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I've seen the term used, but what is a "diffraction limit", when should I worry about it, and what undesirable effects are a result of it ?

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This thread might also be of interest: photo.stackexchange.com/q/6605/1356 –  whuber Feb 5 '11 at 21:46
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There were several good answers here - wish I could have accepted more than one. –  rfusca Feb 7 '11 at 18:51

7 Answers 7

up vote 43 down vote accepted

There have been some very good answers, however there are a couple details that have not been mentioned. First, diffraction always happens, at every aperture, as light bends around the edges of the diaphragm and creates an "Airy Disk". The size of the airy disk, and the proportion of the disk that comprises the outer rings, and the amplitude of each wave in the outer rings, increases as the aperture is stopped down (the physical aperture gets smaller.) When you approach photography in the way Whuber mentioned in his answer:

Think of a scene as comprised of many small discrete points of light.

You realize that every one of those points of light, when focused by your lens, is generating its own airy disk on the imaging medium.

Regarding Image Medium

It should also be clearly noted that the diffraction limit is not actually a limitation of a lens. As noted above, lenses are always creating a diffraction pattern, only the degree and extent of that pattern changes as the lens is stopped down. The "limit" of diffraction is a function of the imaging medium. A sensor with smaller photosites, or film with smaller grain, will have a lower limit of diffraction than those with larger photosites/grains. This is due to the fact that a smaller photosite covers less of the airy disk area than a larger photosite. When the airy disk grows in size and intensity as a lens is stopped down, the airy disk affects neighboring photosites.

The diffraction limit is the point where airy disks grow large enough that they begin to affect more than a single photosite. Another way to look at it is when the airy disks from two point light sources resolvable by the sensor begin to merge. At a wide aperture, two point light sources imaged by a sensor may only affect single neighboring photosites. When the aperture is stopped down, the airy disk generated by each point light source grows, to the point where the outer rings of each airy disk begin to merge. This is the point where a sensor is "diffraction limited", since individual point light sources no longer resolve to a single photosite...they are merging and covering more than one photosite. The point at which the center of each airy disk merges is the limit of resolution, and you will no longer be able to resolve any finer detail regardless of the aperture used. This is the diffraction cutoff frequency.

Diffraction Limitations due to Airk Disk merger

It should be noted that it is possible for a lens to resolve a smaller spot the pixels in an imaging medium. This is the case when airy disks focused by a lens cover only a fraction of a photosite. In this case, even if two highly resolved point light sources generate airy disks that merge over a single photosite, the end result will be the same...the sensor will only detect a single point light regardless of the aperture. The "diffraction limit" of such a sensor would be higher (say f/16) than for a sensor that is able to distinctly resolve both point light sources (which might be diffraction limited at f/8). It is also possible, and likely that point light sources will NOT be perfectly focused onto the center of a photosite. It is entirely plausible for an airy disk to be focused at the border between two photosites, or the junction of four photosites. In a black and white sensor or foveon sensor (stacked color sensels), that would only cause softening. In a color bayer sensor, where a square junction of 4 photosites will be capturing an alternating pattern of GRGB colors, as airy disk can affect the final color rendered by those four photosites as well as cause softening or improper resolution.

My Canon 450D, a 12.2mp APS-C sensor, has a diffraction limit of f/8.4. In contrast, the Canon 5D Mark II, a 21.1mp Full Frame sensor, has a diffraction limit of f/10.3. The larger sensor, despite having nearly twice as many megapixels, can go an extra stop before it encounters its diffraction limit. This is because the physical size of the photosites on the 5D II are larger than those on the 450D. (A good example of one of the numerous benefits of larger sensors.)

Wrenches in the mix

You may often come across tables on the internet that specify a specific diffraction limited aperture for specific formats. I often see f/16 used for APS-C sensors, and f/22 for Full Frame. In the digital world, these numbers are generally useless. The diffraction limiting aperture (DLA) is ultimately a function of the relation of the size of a focused point of light (including the airy disk pattern) to the size of a single light sensing element on a sensor. For any given sensor size, APS-C or Full Frame, the diffraction limit will change depending on the size of the photosites. An example of this can be seen with Canon's EOS Rebel line of cameras over the years:

Camera   |   DLA
--------------------
350D     |   f/10.4
400D     |   f/9.3
450D     |   f/8.4
500D     |   f/7.6
550D     |   f/6.8

The story should be similar for film grain size. Films with finer grain would ultimately be more susceptible to diffraction softening at lower apertures than films with larger grains.

The Diffraction Cutoff Frequency

Diffraction is often touted as an image killer, and people talk about the "diffraction limit" as the point at which you can no longer resolve an image "usefully". On the contrary, the diffraction limit is only the point where diffraction starts to affect an image for the particular image medium you are using. The diffraction cutoff frequency is the point at which additional sharpness is impossible for a given aperture, and this is indeed a function of the lens and physical aperture.

The formula for diffraction cutoff frequency for (perfect) optical systems is as follows:

fc = 1 / (λ * f#) cycles/mm

This states that the reciprocal of the wavelength of the light being focused multiplied by the f-number of the lens is the number of cycles per millimeter that can be resolved. The diffraction cutoff frequency is generally the point where resolution reaches the wavelength of the frequencies of light itself. For visible light, λ between 380-750nm, or 0.38-0.75 microns. Until the cutoff frequency has been met for a given aperture, more resolution can be achieved.

Visual Examples

Whubers sequence of images above is a decent example of the effect of diffraction, as well as the effect of optical aberrations when the lens is wide open. I think it suffers a bit from some focus shift due to spherical aberration, so I have created an animated GIF that demonstrates the effects of changing the aperture of a Canon 50mm f/1.4 lens down from its widest aperture to its narrowest, in full stops.

Diffraction Sequence

(Note: The image is large, 3.8meg, so let it fully download to see the comparison of sharpness at each stop.) The image exhibits marked optical aberration when shot wide open, particularly Chromatic Aberration and some Spherical Aberration (there may be some slight purple fringing...I tried to get focus dead on.) Stopped down to f/2, CA is lessened considerably. From f/2.8 through f/8, sharpness is at its prime, with f/8 being ideal. At f/11, sharpness drops ever so slightly, due to diffraction. At f/16 and particularly f/22, diffraction visibly affects image sharpness. Note that even with diffraction blurring, f/22 is still considerably sharper than f/1.4 or f/2.

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@whuber: My apologies. I finally found my large format references, however it appears that their assertations were based solely on "contact prints" for 4x5 and 8x10. With contact prints, the CoC is FAR larger than is necessary for 35mm or APS-C size formats. With 4x5 film, the "acceptable" CoC was listed as 0.2mm, while for FF digital it is about 0.02mm, a difference of a factor of ten. I'll have to correct my answer, since contact prints are only one form of printing, and any enlargement will change the CoC, reducing the acceptable aperture. –  jrista Feb 7 '11 at 17:57
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This, especially the GIF animation, perfectly answers the question and points out why you have to care about it. –  You Feb 8 '11 at 9:47
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Wow, the 1.4 results are terrible... What's the point of buying a fixed 50mm with a large aperture of 1.4 if you can't use it (due to its lack of sharpness)?! –  dialex Aug 12 '11 at 18:49
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@DiAlex: You won't always get that kind of CA. In this particular case, the CA is so apparent due to the closeup nature of the shot...which is heightened due to the magnification. At a more normal shooting distance, the effect of CA would appear to be considerably less, even though the white text is blurring just as much. The shot above, if photographed at say 10 feet, would result in the white text appearing a bit soft at f/1.4, but since the text takes up so much less area of the photo than it would in a close-up shot like this, it really wouldn't matter. –  jrista Aug 12 '11 at 21:15
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In the case of portraits, that amount of softening is often a desirable attribute for a lens. At a decent distance for photographing a portrait, the CA caused by such an extremely wide aperture will blur out blemishes and create a slightly glowing halo around strands of hair, possibly around the edges of your subject. In such a case, even though the shot IS less sharp than it might be at f/22, it is ultimately a better shot. –  jrista Aug 12 '11 at 21:17

Think of a scene as comprised of many small discrete points of light. A lens is supposed to convert each point to another point at an appropriate place on the image. Diffraction causes every point to spread in a circular wave-like pattern, the Airy disk. The diameter of the disk is directly proportional to the f-number: that's the "diffraction limit."

As the f-number is increased from its minimum (a wide open lens), the light falling at a point on the image will come from a narrower region of the lens. That tends to make the image sharper. As the f-number is increased, the Airy disks get larger. At some point the two effects balance to make the sharpest image. This point is typically in the f/5.6 to f/8 range on SLR cameras. With smaller f-numbers, overall properties of the lens (its aberrations) take over to make a softer image. With larger f-numbers, the softness is dominated by the diffraction effect.

You can measure this reasonably well with your own lenses and no special equipment. Mount the camera on a tripod in front of a sharp, detailed, well-lit flat target having lots of contrast. (I used a page from a magazine; it worked fine.) Use your best settings: lowest ISO, proper exposure, mirror locked up, medium focal length for a zoom lens (or vary the focal length, too), middle distance, perfectly in focus, RAW format. Take a series of photos in which you vary only the f/stop and the exposure time (to keep the exposure constant). Look at the sequence of pictures at 100% on a good monitor: you will see where your camera's "sweet spot" is and you will see the effects of using wider or narrower apertures.

The following sequence is taken from a series for the Canon 85 mm f/1.8 lens, which is a pretty good one. From top to bottom are 100% crops (converted to high-quality JPEG for Web display) at f/1.8, 2.8, 5.6, 11, and 22. You can see the increasing effects of diffraction at f/11 and f/22 in the bottom two images. Note that for this particular lens used with this particular camera (EOS T2i, an APS-C sensor), the diffraction softness at high f-numbers doesn't approach the softness seen with the lens wide open. Having comparable information for your own lenses, which can be obtained in a few minutes, can be valuable for choosing exposure parameters in important photos.

f/1.8 f/1.8

f/2.8 f/2.8

f/5.6 f/5.6

f/11 f/11

f/22 f/22

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Good examples ! –  rfusca Feb 5 '11 at 22:00
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I think your f/1.8 and f/2.8 images are suffering a bit from focus shift. The blurriness of those images wide open does not appear to be purely due to optical aberration, which usually exhibit as slight softness and some CA. The CA is apparent, but particularly in the first image, it also seems clearly apparent that the image is out of focus. The f/2.8 also looks clearly out of focus, just to a lesser degree. –  jrista Feb 6 '11 at 5:31
    
yeah longitudinal CA (the purple and green fringes to the text) indicates the focus may be off in the first two images. Plus I would certainly hope the 85 f/1.8 is sharper than that at f/2.8! If you do this again I would focus stopped down with live view. –  Matt Grum Feb 6 '11 at 15:02
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I've thrown together an animated GIF sequence that demonstrates the effect of diffraction in an answer below. I used a Canon 450D, so the DLA is f/8.4, which means f/11 and below start to exhibit diffraction softening. Its interesting that even with the diffraction softening of f/22, it is still sharper than f/2 or wider. –  jrista Feb 7 '11 at 1:47
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@jrista Thank you. Although the series of images I posted here is likely marred by the focusing issue, I have created comparable series every time I bought a new lens and consistently have made the same observation. This is especially useful information for landscape and other wide DoF photographers, who might have been avoiding the more extreme f/stops. Another intriguing aspect of diffraction is that, due to its physical regularity (the spreading on the image depends only on the color and the f/stop) it should be easy to deconvolve (sharpen away) in post-processing. –  whuber Feb 7 '11 at 13:40

Diffraction happens. It's a fact of life. When lenses are used wide open, other lens abberations are far too prominent for you to notice a minor sharpness loss due to diffraction. Stop down a little bit, and those abberations are minimised -- the lens seems to just get better and better. Diffraction is there, but you still don't really notice it because light that is not passing near the edges significantly outvotes the light that is passing getting a little too close to the aperture blades.

At some point while you are stopping the lens down, the gains you make by eliminating the optical differences between the center and outer parts of the lens elements starts to go away -- there is no longer enough crisply focused light to drown out the out-of-focus image caused by light bending around the edges of the optical path (diffraction). The lens isn't going to get any better when you stop down anymore -- too much light is being diffracted compared to the light that's getting through the middle. From this point on, stopping down will make the image softer.

The point at which the lens is stopped down as far as it can go without increasing softness is the diffraction limit. On some lenses, that's as far as you can stop down -- Nikon, for example, has traditionally kept a relatively wide minimum aperture (f/16) on many of their designs. On other lenses (macros, especially) you might still have a couple of stops or more available to you; depth of field considerations may be more important than absolute sharpness in some applications.

All of photography is a compromise. There may be times when you want to stop down farther than the optimum, but it helps to be aware of the compromises you're making. Stopping down is an easy answer to DOF, but if you're hooked on landscapes and taking them all at f/22 or f/32, it may be time to take a look at a tilt/shift lens.

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+1 - nice answer. –  ysap Feb 5 '11 at 21:12
    
How does a tilt shift differ in this respect? –  Winston Smith Feb 7 '11 at 22:59
    
It doesn't, at least in terms of the amount of diffraction for a given aperture. What does change is the way you achieve depth of field in the image. By using tilt, you change the plane of focus, so in a lot of cases you can get more of the scene in focus with a wider aperture -- you can put both the foreground grass/rocks and the mid-point of distant trees/mountains on or near the plane of sharp focus, so the aperture setting has less to make up for. Tilt is of no real use, though, if you want both foreground and background trees in focus; for that you need a small aperture. –  user2719 Feb 7 '11 at 23:44

While the answers already here describe diffraction well. Diffraction limit is most often used to describe the point at which stopping down your lens does not give you more details in relation to the pixel-size of your camera's sensor.

When you have reached the diffraction limit of your camera, ANY lens stopped beyond that aperture will give you softer results. It is directly related to the size of individual pixels, not the sensor size.

On modern DSLRs, the diffraction limit will be hit between F/11 and F/16. On cameras with small sensors, it may be F/8 or even less. You'll notice that most tiny cameras do not use apertures smaller than F/8 for this very reason. Some even use a fixed aperture (F/3.5 or so) and simulate less light coming in by slipping a ND filter instead of stopping-down. Unfortunately, they actually put the simulated F-stop in the EXIF, so you need to know the camera to realize it uses an ND filter rather than a normal aperture.

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+1 Excellent points, especially noting that the diffraction limit is independent of focal length. To reiterate your first point, its relationship to pixel size is due to the fact that pixels much larger than the Airy disk cannot show what's going on as clearly. However, the softness due to diffraction is there regardless and is independent of pixel size. –  whuber Feb 5 '11 at 22:47
    
Actually, diffraction is very much dependent on focal length. Diffraction depends on the wavelength of a photon and its path probability relative to an edge. The area of total transmission is proportional to the square of the radius of the aperture; the area of diffractive influence is (almost) directly proportional to the radius. It's the high proportion of diffraction and the close spacing of sensels, that makes small sensor/short focal length lenses crap out at higher fractional apertures than larger/longer combinations -- the hole is smaller, and the diffracted light hits more sensels. –  user2719 Feb 6 '11 at 4:03
    
@Stan Could you then please explain why the formula for the Airy Disk diameter on Wikipedia is independent of focal length? (en.wikipedia.org/wiki/Diffraction#Diffraction-limited_imaging ) –  whuber Feb 7 '11 at 13:35
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The confusion stems from the fact that the numbers we use to represent aperture depend on focal length (F/4 = 100mm focal-length / 25mm aperture diameter). In fact, all you really need is the aperture diameter and the pixel size to define the diffraction limit. –  Itai Feb 7 '11 at 14:25
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(Continuation - 4) In general, though, prime lenses of longer focal lengths will have larger physical apertures at any given f-stop than lenses of shorter focal lengths. That's why you can get away with f/64 at 300mm on a view camera (everything is sharp and contrasty) while the same scene shot at f/32 at 50mm looks like hell on a 35mm-format camera (everything's soft and washed out) even when both are enlarged to the same degree -- the physical aperture is at least three times as large, making it three times less probable that a given photon will be redirected. –  user2719 Feb 8 '11 at 0:48

This page at the Cambridge In Color site has a detailed technical explanation of the diffraction limit. It's also got an on-line calculator for checking whether a particular combination of aperture, camera, print size, and viewing distance is diffraction-limited or not.

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Short Answer…

The Diffraction Limit is the smallest spot a given lens system can create/resolve/focus.

Arm-waving: Lenses can focus light to a small spot but not a point. The spot size can vary with the wavelength, with short wavelengths forming smaller spot sizes than longer ones. When a very good, aberration-free (diffraction-limited) lens is used, collimated light will produce an airy disk as a spot at the focus. An airy disk is still the smallest spot that can be produced with that lens at that aperture with that wavelength (using collimated light). Larger apertures produce smaller spot sizes with tighter focus and reduced depth of focus than smaller apertures.

Note that you cannot produce an airy disk with a pictorial scene. Collimated light does not form an image.

Whoa, Stop right there: Larger numerical apertures produce smaller spots makes sense if you consider that in the formula, the aperture is used as a reciprocal value. Dispersion also plays a role here, too.

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"Diffraction limit" is used in x-ray diffraction- a common experiment in material science. The Bragg equation (sin theta = wavelength/2 x crystal spacing) determines the diffraction limit (angle theta) for a given wavelength. Thus the wavelength used will limit the d-value (spacing) which can be measured.

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I don't think this answer will help a non-scientist. –  eWolf Feb 6 '11 at 3:38
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That definition applies to more than x-rays; it's also used in radio/radar for antenna designs, shielding and so forth. It's a perfect example of collision between two realms with their own jargon. In photography, it refers to diffraction-limited performance, the conditions where performance can no longer be improved by stopping down due to the influence of diffraction. It's influenced by the unrestricted lens performance, actual aperture size at a given setting, the thickness of the iris relative to the wavelength and the available acuity of the recording medium. –  user2719 Feb 6 '11 at 10:49

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