I first read about the “digital linear effect” in Chris Johnson’s book The Practical Zone System for Film and Digital Photography (4th edition, 2007). Apparently digital camera sensors respond to light in a very linear manner and he explains it as follows:
Imagine that a digital light sensor is like a container that responds to light by filling up with photons until it reaches its capacity. The brightest light values make the strongest impact on the sensor, so are the ones collected first. (He assigns 6 stops of contrast and 12 bits of data range to his “sensor”.) Now, since the sensor can record up to 4096 levels of tone,
- the first and brightest stop of exposure fills up with half the total tonal range, i.e. 2048;
- the second stop of exposure fills up with half the remaining tonal range, i.e. 1024;
- the third stop of exposure fills up with half the remaining tonal range, i.e. 512;
- the fourth stop of exposure fills up with half the remaining tonal range, i.e. 256;
- the fifth stop of exposure fills up with half the remaining tonal range, i.e. 128;
- the sixth, last and darkest stop of exposure fills up with the remaining tonal range, i.e. 64;
This produces a six division zone system map, from darkest to brightest, of 64–128–256–512–1024–2048.
Johnson now makes two deductions based on this information:
- the fact that so few levels of tone are available for the shadows explains why banding, noise and posterization occurs when the contrast of underexposed images is expanded; and
- if images are exposed for the highlights, then the shadows will fall on exposed stops as near to the middle of the tonal range, giving us more levels for editing.
Unfortunately Chris Johnson is completely wrong. Digital camera sensors do not work as he describes them. A digital sensor is, for simplicity sake, millions of photovoltaic cells. Each cell produces a voltage depending on the amount of photons falling on it. The more photons, the higher the voltage. This voltage is then read by the electronics in the camera and converted to a digital value.
For example, say that at saturation (brightest recordable level of light) a cell has a potential difference of x volt. At this voltage the A/D circuitry records a value of 4096 and, since the linear sensor can record 4096 values, that means each bit equals x/4096 volts. Now, given the same 12 bits of tone as above, a digital sensor responds to light from shadows (0 and 0 volts) to highlights (4096 and x volts) — same as film — and not from highlights to shadows, as Johnson says.
A digital sensor also does not work in “stops”. It is a linear device. The data from the sensor, and therefore (hopefully) also of the RAW file, is the linear values of each photovoltaic cell in the sensor. These values are only converted to a logarithmic scale based on how we see and which is similar to film, during post-processing — either by the camera or in the digital darkroom.
Let’s get back to Johnson’s deductions,
- the garbage we see in the shadow areas of a digital photograph are electrical in origin and has nothing to do with the “digital linear effect”. The causes are a combination of electrical cross-talk (an electrical conduit generates a magnetic field, which induces a potential difference on adjoining conduits) and the noise of the op-amps boosting the voltage for use by the A/D converter (the lower the voltage, the higher the amplification — we know the amplification factor, so just divide the read voltage by that value to get the real voltage).
- exposing for the highlights generally produce an over-exposed image and throws the whole zone system out the window. Remember that camera designers strive to recreate the characteristics of film as far as possible, for not only is it traditional but also reflects how we humans see. All spot and centre-weighted average meters in every digital camera still uses 18% grey, i.e. Zone V.
Conclusion is that although digital sensors are linear in nature, the electronics inside the camera are designed to convert it to the traditional, zone system complient, same as film, non-linear, logarithmic tonal range. Furthermore, the electronics are designed around the specific sensor to which it is coupled. By shooting in RAW, you remove this carefully designed system and replace it with a one-size-fits-all programme. This is why it is necessary to shoot straight to JPEG: so the camera can do its work correctly.
However, as a general rule it is much better to over-expose a digital image by half a stop than to under-expose it, as I tended to do with negative film. But this is still no substitute for getting the exposure right the first time at the moment of pressing the shutter release buttom, like we must do with slide film.
On the other hand, suppose digital sensors are not linear... then this whole page is moot, as well as the reasons for shooting in RAW.