Diffraction Limit

Started Aug 28, 2013 | Discussions thread
Great Bustard
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Re: The plain truth can indeed be phrased in very misleading ways...
In reply to Paul De Bra, Aug 28, 2013

Paul De Bra wrote:

LTZ470 wrote:

From a very credible source:

"Diffraction thus sets a fundamental resolution limit that is independent of the number of megapixels, or the size of the film format. It depends only on the f-number of your lens, and on the wavelength of light being imaged. "

This statement is absolutely factually correct. It is also a useless statement for anyone trying to decide which higher f-numbers to avoid to not suffer from softening due to diffraction.

Diffraction indeed defines how light is "scattered" over an area of the sensor, depending on the f-number. The size of the "airy disk" is independent of the number of megapixels or the size of the film format. But, now let's see whether that has influence on the image we can capture:

Suppose the diameter of the airy disk is X. If the size of our sensor is of the same order of magnitude as X the total image captured will have absolutely no detail whatsoever, even if that tiny X-sized sensor has 100MP. If the size of our sensor is in the order of 1000X we can resolve in the order of 1000 lines and get a fairly detailed image. The size of the airy disk is the same but on a larger sensor the *relative* size of that airy disk to the total size of the image is way smaller.

So what matters is the size of the airy disk that corresponds to a certain f-stop versus the size of the pixels relative to that airy disk.

Not the size of the pixels, but the size of the Airy Disk as a proportion of the sensor size. Smaller pixels, for a given sensor size, always resolve more detail at any given f-ratio.

When you look at pixel-level detail of an image (which is not overall sharpness) what counts is the size of the pixels. Diffraction at the pixel level at say f/16 on a 12MP 4/3 sensor will be roughly equivalent to diffraction at f/16 on a 48MP 35mm full frame sensor, when you look at the image from the same distance relative to the pixel size. So if you look at a 30x20 print from that 12MP sensor from 2 feet you should look at a 60x40 print form the 48MP sensor from the same 2 feet.

Diffraction does play a different role on smaller versus larger sensors because the way I described above is not the way we look at pictures. We blow up the pictures captured by small sensors and/or shrink the pictures captured by large sensors so that the printed images are of the same size. When you do that we are effectively changing the effect the size of the airy disk has. We are blowing up the airy disk seen by the small sensor and/or shrink the airy disk seen by the larger sensor. Which means that the diffraction caused by a certain f-stop becomes much more visible in the blown-up image from the small sensor and less visible in the shrunk image from the larger sensor.

So while the "fundamental" statement is correct the reality is that smaller sensors suffer from diffraction at larger apertures than large sensors because we change the magnification of the image captured by the surface of the sensor.

Let's see if this doesn't sum it up:

http://www.josephjamesphotography.com/equivalence/index.htm#diffraction

In addition to DOF and sharpness, the is also intimately connected to diffraction. Diffraction softening is the result of the wave nature of light representing point sources as disks (known as Airy Disks), and is most definitely not, as is misunderstood by many, an effect of light "bouncing off" the aperture blades. The diameter of the Airy Disk is a function of both the f-ratio and the wavelength of light: d ~ 2.44·λ·f, where d is the diameter of the Airy Disk, λ is the wavelength of the light, and f is the f-ratio. Larger f-ratios (deeper DOFs) result in larger disks, as do longer wavelengths of light (towards the red end of the visible spectrum) so not all colors will suffer from diffraction softening equally. The wavelengths of light in the visible spectrum differ by approximately a factor of two, so that means, for example, that red light will suffer around twice the amount of diffraction softening as blue light.

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While the diameter of the Airy Disk is the same for the same color and f-ratio, regardless of the sensor size, the effect of the diffraction softening is not the same across formats. The reason is that the proportion of the sensor that is covered by the Airy Disk is not the same since the sensors are not the same size. For example, while the Airy Disk diameter at the same f-ratio, the effect of the diffraction softening on 35mm FF is half as much as on 4/3, if the final images are displayed with the same diagonal dimension, .

Let's work an example using green light (λ = 530 nm = 0.00053mm). The diameter of the Airy Disk at f/8 is 2.44·0.00053mm·8 = 0.0103mm, and the diameter of the Airy Disk at f/4 is half as much -- 0.0052mm. For FF, the diameter of the Airy Disk represents 0.0103mm / 43.3mm = 0.024% of the sensor diagonal at f/8 and 0.005mm / 21.6mm = 0.012% of the diagonal at f/4. For 4/3, the diameter of the Airy Disk represents 0.0103mm / 21.6mm = 0.048% at f/8 and 0.005mm / 21.6mm = 0.024% at f/4.

Thus, at the same f-ratio, we can see that the diameter of the Airy Disk represents half the proportion on FF as 4/3, but at the same DOF, the diameter of the Airy Disk represents the same proportion of the sensor. In other words, all systems will suffer the same amount of diffraction softening at the same DOF and display dimensions. However, the system that began with more resolution will always retain more resolution, but that resolution will asymptotically vanish as the DOF deepens. In absolute terms, the earliest we will notice the effects of diffraction softening is when the diameter of the Airy Disk exceeds that of a pixel (two pixels for a Bayer CFA), but, depending on how large the photo is displayed, we may not notice until the diameter of the Airy Disk is much larger.

In addition, it's important to note that, for two sensors of a given size, the sensor with a greater pixel density does not suffer more from diffraction softening due to the smaller pixels. We will simply notice the effects of diffraction softening earlier (at wider apertures) since we had more resolution to begin with as a result of the smaller pixels (presuming, of course, that we display the photo large enough that we can resolve individual pixels). Of course, the effects of diffraction softening are also offset by lessening lens aberrations (to a point) as well as more of the photo coming within the DOF as we stop down.

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