The encoding of pixel values in binary digits involves precisely this phenomenon. If we first assume we have a 4 bits, i.e. 4 zeros and ones available for each pixel, then these 4 bits can be combined in 16 different ways:

Here, the number after the arrow shows how each sequence of bits could be interpreted. We do not have to interpret these particular combinations as the integers from 0–15, but it is common to do so – this is how binary digits are understood using an unsigned integer type. But we could also easily decide to devote one of the bits to giving a sign (positive or negative), in which case we could store numbers in the range -8 – +7 instead, while still using precisely the same bit combinations. This would be a signed integer type.

Of course, in principle there are infinite other variations of how we interpret our 4-bit binary sequences (integers in the range -7 – +8, even numbers between 39 to 73, the first 16 prime numbers etc.), but the ranges I’ve given are the most normal.

In any case, the main point is that knowing the type of an image is essential to be able to decipher the values of its pixels from how they are stored in binary.

So with 4 bits per pixel, we can only represent 16 unique values. Each time we include another bit, we double the number of values we can represent.

Computers tend to work with groups of 8 bits, with each group known as 1 byte. Microscopes that acquire 8-bit images are still common, and these permit 2⁸ = 256 different pixel values, which, understood as unsigned integers, fall in the range 0–255. The next step up is a 16-bit image, which can contain 2¹⁶ = 65536 values: a dramatic improvement (0–65535). Of course, because twice as many bits are needed for each pixel in the 16-bit image when compared to the 8-bit image, twice as much storage space is required - leading to larger file sizes.

Although the images we acquire are normally composed of unsigned integers, we will later explore the immense benefits of processing operations such as averaging or subtracting pixel values, in which case the resulting pixels may be negative or contain fractional parts. Floating point type images make it possible to store these new, not-necessarily-integer values in an efficient way.

Floating point pixels have variable precision depending upon whether or not they are representing very small or very large numbers. Representing a number in binary using floating point is analogous to writing it out in standard form, i.e. something like 3.14 × 10⁸. In this case, we have managed to represent 314000000 using only 4 digits: 314 and 8 (the 10 is already known in advance). In the binary case, the form is more properly something like ± 2^M × N: we have one bit devoted to the sign, a fixed number of additional bits for the exponent M, and the rest to the main number N (called the fraction).

A 32-bit floating point number typically uses 8 bits for the exponent and 23 bits for the fraction, allowing us to store a very wide range of positive and negative numbers. A 64-bit floating point number uses 11 bits for the exponent and 52 for the fraction, thereby allowing both an even wider range and greater precision. But again these require more storage space than 8- and 16-bit images.

Of the two problems, clipping is usually the more serious, as shown in Figure 1. A clipped image contains pixels with values equal to the maximum or minimum supported by that bit-depth, and it is no longer possible to tell what values those pixels should have. The information is irretrievably lost.

Clipping can already occur during image acquisition, where it may be called saturation. In fluorescence microscopy, it depends upon three main factors:

If clipping occurs, we no longer know what is happening in the brightest or darkest parts of the image – which can thwart any later analysis. Therefore during image acquisition, any gain and offset controls should be adjusted as necessary to make sure clipping is avoided.

Rounding is a more subtle problem than clipping. Again it is relevant as early as acquisition. For example, suppose you are acquiring an image in which there really are 1000 distinct and quantifiable levels of light being emitted from different parts of a sample. These could not possibly be given different pixel values within an 8-bit image, but could normally be fit into a 16-bit or 32-bit image with lots of room to spare. If our image is 8-bit, and we want to avoid clipping, then we would need to scale the original photon counts down first – resulting in pixels with different photon counts being rounded to have the same values, and their original differences being lost.

Nevertheless, rounding errors during acquisition are usually small. Rounding can be a bigger problem when it comes to processing operations like filtering, which often involve computing averages over many pixels (see Filters). But, fortunately, at this post-acquisition stage we can convert our data to floating point and then get fractions if we need them.

From considering both clipping and rounding, the simple rule of bit-depths emerges: if you want the maximum information and precision in your images, more bits are better. This is depicted in Figure 2. Therefore, when given the option of acquiring a 16-bit or 8-bit image, most of the time you should opt for the former.