Photography Tips 7: Photography Math

Hopefully by now you all know that I am an engineer, which for me partly means that math always has been quick for me to pick up. It also means that one of the things that drew me towards photography was the fact that it involved math. I knew that part would make sense to me and the creative stuff would be what I would have to work a bit harder at (still true by the way).

The most fundamental math concept in photography is exposure. This includes the exposure triangle of aperture, shutter speed and ISO, along with understanding different stops of exposure, full, 1/2, 1/3 stops and what that means in terms of the exposure of your image.

Going back to the exposure triangle, a quick review, after which we will get to the numbers and math! All three variables of aperture, shutter speed and ISO, work together to determine the exposure of your final image, how bright/dark it will be.
Aperture: This is the opening in your lens that allows light to pass through it back to the shutter and your sensor or film. It opens and closes like the pupil of your eye depending on how much light you want to let in. The more open it is the more light is allowed through. (Imagine in a dark room how big your pupils are or outside on a bright day they get really tiny). So the less light that is available to make your image the more of it you will need to let in to get a properly exposed photograph.
Shutter Speed: This is how long the shutter in your camera body stays open to let light into the camera to land on the sensor or film. The longer it is open the more time the light will have to enter the camera. If you have a lot of light available you will only want it open for a shorter time.
ISO: This is a measure of how quickly your sensor or film responds when light hits it. This is similar to film speed. The faster it responds the less light you will need to make the final image.

There are other considerations for how each of these three items will impact the look of your final image but we can talk about those in another post, for now we are focusing only on how your exposure is impacted.

Now getting to the numbers:
The light getting into your camera is measured in stops. Lowering your exposure by 1 stop means you allow half is much light into the camera, raising it means you double the light. 1 stop of aperture, shutter speed or ISO is equal in light to one stop of any of the others. 1 stop of aperture = 1 stop of shutter speed = 1 stop of ISO. So if you want to keep your exposure the same but adjust one of the settings you have to adjust either one or both of the others to make up the difference.

All three variables report their values differently:

Aperture is recorded in numbers like f/1.4, f/2.0, f/5.6, f/8, f/11 etc. Those numbers represent the fraction of the lens that is NOT covered up by the aperture blades, or more accurately the portion of the lens available that is left uncovered by the aperture blades. Because it is a fraction f/1.4 means LESS of the lens is blocked which lets in MORE light, f/11 means more of the lens is blocked allowing less light to get in to make your image. Above I had mentioned stops of light the full stops for aperture can be listed out by starting with f/1.4 and f/2 and alternatively doubling them to get the list of full stops:
f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22, f/32 etc.
So f/4 lets in half the light of f/2.8. To make it a bit more confusing most cameras these days have the ability to adjust aperture in 1/2 or 1/3 stops. These are a little harder to memorize but there are easy references like this handy table:
f/# 1.0 1.1 1.2 1.4 1.6 1.8 2 2.2 2.5 2.8 3.2 3.5 4 4.5 5.0 5.6 6.3 7.1 8 9 10 11 13 14 16 18 20 22
Each number is 1/3 of a stop, note how the green numbers match up with the list of standard full stops. Your camera may also let you put it on half stops, those numbers would be
f/# 1.0 1.2 1.4 1.7 2 2.4 2.8 3.3 4 4.8 5.6 6.7 8 9.5 11 13 16 19 22
I prefer to stick with the 1/3 stops.

Shutter Speed is measured in seconds of time the shutter is open. Examples include 30 seconds, 1/100th of a second, 1/8th of a second etc. The math on stops here is a little easier, take any shutter speed, 1/100 for example and cut it in half giving you 1/200 and you cut the light in half, double it giving you 1/50 and you get twice as much light. This one seems pretty easy to grasp (at least to me) you are keeping your shutter open twice as long at 1/50 vs 1/100 so you allow in twice as much light. Again most cameras can do these in 1/3 and 1/2 stops, and again I keep mine on 1/3. The range on my camera goes from 30 seconds to 1/8000th of a second.
30, 25, 20, 15, 13, 10, 8, 6, 5, 4, 3.2, 2.5, 2, 1.6, 1.3, 1, 0.8, 0.6, 0.5, 0.4, 0.3, 1/4, 1/5, 1/6, 1/8, 1/10, 1/13, 1/15, 1/20, 1/25, 1/30, 1/40, 1/50, 1/60, 1/80, 1/100, 1/125, 1/160, 1/200, 1/250, 1/320, 1/400, 1/500, 1/640, 1/800, 1/1000, 1/1250, 1/1600, 1/2000, 1/2500, 1/3200, 1/4000, 1/5000, 1/6400, 1/8000

ISO is measured in film speed equivalents. The standard full stops being 50, 100, 200, 400, 800, 1600, 3200, 6400. Notice how they double? Again the doubling of the number also matches up with doubling the light. ISO 100 will need twice the light of ISO 200, and half the light of ISO 50. Again some cameras give you the option of incremental stops (not all do though, my XT only had the option of 100, 200, 400, 800 and 1600). I prefer to stick with the 1/3 stops. My camera allows 1/3 stops between ISO 100 and 6400, but only whole stops from 50 to 100 and from 6400 to 12,800 and 25,600. The sequence for 1/3 stops is:
100, 125, 160, 200, 250, 320, 400, 500, 640, 800, 1000, 1250, 1600, 2000, 2500, 3200, 4000, 5000, 6400
Do you see the pattern there? If you can remember 100, 125 and 160 you just keep doubling those to get the full sequence.

Okay now we know how each is measured and reported, and what those numbers mean to an extent. How do we use them to adjust our exposure or adjust our settings and keep the same exposure?

Example 1: Correct underexposure
What if you have settings of f/4, SS 1/200, ISO 250 and your image is under exposed? You can increase your exposure by adjusting any single variable (just ISO, just aperture or just shutter speed) or all of the three variables in combination. If you need 1 more stop of light some of your possible combinations are
f/2.8, SS 1/200, ISO 250 (adjusting just aperture)
f/4, SS 1/100, ISO 250 (adjusting just shutter speed)
f/4, SS 1/200, ISO 500 (adjusting just ISO)
f/3.5, SS 1/160, ISO 320. (adjusting all three)
There are quite a few more as well. You could adjust just two of the variables but that makes my list even longer. You can apply similar thinking with an overexposed image just adjust in the opposite direction.

Example 2: Correct too shallow depth of field.
Back in my tips post 5 we talked about what controls depth of field (how much of your image is in focus), focal length, focusing distance (ie distance to the subject you put your focus on) and aperture. What if you take an image and realize you don't have enough depth of field to include all of your subject you intended? You can of course consider shortening your focal length or backing up so your focusing distance is longer but lets say you can't do either of those so you want to control it with just your aperture. Making the assumption that your exposure was spot on and your settings were f/1.4, SS 1/1000 and ISO 100. You look at an online depth of field calculator or use an app on your iphone and enter your information (Canon 5D mark ii, focal length 50mm, distance 5 feet) and find out your depth of field was 0.25 feet. Looking at your subject you want your depth of field to be at least 1 foot. Playing around with the aperture variable shows you that at an aperture of f/5.6 your depth of field will be 1.01 feet, perfect! But we don't want to mess up our exposure so how do we compensate? f/5.6 is 5 full stops away from f/1.4 so we need to make up 5 stops in either shutter speed, ISO or using both. I always look at the shutter speed first before bumping the ISO to see if I have room to drop it. Lets say in this case you can lower it to 1/125 that gains you back three stops, you need to make up the other 2 with ISO so you up that from 100 to 400.
Results: f/1.4, SS 1/1000 and ISO 100 = f/5.6, SS 1/125 and ISO 400 in terms of exposure.

Example 3: Adjust for a slow shutter speed
What if you have the proper exposure with settings of f/11, SS 1/6, ISO 100 but you don't want to use a tripod (which you should if you want a sharp picture at a shutter speed of 1/6th of a second), and you know that for you to handhold in this situation you need a shutter speed of at least 1/200. First determine how many stops of light you will lose by slowing down your shutter that much, counting off it is 15 one third stop increments. That means 5 full stops of light will be lost by increasing your shutter speed. Now we need to make that up in the other settings, we can make it all up with one or split it. Based on the depth of field you need you are willing to go down to f/4, that will gain you back 3 stops of light, 2 left. Now the ISO, 2 stops from ISO 100 is 400. So our final result is that an exposure of f/11, SS 1/6, ISO 100 is also equal to f/4, SS 1/200, ISO 400.

For example one and two, if you aren't sure how to know how much to adjust by, it's not like your camera is going to say "you need to add 2 stops of light". If you learn how to read your histogram with enough practice you will get really good at guessing how much you need to adjust by. If you don't know how to read your histogram, or you want to see the steps I follow to determine my settings when shooting in manual, check out these other posts:
Photography Tips 3: The Histogram

Photography Tips 2: Shooting in Manual

You also don't always have pull up a table to count the stops if you are trying to keep your exposure the same, as long as all three variables are set in the same increments full, half or third stops you can just count how many steps you adjust each one and make sure they balance out.

Thank you to my friend Amy for reading this first for me and giving me feedback on it.

1 comment:

renee said...

Just found your site recently. This is a really great post - the best explanation on the #s related Aperture that I've read!!!


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