Does sensor size impact the diffraction limit of a lens?

Question

My understanding of diffraction, is that with a small aperture the 'airy disk' (which I understand is the pattern light from a given direction relative to the lens will form on passing through the lens), becomes larger, and thus overlapping of these airy disks occurs. The lens diffraction limit is when two or more of these airy disks overlap on a single photo-site on a sensor or cross over onto two photo-sites, causing reduced sharpness. Therefore, if the sensor is larger, and the photo-sites for the same resolution can also be larger, does this influence the diffraction limit of a lens? if so, how?

Answer 1

Does sensor size impact the diffraction limit of a lens?

No.

Therefore, if the sensor is larger, and the photo-sites for the same resolution can also be larger, does this influence the diffraction limit of a lens?

Not really. What it does affect is the sensor's (not the lens') diffraction limit.

If so, how?

If the size of the Airy disc caused by diffraction is smaller than the ability of the sensor (or film grain) to resolve it, then the image will not be diffraction limited. Only when the size of the Airy disc is large enough to be resolved by the sensor will the image be diffraction limited. The resolution limit of the sensor is determined by the pixel pitch: that is, the distance of the center of each pixel well from adjacent pixel wells. The aperture at which the sensor can resolve the Airy disc is what we refer to as that sensor's Diffraction Limited Aperture (DLA).

Diffraction Limited Aperture (DLA) is only applicable at 100% viewing size. This is because DLA assumes a Circle of Confusion (CoC) equal to the pixel pitch of a particular sensor. The effects of diffraction at the DLA are only observable if the resulting image is magnified enough that the viewer can discretely resolve individual pixels. For an 18MP image viewed on a 23" HD (1920x1080) monitor that is the equivalent magnification of a 54"x36" print!

Take for example the 20.2MP full frame Canon 6D and compare it to the 20.2MP APS-C 70D. Both have the same resolution: 5472x3648.

• The 6D has a pixel pitch of 6.54µm and DLA of f/10.5
• The 70D has a pixel pitch of 4.1µm and DLA of f/6.6

The lower DLA of the 70D is due to its smaller sensor/pixel size that requires higher magnification to display images from the 70D at the same size as an image from the larger sensored 6D.

Diffraction at the DLA is barely visible when viewed at 100% (1 pixel = 1 pixel) on a display. As sensor pixel density increases, each pixel gets smaller and the DLA gets wider. DLA does not mean that narrower apertures should not be used. It is where image sharpness begins to be compromised for increased DOF. Higher resolution sensors generally continue to deliver more detail well beyond the DLA than lower resolution sensors until the "Diffraction Cutoff Frequency" is reached (a much narrower aperture). The progression from sharp to soft is not an abrupt one. For more about diffraction, read this question. Current Canon DLSRs may have a DLA as low as f/6.6 (70D, 7DII) and as high as f/11 (EOS 1D X). Most other manufacturers' DSLR offerings fall somewhere along the same lines.

Ultimately you must consider all of the factors involved to decide what is the best aperture to use for a particular photograph. Many times, it will be a compromise between several factors such as more depth of field (narrow aperture) and usable shutter speed and ISO (wide aperture).

Answer 2

No. Diffraction depends on the aperture and pixel size. The sensor size itself has no influence in the equation. A larger sensor as you say can have larger pixels but it can also have smaller ones. It really makes no difference when it comes to determining the diffraction limit.

Answer 3

The diffraction limit is the resolution where the Airy disks significantly overlap, completely independent of whatever they're falling on.

But if that diffraction limit is at a higher resolution than the recording medium? Then for that aperture+lens+sensor combination you're sensor-limited, not diffraction limited. So sure, pixel resolution matters... sort of.

(Yeah, yeah, I'm acting as if resolution limits are hard limits, which is false. But explaining it accurately in terms of modulation transfer function takes more brain cells than I have to spare lately. Hard limits are a good enough approximation.)

Answer 4

I would say "yes and no". :) Favoring No.

The smaller sensor will normally use a shorter lens, for which say f/4 is a smaller diameter than f/4 on a longer lens. First glance would see that as a Yes.

But Wikipedia at http://en.wikipedia.org/wiki/Airy_disk#Cameras explains that in the Airy formula (for discernible difference of two points due to Airy disks, i.e., the resolvable resolution), that f/d is simply just f/number. So resolution due to diffraction actually instead depends on f/stop number, for which f/4 is f/4, on any sensor size.

Diameter is the factor causing it, but focal length is a magnifying factor of seeing it.

However, in photography, it does seem obvious in practice (IMO) that f/40 is little problem on a longer lens (say 100mm), and not very effective on a short lens (say 15mm).

Answer 5

Diffraction is a feature of the lens. The sensor cannot alter properties of the lens!

There is a lot of garbage "information" on the web that is misleading to photographers that don't have a background in maths/physics/optics/sampling-theory.

For correct and accurate information on matters like these I recommend the web site "Cambridge in Colour": http://www.cambridgeincolour.com/

What happens when you use a smaller sensor is that a smaller part of the image created by the lens is captured. The image is then enlarged more for viewing so any loss of detail or sharpness caused by diffraction is more visible. The behaviour of the lens itself does not change, nor is there any change in the aperture at which diffraction becomes the limiting factor the image quality.

To put that more usefully, the optimum aperture of the lens (i.e. the point between limits set by aberrations and limits set by diffraction) is unchanged.

Another pointless worry is "do the latest sensors out-resolve my lenses?"

We WANT our sensors to out-resolve the lenses. That is over-sampling which more accurately captures the resolution of which the lens is capable.

p.s. Resolution is also a property of the lens. It is not a number of pixels. Not even "perceptual megapixels", whatever they might be. The more megapixels on the sensor, the more nearly the full resolution delivered by the lens can be captured.

Answer 6

When we talk about the resolving power of lenses, we are talking about the Rayleigh Criterion researched and published by John William Strutt, 3rd Baron Rayleigh, England, 1842–1919. Astronomer Royal, Nobel Prize for Physics 1904. The Rayleigh Criterion remains valid today, to my knowledge, no one has made a lens that exceeds this benchmark.

The Criterion:

The resolving power of a lens decreases with aperture, as this increases the Airy disc diameter. The resolution also decreased with increasing wavelength; it is almost twice as great in extreme blue as in extreme red. For wavelength 589 millimicrons (middle of visible spectrum) – - Resolving power in lines per millimeter = 1392 ÷ f-number

f/number	line-pairs per mm (lpmm)
f/1	1392
f/1.4	994
f/2	696
f/2.8	497
f/4	348
f/5.6	249
f/8	174
f/11	127
f/16	87
f/22	63
f/32	44

Note: The resolving power of the camera lens set to f/8 is higher than what is pictorially useful.