Dynamic Range

Exposure and Dynamic Range

By Bob Newman, first published December 2012

Revisiting exposure

In my last article, the nature of the photographic quantity ‘exposure’ was explored. To recap, exposure refers to the amount of light incident on the sensor, the sensor illumination times the exposure time. The amount of light determines the number of photons making up in the image, which in turn sets the amount of visible noise, according to the square root of the number of photons compared across like sized patches, be they input pixels, output pixels or just a size dictated by the limit of human acuity. This article will consider exposure in the context of a frequently discussed quality of digital photography, dynamic range.

What is dynamic range?

Dynamic range is a term which has been borrowed from electronic engineering and considering that digital cameras are electronic, this rifling of terminology is hardly surprising. However, it’s meaning has become somewhat more diffuse as photographers try to equate this abstract engineering term with what they see in their photos. Strictly, ‘dynamic range’ is the ration between the largest recordable (or transmittable) signal and the smallest one. The largest is usually determined by the signal capacity of the storage medium or transmission channel. What determines the smallest is somewhat more complicated, but that will be addressed later on. Since it is a ratio, it is simply a number, there are no units involved. Rather than expressing it as a straightforward denary quantity, it is generally more convenient to use a logarithmic representation. In Electrical engineering this would be as a logarithm to base ten, the conventional term being the ‘decibel’, which is 20 times the logarithm to base ten of the ratio. For photographic purposes a more convenient radix is two, since we are used to dealing with it in the form of Exposure Values (EV) or ‘stops’. For the rest of this discussion, we’ll use ‘stops’. Table 1 gives the equivalence between the raw ratios, stops and decibels.

Figure 1: Sixteen different shades (top) become blurred together when subjected to noise (bottom).

Back to what determines the minimum possible signal. This is the point where electronic engineering and imaging begins to diverge. For the electronic engineer, the minimum possible signal is determined by the irreducible level of noise, or random variation, in the channel – if the signal is lower than this it cannot be easily retrieved. So, the conventional definition of dynamic range is the magnitude of the maximum possible signal divided by the magnitude of the ‘noise floor’. This definition is commonly used when measuring cameras and in this case the noise floor is defined by the read noise. However, photographically having image detail at the same level as the noise is unacceptable for photographic purposes, so the ‘dynamic range’ measured this way does not give a good indication of the tonal range available in a photograph.

Dynamic range and tonal range

A photographer is interested in what range of tones can be rendered in an image, which we might call the ‘tonal range’ as opposed to the ‘dynamic range’. Simply, the ‘tonal range’ would be an estimate of the number of tones available from the brightest to the darkest that the camera can capture. The number of tones available is determined by the noise level. Figure one shows a range of sixteen tones from white to black at the top. They are clearly distinguishable. Below are the same range of tones with noise added – they are no longer discernible as separate tones. Thus to determine the tonal range of an image it is necessary to take into account the amount of noise in the image. As was discussed in the last article, the amount of noise is dependent on the exposure, since the exposure determines the number of photons collected, and that in turn determines the signal to noise ratio due to shot noise, which is the square root of the number of photons per observed sample. So, as the exposure is greater the signal to noise ration is higher (meaning less noise), and a greater number of tones may be differentiated. The outcome of this is that the dynamic range does not by itself determine the available tonal range.

Same DR, different tonal range.

The see why, examine the two photographs in Figure 2. Both of these have eight stops of dynamic range – the largest signal is 256 times the smallest. However, the level of the smallest signal is different. In Figure 2a the camera, a Canon 5D, has been set to 100 ISO, at which setting the residual read noise is 32 electrons per pixel. Thus the level set for the upper end of the dynamic range is 32 ´ 256, or 8192 photoelectrons per pixel. In figure 2b the camera has been set to 3200 ISO, where the read noise is 4 electrons per pixel. The upper end here is 8 times lower or 1024 electrons per pixel (note that to achieve the same DR the nominal ISO exposures have not been used, there is in fact three stops between the exposures, not the five that the ISO settings would indicate – using the camera in manual mode allows the exposure to be chosen at variance with the meter).

Figure 2 (a) and (b): Two shots with the same dynamic range but different noise. (a) has 8 stops above 32 electrons per pixel of noise. (b) has 8 stops above 4 electrons per pixel of noise. (c) the crops reveal that (b) is noisier, even though it has the same dynamic range.

Figure 2 (c) and (d). Crops from different areas.

Looking at the images overall the same features are visible in both the bright parts and the shadows, because the dynamic range is the same. Thus, in both the shadows become featureless blackness at the same level of darkness. However looking at the crops from the two, it can be seen that the lower exposure image (Figure 2b) is decidedly noisier at all brightness levels – there is even appreciable noise in the sky. This is to be expected, because lower exposure causes more noise, regardless of the dynamic range. It shouldn’t however be thought that this result means that the high read noise of this camera is a good thing, it is the high exposure that has caused the lowering in noise and that could have been used even had the read noise been lower. The effect of lowering the read noise would be an increase in dynamic range and in this case visibility of features in the shadows, rather than the ‘plugged’ appearance in these pictures.

The other lesson to be drawn from this experiment is that it is the actual exposure that determines the top end of the dynamic range (and also the tonal range) rather than the ISO nominal exposure or the sensor’s saturation exposure. In this case the camera had capacity for at least two stops more exposure and using those would have increased both the available dynamic range for the shot, and the tonal range.

In summary, if noise and dynamic range is your criterion for image quality, then the aim of exposure management must be to maximize exposure, that is for a given light use the longest shutter speed and largest aperture you can, and the result will be the best dynamic and tonal range that can be achieved in those conditions with your camera. Of course, there are limits to both shutter speed and aperture. Shutter speed will usually be limited by the amount of motion blur that can be tolerated, caused either by camera shake or subject movement. Aperture will be limited by depth of field requirements or by a desire to use the lens near its peak performance. In either case, it is often the desire to take the picture that you want that limits the possible image quality, less frequently is it the limitations of the camera or the absolute dynamic range that it can achieve.

Table 1

Ratio	Stops/EV	decibels
1	0	0
2	1	6.02
4	2	12.04
8	3	18.06
16	4	24.08
32	5	30.10
64	6	36.12
128	7	42.14
256	8	48.16
512	9	54.18
1024	10	60.20
2048	11	66.22
4096	12	72.24
8192	13	80.26
16384	14	86.28