every lens would be able to resolve these effects, even if they were produced, since not every lens has inherent resolution high enough to be considered diffraction limited.

I'm certain that someone will expand on this with more clarity, and correct my errors.


Cheers,
--joe.
 
Check the diffraction calculator on this page:
http://www.cambridgeincolour.com/tutorials/diffraction-photography.htm

Try different sensors, and f-stops. The Airy disk diameter is correlated only with the f-stop. Thus, with a larger film size, the Airy disk takes up a smaller proportion, and produces a sharper image. However with a digital P+S, the Airy disk (which doesn't change in absolute size) will be a larger part of the image, and thus decrease sharpness.

The Airy disk is what your camera sees when it looks at an infinite point, such as a star. As the aperture becomes smaller, the disk spreads in diameter.
 
I agree that the wavelength of light is important . But as we are talking about camera lenses and visible light (not x rays or gamma rays etc) I have not mentioned it as in this case, as its basically a "constant" as the physicists might say - with only slight variations depending on whether there is a red cast (as at sunrise) or a blue cast as at midday but assume these would be far too small to have an effect in practice.
 
peterm1 said:
...but assume these would be far too small to have an effect in practice.
Click to expand...

You're right, of course; I was being overly expansive in my explanation.

But realize that the average human eye responds to light in the range of 380-750 nm, roughly a 2x change in wavelength. Consider the empirical formula for the Airy disk (link above), where the minimum resolvable size on the film/sensor is given by

x = 1.22 * L * F,

where L is wavelength, F is the f-stop, and x is the smallest feature visible on the film/sensor. In this way, doubling the wavelength actually doubles the minimum resolvable size (or, rather, halves the resolution limit), so that even within the range of visible light, a significant coma/chromatic effect can probably be generated.

Take this with a grain of salt for the moment, however; I may have no idea of what I'm about.


Cheers,
--joe.
 
"Take this with a grain of salt for the moment, however; I may have no idea of what I'm about."

Me neither of course, which is why I am trying to work it thru from first principles rather than just relying on the ability to parrot something from a book..... which is what happened, when this was last discussed a year or two back and whats more, I was convinced some were doing it rather imperfectly. So I appreciate the logical and thoughtful repsonses from you and other contributors this time around.

And I think working it out from first principles is often the ebst way. It should give deeper insight and more comprehensive understanding of the theory.
 
I've experimented with using a pinhole aperture in contact with the front element of the 75mm f/3.5 lens of a Minolta Autocord. It definately gives you diffraction effects! You'll need a tripod and you'll also run into reciprocity failure also, where you need to expose several times as long as your meter says when your exposure is many seconds or even minutes in duration.

I used a piece of black paper to make the pin hole aperture. In order to get a nice clean hole with no fuzz around the edges I held the needle with pliers and heated it glowing red hot on the stove. I actually burned the hole through the paper. You can measure the exact diameter of the pin hole with a micrometer, and there are also published charts of the diameters of various needle sizes.
 
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peterm1 said:
And I think working it out from first principles is often the ebst way. It should give deeper insight and more comprehensive understanding of the theory.
Click to expand...

Oh, I couldn't agree more. I've found that doing so usually gives me a grasp of the topic somehow "greater than the sum of its parts", if you see what I mean.

I love that RFF seems to generate these thoughtful side-topic discussions as often as it does. Reminds me that I'll have to look up that old thread you mention, as contentious as it is.

The topic of diffraction has always been of interest to me; in my former life as a high-school physics teacher, the Young's Double-Slit experiment was one of my favorite demonstrations. There are so many implications represented by the results, though, that using the lesson to its fullest extent was limited by the students' basic level of understanding - and, as it turns out, my ability to teach it.

Good stuff.


Cheers,
--joe.
 
I didn't invent the hole burning technique. I read it someplace years ago. Just another bit of long forgotten old lore I guess. The best paper I've found is the black interleaving sheets between sheets of sheet film. I've considered, but never tried, unscrewing a lens cell from the shutter so you can put the pinhole right next to the diaphragm.

If you put it in front of the lens leave the diaphragm wide open or you might get some corner vignetting on the negative.
 
"The topic of diffraction has always been of interest to me; in my former life as a high-school physics teacher, the Young's Double-Slit experiment was one of my favorite demonstrations. There are so many implications represented by the results, though, that using the lesson to its fullest extent was limited by the students' basic level of understanding - and, as it turns out, my ability to teach it."

The whole double slit - implications for reality - discussion that comes out of quantum theory is a whole other field of interesting but mind boggling fascination for me too. Studies have now been carried out confirming the theoretical predictions that if you are observing the behaviour of this double slit "system," you will get a different result from when it is not being observed. In other words light behaves like a wave OR like a particle depending on what observations you are - or are not , making. Here is a lovely you tube cartoon explaining it all - or at least explaining why it is so mystifying - as no one can really explain what is going on. The best physicists in the world are still arguing why and how the act of observation can actually change the way something "out there" in the real world, behaves.

http://www.youtube.com/watch?v=DfPeprQ7oGc
 
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Well, I actually am a physicist, but as I am not really into optics professionally, take some reserve to what is written below.

In the original post is stated that it is actually size of the whole which matters is correct and I have to admit when thinking of diffraction as a limiting factor for a lens resolution I have never realized this (shame on me). But there is one more trivial factor that is directly related to size of the circle of confusion which tells us whether the out of focus area will be sharp or not. And that is the distance of the aperture to the film plane. So (naively) if we would compare a 50 and 100 mm lenses both set at the same aperture - the "hole" for the 100 will be twice the size than the hole for the 50 - but will be also twice as far. So if we would consider a light ray that diffracts a give angle - it will fall twice as far from the non diffracted ray for the 100mm lens when compared to 50mm lens. But - as noted in the first post - the hole for the 100mm lens is larger and therefore fewer light rays will diffract.

So - my guess is that these two effects more-less cancel (save for higher order effects) and therefore is the f/stop a rather good measure for diffraction limits for different focal lengths.

Now - when it comes to different film/sensor sizes - it is purely a matter of enlargement factor. If one needs say 5 line pair per millimeter for a sharp looking print - the smaller is the film/sensor (= the larger is the enlargement factor) the more lines per mm are necessary during the image capture.

With a 35mm film to get about 8x10" print we are speaking of about 8x enlargment - so we need at least 40 line pairs per mm (you need more as you lose during scanning or classical enlargement process and also the film limits the final resolution - I will save one stop for that) - so you do not want to shoot bellow f22 if not necessary.

See HERE for example

Now - imagine doing the same print from a 1/2.33" (e.g. Panasonic LX3) sized sensor - the enlargement factor to 8x10" print is about 25 so you need at least 125 line pairs per mm to get a sharp print - so you do not want to go bellow f/8 if possible.

It is all just +/- but I guess it should not be completely wrong
 
Oh, and do keep in mind that almost every lens is diffraction-limited, you just have to stop it down far enough for the diffraction effect (airy disk width) to outweigh the lens' abberrations.

This should be possible with all but the crappiest lenses. 😀

So, what people mean when they say that a lens is diffraction-limited, is that it is so at open aperture. Now that's a distinction.

EDIT: And yes, I am a physicist.
 
According to an old article by Bob Schwalberg:

FL : 4 = Maximum aperture size before diffraction starts to be evident in Pictures

Examples (24x36mm):

15mm f2.8 - f4 at f4 diffraction would start to be a problem
20mm f4 - f5.6
24mm f5.6 - f8
28mm f5.6 - f8
35mm f8 - f11
50mm f11- f16
 
rlouzan said:
According to an old article by Bob Schwalberg:

FL : 4 = Maximum aperture size before diffraction starts to be evident in Pictures

Examples (24x36mm):

15mm f2.8 - f4 at f4 diffraction would start to be a problem
20mm f4 - f5.6
24mm f5.6 - f8
28mm f5.6 - f8
35mm f8 - f11
50mm f11- f16
Click to expand...

So the 12mm f5.6 would be useless stopped down then?

 
For your viewing pleasure.

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