Finally, we need to consider how computers store those intensity measurements.

Most will be familiar with the concept that computers store values as 1s and 0s. When storing image data, each pixel will represent a given number of bits that can be 1 or 0, the number of bits we use to store the value is called the bit depth.

An image with a bit depth of 1 will have 1 bit per pixel, so each pixel in the image will be either 0 or 1. If we had 2 bits, each pixel can be 00, 01, 10, or 11. Those binary numbers aren't very intuitive for humans, so we instead translate this as 0, 1, 2, and 3. As we increase the number of bits, we increase the range of values by 2 to the power of the bit depth. So, in a 4-bit image, we can have 2^4 = 16 degrees of variation, and if a pixel collected no light it would have a value of 0 and if it collected as much light as we're able to collect its value would be 15. 

What does this mean for our digital camera images? As we saw, if we have a read noise of 10 electrons we need more than 10 electrons difference to know that a pixel is truly brighter. Our camera might have the capacity to store up to 10 000 electrons per pixel. We call this the full well capacity. If our camera's full well capacity is 10 000 electrons, and our read noise is 10 electrons, the degree of variation accuracy is 10 000 / 10 = 1000. So this camera could reliably measure 1000 levels of intensity, and we call this the dynamic range of the camera. 1000 isn't an exact power of 2, so instead we would most likely store the image in 10-bit, or 1024 greyscales, with the remaining 24 greyscales not making a significant difference to the overall accuracy of the measurement. 

However, for a variety of reasons, computer data structures are easier to handle if they are made up of groups of 8 bits. So the most common image file formats usually store the intensity data as either 8 or 16-bit. 

8-bit gives us 256 greyscales, for values going from 0 to 255. This is not a lot compared to the 1000 greyscale dynamic range of the sensor we just discussed above, but it is also roughly twice as good as the human eye can normally manage. In fact, because of this, most computer displays are limited to 8-bit display ranges, and conversely, higher bit depth images are displayed with this 8-bit display range.

With this in mind, we might ask what the utility is of storing the images in 16-bit, and this brings us back to what we mentioned earlier about measuring low levels of light.

A camera with a full well capacity of 10000 electrons and a read noise of 10 electrons might be OK for a brightfield system where we are collecting a lot of light, but a high-end fluorescence imaging sensor for low light imaging might more likely have a full well capacity of 80 000 electrons and a read noise of 2 electrons, which would give us an effective dynamic range of 40 000 greyscales. However, in low light imaging scenarios, the exposure time required for the highest intensity pixel to collect 80 000 photo-electrons might be measured in seconds. Exposing our sample for that length of time will probably be impractical for a range of reasons:

• our sample might be very dynamic and might move or change during that time
• such long exposure time might cause our excitation light to bleach the sample or kill it through photo-toxicity
• waiting several seconds to take a single snapshot would also make the acquisition of multiple Z planes less practically feasible

For all these reasons we might compromise and settle for a much shorter exposure time. 

So, let's consider a case where we might have an ideal exposure time of 10s to collect 80 000 in at least 1 pixel. Instead, we might compromise and choose a 100ms exposure time and only collect 800 photo-electrons or 1/100th of the maximum intensity range. If we stored this image in 8-bit, we would only have 2, maybe 3, greyscales. If we stored these images in 16-bit instead, we would have 600 greyscales, and measurements of the difference between the brightest and darkest pixels in the image would be a lot more precise.

So, in the end, we store the images in 16-bit, not because we expect to accurately differentiate between 65 536 levels of intensity accurately, but because we might only collect a small fraction of the maximum intensity range and we still want to be able to work with that.