The ‘Nitty Gritty’ of Image Sharpness

I have shown different ways of making images look as sharp as possible, both on the screen and more importantly, in print. All this has assumed that the image is reasonably sharp in the first place – as sharp as the lens can make it.

 

In film days the resolving power of film was often less than that of the lens itself, any aberrations in lens design would be too fine for the film to record so the film was generally considered the limiting factor – at least with high quality lenses from the major manufacturers. It was also known that even the best lenses were often slightly less sharp at their maximum aperture that at, say, F8, so to get the most out of a lens and film combination you might have shot on a tripod, at F8 or F11 and used a fine grained film.

With the advent of cameras with sensors up past 12Mp the resolving power of the capture device has exceeded even the best films, the Canon 1Ds Mk3, at 21Mp is the current king of the hill with respect to image size but the newer camera like the Nikon D2X and the Canon EOS450D actually pack more photosites into each millimetre of sensor – 175 per mm as opposed to 155/mm for the bigger Canon. Let’s put this into practical perspective; designed for film, the standard PIMO/ISO resolution test charts had arrays of lines which became closer and closer together and the point at which the lines could no longer be recorded as distinct was called the ‘extinction limit’ for the film. Now, any camera over about 12Mp needs to be placed at double the camera-to-chart distance – otherwise the camera can simply resolve the whole chart, right up to its limits.

Having so much resolution in a 35mm-style camera is wonderful, the best cameras now match 6×7, or even 6×9, format for sheer quality and are considerably lighter and easier to handle than the older film cameras. Unfortunately there is no such thing as a free lunch and this high resolution has come up against not only lens design limits but also the very physics of light itself.

When light passes through an aperture some small part of it will be bent slightly by the edges of the hole. This is known as diffraction; those of you who did high school physics may remember diffraction and interference patterns.

Normally this distortion is very small compared to the amount of light passing through the aperture but as the aperture size gets smaller, so the diffraction become proportionally more significant. In camera lenses the aperture gets smaller as we stop down for extra depth of field so what effect does this have on image sharpness?

Imagine a single point of light, like a star in the night sky, focussed by a lens onto a sensor. In a perfect world this will appear as a single point on the sensor but, since lenses are not perfect, different colours of light focus at different points and the light is passing through an aperture, this will be in reality a small disc rather than a single point – called an ‘airy disc’. The size of the airy disc, assuming once again a perfect lens, is inversely proportional to the size of the aperture – as the aperture gets smaller the airy disc gets bigger.

A point of light becomes diffracted into an Airy Disc.

The Airy Disc as seen in perspective.

When two close points are diffracted they blend into each other, making them hard to distinguish, or simply ‘soft’.

The Impact on Sharpness

As the effects of diffraction become more pronounced and the airy discs become larger the image becomes visually degraded and will look ‘soft’. The crucial aspect here is at what point does this diffraction effect become visible in a practical sense?

On a digital sensor this is quite easy to define – an airy disc will be too small to resolve if it is smaller than one pixel on the sensor but will begin to seriously degrade an image when it is about the size of two pixels on the sensor. We will come back to this later.

“Circles of Confusion” or CoC is another term used when discussing sharpness. A CoC is a disc which is just small enough to look like a point to the unaided eye – a full stop on a newspaper page would look like a point of black from a metre away even though on closer inspection it’s actually a small black disc. This is very important in photography because when an image is enlarged to make a print, what once looked like a point of detail can become enlarged enough to appear as a disc, not a point. Put simply, the image looks soft.

Depth of field is based around the concept of CoCs. Only the subject at the single point of focus can be said to be fully ‘in focus’ – in front and behind that point the image becomes progressively less sharp until the out of focus detail becomes larger than a certain sized CoC and the lack of sharpness is actually visible. Depth of field is an illusion based on the fact that the eye can only resolve a certain amount of detail and as long as the imperfections in the image are smaller than this, the image will look sharp.

So how small does a CoC need to be before it looks like a point, not a disc? The standard used by camera manufacturers over the years has been about 0.25mm. A person with excellent vision can probably resolve fine detail to 0.1mm. However because this CoC size is measured on the final print, not the original image capture, it is clear that the degree of enlargement from the original capture is crucial too – as we all know the bigger the print, the softer it looks. But we also know that an image will look perfectly sharp up to a certain point, beyond which it starts to look soft.

And this is the crux of the matter. If the image sharpness is ultimately limited by the physics of light then no matter how many pixels are crammed onto a sensor then image can only be so sharp.

OK, so exactly how much does the aperture affect the sharpness?

I said before that if the airy disc is bigger than 2 pixels on the camera sensor then it will be degrading the image. This is true, but it’s complicated by the fact that different cameras have pixels of different sizes. The Canon 5D has pixels 0.0084mm across, the Nikon D2X 0.0055mm across.

 

Airy disc sizes depend only on the aperture, not the focal length or anything else.

Diffraction Limiting
Now, compare these sizes with the pixel sizes from the cameras above and an interesting pattern emerges.

The Canon 450D has a pixel size of 5.2 microns but at F8 the airy disc is 10.3 microns across. This means that the camera is ‘diffraction limited’ at F8 or smaller. Only at F4 is the airy disc the same size as the sensor pixel and so after about F5.6 (!) the image is becoming degraded.

What is also evident is that the bigger the pixel size, the less significant diffraction degradation there will be at any given aperture. Look at the Nikon D3, this is diffraction limited at about F11 – 16. Compared to the Canon the Nikon image will be more ‘enlargeable’ when both are at F11 even though they have a similar total pixel count simply because of the bigger sensor and pixels.

The trade off for camera designers is that more pixels per mm on the sensor appears to mean more detail but, conversely, bigger pixels mean less diffraction errors. That’s why compact camera with high pixel counts are rubbish compared to a dSLR with the same pixel count, and also why the hugely expensive digital backs give such good images because the only way to get lots of big pixels into a camera is to have a bigger sensor.

The upshot of all this is that resolution is limited not so much by a sensor’s pixel density but by the optical quality of the lens and the effects of diffraction. The first can be solved by using lenses of the highest quality but the second is an absolute and cannot be avoided.

Don’t Panic !!!

Fortunately there is no need to panic – with real world lenses and other factors influencing sharpness, this diffraction limit will be less significant that it might appear. But, as this shot of a newspaper (exciting I know) shows, the effect is real and stopping down to F32 can seriously degrade the image. The top row is the Canon 400D (at F5.6 and F22) and the bottom row the Canon 5D, what is also interesting, if it shows up in print is that whilst the 400D is slightly sharper than the 5D at F5.6(higher pixel density) the 5D is marginally better at F22 (bigger pixels).

 

Optimising Sharpness and Depth of Field (DoF)

We have seen that lenses produce their best details stopped down a bit, but not too much. F5.6 to F11 would be the sweet spot for most cameras but what if we need the DoF provided by F32?

One way is to use a Perspective Control Lens or a large format camera and use the tilt facilities to get maximum DoF even at apertures as wide as F5.6. This technique requires specific equipment that might not be available to everyone but it is extremely effective as this image shows. This shot from Orpheus Island shows the depth of field extending from the closest point right to the horizon. You can also the that whilst the tree is sharp in the foreground, the pebbles beneath are not. This is because the lens tilts the plane of focus but does not actually increase it.

Airy Disc Graphics reproduced with the kind permission of Sean T. McHugh (www.cambridgeincolour.com/tutorials/diffraction-photography.htm)