Tonal Range in Digital Cameras

Or, to continue with this analogy will the 4-bit processor simply position itself toward the mid greys (partially filled pixels) recorded by the sensor and simply ignore the very bright and very dark areas' and then as you add bits more and more shades of grey at either end are added.

The photographer chooses the "position" of the bits when he chooses exposure so a 4 bit converter can't position itself in the middle, it will always be placed at the "top". Doing otherwise would be kind of like using mismatched ISO processing.

If you assume a 4 bit converter with today's modern DSLR photosites, there would be 6-11 stops of wasted dynamic range that the converter couldn't take advantage of. That would mean that you could increase ISO at least 6 stops from base without increasing noise. We see an example of that in the first generation 5D. Its photosites were capable of well in excess of the 12 bits its converter offered so you could bump the ISO several stops without penalty.

OK; clear. So one final clarification then. A 4 bit convertor would be able to record the increased high end DR of a high end sensor, or possibly the low end if so exposed, but not both.

To answer that, does the 1 bit case have 1 stop of range or almost 2?

1 Stop is 1 stop. sure...

But what is 1.9?

OK; clear. So one final clarification then. A 4 bit convertor would be able to record the increased high end DR of a high end sensor, or possibly the low end if so exposed, but not both.

Yes.

1 Stop is 1 stop. sure...

But what is 1.9?

This is tricky.

The total dynamic range of light is 2^n where n is what we call "stops". The total dynamic range of an integer is 2^m where m is the number of bits in the word. As you can see, the number of bits is directly analogous to the number of stops in an ideal linear system. It can't be any other way. Of course, that doesn't help with the confusion but hopefully it tells you what the answer is when intuition is telling you otherwise. It also doesn't help when there is fractional stops since you can't have fractional bits. It does tell you how many bits are needed for a given sensor capability though.

I'll attempt to describe this another way. I'm not a teacher and my engineering classes are 25+ years old at this point.

Any given intensity of light can be approximated by a sum of light sources of fixed intensities that are properly chosen. Let's say we have 3 different light sources where the first light source, A, is the brightest, the second, B, is precisely half as bright as the first, and the third, C, is half as bright as the second. In this case, we can describe any light source that isn't too bright using one of 8 values:

A B C : 0=off 1=on

=============

0 0 0 - darkest

0 0 1

0 1 0

0 1 1

1 0 0

1 0 1

1 1 0

1 1 1 - brightest

There may be considerable error in our crude representation of light because we have only 3 measurements. That error is called quantization error.

A 3 bit linear A-D converter will generate a value that directly corresponds to the control word that determines which lights are turned on and off above. The reason for that is the converter outputs binary and we carefully chose our light sources to work in powers of two. As I've said before, a 3 bit converter will have 3 stops of range so that's what this system has, yet there is only 2 stops difference between the 3 reference light sources. The reason for that is that we can turn all the lights off or all of them on. That's what you are observing, rachid. All those "extra bits" are producing almost an extra stop; those combined with all zeros yield the last stop that means that 12 bits is 12 stops rather than just 11.

I hope that explanation helps. I've considered these things as one in the same for so long because of my background that I struggle to even explain it.

I hope that explanation helps. I've considered these things as one in the same for so long because of my background that I struggle to even explain it.

Hi Craig,

it helped! i understand you and now i have to think about.

I should drink one espresso more. That helps

rachid