Basics of Image Noise

Noise in images seems to create a fair bit of confusion.  In particular the whats and whys of noise in images.

Noise is often referred to as the digital equivalent of grain in film.  The thinking is that noise sort of resembles film grain.  Well, no, it doesn’t really.  Not if you look at it moderately closely.

In this article we’re going to look at the basics of noise in digital images and hopefully dispel a myth or two about noise and sensor ISO settings.  Unfortunately there’s going to be a bit of math but it’ll be kept to a minimum.

This article is actually an offshoot from another writing project I’m working on and I thought it’d make a good addition to the blog.

Noise is in every digital image captured.  Even where ETTR (Expose to the Right) has been used to minimise the evidence of noise, it still exists.  There are three components to noise in digital images.  Photon or Shot noise, Read noise and Dark noise.

Photon or, more commonly, shot noise results from the fact that light travels in particles and these particles reach the sensor at different times for a given exposure setting. So if one pixel recorded 10,000 photons and the pixel next to it captured only 9,000 photons at the same exposure, the difference shows up as shot noise. It, essentially, represents gaps in image information. Information from each pixel is not considered discretely in determining the total signal. Information from all pixels is accumulated to generate the total signal. The value of shot noise is the square root of the signal.  This is the rationale behind ETTR.

Read noise is the inherent interference in electronic components that results in the conversion from analogue photons to digital voltage. Not all of the photons captured will be converted to voltage. This ‘leakage’ or inefficiency in the system is read noise. Read noise is a constant but it does get multiplied by the ISO amplification factor.

Dark noise is another type of shot noise. It occurs due to electrons released within the system (which subsequently get converted to voltage) that are not the result of photons hitting the sensor. Because these electrons are not being released as the result of light hitting the sensor they show up as noise in the image. Dark noise is affected largely by temperature. Long exposures and shooting in high heat environments will contribute to increased dark noise. Dark noise is also amplified by the ISO. Dark noise is predictable; however, so it can be very successfully eliminated by a process called ‘dark frame subtraction’. This is what long exposure noise reduction in camera actually is. A second exposure is taken at the same exposure setting but with the shutter closed. The noise in this ‘dark frame’ is subtracted electronically from the original image, thereby reducing dark noise.

The light sensitivity of a given imaging sensor is fixed.  Increasing ISO doesn’t increase the sensitivity of the sensor as many writers state.  That’s a myth.  The signal off the sensor is actually reduced by increasing the ISO setting.  Increasing the ISO simply amplifies the signal to artificially increase it.

So how does ISO affect noise and signal to noise ratio (SNR)?  Here comes the math.

The actual calculation is a bit more complex than this but the gist is basically the same.  SNR = Signal/Noise.  More precisely it’s Signal/((Signal + Read Noise^2 + (Dark noise*shutter speed))^.5

Let’s take a shot at ISO 100 for 1 second and assume the signal is 10,000.  Let’s assume the Read noise is 50 and Dark noise is 10.  Remember that Dark noise is affected by shutter speed.  The equation is SNR = 10000/((10000 + 50^2 + (10 * 1))^.5 or 89.4.

Now let’s boost the ISO to 200 for .5 seconds.  The signal now is 5,000.  Read noise is 100 (50 multiplied by the ISO amplification factor).  Dark noise is 10.  The equation is 5000/(5000 +(50*2)^2+ (10*.5))^.5 or 40.81.

If we go to ISO 400 for .25 seconds the signal drops to 2,500.  Read noise is 200 (50 * ISO amplification factor) and Dark noise is 10.  SNR = 2500/(2500 + (50*4)^2 + (10*.25))^.5 or 12.12.

Quite a difference, right?  The SNR is less than half, in this made up example, as we boost the ISO from 100 to 200 and drops to nearly 1/7 the original level when we move the ISO up by 2 stops.

A couple things should be evident.  As the amount of signal is reduced the proportion of shot noise in the image increases (100 is 1% of 10,000 but 70.71 is 1.4% of 5,000 and 50 is 2% of 2,500).  Also, the impact of Read noise becomes more significant as ISO is increased.

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