Digital Photographic Exposure, the bucket analogy
Larry Colen
160203 0800
Getting the right exposure with a digital camera is both so complex that you can spend years learning about it, finding new subtleties every year, and so simple that, and I know this from experience, a 12 year old boy can learn the basics in an afternoon. When I was teaching performance driving (car racing) I realized that there were two types of learning, “brain learning” and “butt learning”. Brain learning is understanding how things work, and butt learning is being able to do things without having to think about them. In many activities, the primary point for brain learning is to make the butt learning easier.
You will not be able to fully learn this material simply by reading this, you will need to set your camera in manual mode, go out, take pictures, then look at the results. It may also take reading things a couple of times through to get a good understanding. So, read it through fairly quickly the first time, and become familiar with the material, then go back, read a little bit, pull out your camera and try things out.
I am not going to try to cover everything in depth, and a lot of the things I say will not be totally technically accurate. One does not need to know about electron band gap, Schottky noise, or understand the particle wave duality of photons, in order to correctly expose your photos.
In short, there are four things that affect the exposure of your photo. First is how much light is coming off of your subject. The second is how sensitive your sensor (see, sensor/sensitive) is to light. The third is what fraction of light from your subject hits your sensor. The fourth is how long the light from your subject hits your sensor.
The word aperture means hole. There are metal leaves inside your lens which affect what fraction of the light gets through your lens. This value is measured in f/stops. Technically the f/stop is the ratio of the diameter of the hole to the focal length of the lens, but you can think of it as the fraction of light that gets through your lens. f/2.0 would let 1/2 the light through, f/4 is 1/4, f/8 is 1/8, and so forth.
Shutter speed, is how long the shutter is open. 1/50 of a second is twice as long as 1/100, which is twice as long as 1/200.
The sensitivity of your sensor is measured according to a formula specified by the International Standards Organization, or ISO. It is roughly equivalent to the one that used to be used for film defined by the American Standards Association, or ASA. That is why your camera at ISO 200 will need about the same exposure values as if you were using ASA 200 film. That number is approximately the fraction of a second you need to expose film for, in bright sunlight at f/16. So, if your ISO is set to 100, and your aperture is set to f/16, and you go out in the sun, a shutter speed of 1/100 Second will be close enough to get a decent exposure. If you bump your ISO to 200, then you'll need a shutter speed of 1/200, at ISO 400 it would be 1/400 of a second.
You may have noticed that every thing that I've mentioned has been a doubling, or halving. Double the sensitivity, and you cut the exposure time in half. Each one of these doublings is called a stop. If you open your aperture up an f/stop then you need to change your shutter speed or your ISO by a stop. Technically, what you are changing is your sensitivity, not the International Standards Organization in Geneva Switzerland, but it is the slang people use. 
You will notice that your camera will allow you to change your values by either 1/2 or 1/3 of a stop. First of all, a full stop is a big change, and sometimes you need to just make a small adjustment. Also, 1/3 of a stop is a ratio known as a decibel or dB. If you have your camera set to 1/3 of a stop per click, and you set your shutter speed to 1 second, three clicks and it will be 1/2 second, three more 1/4, three more will be 1/8 and so forth. However, if you then turn it two more clicks to make ten, it will be 1/10 of a second. If you turn it ten more clicks it will be 1/100, and ten more will be 1/1000. Where every three dB is roughly a stop, or a doubling, every ten is a factor of ten. Knowing these fractions isn't critical, but it can make it easier for some people to understand where things are coming from.
Another important thing to know is that exposure is a two step process. With film cameras you would expose and develop the negative and then use that to expose and develop the paper for the print. With digital cameras you expose the sensor, then the camera reads that data into the raw file. You then take that raw file, and process the data in it to create your final JPEG. If you go straight to JPEG in your camera, that is like taking your film to the drugstore, and when you get your prints throwing away the negative, so that if you want an enlargement you then need to take another picture, which won't be as sharp and make the bigger print from that.
Now, we finally get to the analogy that I was mentioning. You can think of the light coming off of your subject as a stream of drops of water. The aperture is a hole that allows some fraction of them through. The shutter is a valve that won't let any of those through to the sensor except for the short period when it is open. Think of your sensor as an array of a bunch of buckets. Each pixel is a different bucket. How full it is determines how bright it is, up until the point that it starts to overflow. Once it overflows we don't know anything more about how much water was in it, we just know that it overflowed. 
Likewise, the bottoms of these buckets are not smooth, they are pretty rough. That means that if there isn't much water in them, it's hard to measure exactly how much there is, it might look empty, or it might look like there's a bit of water in it. This roughness of the bottom of those buckets is like the noise in your sensor. When we expose the raw file correctly, we want the fullest buckets (brightest pixels) to be nearly full, but not overflowing, so that the emptiest buckets (darkest pixels) have enough water to cover up the rough bottom of the bucket (noise floor of the sensor). 
When the buckets overflow, we call it blowing out, or clipping. There is a mode on your camera that will show which pixels are so over exposed that they blew out, and which ones are so dark that the information is lost in the noise. When you are reviewing the images in this mode one may blink in one color (yellow) and the other spots will show up blinking in another color (red). 
There is another way to tell how well your raw file is exposed, and that is the histogram. The histogram is a graph that shows how many buckets are how full. They will put the empty buckets on the left and the full ones on the right. It's like taking that array of buckets that each hold a quart. Stacking up all of the ones that are empty on the left side, all the ones with one ounce next them, then the ones with two ounces, four, eight, sixteen and the ones that overflowed all of the way to the right. When you expose your raw file so that the buckets are as full as they can be, without overflowing any, that is called "Expose To The Right".
You may ask "But won't that make my final image too bright?". No, it won't because when you process your raw files on your computer, you just darken them back to what you want. There are many other reasons to do the final processing on the computer as well, but in short you have a much more powerful computer on your desk that can spend longer processing each image than the one in your camera. Also, desktop image processing software, like lightroom, gets better every year, so a raw file that may have been too noisy to get a good final image when you took it, is one that lightroom might be able to do a good job of cleaning up five years later. 
The other problem with going directly to JPEG in your camera, is that the conversion to JPEG is what is called "lossy". The reason JPEG files are so much smaller is that they throw away any information that they don't think you need, and you can never get that information back. You can make small adjustments to a JPEG file, maybe as much as a stop, but I have gotten fine images out of raw files that were underexposed by four or five stops and which looked practically black.
There is another subtlety to using the histogram, and that is the RGB histogram. Each pixel (or bucket) is only sensitive to red, green or blue light. Not all images have an equal balance of red, green and blue light. If you are taking pictures of something with saturated colors, or musicians on a stage with colored lights, one of the color channels might over expose (or blow out, or overflow the buckets) much sooner than the others. If you check your exposure with the RGB histogram, you can see when this is happening, reduce your exposure to prevent it, then correct things in lightroom for your final image.
At this point, we've learned three different ways of adjusting the exposure of your raw file. We can increase or decrease our exposure time (change the shutter speed), open or close the aperture (change the f/stop), or change the sensitivity of the sensor. There are also a couple of other things we can do, and that is change the amount of light hitting the subject, or putting a filter over our lens to reduce the light going into it in the first place. We won't discuss these last two in any detail right now. Each of the other three do things other than just affect how bright your raw file is.
The slower your shutter speed is, the more that things can move when you are taking the photo. If you are taking a picture of a bowl of fruit on a table, and nothing is moving, then all you have to worry about is whether your camera moves while you are taking the photo. Put it on a tripod and you can expose the image for several seconds without any problem. Learn how to properly hold your camera and even without a tripod you can often get reasonably sharp pictures as slow as 1/10 or 1/5 second. However, if you are photographing something that is moving, then you need to choose a shutter speed that will either freeze the motion, or show just enough blur to show that there is motion, but which will still leave the subject sharp enough to see the important details.
For example, a car traveling at 60 MPH (100 KPH) is travelling about 100 feet (30m) every second. That means with a shutter speed of 1/100 second, the car will still move a foot. At 1/1000 of a second it still moves about an inch. So, if you are shooting outside at ISO 100 at f/16 and the car is blurring at 1/100 second, you will need to either increase your sensitivity ten clicks (3 2/3 stops) to ISO 1000, or open up your f/stop to f/5.0 to shoot at 1/1000 of a second. There are, of course, many alternate values where you increase your ISO a bit and open up the lens a bit.
There are a lot of things that contribute to choosing what aperture to use. If you are being super fussy about getting the sharpest possible image of the subject at the best focus, different lenses are at their sharpest at different f/stops. Generally the sharpest aperture is a closed down a couple of stops from wide open. However, it is hard to go wrong in the f/8-f/11 range. Likewise with a super high resolution sensor, after you stop down beyond a certain point (which varies from sensor to sensor), you run into something called diffraction limiting. I am only mentioning this because there is a good chance that you will hear someone else talk about it. In the real world, if you are reading this in order to learn how to set the exposure of your camera, you don't need to worry about diffraction limiting.
The important thing to know about changing your aperture is that it will change something called depth of field. What this means is that at a smaller aperture (higher f/stop or stopped down), more will be in focus than with the lens wide open. Sometimes this is a good thing, such as when you are photographing a group of people, they aren't all the same distance from the camera, and you want them all in focus. On the other hand, sometimes you want to limit your depth of field. If you are photographing someone, and you don't want details in the background to distract from your subject, you can open up the lens so that only their face, or even part of their face, is in focus, and the background will be blurred out.
There are a lot of other things that affect depth of field, the focal length of the lens, the distance to the subject, the ratio of the distance to the subject and to the background. None of these terribly matter at the moment, the important thing to remember is that if you stop down your lens, to let in less light, a wider range of distances will be in focus. When you do this, however, you will need to either decrease your shutter speed (increasing motion blur) or increase the ISO sensitivity of your sensor.
The third element of the exposure triangle is the ISO sensitivity. The higher the ISO, the less light you need to properly expose your image (fill up the buckets).  At this point, you may be thinking that all you need to do is to crank up the ISO all of the way, and you'll be able to stop the pictures way down for more depth of field, and crank up the shutter speed to stop all motion blur, and your pictures will be amazingly sharp.
Unfortunately, you can't get something for nothing. Increasing ISO does two things that we don't necessarily like. First of all it increases the noise, and secondly it decreases the dynamic range. To understand this, let's go back to our bucket analogy. You can think of increasing the ISO as raising the bottom of our pixel bucket. That means that it will take fewer drop to fill up the bucket. However, remember how I said the the bottom of the bucket is rough and if there's just a little bit of water in it, it's hard to tell how much it is. This means that the noisy region near the bottom of the bucket is now much closer to the top of the bucket, so your measurement of whether the bucket is 1/8, 1/16 or 1/32 full is going to be a lot less accurate, or in other words, noisier. The other thing that it does, is to make the bucket smaller. Rather than being able to hold 32 ounces, it can now only hold four ounces, so it will overflow (or clip, or blowout) a lot easier. This is why we generally want to use as low of an ISO as we can, and still get the shutter speed and depth of field that we need.
It is important to know, however, that far more photos are ruined by using too low a shutter speed, or too wide of an aperture than by too high of an ISO. Also, noise reduction software gets better every year, so that a photo that is so noisy that it is barely acceptable now, is one that good software can clean up much better a few years from now. 
We have now covered the basic exposure triangle: sensitivity, shutter speed and aperture. We have discussed how each of these affects the basic exposure of the raw file, and some of the other effects that changing each of these have. We have also discussed the basics of using the histogram, and in particular the RGB histogram, and the blinkies, to check the exposure of your image immediately after you take it. In short, we have covered the basic brain learning. It is now time to work on the butt learning so that in addition to an intellectual understanding, you also have an intuitive understanding of how this all works.
What you need to do, is to put your camera in manual mode, go out and take some photos, adjusting the various values, and seeing how they affect the final image. Most DSLRs have something in the viewfinder that in manual exposure mode will tell you how far you are from what it thinks is the correct exposure. Some cameras have a button (on Pentax it is the green button) that in manual mode will set your exposure in manual mode. You can buy a manual light meter, use it to measure the light, and use that to set your exposure. Or, with a little bit of practice, you can look at a scene, take an educated guess and generally be pretty close. To learn the most about exposure, I recommend this last method.
Once you have set your initial exposure, take a test photo and look at it, with the histogram on the back display. Adjust your exposure based on the histogram and the blinkies, until you are happy with the results. Once you have a decent basic exposure, try adjusting your ISO, aperture and shutter speed, and the other ones to compensate. Explore with how changing your aperture changes your depth of field. Note: many cameras allow you to stop down the lens and see the actual depth of field through the viewfinder.
There is also a technique called bracketing, where when you press the shutter, you take several images, one "under exposed", one "nominally exposed" and one "over exposed". In challenging lighting, this can ensure that one of the images is probably exposed correctly. Bracketing can be done manually, or on some cameras it can be done automatically. 
Many cameras also allow you to simultaneously capture both raw and JPEG files. While you are learning, you may want to try doing this.
Taking the photos is only the first half. You then need to load the raw files into a program like lightroom and process the final image. You will find that with good image processing software, it actually takes less time to get your final image using raw files than jpeg files. If you have shot both raw and jpeg, you can see directly how much more adjustment you can make on raw files.
Once you have a good understanding of setting your exposure manually, then you will have a better understanding of how the various automatic exposure modes work, and when you may want to have the camera automatically set your shutter speed, aperture or ISO based on which values you decide are critical to choose yourself.