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The Essentials (and Math) to Understanding Aperture

Photography is all about capturing light. In order to make a photograph that we can see, we have to control both the amount of light that is exposed to a photosensitive surface, be it film or a digital sensor, and also control the sensitivity of that surface to the light. In this three-part series, I will discuss light and how a camera and lens combine to control exposure.

Exposure can be defined as the amount of light that falls onto the camera's light-sensitive surface. In any given scene, regardless if there is natural or artificial light being emitted, there is a measurable amount of light that illuminates your subject.

This amount of light varies due to four basic factors: intensity, duration, distance between light source and subject, and modifications to the light. This is not going to be a dissertation on light, but let's touch on some basics and those four factors before talking about controlling exposure.

Light is fascinating in that it behaves with the properties of both waves of energy and particles. This wave-particle duality affects the way light behaves inside and outside of a camera and lens.

Intensity, the brightness of the light: A light source emits photons and the more photons that are emitted by a light source, or reflected by an object, the brighter it is. A brighter photograph is created from a sensor or piece of film that has been hit by more photons. A darker image was exposed to a lower quantity.

Duration: The sun is a constant light source, but you can escape the light by riding the Earth as it rotates or by going inside! Artificial light can be turned on or off and some is emitted in a short-duration flash. If you increase the amount of time that a given light is emitted from a light source, you can increase the number of photons that are collected by the camera.

Distance: Photography, unfortunately for some of us, involves mathematics. This lesson on exposure cannot escape its pull. For those of you with math skills similar to mine, I apologise in advance. The closer to the light source, the more photons you can capture with a camera. The further you are away, the fewer photons you can collect. Easy, right? Well, what if you double your distance from the light source? There should be half the photons and half the light, correct? Nope. Thanks to something called the Inverse Square Law, you get 1/4 of the light when you double the distance. Why? This is because we are talking about area, not just distance. As light is emitted from most sources, it spreads out (lasers are an exception). So, a light bulb at 5 feet appears 4 times as bright as it was at 10 feet. Similarly, a fictional planet orbiting our sun at a mean distance of 186 million miles gets only 1/4 of the sunlight that we enjoy on Earth.

The Inverse Square Law, applied to light

Modifications: There are a numbers of light modifiers that help control and shape both artificial and natural light. You cannot dim the sun, but the clouds certainly can. You can also have your subject move into the shade — or you can create shade. Reflectors, diffusers, and gels are just a sliver of the available tools you can use to modify light.

Measuring Light

OK, now that we know how the amount of light can be altered, we need to assign a value to light so that we can measure its intensity, adjust our camera settings accordingly, and then adjust them further to brighten or darken an image. It is this image adjustment that leads us to the mathematical concept of "exposure value" or EV; sometimes referred to as "stops."

The intensity of light is its luminance but, even with a number assigned to luminance, we really aren't interested in quantifying that because cameras can capture images in all kinds of light, or even in darkness. What we do care about is setting a baseline so that when we change camera settings we are aware of how the changes will affect the exposure and how to compensate, if compensation is desired.

Photos taken with the same shutter speed at different apertures (note differences in depth of field)

Simplified, a "properly exposed" image can be given the baseline of EV 0. If we change something on the camera to make the image darker, we venture into a minus EV. Brighter is a positive EV. This is where the previously mentioned quantitative value comes in. EVs are given numbers so that we can measure the change from the baseline EV.

Why do we care about EVs? Well, you'll find out by reading on...

The goal in creating an exposure is to allow a specific amount of light into your camera and lens to capture your subject in a way that matches your artistic vision. Note that I did not say that the goal is a "proper exposure" and I have twice now used quotation marks around the phrase. Photography is art, and if you want to alter the image to be brighter (overexposed) or darker (underexposed) to better express your vision, then never think that every frame you shoot needs to meet the definition of "proper exposure." It does not. I will keep using the word "proper," but do not read deeply into the term and feel free to add your own "air quotes" when you read it!

So, what you want to do is set up your camera and lens to allow the correct (for you) amount of light into the system to create the image you want. In order to control this light, you have the ability to control three separate settings inside the camera. There are two ways to control the amount of light that enters the camera and exposes the photosensitive surface (aperture and shutter speed) and one way to control the sensitivity of that surface (ISO).

Light's journey through the camera lens to the sensor

One way to simplify these adjustments is to compare the camera to certain elements of the human eye. Aperture functions like the eye's iris that opens and constricts the diameter of its opening to limit the amount of light allowed into the eye. Shutter speed is similar to blinking, except the eyelid is usually open when we are awake. However, if you can imagine your eyelids opening momentarily to capture a single image before closing, that is like a camera's shutter. And, finally, ISO is similar to the sensitivity of the rods and cones at the back of the eye.

It is important to know that in almost every camera that has a variable aperture, shutter speed, and ISO, there is a way to manually control these settings. Of course, you can find adjustable aperture rings and shutter speed dials on older cameras and lenses for SLRs, but you can also likely control aperture, shutter speed, and ISO on today's point-and-shoot cameras as well. Learning how and when to adjust these settings can help improve your photography, as it will give you more control over your images.

In Part One of this three-part series, we will start by talking about aperture.

Diaphragm blades open and close to determine the size of the aperture


Aperture is the size of the opening in the lens. Some lenses have fixed apertures, but most photographic lenses have variable apertures in order 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.

Like the pupil in your eye, the aperture diaphragm opens and constricts to control the amount of light passing through the lens. In order 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!

Graphic representation of apertures at different f-stops

The ratio of the opening of a lens aperture when compared to the size 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.

Do the math: Double the radius of the aperture means four times as much light entering the camera

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.

Example of deep depth of field

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.

Shallow depth of field (large aperture)

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.

Large depth of field (small aperture)

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 centre of the image. Many photographers, when they are starting to understand aperture, think that the key to maximising 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.

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. Stay tuned to for the next segment of the three-part series, Understanding Shutter Speed.

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