"Diffraction Limited" in Simple Terms

[Ken Lee]

With apology that this subject has been discussed before...

Stopping down a lens from wide open, inspecting the ground glass with a loupe, it's easy to determine the sharpest aperture, after which the image begins to degrade due to diffraction. That's the empirical method: OK. My question is about the underlying optics.

Given light of the same wavelength, is the diameter of the hole through which the light passes, the limiting factor at which diffraction becomes an issue ?

A 50mm lens at f/8 has the same sized aperture as a 100mm lens at f/16, or a 200mm lens at f/32. All things being equal would those 3 lenses exhibit the same amount of diffraction ?

Here I'm not considering other factors like film grain, pixel size, degree of enlargement, just the effect of diffraction... or is that unwise ?

[Dan Fromm]

Ken, Emmanuel Bigler has posted a lucid explanation of diffraction in which he points out that relative aperture, the f/ number, not absolute aperture, the size of the hole is what matters. Come to think of it, he's posted the explanation more than once.

Don't worry, be happy. Just remember than no lens delivers as much resolution on film as its diffraction limit and that the resolution you need on film is determined by the resolution you need in the final print. If you believe that 8 lp/mm is the lowest tolerable resolution in the final print -- many posters here think that less resolution in the final print is perfectly ok -- then you need 8 x enlargement lp/mm in the negative. Don't worry, be happy.

[Heroique]

Another simple way to think about it in layman's terms.

Take a typical prime macro lens.

The aperture ring on the lens might indicate one relative aperture (say f/22), but as magnification grows larger and larger, the effective (real) relative aperture gets narrower and narrower, introducing more and more diffraction – even though the absolute size of the hole isn't changing.

[Peter De Smidt]

On a related note, here a paper by Rik Littlefield on depth-of-field of a diffraction limited lens: http://janrik.net/MiscSubj/2014/DefocusAnalysis201405/WhatIsTheDOF_DiffractionLimitedLens_v01.pdf

[Jim Jones]

As Dan reminds us, the blur on film due to diffraction is proportional to the f/number. However, images from smaller format cameras are often enlarged more, increasing the blur. When images captured from the same position with large and small formats at the same aperture diameter are presented at the same size, both the diffraction blur and Depth Of Field will be similar. f/64 has been used for 8x10 negatives to be contact printed as a compromise between diffraction and DOF. In my experience, a 50mm lens at f/11 on a 35mm enlarged to 8x10 is likewise on the verge of being diffraction limited.

[Dan Fromm]

In my experience, a 50mm lens at f/11 on a 35mm enlarged to 8x10 is likewise on the verge of being diffraction limited.

Jim, at f/11 the diffraction limit -- the highest resolution attainable -- on axis is approximately 1500/11 = 136 lp/mm at very low contrast. Resolution attainable in the corners will be lower.

No one gets 136 lp/mm on axis consistently. Here's an account of an attempt to find out what's possible in practice: https://www.flickr.com/photos/nesster/4424744296/sizes/o/ (part 1) and https://www.flickr.com/photos/nesster/4424744224/sizes/o/ (part 2). Short answer, around 100 lp/mm can be attained with impeccable technique, high resolution film and focus bracketing. Sometimes. Doing it consistently is very hard. Most of us do well to get 70 lp/mm.

The practical implication is that more-or-less the largest print possible from 35 mm still that will stand close inspection (> 8 lp/mm) in the print is 8x10. Doing that requires very good technique and equipment at every step in the process.

Fortunately for us mere mortals, many images with < 8 lp/mm in the final print will please. The highest possible resolution in the final print won't save a weak image, so-so resolution in the final print doesn't often ruin a strong image. Just ask the soft focus cultists.

[ic-racer]

A 50mm lens at f/8 has the same sized aperture as a 100mm lens at f/16, or a 200mm lens at f/32. All things being equal would those 3 lenses exhibit the same amount of diffraction ?


"Amount of Diffraction" is an ambiguous term.

In the example above the three lenses will NOT have the same size Airy disk on film (that only happens if they are all at f8) However, in the example above, the relationship of Airy disk size to image size will be the same.

[Ken Lee]

Jim, at f/11 the diffraction limit -- the highest resolution attainable -- on axis is approximately 1500/11 = 136 lp/mm at very low contrast. Resolution attainable in the corners will be lower.... largest print possible from 35 mm still that will stand close inspection (> 8 lp/mm) in the print is 8x10.

I've been looking for just such a rule of thumb.

Apparently we divide 1500 by f/stop to get lp/mm - and then divide that by 8 to get a limit of enlargement.

Making it simpler and rougher, can we divide 1500/8, namely 185 by the f/stop and get the limit of enlargement ?

Reversing it, can we divide 185 by the degree of enlargement that we want, and get maximum f/stop ? For example, if we want to enlarge by a maximum of 4x, can we use an f/stop of 185/4 or f/45 ?

Since these are theoretical limits for perfect equipment and technique, could we simply cut the numbers by roughly half ? For example, divide 100 by max enlargement to get max f/stop ? If we plan to enlarge no more than 4x, then we can get away with f/25... etc.

Is this reasonable ?

[Darin Boville]

I think we've made a jump from the idea of "diffraction limit"--which can be defined and measured--to maximum print size which is subject to many more variables and is much more subjective.

For example, the presence of sharp grain will usually allow you to make a bigger print than you otherwise would.

The subject matter may have a pronounced effect as well. A subject with plentiful fine detail might resist enlargement beyond a point. Other subjects without fine detail, or which are intentionally blurry, might allow a much greater degree of enlargement.

The substrate upon which you are printing will matter. Smoother surfaces show the fuzziness more readily, textured surfaces not so much.

And some photographs just look better smaller than a diffraction limit calculation would allow.

Diffraction limit is certainly an issue but sometimes (usually?) it can be quite a minor one in determining print size.

--Darin

[Bill Burk]

Have you seen the graph from Way Beyond Monochrome by Ralph Lambrecht? It's a great visualization of the limits of diffraction, in a way that you can comprehend in a glance and probably settle the matter in your mind once and for all...

Basically, with 35mm the diffraction limit is somewhere around f/11-16 while with 4x5 it's somewhere between f/32-45

[Emmanuel BIGLER]

A 50mm lens at f/8 has the same sized aperture as a 100mm lens at f/16, or a 200mm lens at f/32. All things being equal would those 3 lenses exhibit the same amount of diffraction ?

Hello Ken

I found in the archives this discussion where you can probably find some useful elements.

http://www.largeformatphotography.info/forum/showthread.php?103382-Stopping-down-and-quot-Diffraction-quot

A 50mm lens at f/8 has the same sized aperture as a 100mm lens at f/16, or a 200mm lens at f/32. All things being equal would those 3 lenses exhibit the same amount of diffraction ?

This a very good question regarding how diffraction effects scale with physical aperture sizes and focal length, and the answer can be

1/ no if you look at the diffraction spot size or diffraction cut-off spatial frequency in the image plane;

2/ definitely yes if you look at the angular resolution in object space.


point 1/ can be summarized as follows

- consider a thin positive lens element of focal length f with an iris of diameter a located at is center, hence its f-number is N=f/a, and make a dream: this lens element is aberration-free! Of course this does not exist in the real world but does exist in optical design softwares, and this purely theoretical element is very useful to understand about 95% af all our photographic and theoretical questions regarding depth of field, illumination in the image plane, bellows factors, and of course: diffraction effects.

- consider, as a starting point, that you look at the center of the field, on the optical axis and assume that N is not too small, not f/1 or f/2 but f/8 or more like in real life of LF photography. This hypothesis of N not being too small greatly simplifies the expressions for the diffraction limits. And assume, this is even more unrealistic for photographers (except those who insists on take pictures only with sodium street lights) that the wavelength of light is unique, equal to lambda.

Then the absolute, non negociable, non digitally post-processable diffraction limit can expressed either in terms of diffraction spot size in the image plane, or diffraction cut-off spatial frequency:

diffraction spot-size ~= 1.2 N . lambda
diffraction cut-off spatial frequency = 1 / (N . lambda) (no fuzzy 1.2 factor here)

Now, from those exceedingly simple formulae (** note#1), we get the answer to point 1/, the relative aperture size N=f/a directly determines the diffraction limit in terms of spot size or cut-off frequency in the image plane. If we are operating not in the infinity-focus position but at a certain magnification ratio M, simply replace N in the above formulae by Neff=N(1+M).

And regarding problem /2, this is a typical problem for surveillance cameras, where you have to take high-resolution pictures of objects located at a fixed distance D; e.g. 10 meters for one of those machines that flourish along French roads and that try to automatically decipher your licence plate if you are caught overspeeding; or 100 km, if you are operating a satellite-based surveillance camera.

In problem /2, you want to been able to get the smallest possible resolution at a fixed object distance. Starting from the diffraction spot size in the image plane, which is located in the focal plane for those far-distant objects, you can convert the image diffraction limit into an object diffraction limit simply by muliplying by a basic geometrical magnification factor D/f.
Hence the diffraction limit on the object itself is simply lambda . D / a; in terms of angular resolution, this is simply lambda / a.
And in this case, the 50mm lens at f/8, the 100mm lens at f/16, or a 200mm lens at f/32 yield exactly the same (angular) diffraction limit (in object space)!


** note#1: the Holy "Marxist" legend says that once, somebody tried, in vain, to explain something to Groucho; "Eh, a 8-year old boy could understand this!"
And Groucho answered: "So, please, bring here immediately a 8-year old boy and ask him the question".

[Struan Gray]

Executive summary: the size of the hole determines the angular spread of the light. The focal length determines the distance to the film, and hence how much the light can spread sideways.

A 50 mm f8 and a 100 mm f16 have the same size hole, so the light has the same angular spread. But when focussed on infinity the 100 mm lens is twice as far from the film, so diffraction is twice as bad.

A 50 mm lens focussed at 1:1 (100 mm from the film) has the same sized hole *and* the same distance to the film. The diffraction is also the same, but in photography we prefer to say that the effective aperture has changed to f16 rather than deal explicitly with image-side distances and aperture sizes.


There are finesses to do with the nature of the glass in the lens too. The glass up front magnifies or reduces the apparent size of the aperture, which affects how much light is let in and so influences exposure. The glass at the back changes the angles of the light, shifting the apparent position of the aperture, and so the distance the light has to travel, and so the diffraction. Again, in photography, it is preferred to keep a constant f-number and express these changes through factors like the pupillary magnification - but if you wish you can arrive at the same answer using holes and distances.

[ic-racer]

Is this reasonable ?


Just like the circles of confusion that determine depth of field, the effect of large Airy disks in the viewed image is related to the observer's acuity, magnification and viewing distance.

You can set your 'limit' if you take that all into account.

[BetterSense]

"Amount of Diffraction" is an ambiguous term.

In the example above the three lenses will NOT have the same size Airy disk on film (that only happens if they are all at f8) However, in the example above, the relationship of Airy disk size to image size will be the same.

This is correct understanding.

Others have pointed out that when considering resolution on film, it is the f-number that matters; their analyses are correct but vacuous. I will never understand the compulsion to consider resolution on film, when the only thing that matters in pictorial photography is the final print. When comparing equal prints (that is to say, equal final magnification), equal size aperture holes (entrance pupils) give the same amount of diffraction blur. The same is true of depth-of-field.

F-number is really a rubbish unit for photography once you introduce multiple camera formats. F-numbers simplifies exposure calculations at the expense of obfuscating fundamental image formation factors like depth of field and diffraction.

[Jim Jones]

I think we've made a jump from the idea of "diffraction limit"--which can be defined and measured--to maximum print size which is subject to many more variables and is much more subjective.

For example, the presence of sharp grain will usually allow you to make a bigger print than you otherwise would.

The subject matter may have a pronounced effect as well. A subject with plentiful fine detail might resist enlargement beyond a point. Other subjects without fine detail, or which are intentionally blurry, might allow a much greater degree of enlargement.

The substrate upon which you are printing will matter. Smoother surfaces show the fuzziness more readily, textured surfaces not so much.

And some photographs just look better smaller than a diffraction limit calculation would allow.

Diffraction limit is certainly an issue but sometimes (usually?) it can be quite a minor one in determining print size.

--Darin

Yes, indeed. Some of Edward Weston's macro photographs were taken with a lens modified for very small apertures. Given the subjects and his technique, diffraction was certainly not a conspicuous problem.

[Bill Burk]

In Post #5 at APUG, Ralph Lambrecht shared the graph which indicates several dimensions of information related to diffraction limit... Formats, f/stops, circle of confusion, actual resolution and wavelength.

I think this is one of the most effective graphic representations of information I have ever seen! Also, if resolution is your quality aim, the graph reveals why you want to shoot MF or LF, the only formats where you have resolution headroom...

http://www.apug.org/forums/forum48/88939-puzzled-about-diffraction.html