These are independent issues. I can start counting the photons with 10, then 510, 1010, 1510, etc. Then the dynamic range is 60000/10.

But I can start counting with photon 1, then 501, 1001, etc.

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Do you really think you can increase the dynamic range of a sensor by a factor of ten simply by counting {1, 11, 21, ...} instead of {0, 10, 20, ...}? Doesn't that sound ridiculous?

We all agree that it is possible to concoct non-linear counting schemes which provide extended dynamic range with fewer bits. But such a scheme is mathematically impossible for a linear sensor (with an offset of zero).

Here is a thought exercise which might prove interesting. Imagine an array of 120 light bulbs which I want to photograph. The light bulbs have different brightness, with a linear progression. The first light bulb is turned off. The second light bulb emits 500 photons/second into the aperture of my camera. The third light bulb emits 1000 photons/second.... The last light bulb emits 60000 photons/second.

Now I photograph this array of light bulbs with two different cameras in three different scenarios:

1) Camera full well 60000 photons, linear scale counting one photon out of 500, exposure 1 second. This camera images the light bulbs with readings {0, 1, 2, ... 120).

2) Camera full well 60000 photons, linear scale counting single photons, exposure 1 second. This camera images the light bulbs with readings {0, 500, 1000, ... 60000}.

3) Camera full well 60000 photons, linear scale counting single photons, exposure 1/500 second. This camera images the light bulbs with readings {0, 1, 2, ... 120}.

Would you agree with the following statements?

1) The first camera uses its entire dynamic range to capture the scene. If the scene had brighter light bulbs, this camera could not capture them. If the scene had light bulbs with intermediate brightness, this camera could not resolve them.

2) The second camera, with the same exposure, captures the scene with resolution to spare. The captured dynamic range appears to be the same (because the dimmest bulb still has brightness 500 photons/second), but there is plenty of unused space to capture light bulbs with intermediate brightness.

3) The second camera, with reduced exposure, captures the scene with the same resolution (in fact the same numerical output values), but with dynamic range to spare. This camera could capture a larger range of light bulb brightness.

Clearly the two cameras do not have the same dynamic range!