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The easiest way to describe noise is as the photo being randomly "off" from what it "should" be.
A photo that is "too dark", "too bright", "too red", "too blue", etc. isn't "noisy". Instead, a noisy photo would be where a swatch that "should all" be roughly one color at a certain brightness and/or color vary "too much".
The two basic types of noise are luminance noise (where the brightness varies "too much") and color noise (where the color varies "too much").
So, what causes noise? There are two principle sources of noise: the total amount of light that falls on the sensor and the efficiency of the sensor.
If we think of the sensor as a swimming pool, the total amount of light is analogous to the amount of water in the pool, and the sensor efficiency is analogous to amount of contamination that was in the pool before water was ever added.
The weird thing is, that the water itself is contaminated by the light itself. But the contamination isn't as simple as a percent of the water, rather it's the square root of the amount of water. I know that's weird, but that's how it is, and this is called the photon noise (also called the "shot noise"), which is the primary source of noise in a photo.
So, for example, if you have 10,000 gallons of water in the pool, then sqrt 10,000 = 100 gallons are contaminated.
Now here's where it gets a bit weirder still. If the pool had 100 gallons of contaminents before the water was added (this is called the "read noise"), then the total amount of contamination isn't the linear sum of the photon noise and the read noise. That is, the total contamination isn't 100 gallons + 100 gallons = 200 gallons.
Instead, the total noise is root sum square: sqrt (100² + 100²) = 141 gallons. But, if that's a bit too technical, then just think of the total noise as the linear sum -- it's not that important a distinction to make at this point in the game.
The noise in the photo is the analogous to the density of the contaminants in the water. For example, if we have 141 gallons of the 10,000 gallons of water is contaminated, then the contamination is 141 / 10,000 = 1.41%.
This measurement of noise is called the NSR -- Noise to Signal Ratio. Often you will here people refer to the SNR which is simply the reciprocal of this value. For example, an NSR of 1.41% means the SNR = 1 / 1.41% = 71.
OK, moving on. How does the water get into the pool? Well, think of the scene as rain falling down on the pool, and as the shutter as a covering over the pool. The amount we open the cover is analogous to the aperture in the lens, and the length of time we keep the pool uncovered is analogous to the shutter speed.
Thus, how much water gets in the pool depends on how hard it's raining, how wide we open the covering, and how long we keep it open. How much light gets on the sensor depends on how bright the scene is, how wide we open the aperture, and how long our shutter speed is.
The exposure is analogous to the depth of the water in the pool. Clearly, a larger pool will hold more water for a given depth. In the same way, a larger sensor will collect more total light for a given exposure. That's the reason that larger sensor systems usually have less noise.
I say "usually have less noise" because a big pool with lots of contaminents in it before the water began falling may still be more contaminated than a smaller, cleaner, pool would be. In other words, a smaller, more efficient, sensor may outperform a larger, less efficient sensor even for the same exposure.
So, where does ISO fit into all this? In an AE (auto exposure) mode, such as Auto, P, Av, Tv, etc., choosing a higher ISO results in the camera selecting a smaller aperture (higher f-ratio), faster shutter speed, and/or less flash power, any of which will result in less light falling on the sensor.
What about pixel size? Well, the effect of pixel size is a secondary effect on noise, and is a bit more technical. This link:
http://forums.dpreview.com/forums/read.asp?forum=1018&message=35068712
and, even more detailed, this link:
http://forums.dpreview.com/forums/read.asp?forum=1018&message=32064270
cover the topic pretty thoroughly, and this link:
http://forums.dpreview.com/forums/read.asp?forum=1018&message=37714016
provides a pretty clear demonstration of what the previous two links discuss. But, if anyone's read this far, and has questions, I'd be happy to answer them.
I really hope this discussion was helpful to beginners. I sincerely apologize if it was overly technical. Clearly, the issue of noise is more complicated than my post makes it out to be, but I'm trying to keep my post and accurate as possible, at the expense of being more complete.
EDIT: I also apologize for any typos and/or errors that may be in the post. If you feel I made an error anywhere, please don't hesitate to bring it to my attention, so that I can acknowledge it if I agree, or so we can discuss it if I disagree.
A photo that is "too dark", "too bright", "too red", "too blue", etc. isn't "noisy". Instead, a noisy photo would be where a swatch that "should all" be roughly one color at a certain brightness and/or color vary "too much".
The two basic types of noise are luminance noise (where the brightness varies "too much") and color noise (where the color varies "too much").
So, what causes noise? There are two principle sources of noise: the total amount of light that falls on the sensor and the efficiency of the sensor.
If we think of the sensor as a swimming pool, the total amount of light is analogous to the amount of water in the pool, and the sensor efficiency is analogous to amount of contamination that was in the pool before water was ever added.
The weird thing is, that the water itself is contaminated by the light itself. But the contamination isn't as simple as a percent of the water, rather it's the square root of the amount of water. I know that's weird, but that's how it is, and this is called the photon noise (also called the "shot noise"), which is the primary source of noise in a photo.
So, for example, if you have 10,000 gallons of water in the pool, then sqrt 10,000 = 100 gallons are contaminated.
Now here's where it gets a bit weirder still. If the pool had 100 gallons of contaminents before the water was added (this is called the "read noise"), then the total amount of contamination isn't the linear sum of the photon noise and the read noise. That is, the total contamination isn't 100 gallons + 100 gallons = 200 gallons.
Instead, the total noise is root sum square: sqrt (100² + 100²) = 141 gallons. But, if that's a bit too technical, then just think of the total noise as the linear sum -- it's not that important a distinction to make at this point in the game.
The noise in the photo is the analogous to the density of the contaminants in the water. For example, if we have 141 gallons of the 10,000 gallons of water is contaminated, then the contamination is 141 / 10,000 = 1.41%.
This measurement of noise is called the NSR -- Noise to Signal Ratio. Often you will here people refer to the SNR which is simply the reciprocal of this value. For example, an NSR of 1.41% means the SNR = 1 / 1.41% = 71.
OK, moving on. How does the water get into the pool? Well, think of the scene as rain falling down on the pool, and as the shutter as a covering over the pool. The amount we open the cover is analogous to the aperture in the lens, and the length of time we keep the pool uncovered is analogous to the shutter speed.
Thus, how much water gets in the pool depends on how hard it's raining, how wide we open the covering, and how long we keep it open. How much light gets on the sensor depends on how bright the scene is, how wide we open the aperture, and how long our shutter speed is.
The exposure is analogous to the depth of the water in the pool. Clearly, a larger pool will hold more water for a given depth. In the same way, a larger sensor will collect more total light for a given exposure. That's the reason that larger sensor systems usually have less noise.
I say "usually have less noise" because a big pool with lots of contaminents in it before the water began falling may still be more contaminated than a smaller, cleaner, pool would be. In other words, a smaller, more efficient, sensor may outperform a larger, less efficient sensor even for the same exposure.
So, where does ISO fit into all this? In an AE (auto exposure) mode, such as Auto, P, Av, Tv, etc., choosing a higher ISO results in the camera selecting a smaller aperture (higher f-ratio), faster shutter speed, and/or less flash power, any of which will result in less light falling on the sensor.
What about pixel size? Well, the effect of pixel size is a secondary effect on noise, and is a bit more technical. This link:
http://forums.dpreview.com/forums/read.asp?forum=1018&message=35068712
and, even more detailed, this link:
http://forums.dpreview.com/forums/read.asp?forum=1018&message=32064270
cover the topic pretty thoroughly, and this link:
http://forums.dpreview.com/forums/read.asp?forum=1018&message=37714016
provides a pretty clear demonstration of what the previous two links discuss. But, if anyone's read this far, and has questions, I'd be happy to answer them.
I really hope this discussion was helpful to beginners. I sincerely apologize if it was overly technical. Clearly, the issue of noise is more complicated than my post makes it out to be, but I'm trying to keep my post and accurate as possible, at the expense of being more complete.
EDIT: I also apologize for any typos and/or errors that may be in the post. If you feel I made an error anywhere, please don't hesitate to bring it to my attention, so that I can acknowledge it if I agree, or so we can discuss it if I disagree.