I know digital cameras have ISO options, and that ISO is the camera's sensitivity to light, but if you set higher ISO then you can get a noisy image. I also know there are two other camera options, shutter speed and aperture.
What is the relationship of between them? Is there any equation, or something like that?
For example, if I set the ISO to 640, then how should I set the shutter speed and aperture?
There is an equation, and by convention, it's set up to be really simple. There are basically five factors to consider together:
and, finally but not least:
That's kind of a lot to take in, which is why switching out of Auto mode can be so intimidating. But, let's start with simple.
Photography has a convention called the exposure value scale. That's a series of numbers generally in the range of single or double digits on either side of zero. Each number corresponds to aperture and shutter speed settings which will result in the same amount of light collected — which means, with the same scene and sensitivity, the same exposure in the final result.
It's often convenient to think of these numbers in terms of typical scenes which will be exposed in a typically-regarded-as-correct fashion at that EV. For example, at ISO 100, full sun is around 15, home interiors usually around 6, and a landscape lit by a quarter moon something like -6. More details here, or summarized in this handy circular chart:
Each factor has its own scale, but we call each full step on any of the scales "one stop", and — finally, I've gotten to the simple thing! — the cool thing is that in terms of resulting brightness, you can exchange one stop of any factor for a stop of any other.
Why would you want to do that? Two basic reasons. First, each factor has limits:
But second, in addition to exposure, each factor affects the image in the other way, and this is fundamental to the creative process of photography:
No matter the factor, changing by one stop means doubling or halving the amount of light from that factor.
I said there was an equation, and then didn't give one. It's basically this:
aperture × shutter duration × sensitivity × light = exposure
BUT, don't go worrying about multiplying anything — you just need to add and subtract stops.
(If math makes your eyes glaze over, skip this parenthetical. If you're curious, though, it's because the stop system is a log scale, and we're effectively just adding exponents, which is the same as multiplying. But, again, the awesome thing is that this is pre-factored into the way we work with cameras, so you don't ever have to think about this again if you don't want to.)
For each of the individual scales:
and, on exposure itself, see How to choose the correct exposure?.
How do you know what the EV of a scene is and what values to start with? You can guess, or you can use an exposure meter. It used to be very common to have these as separate devices, but now, every camera has a very nice one built in. (The separate devices still have their use, but that's a more advanced topic.) This is what your camera uses in its automatic modes — they take a meter reading, and then use a program to choose exposure factors to match. (More at How do DSLRs figure out what aperture to select in P mode?.)
The automatic meter will give you settings for aperture, shutter, and ISO which should give you a middle, average brightness. You can tell it otherwise, though, with "EV compensation" — see When I change the EV compensation, how will that affect my aperture, shutter speed, or ISO? for a lot of detail.
You ask: "For example, if I set the ISO to 640, then how should I set the shutter speed and aperture?", and the answer is: it depends. You meter to find out, and either consult an EV table or — more practically — simply let the camera suggest a starting point (if your camera doesn't have a button in manual mode to do this, simply take note of what it's chosen in automatic mode). And then you're ready for...
If you want to darken or lighten the resulting image, you can change any one of aperture, shutter duration, ISO, or scene lighting (up until the inherent limits of each factor). For example — keeping the lighting the same for now — if you want to brighten an image taken at ISO 400, f/8, and shutter speed ¹⁄₁₂₀th of a second by one stop, you could change any one factor: ISO to 800, aperture to f/5.6, or shutter to ¹⁄₆₀th. (If you change all three, that'd make a three stop change, of course.)
If you want to keep the exposure the same but change a factor, you can change either of the other factors in the opposite direction. So, for the example of ISO 400, f/8, ¹⁄₁₂₀th, if you wanted to freeze motion better with a shutter of ¹⁄₂₄₀th, you could keep the exposure the same by changing either ISO to 800 or aperture to f/5.6. Or, you could change the lighting by one stop and leave ISO and aperture alone.
The "exposure triangle" is a term popularized by photography author Brian Peterson for aperture, shutter duration, and ISO. I'm not fond of it for two reasons — first, there really are more factors than three, and second even if we just consider those three, there's nothing triangle about them. You can read much, much more about this at What is the "exposure triangle"? — including an alternate representation which you might find more helpful if you want to think about it in terms of geometry.
The total exposure you get is governed by four factors:
The last three are tradeoffs we get to control in the camera, and together are often termed the "exposure" that was used to take a picture. In some cases we can control the scene brightness, like with lights in a studio or with a flash. Cameras do control flashes sometimes, but for the sake of this answer we'll say the scene brightness is given, and we want to adjust the other 3 items to get the desired exposure.
The ISO setting controls how sensitive the sensor is. Back when sensors were film, you decided this by what you loaded into the camera. Films had various tradeoffs between sensitivity and grain. The more sensitive films were more grainy.
With today's digital sensors, you can chose the sensitivity frame by frame. However, just like with film, there is a tradeoff. Actually most sensors have a single native sensitivity, then the output of the sensor is amplified (or in some cases actually attenuated) before being digitized. The problem with amplifying the sensor signal is that you amplify the inherent noise along with the image signal. Some sensors are better (less noisy) than others, so allow for more amplification before the noise gets large enough compared to the image signal to be objectionable.
The shutter speed is pretty much what it sounds like, and is how long the image is projected onto the sensor. Longer times let the sensor accumulate more data relative to its noise and are therefore better from that point of view. However, of course there is a tradeoff. Anything that moves in the scene, or the whole scene if you move the camera, will be blurred more the longer the shutter is open.
For example, if you're taking a picture at a sporting event and someone is running at 3 m/s sideways to your view, he would look like a 3 meter wide blur at 1 second shutter speed. At 1/100 second the blur would be 3 centimeters, and at 1/1000 second only 3 mm. There is no single answer as to what is better, which is one reason cameras give you these choices. You may want someone running being blurred to show speed. On the other hand you might want to show the instant expression on the face with drops of sweat hanging frozen in mid air.
In any case, the 1/1000 exposure gives the sensor 10 times less light to work with, so its signal will be 10 times closer to its noise level.
This is somewhat of a aside, but digital sensors also accumulate some noise over time. This is why digital cameras usually limit exposure times to 30 seconds or so. Unlike film, you can't just leave a digital sensor sensing for long periods of time with dim light.
The f-stop or aperture controls how much light the lens lets thru. The f-stop number is actually the ratio of the effective diameter (for the purpose of letting light thru) of the lens divided by its focal length. This is done because that normalizes the light-letting-thru measure of lenses independent of focal length. For example, a 50 mm lens set to f/8 will project the scene with the same brightness as a 200 mm lens set to f/8. The 200 mm lens will make each scene element 4 times larger across, so it will be spread out over 16 times more area. That means it needs to collect 16 times more light from the scene to get the same brightness. However, all that is taken into account with this normalized aperture measure we call the f-stop.
Of course again there is a tradeoff. A wider open lens (lower f-stop number) gives the sensor more light, which results in a better signal to noise ratio. However, the depth of field (the distance over which scene objects will be in focus) will be lower. Imperfections in the lens will also be more prominent.
At really small apertures (larger f-stop numbers), diffraction becomes a issue. The light rays that just glance past the edges of the aperture diaphram get bent a little instead of continuing on straight. This only happens when they pass close to something that would block them, so this only matters to the ring of light rays that pass just inside the aperture. As the aperture is set smaller, a larger fraction of lights rays are close to the edge, and these bent rays make up more of the light hitting the sensor. The result is that bright objects in the scene cause other areas of the projected image to get lighter too. The overall affect is to reduce contrast and give the appearance of less sharpness.
Usually f/5.6 or so is the sweet spot, but that depends on the specific lens. Most of the time you don't worry about this too much, and good quality lenses will still take good pictures at f/2, and diffraction is hard to notice at f/22. I've taken macro pictures at f/64, and the loss of sharpness due to diffraction was quite evident.
Most of the time, however, we trade off f-stop between letting more light thru and too small a depth of field.
Overall exposure is therefore controlled by the ISO setting, shutter speed, and f-stop. The various results you trade off against each other are mostly giving the sensor enough light so that the image signal is large compared to the noise, motion (or camera shake) blur, and depth of field.
As a general guide, a normal scene in full sunlight is well exposed at f/16 and the shutter speed set to 1 divided by the ISO value. For example, that can be f/16, 1/100 second, and ISO 100. Or it could be f/16, 1/250 second, ISO 250.
In photography, a factor of two in exposure is a clearly noticable step, but not a particularly large one. We usually think of adjusting exposure in numbers of 2x steps. You can think of a factor of 2 as being a "standard increment" in photography.
ISO adjusts linearly. ISO 200 is twice the exposure of ISO 100.
Shutter time is also linear. However, since we usually write the shutter speed numbers as reciprocals (1/100 second, 1/250 second, etc), the bottom number goes down to increase exposure. 1/50 second is twice the exposure of 1/100 second.
The f-numbers math is more complicated. The exposure goes with the logarithm of the reciprocal of the f-number. Since this gets complicated to do mentally, a bunch of f-numbers have been pre-computed that cause half the exposure from the previous. Each of these f-numbers must be the square root of 2 higher to make half the exposure. Starting at f/1 (almost never happens), we therefore get the progression f/1, f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22. These values are so commonly used that early cameras often had detents on the aperture ring to allow positively setting to one of these values, and to allow adjusting up or down by feel while looking thru the viewfinder. These detents were also called "stops", which is where the term "f-stop" came from.
Since the common f-stops each represent a factor of 2 brightness from the next, the term "f-stop" has come to be used as a factor of two in exposure, even if the aperture itself isn't changed. For example, it is common in photography to say that ISO 400 is "2 f-stops" more than ISO 100, or that 1/500 shutter speed is 1 f-stop down from 1/250 shutter speed.
We usually think of exposure in terms "f-stops" up or down. For example let's say you took a picture at ISO 200, f/5.6, and 1/250 second. This came out too dark, and you felt that it needed 2 f-stops more exposure (factor of 4 more light). You might try any of the following to get this additional 2 f-stops of exposure:
ISO 200, f/2.8, 1/250 s
ISO 400, f/4, 1/250 s
ISO 400, f/5.6, 1/125 s
ISO 200, f/4, 1/125 s
However, while the exposure of each of these four examples above is equivalent, the depth of field, motion blur, and sensor signal to noise ratio won't be. Most modern sensors have little noise relative to full exposure at ISO 400, so the last tradeoff in these examples wouldn't likely be a issue in most cases.
Again, it's all about tradeoffs. There are no right or wrong answers, only what works with your camera, with your scene, and with what you are trying to show.
If you think of a camera as simply a light collector / recorder or photon counter and ignore actually taking a picture of a scene, there is a very simple relationship between ISO, aperture, and shutter speed:
Total light recorded1 is proportional to ISO × aperture × shutter speed × available light in the scene
For the remainder of this explanation, treat available light as a constant that you can't control.
Thus, if you increase any of the three controls (ISO, aperture, shutter speed) by a factor of 2, for example, then you must halve one of the remaining two controls to maintain the same total light collected.2 (Note 1 below)
So we have three input controls (ISO, aperture, shutter speed) to produce a single output, the total light collected. While we don't think in terms of total number of photons collected, we do think in terms of correctly exposed images. So in order to get a desired correctly exposed image, we adjust the three controls based on their effect in the desired image, based on the individual scene being shot.
Practically, ISO is typically the last of the controls to set, the one you tend to care about the least.3 Usually, you are composing for depth-of-field (aperture), or stopping action or implying motion (short vs. slow shutter speed), or some combinations thereof. Once those are dialed in, ISO is more or less chosen for you, in order get the desired exposure. Of course, if your choice of aperture and shutter speed requires an undesirably high ISO (i.e., graininess or noise) to get the correct exposure, you have some choices to make:
Notes:
In the context of film, ISO is a measure of the recording medium's sensitivity to light. The higher the ISO, the more sensitive the film is to proportionately less incoming light, with the tradeoff that the film grain ("noise" of the film) increases with ISO.
In the context of digital photography, ISO does not describe the sensitivity of the image sensor to light; the sensor has a fixed sensitivity to a given amount of incoming light, producing a certain voltage. However, the resulting voltage is either amplified (multiplied) before being converted to a digital value, or the post-conversion digital value is multiplied, or both, according to the ISO value set for the shot. Thus, with respect to the recorded image, digital ISO functions similar to film ISO.
With regards to aperture, I didn't say halving the ƒ-number. The meaningful measure of aperture is a cross-sectional area. Recall that area is proportional to the square of the linear measure across the area, i.e.: A ∝ d². Thus to double/halve the aperture area, the ƒ-number must be increased/decreased by a factor of √2, or approximately 1.414...
When using film, ISO was both something you cared about a lot more, and something you had relatively less control over (both in terms of ISO range, and ability to choose ISOs based on which film you had available). For DSLRs, in a sense, ISO is the compensation factor to allow you better choose your aperture and shutter speed. It still matters, but not really as a priority choice. I can't imagine many photographers approach a scene thinking "regardless of the other settings, I want ISO 400 for this shot".
This explanation completely ignores issues such as composition, depth of field, noise (grain), etc. Of course, those are extremely important in making a good picture.
All photographers should memorize the basic full "Stops" in exposure as expressed in shutter speed, aperture, and ISO.
Once you are familiar with them, any time you change one of the variables it is very easy to adjust one of the others to equal the same exposure.
1/30 1/60 1/125 1/250 1/500 1/1000 etc. (half or double is 1 full stop)
f/1.4 f/2.0 f/2.8 f/4.0 f/5.6 f/8 f/11 etc
ISO100 ISO200 ISO400 ISO800 ISO1600 ISO3200 ISO6400 etc (half or double is 1 full stop)
As per the original question, if you are using ISO640 and you change the ISO by 1 full stop, (halve or double the ISO to 320 or 1250), then you would adjust the aperture or shutter speed by 1 full stop.
