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Understanding the Effects of Diffraction (Part 2)

This article is a continuation of my previous post on understanding the effects of diffraction. That article has caused a long-winded discussion because some people decided to go deeper in the discussion of diffraction without fully understanding some fundamental concepts. Add to that some bogus resolution graphs and the discussion went from bad to shite.

In the interest of further learning, let’s go back to the very basic principles behind lenses and light.

LENS ABERRATION

The main purpose of a photographic lens is to focus light into the camera’s sensor. Ideally, an incoming point light source is projected into the sensor as a point. The reality is not quite that simple. Light rays near the center of the lens just pass straight through the glass without any problems. However, light rays that do not pass through the center will have to bend so as to meet with the other light rays towards the same focal point. The farther the light ray is from the center, the sharper it has to bend. The problem here is that lenses are not perfect. These imperfections or aberrations result in imprecise bending of light. Light rays near the edges of the glass don’t quite hit the focal point. Some of them will fall just before the sensor and some of them will fall after the sensor. The point light source then is projected into the sensor no longer as a point but something that is much larger. Refer to the simple illustration below. The red ray hits the focal point, the blue ray almost hits the focal point but the green ray which is very near the edge totally misses it.

Screen Shot 2014-10-21 at 8.29.24 pm

There are ways to work around lens aberrations. The most common method is by closing down the pupil to eliminate light rays that are near the edges of the lens. In photography, this is what happens when you close down or “stop down” the aperture. In the illustration below, the narrow pupil has eliminated the out-of-focus green ray leaving only the red and blue rays that are more focused.

Screen Shot 2014-10-21 at 8.27.30 pm

The result is a smaller projected point that is truer to the original point source. The overall image that is projected into the sensor will look sharper. The lens’es performance has therefore improved by utilising only the center of the glass by closing down the pupil. The downside though is that since the pupil has eliminated other light rays, the resulting image will also look darker. Bottom line is that you will have to trade sharpness with brightness.

DIFFRACTION

As discussed above, closing down the pupil improves the performance of the lens. You can make the pupil as narrow as you want and the lens performance will improve proportionally.

There is a problem though that is not quite the fault of the lens itself. This problem is attributed to a property of light. Light changes direction when it hits edges or when it passes through holes. This type of change of direction is called diffraction. Diffraction is ever present as long as there is something that is blocking light. So although a narrower pupil improves lens performance, light goes out-of-control when it passes through a narrow opening. The narrower the pupil, the more that light changes direction uncontrollably. It’s like squeezing a hose with running water. The tighter you squeeze, the wider the water spreads. In the end, light rays will still miss the focal point and we are back to the same dilemma where our point light source is now projected at a much bigger size on the sensor.

DIFFRACTION-LIMITED LENS

We are now ready to understand what a diffraction-limited lens means.

Recall that depending on the size of the pupil, light rays that are farther away from the center of the lens will miss the focal point thus causing a point light source to be projected much larger on the sensor. Let’s assume for now that this point source is projected with a much larger diameter, X, on the sensor.

Now forget for a moment that the given lens has problems and is perfect with no aberrations whatsoever. Recall that at the same pupil size, light diffracts (spreads) in such a way that will cause some of the light rays to miss the focal point and again resulting in a larger projected point of diameter Y.

So now we have two different sizes of the projected point: size X caused by lens aberrations and size Y caused by diffraction (assuming that the lens was perfect).

If X is smaller than Y then the lens is said to be diffraction-limited at that pupil size or aperture. This means that the main contributor to image softness is diffraction instead of lens imperfections. The optimum performance of the lens is the widest aperture in which X remains smaller than Y. Simple.

If X is larger than Y, the problem becomes a bit more complicated. It means that lens imperfections are more dominant compared to diffraction and therefore you can choose to make the aperture narrower to improve lens performance. Stopping down will of course decrease X but will increase Y. It becomes a delicate balancing act between lens imperfection and diffraction. This is a common problem with cheap kit lenses. At larger apertures, kit lenses have aberrations so bad that the image they produce look soft. So you stop down to f/8 or f/11 and by then diffraction kicks in causing the image to soften. It’s a lose-lose situation. That is why premium lenses are expensive. They are sharp wide open where diffraction is very negligible.

A lens that is diffraction-limited at f/5.6 is considered very good. A lens that is diffraction-limited at f/4 is rare. A lens that is diffraction-limited at f/2.8 is probably impossible.

Let’s summarise the discussion:

1. Lenses are not perfect. Aberrations will cause the light rays to miss the focal point thus resulting in loss of sharpness.
2. Lens performance improves as you stop down the aperture.
3. Diffraction is a property of light that forces it to change direction when passing through holes. This causes light rays to miss the focal point thus resulting in loss of sharpness.
4. Diffraction is always present and worsens as you stop down the aperture.
5. A lens is diffraction-limited at a given aperture if the effects of aberrations are less pronounced compared to the effects of diffraction at that aperture.

That’s it for now. In the next article, we will discuss the effects of lens aberrations and diffraction on sensors.

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