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Diffraction: When Smaller Apertures No Longer Mean Sharper Pictures

Conventional wisdom is that one can achieve a sharper image by stopping down to a smaller aperture, but this misses the mark in two fundamental ways. First, the image will always be sharp at the point of focus. What a smaller aperture gives you is an apparent sense of greater sharpness by extending depth of field over a wider range of distances in front of and behind that focus point. Second, a phenomenon known as diffraction can cause you to actually get progressively less sharp images beyond a certain aperture, even at your focus distance. The effect of diffraction at various f/stops on Nikon DX-format digitalAnd it is this second point that is the subject of this week's PhotoTip article.

At a sufficiently large aperture, light rays can pass through unobstructed on their way to the film or sensor. But as the aperture gets smaller, less light can get through. This is well known and is the reason why you have to use slower shutter speeds to achieve an equivalent exposure. But at really small apertures light rays can barely squeeze through at all and are actually bent slightly on their way to your film or sensor and begin to interfere with one another.

You can actually see this effect in everyday life. If an object is placed in front of a light source, it will cast a shadow on whatever is behind it. Light rays passing beyond the edges of the object still continue unimpeded, but those that strike the object get blocked by it, resulting in a shadow. But if you look closely, no shadow ever has a perfectly sharp edge. The light rays that pass closest to the object without actually being blocked get diffracted or bent slightly, blurring the edge of the shadow. This same effect occurs as light passes near the edges of the aperture opening in your lens. The effect is negligible for large apertures, but it becomes increasingly more significant as the aperture gets smaller.

Diffraction bent light rays will have to travel further than those not being diffracted. This means they will also take longer to reach the sensor than rays able to pass straight through the aperture unaffected. As they become increasingly out of phase with their neighbors, light waves will begin to interfere with each other, lessening sharpness.

The interference pattern thus produced includes a central spot called the Airy disk, named after Sir George Airy and a number of surrounding diffraction rings. The size of the Airy disk depends only on the wavelength of light and the aperture, but as it approaches the diameter of the Circle of Confusion for the film or sensor format being used, it limits the resolution possible.

Interference pattern caused by diffraction
Interference pattern caused by diffraction
Airy disk surrounded by diffraction rings
Airy disk surrounded by diffraction rings

The actual calculations are somewhat complicated, but the diameter of the Airy disk in millimeters can be approximated by dividing the aperture by 1500. Thus, for a lens set at f/11, we get an Airy disk of around 11/1500 = 0.0073mm and once we stop down as far as f/22 the Airy disk will have grown to about 0.015mm (22 divided by 1500). If objects are close enough to each other, their Airy disks will overlap, blurring each other. Indeed, to clearly see that two objects are distinct, the distance between them must be at least twice this limit to allow room between them for the diffraction pattern of what separates them. This means that resolution will be limited by diffraction if the Circle of Confusion for the film or sensor format we are using is less than twice the diameter of the Airy disk as determined by the aperture being used.

 Aperture (f/stop)   Airy disk diameter (mm)   Airy disk diameter doubled 
f/4 0.003 0.005
f/5.6 0.004 0.007
f/8 0.005 0.011
f/11 0.007 0.015
f/16 0.011 0.021
f/22 0.015 0.029
f/32 0.021 0.043
f/45 0.030 0.060

Let's take a look at what all this translates to in actual practice. Shown here is a 200% view at various apertures of a lens test chart taped to a wall on the other side of the room from my Nikon D2x camera. Up through around f/16, each row looks reasonably the same as the one before it. From there on down though, successive apertures yielded progressively worse resolution. The f/40 shot (the limit of the lens I was using) is downright horrible on the right-hand end of the chart where the lines are closest together.

The effect of diffraction at various f/stops on Nikon DX-format digital
The effect of diffraction at various f/stops on Nikon DX-format digital

Most lenses designed for 35mm film have f/22 as their smallest aperture which makes sense from the above. The approximate size of an Airy disk at f/22 would be 0.015 as shown in the table above. Doubling that gives us 0.03 which is the same as the commonly accepted Circle of Confusion value for 35mm film. A DX format Nikon DSLR though has a CoC value of only 0.02. Consulting the chart above shows that on the smaller sensor we will start to become diffraction limited at only f/16. But due to other effects of the smaller sensor, we will actually get more depth of field at f/16 on digital than we will on film so the need to go to f/22 is less.

How much difference all this will make in practical terms depends a lot what you shoot and what you do with your images. The lines used as an example here where quite small and relatively far away. From my vantage point behind the camera, I couldn't even see with my naked eyes the detail that does remain at f/40. Neither would a moderately sized print of the entire image these crops were taken from. But if your needs are critical, the strategy of using a smaller aperture in the hopes of getting a sharper image can in fact become a self defeating one. In particular, if you are shooting digital with a format smaller than standard 35mm film, resist the temptation to always stop down to f/22 when you need a lot of depth of field. It may not be your best option.

Update 04/30/2006 - Just a short note of clarification in response to questions and feedback I've gotten on this article: Diffraction always occurs, even at wider apertures. What makes it a problem is when the percentage of light being diffracted gets to be high enough in relation to the non-diffracted light. At sufficiently large apertures, most of the light getting through passes far enough away from the edge of the hole to be unaffected and totally drowns out any loss of sharpness from the light that is being diffracted. In terms of impact on the overall exposure, the diffracted light just doesn't even register. As you stop down and the opening gets smaller though, the ratio of diffracted light to non-diffracted light goes up. As it does, there gets to be enough diffracted light contributing to the exposure that it causes a noticeable decrease in the sharpness of the resulting image.

Date posted: April 9, 2006 (updated April 30, 2006)


Copyright © 2006 Bob Johnson, Earthbound Light - all rights reserved.
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