The Exposure Triangle

by Nigel Cooper

What is the Exposure Triangle?

 

The exposure triangle is the relationship between the camera’s ISO, shutter speed and aperture settings. These three key components work together to determine the exposure (EV, exposure value) of a photograph, or an incorrect one if it is not understood or if used incorrectly i.e. an incorrect mathematical equation is calculated while implementing it.

 

It is referred to as the ‘exposure triangle’ simply because there are three elements (different ways) of adjusting the exposure on a camera: ISO, shutter speed and aperture. When the photographer adjusts one element of the exposure triangle, one, or both, of the other two elements must be changed to retain the same exposure.

 

Not only does the exposure triangle affect the exposure, it also affects the global ‘look’ of the image too i.e. the ‘depth of field’ (how much of the image from foreground to background is in focus and how much is blurred out of focus) and ‘image noise’ (this was known as ‘film grain’ back in the days of film) for example.

 

The three elements of the exposure triangle – the three ways of adjusting exposure – are: ISO, shutter speed and aperture. ISO adjusts the camera sensor’s sensitivity (how easily it can absorb light). A higher ISO setting – 1600 for example – makes the sensor more sensitive to light while a low ISO setting such as 100 makes it less sensitive to light.

 

Changing the ISO setting up from 100 to 200 will double the sensor’s sensitivity and the amount of light reaching it. The next element in the exposure triangle is the aperture, which is a mechanical set of blades (the iris) inside the lens that open/close to form a larger/smaller hole in the centre of the lens to allow more/less light through the lens to reach the camera’s sensor. Opening up the aperture of the lens from f5.6 to f4 creates a larger opening in the iris of the lens by one full f-stop and thus doubles the amount of light reaching the sensor. The third element of the exposure triangle is the shutter speed, which is the mechanical shutter curtain (trap door if you like) that quickly opens and closes just in front of the camera’s sensor to allow light to come through and hit the sensor for a given period of time. If the photographer has set the shutter speed to 1/100th of a second and then changes the shutter speed to a faster one of 1/200th of a second the effect of this change is the equivalent of one stop and will reduce the amount of light reaching the sensor by half. To clarify, one stop via the ISO, aperture or shutter speed will either double the amount of light reaching the sensor, or halve it, depending on the up/down adjustment made to any of the three elements of the exposure triangle.

 

Mastering and having a thorough understanding of the exposure triangle is crucial for achieving perfectly exposed images, and when I say ‘perfect’ I don’t mean one stop underexposed and then pulling back the exposure and/or brightness in software to fix the glitch later, which can introduce image noise and lessen the overall image quality of any given shot, especially if the photographer shot in JPEG and not RAW.

 

Why photographers should implement the exposure triangle?

 

It continues to astonish me how many photographers (especially so-called ‘professional’ photographers at least) do not understand the exposure triangle, and even those who do don’t implement it regularly in their work. Instead, many choose to rely on one of the camera’s automatic modes: programme, shutter priority, aperture priority or auto ISO. For me, this is professional (and creative) suicide, Russian roulette, at best.

 

Here is a prime example of when the exposure triangle should have been implemented. Just recently a photographer showed me some images on his computer that he’d taken at an indoor badminton competition. He was proud of his shots, for the most part at least, i.e. composition and the action element that he’d caught. But, he could not understand why his exposure was jumping all over the place from one shot to the next; some were underexposed while others were a little overexposed. Also, he was not entirely happy with the way his camera did not quite freeze the action on some shots he’d taken of players jumping in mid air as they leaped up for smash shots close to the net.

 

When I checked the metadata to ascertain what camera settings he’d chosen, I was shocked to see that his camera had been set to ‘Shutter Priority’ mode i.e. he’d set the shutter speed and then relied on the camera to decide what the appropriate aperture should be to attain a correct exposure, but, as is often the case with camera’s built-in ‘reflective’ metering systems, it doesn’t always achieve the correct exposure and is, more often than not, a hit and miss affair. The camera’s built-in metering system assumes that everything it sees is a mid-tone grey (18% to be exact) and exposes accordingly. In a nutshell, if you switch a camera into any of its ‘automatic’ settings i.e. fully auto (programme mode) aperture priority or shutter priority and even auto ISO, and you fill the frame with a pure white wall, that white wall will actually come out grey in the final image. Likewise, if you fill the camera frame with a jet-black wall it will also come out grey – 18% mid-tone grey. This is why ‘any’ automatic setting on a camera simply cannot be relied upon to achieve anything that could be considered an accurate exposure. I see all these various auto settings as the equivalent to playing Russian roulette with your exposure, you really don’t know what you are going to get, unless you are photographing a scene that is made up of 100% mid-tone 18% grey of course, but that never happens.

 

I asked my friend why he’d chosen to shoot in shutter priority mode. He explained that he wanted to freeze the action of the badminton players so he’d switched to shutter priority mode and dialled in 1/500th of a second to be sure he’d freeze the action, while leaving the camera to ‘automatically’ set an appropriate (or inappropriate in this instance) aperture setting. I explained to him that shutter priority mode was just plain wrong because he was shooting in an indoor arena that was lit with large ceiling lights i.e. the light in there was never going to change during the games. It was not like he was shooting outdoors and the sun kept coming out from behind a cloud before hiding behind another and the light was constantly changing. An indoor-lit arena has no such light changing conditions so why set the camera to shutter priority? 

 

I went on to explain why some shots where under and others overexposed. This had happened because as he was panning around the court framing up and shooting players, some close and some wider shots, the scene was not a constant mid-tone grey. One shot, that was hugely underexposed, was a wide shot of a player, but behind the player was a large advertising board that was made out of white backlit Perspex. The camera’s metering system had taken this bright white sign into account and darkened everything down to try and make it a mid-tone grey and in doing so the player in front of it was about two stops underexposed. 

 

He had a few other shots that were overexposed from when he’d panned over to the right side of the court to shoot the other two players and in that half the seating area in the background had no lighting in it and although the court was lit, the seating/stand was quite dark. The camera’s exposure system had tried to compensate for this large dark area in the background by overexposing to bring it up to a mid-tone 18% grey, which resulted in overexposing the court area and the players by at least one stop.

 

If he’d put his camera into spot metering mode in shutter priority with his 1/500th second shutter speed and taken a few spot readings off mid-tone grey areas of the court and players skin and mid-tone clothing that were under the arena’s lighting and then checked the histogram on the back of the camera to confirm the exposure was spot on then he could have taken that resulting aperture suggestion, switched the camera into full manual mode, left his 1/500thsecond shutter speed and then dialled in the correct aperture that he’d attained via his spot meter readings. This way, in full manual, the camera would be firing off at 1/500th second shutter speed and at the same aperture, time and again, all evening. The lighting in the arena was constant remember, it was not going to change. With this full manual method he could have shot all evening, knowing that every single shot would be consistently, and perfectly, exposed.

 

However, he complained to me that if he decided to take some shots at a slower shutter speed – for blurring effect – he would screw up this perfect exposure, which would have been true as he did not know (he does now) how the exposure triangle worked and he did not fully understand that one full f-stop up or down allowed double or half the amount of light to reach the camera’s sensor.

 

I explained to him that it is all a simple mathematical equation and that if he was shooting at 1/500th of a second shutter speed (for example) with an aperture of say f2.8 and he then decided he then wanted to shoot at 1/60th of a second to get a little bit of motion blur while a player jumped and smashed the shuttlecock, all he had to do was a little mental arithmetic in his head, which goes something like this. Halve 1/500th shutter speed to 1/250, that’s one stop of extra light that will now reach the camera’s sensor. Halve that again to 1/125th of a second, that’s another full stop of light, then halve that again to 1/60th of a second shutter speed, which is where he wants to be at. But we have now added three full stops of light, which we need to compensate for somewhere else in the exposure triangle. He was shooting at 400 ISO so we could drop that by half to 200 ISO to lose one stop, and halve it again to 100 ISO to lose another stop. As his camera did not go down to 50 ISO we could not lose the extra third stop required this way so, instead, we now move to the third element of the exposure triangle, the aperture, and close the lens down one full f-stop from f2.8 to f4, bingo. We gained three stops of extra light sensitivity when dropping the shutter speed from 1/500th down to 1/60th and then we compensated and lost three stops of light by bringing the camera’s ISO setting down two stops from 400 to 100 and then we lost the other stop by stopping the lens’s iris (aperture) down one full f-stop from f2.8 to f4. If my photographer friend had a thorough understanding of full, half and 1/3rd stops and the exposure triangle this mathematical equation would have taken just a few seconds to work out and dial into his camera, assuring perfect exposures at any given shutter speed while photographing an indoor sporting event.

 

To clarify further, if the camera was set to 1/500th second shutter speed at f8 with an ISO setting of 800 and the photographer wants to change his/her shutter speed to 1/2000th of a second to totally freeze the action at a sporting event the equation would go like this. From 1/500th up to 1/1000th is double i.e. one stop and from 1/1000th up to 1/2000th is double i.e. another stop. So, change the shutter speed up from 1/500th to 1/2000th and then figure out where else on the exposure triangle you are going to get those three stops of light back from. Remember, going from 1/500th to 1/2000th of a second shutter speed will lose three stops of light as the shutter curtain is going to open and close so much quicker. There are a few ways we can correct this and retain the same exposure. In this instance the photographer is shooting at f8, perhaps he wants to stay at f8 to retain some depth of field so he does not have to be quite so critical with focusing on the eye, which can be difficult with fast moving players. If this is the case the photographer could regain those three stops of light by changing the ISO setting up from 800 to 1600, which is one stop, then up from 1600 to 3200, which is two stops and then up from 3200 to 6400, which is three stops – sorted. But, if the photographer is worried about introducing grain/noise into the image at such a high ISO setting he could leave the ISO at 800 and get those three stops of light back by adjusting the lens’s aperture setting by changing it from f8 to f5.6, that’s one stop back, then from f5.6 to f4, that’s two stops back and then from f4 to f2.8 that’s the three stops back. Or, finally, a combination of the two, so change the ISO from 800 to 1600 to get one stop of light back then change the aperture from f8 to f4 to fix the other two stops. It’s that simple.

 

If you find yourself shooting a similar indoor sporting event and the lighting in the arena is not amazing, there is a little trick that can help. Rather than crank the camera’s ISO up to something like 3200 that will likely result in noise (grain) in the final image (yes, even on modern DSLR and Mirrorless cameras) you can underexpose the image on purpose by keeping the ISO one full stop lower, 1600 in this instance, and then, as long as you are shooting in RAW, you will be able to pull that stop of light back in post production without introducing any noise into the image. It’s only when you try and pull back about three stops of light that you will start to introduce noise, even when shooting RAW. Again, having a good understanding of f-stops, shutter speeds and ISO sensitivities, will allow you to achieve a shot that is underexposed by a stop, but by design, not fault.

 

To clarify

 

To increase the exposure by one stop you would double the exposure and to decrease the exposure by one stop you would halve it.

 

Let’s start with the easiest of the three elements of the exposure triangle; ISO. One stop up from 100 ISO is 200 and one stop up from 200 is 400. Moving up full stops from 400 is 800, 1600, 3200, 6400, 12800.

 

Now let’s look at shutter speeds, the second element of the exposure triangle; shutter speed (for the record, ISO, shutter speed and aperture, although the three make up the exposure triangle, there is no order to them). This element is nice and simple too. When shooting with longer shutter speeds you simply double the time to increase the light reaching the sensor by one stop i.e. going from 1 to a 2 second shutter speed is one stop of light, from 2 to 4 seconds is another stop, then each doubling of the shutter speed thereafter is another stop of light from 8 seconds to 16 seconds then to 32 seconds, then 64 seconds and so on and so forth.

 

The same math applies when shooting at fractions of a second (which is what we do most of the time) changing from 1/100th of a second to 1/200th will halve the amount of light reaching the sensor and is full stop. From 1/200th to 1/400th is another stop and from 1/400th to 1/800th is another stop. The same applies when working from fast shutter speeds down to slower ones. These are full stops of light moving from 1/800th down through 1/400th, 1/200th, 1/100th, 1/50th.

 

Finally, the third, and final, element of the exposure triangle; aperture. Now, I’m afraid that things are going to get a little more complicated here and somewhat mathematical. Using logic you’d be forgiven for thinking that f2 would let in twice as much light as f4, but this is not the case. In reality, f2.8 actually doubles the amount of light reaching the sensor than f2. The aperture scale does not share the simple mathematical principles as its shutter speed and ISO cousins. Aperture settings are measured using what’s called the f-stop scale.

 

The f-stop scale (in full stops) looks like this: f1.0, f1.4, f2, f2.8, f4, f5.6, f8, f11, f16, f22.

 

Changing the aperture setting on the camera from f2.8 to f4 is one stop of light and reduces the light reaching the sensor by half. Likewise, changing the aperture setting from f11 and opening up the lens one stop to f8 will double the amount of light reaching the sensor. The complex math involved in these aperture f-stop numbers do not need to be known, but for those who care it goes something like this (feel free to skip, it’s rather boring).

 

F-stop numbers come from an equation that is used to work out the size of the aperture from the focal length of the lens. The ‘f’ in f-stop numbers stands for the focal length and the number that comes after it is a fraction of that focal length, which tells you the size of the aperture. Example, to find the width of the aperture of a 50mm lens with an aperture of f2 (for mathematical simplicity) you would divide the 50 by the aperture of 2, which gives a diameter of 25. Then take the radius – half the diameter: 12.5 – and multiply it by itself to create the radius squared, resulting thus 156.25, and then multiply that by pi, resulting in 490.9. The whole equation looks like this: Area = pi * r². Like I said, boring and it is not necessary to know this and, personally, I don’t even think it helps to get your head around it. The important thing is to simply memorize the full f-stop scale, which, again, looks like this: f1.0, f1.4, f2, f2.8, f4, f5.6, f8, f11, f16, f22. Once you have committed this full f-stop scale to memory you’re all set. 

 

There is a little more though, there are third stops too, which give you even finer control over exposure. Between f2.8 and f4 lies f3.2 and f3.5. The same goes for shutter speeds, between 1/100th and 1/200th you’ll find 1/125th and 1/160th. Same for the ISO, between ISO 100 and 200 you will find ISO 125 and 160. However, you don’t have to memorise these third stops as on all modern digital cameras as you dial through the shutter speeds, f-stops and ISO settings the camera cycles through them for you to see. But, if you can memorise the full f-stop aperture scale, full stop shutter speeds (simple, double or halve the number) and full stop ISO settings (again, simple, double or halve the number) and an understanding of the exposure triangle and how changing one of these three elements will require one of the other two to also change to compensate and, hence, retain the same exposure, then you’ll achieve perfect exposures shot after shot.

 

Lens ‘sweet spot’

 

On a final note – and I’m going to digress away from the exposure triangle here – many aperture photographers (usually geeks who spend more time photographing technical charts than actual three-dimensional images) spend too much time trying to shoot at any given lenses’ so-called ‘sweet spot’. Yes, they all have them and, on average the sweet spot on most lenses (the spot that achieves the sharpest/clearest image) is around the f8 to f11 aperture, typically about mid-way through the lens’s aperture range. These fanatics also tend to avoid the extreme ends of the aperture settings of any given lens i.e. a 24-70mm lens with an aperture range from f2.8 to f22 would have a certain photographic demographic avoiding the extreme f-stops i.e. f2.8 in fear of an image that might be a trifle soft and f22 in fear of getting lens diffraction. Sometimes they will avoid the two f-stops at the extremes so f2.8 and f4 would be avoided at the more open end and f16 and f22 would be avoided at the other end. My answer to this is that modern (high end quality lenses at least) do not really suffer from diffraction at smaller apertures anymore so shooting at f16 and f22 does not concern most professional photographers and I’ve never seen lens diffraction on any of my Canon L series lenses at f22. At the other end, the f2.8 end, yes, there can be a ‘trifle’ of softening in an image but unless you are going to ‘pixel’ peep at high magnifications in software you are, generally, never going to see it so don’t concern yourself with this, ‘true’ professional photographers don’t.

 

What a lot of these boffins don’t understand is that they are sacrificing ‘art’ by restricting the image’s depth-of-field and what parts of the image from foreground to background are sharply in focus and what is – artistically and purposely – thrown out of focus. Example, a portrait of a happy couple sitting in the meadows next to a river would look better if the focus was on them and the background was thrown out of focus by using a wider aperture such as f2.8 or f4. Insisting on aiming for the lens’s sweet spot of say f8 or f11, would not allow the photographer to do this. Sure, the image around the edges (where you typically don’t look anyway as the important subject matter is usually always in the central areas, not in the far reaches of those corners) would be sharper, but at the expense of a professional portrait where the background has been thrown out of focus to put all the attention on the happy couple. This is why professional photographers ignore this so-called ‘sweet spot’ on a lens, concentrating instead on being creative and achieving stunning images.

 

This is a true story that leaked a few years back when Canon launched the MK2 version of their famous 70-200 f2.8 L series lens. They had sent some pre-production lenses out to a handful of trusted reviewers, some of whom were boffins who photographed test charts and they complained that in the far corners of the images they were a little ‘soft’. Now, I’m taking in the ‘very’ far corners of the images here, on a 10x8 inch print I’m taking about a centimetre or two away from the four corners, where there is never any important part of the main subject matter, so who cares if things are a trifle soft at the extreme corners? Lens design is a complex and scientific thing and to achieve a pin sharp lens images across 95% of the central image area that tiny, inconsequential and quite insignificant, 5% in the extreme corners has to take a slight hit in the ‘tack sharp’ department. Professionals don’t care about this; they want the main subject matter in the main parts of the image to be tack sharp, as do Canon. But, the geeks who shoot test cards want the entire image to be uniform, from corner-to-corner. So, to avoid these ‘geeky’ negative reviews Canon had to actually retard the lens slightly so these far corners where sharp also, just as sharp as the central parts of the image. On a test card shot with this new retarded lens the image was as sharp in the corners as it was in the centre, but not as sharp in the centre as the original MK1 version of the lens. It was a trifle less sharp across the entire image area of the frame to allow the 5% part in the corners to become the same. This made the test-chart shooting geek happy, but annoyed the hell out of the rest of us – a sad, but true story.

© Nigel Cooper 2019 - 2020

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