Understanding Exposure, Part 2: Aperture

Aperture is the size of the opening in the lens. Some lenses have fixed apertures, but most photographic lenses have variable apertures to control the amount of light entering the lens. This aperture is regulated by a diaphragm made of overlapping blades that can be adjusted to vary the size of the opening through which light passes. The size of the opening also has a secondary effect on the photograph, as the diaphragm also changes the angle at which the light passes through the lens. We will discuss two "side effects" of changing the aperture size after we finish discussing aperture's relationship to exposure.

This article is part of a multi-part series about photographic Exposure.
1. Introduction: The Exposure Triangle
2. Aperture
3. Shutter Speed
4. ISO

Like the pupil in your eye, the aperture diaphragm opens and constricts to control the amount of light passing through the lens. To facilitate a properly exposed photograph, we need to quantify the size of the opening so that we can mathematically incorporate this opening into our calculation for exposure+. Luckily, especially if you have my math skills, this has been done for us already!

The ratio of the opening of a lens aperture when compared to the focal length of the lens—not a measurement, but a ratio—is referred to as an f/number, f/stop, focal ratio, f/ratio, or relative aperture. Regardless of the label you use, aperture values are spaced, for mathematical purposes, in exposure values (EV) or stops.

The benefit of mathematically figuring out EVs is that we can apply this measurement to all three adjustments that affect exposure—aperture, ISO, and shutter speed. With three adjustments all speaking the same "language," we can use them simultaneously or independently as needed.

The formula used to assign a number to the lens opening is: f/stop = focal length / diameter of effective aperture (entrance pupil) of the lens.

Written on the barrel of your lens, or digitally inside your camera and displayed in the viewfinder or LCD screen, you probably see f/stop markings at one-stop increments.

The smaller the number, the wider the opening. Therefore, a lens with a larger-diameter barrel and optics will allow a larger opening represented by a smaller f/stop. Your lens/camera might allow you to "dial up" different numbers than what is shown above; older manual lenses usually "click" at 1/2 stop increments. These numbers, seen on a digital display, like f/3.3 for instance, represent 1/2-stop or 1/3-stop ratios.

To keep things simple for this article, let us work with full stops, shall we?

Moving back to physics with some mathematics, here is how the f-stops change your exposure: If you set your camera to f/8 and then widen your aperture diaphragm to f/5.6 you have doubled the amount of light passing through the lens. Changing from f/8 to f/4 quadruples the amount of light. Going from f/11 to f/16 halves the amount of light.

Do you notice something strange? When we go from f/8 to f/4 we are doubling the size of the opening of the lens. Correct? Why then, is the amount of light quadrupled if the opening is only double the size? The return of math and of the Inverse Square Law.

The formula for the area of a circle is: Area = π multiplied by the radius squared. If you crunch some numbers, you will find out that by doubling or halving the radius of the aperture, you will quadruple or quarter the area just like when we were talking about the difference in the intensity of a given light based on distance.

When we bring this numeric data into a system for EVs, it is quite simple. A change in aperture that results in the light being either doubled or halved means you have changed your exposure by one EV, or stop. So, if you widen the aperture from f/16 to f/11, you have a +1 EV result, as you have doubled the amount of light that will pass through the aperture diaphragm. f/16 to f/8 doubles the size of the opening, quadruples the amount of light, and represents a +2 EV shift. Simple, right?

So, now that you know how aperture effects exposure, let us talk about those two "side effects" of aperture that we alluded to above. The size of the aperture diaphragm not only affects the amount of light passing through the lens, it also affects image sharpness and is one of several factors that affect something called "depth of field."

Depth of field is defined as the amount of distance between the nearest and farthest objects that appear to be sharply in focus in an image. Without depth of field, the lens's razor-thin focal plane would cause problems for photography. Take a photo of a person and, for instance, the tip of their nose would be in focus but the rest of them would be completely blurry. Depth of field allows that focal plane to have a perceived depth.

Depth of field is a function of lens aperture size, lens focal length, the distance between the subject and the camera, and something called the circle of confusion. For the purposes of this article, we will keep the depth-of-field discussion relevant to aperture. Depending on your camera and lens, by opening your aperture to its widest settings, you will narrow the range of the focal plane to a very small distance. This can be used in photography for creative compositions with close-up photography and, most popularly, for making distant backgrounds blurry when taking portraits.

It is important to note that some camera/lens combinations will not produce appreciably shallow depths of field, so do not think that by simply opening up your aperture diaphragm to its maximum, you will achieve extremely small depth of field. Adjusting your aperture diaphragm the other way, to its most narrow setting, extends the depth of that focus plane and allows a large range of the image to be in sharp focus. Deep depth-of-field techniques are used commonly in landscape images.

For a varsity-level, three-part depth-of-field discussion, click here.

Not only does the aperture control the amount of light passing through the lens, it affects the angle of the light rays as they transit the lens. To be clear, we are not talking about how the lenses are bending light, we are talking about how light, when it passes by an object, is slightly bent by that object—in this example, the blades of an aperture diaphragm. This bending of the light is called "diffraction" and is a characteristic of light's wave properties.

When you constrict a lens's aperture diaphragm, you are bringing that diffraction closer to the center of the image. Many photographers, when they are starting to understand aperture, think that the key to maximizing sharpness is a small aperture because of the effect that aperture has on depth of field. However, because of diffraction, this is not true. Although you are increasing your depth of field by constricting the aperture, you are also increasing the amount of diffraction in the image and this causes the image to lose sharpness.

Additionally, even with modern manufacturing precision and computer design, there is no such thing as an optically perfect lens. Because of imperfections in the glass and the way light behaves when it is bent, lenses produce aberrations that have negative effects on an image.

When you open the aperture diaphragm to its maximum size, you allow the maximum amount of light into the lens and, with it, the maximum number of aberrations. By "stopping the lens down," or reducing the size of the aperture diaphragm, you reduce those aberrations and the sharpness of the image created by the lens increases. However, as we discussed above, the downside is that as you make the aperture diaphragm smaller, you will increase the diffraction as the smaller opening causes more bending of the light rays. The middle ground, the region where the aberrations are reduced and the diffraction is manageable, is known as the lens's "sweet spot"—usually in the region between f/4 and f/11 depending on the design of the lens. This sweet spot aperture is where you will get the maximum performance of the lens as far as sharpness and reduced aberrations, as well as getting a middle-of-the-road depth of field.

For more on diffraction, please click here.

So, in summary, aperture not only serves to control the amount of light passing through a lens, it also affects the performance of a lens in terms of depth of field and sharpness. Now it is time to head to the next segment of the eposure series, Understanding Shutter Speed.