raptor3x said:

Neutral said:

raptor3x said:

Sporgon said:

jrista said:

You CAN preserve the highlights, and still have better shadow tonality, than with a Canon camera. I mean, we are talking about total tonality of around 2100-2400 tones on a Canon, and anywhere from 7300 to 8100 tones or more on Exmor-based cameras. The entire tonal range of a Canon camera can fit within the shadow quarter of the signal on an Exmor...I mean, think about it: 8000/2000...if you consider the bottom quarter of the signal to be "the shadows", you could fit an entire Canon exposure in the shadows of an Exmor, and have the same tonality. Earlier highlight clipping? Saturation falloff? That's a total misnomer. You have GOBS more tonality in an Exmor signal than a Canon has in it's entirety, and you have as much tonality just in the shadows as a Canon has in it's entirety. There is no such thing as early highlight clipping or blue saturation falloff with an Exmor...

That sounds so impressive.

You'll be able to see that 8000 / 2000 difference here then.

Just to reiterate, because you may not have caught it, jrista was confusing dynamic range with tonal range. You can't just take 2^(# stop DR) and say that's the number of tones the camera can represent. Dynamic range represents the ratio between the lowest and highest tone that can be represented, but the actual number of tones that can be represented within that range is dependent on the quantization of the signal into discrete levels, which is in turn dependent on the standard deviation of the signal as a function of intensity. Just as an example, no current 35mm camera is anywhere close to being able to represent 8000 levels of grey in a single shot. The D810 would be closest with up to 910 tonal levels at ISO 64. To compare that with the 1DX, the 1DX has up to 648 tonal level at ISO 100 (the D810 has 792 at ISO 100). Comparing the 1DX and A7S at ISO 12800, the 1DX has a potential of 77 tones while the A7S has up to 84 tones; certainly an improvement but not the revolution jrista implies (at least not in terms of tonality). The real strength of the A7S is how amazingly well it preserves color and detail at high ISO, much better than the 1DX once you get above ISO 25600.

Could you please clarify your calculations on numbers of possible tones values?

This does not seem correct to me.

Here some basic math from theory of signal detection:

In general possible number of detected tones has limit of number of quantization levels if signal noise is going to zero.

Each quantizatin level is a decision slot for assigning digital value to the received analog signal at the input of ADC. For 14 bits ADC there are 16384 possible representatin of input analog signal. In theoretically ideal situation (with zero input analog signal noise) there are 16384 possible tonal values that could be assigned to received input analog signal.

Now when we come to real systems with noise (regardless of the noise origin) we have fundamental thing which is called SNR which affects precision of the signal detection - in our case to which tonal slot signal will be assigned. More signal noise more probability that signal will be assigned wrong digital value. Roughly if 99% of the signal energy is within particular decision slot ( in the center of it) then there is possibility that there is 99 percent probability that signal will be assigned correct value and 1% that that will be assigned value from adjucent decision slot. For image sensor this will result in 1% variations in image tonality signal with given noise level and noise distribution pattern. If signal value is on boundary of decision slot with the same conditions as above than there will be 50/50 distribution for output value assignements. This is actually why possible tonal values are less than ADC quantization levels.

This is actual limitation of one dimention signal detector when only signal amplitude modulated with noise is taken into account.

So overall all depends on number of signal detector decision slots and intensity and distribution pattern of the signal noise and actual signal level at the input.

If majority of signal noise power spectrum width becomes wider than width of the decision slot than this is where we would see that number of the possible correct tonal numbers would be reduced.

Also errors in signal values assignmets would be more frequent for lower level signals - this is just signal detector SNR function for two input noise varàibles - read noise and photon noise in our case.

I do not think we need to go more deep into that. These are just basics.

So according to all said above Jrista calculations seem correct to me.

If you can actually prove that this is different and Jrista is not correct somewhere I àm really interested to see that.

Sorry for the delay, I was away all week. You're both missing that the width of the quantization for non-overlapping levels is limited by the STD of the signal as a function of signal level. You have to actually perform the integration, or more realistically the summation, over the entire signal range to get the number of tonal ranges. You don't need to take my word for it though,

DxO does the exact same thing;

that's actually where I took the numbers from.

It is nice to have some interesting and useful discussions.

What you were mentioning and what is illustrated in DXO tonal range chart is basically the same what I was talking about signal detection in presence of noise and having ADC to assigning digital values (combination of analog and digital circuits).

Exactly this relates to the part where I was talking about signal detection decision slot width and width of the signal spectrum containing most of the signal energy (analog tone strip width). Signal detection decision slot width is basically ADC quantization step for ideal (theoretical) signal without noise and for real signal with noise the other limitation is tonal strip width which is STD dependent. Both together puts limit at number of possible tonal values at both ends of dynamic range at the output of ADC.

And DXO tonal range charts bring us to something interesting which might not be actually very obvious.

Even I was not paying attention to this earlier.

Before going there in more details I need to clarify some things related to relations between signal levels , SNR and STD as I feel that this is kind of confusion for most of the people here.

What is important here is what I mentioned before - signal detection decision slot size/width (ADC quantization step) and width of the pure sin(x) signal spectrum with added noise (basically width of the tonal strip before ADC).

Here some simple as possible explanations, by simple steps - simple math and outcomes of that:

1. As a starting point:

STD of ideal signal (e.g. F(x)= A * sin(x) ) without noise is always zero regardless of the signal amplitude. Changes of signal amplitude A do not change STD - it is always zero.

Also number of possible different values between value M and value N is always infinity even if difference between M and N is decreasing to zero (N-M->0).

2. Signal-to-noise ratio is inversely proportional to the relative standard deviation of the signal amplitude

3. STD for signal with the fixed noise level is decreasing if you increase pure signal level and keep noise level at constant value.

What this actually means is that more SNR results in less STD and more narrow is spectrum strip containing 99% of the signal energy.

4. STD for given SNR is constant if you are increasing value of the (signal+noise) not changing SNR - actually doing amplification of the real signal with noise - amplification does not change SNR and as result STD is also not changing. Outcome of this is that noise spectrum width is increasing with the increased level of amplifications. In other words tonal strip width is increasing with amplification and it takes width of more and more signal detection decisions slots.

5. If you decreasing SNR for given pure signal level (adding more noise to the fixed signal) this results in increasing STD of the signal mix with noise . Result of this is that noise spectrum width (or tonal strip) becomes wider. This width eats up more and more ADC signal detection decision slots.

Result of this is that number of distinguishable tonal strips across system dynamic range (before ADC) is also decreasing.

Results for sensor - less tonal values.

6. Worst case scenario when you amplifying signal while decreasing SNR - this results in both increase of STD and non liner but rather exponential increase of noise amplitude spectrum width.

So for sensor this results in even less possible tonal strips across system DR range before ADC and even less values after ADC conversion.

This is actually what is happening when increasing camera ISO settings to compensate for lower input light entering camera - doing more amplification for the signal with less and less SNR to cover full ANC input DR .

All above is illustrates of what we see on the DXO tonal chart and basically this give something which I find interesting for overall systems understanding and understanding better their physical limits.

It seems that the reason why tonal numbers are so close for sensors with different DR and different sensor read noise is the noise factor which is independent from the sensor.

This is actually seems to be photon noise which is reducing tonal range differences between different systems.

Photon noise is basically photons 4D jitter (time+ x,y,z variations).

Result of this that is for given integrating time (exposure ) there will be variations of the signal levels of the optical detector .

It seems that for sensors with low read noise photon noise starts adding more to the overall system noise compared to the read noise. It looks from DXO chart that photon noise is about the same order as read noise for existing Canon sensors (may be somewhat smaller) and more than read noise of best Exmor sensors and as result tonal strip width is bigger than ADC quantization step

As result overall noise (read noise +photon noise) amplitude spectrum width (which is basically visual representation of STD) is very close for all existing systems so we see that that number of possible tonal values (tonal strips) is close for different systems even when system has MF with 16bit ADC compared to DSLR with 14 bit ADC (e.g. look at medium format - e.g. IQ180 chart compared to 1Dx )

Seems that there are not two many ways to have some improvements in this area:

1. Have lower possible in camera native ISO (ability to have longer light (photon noise) integration time and longer read noise integration time)

2. Have higher photocell well capacity (increasing DR by increasing max number of photos received before reaching saturation point). Here is where BSI sensor could be useful. Also still reducing read noise.

3. Both 1 &2 above would reduce tonal strip width and as result increase tonal range at low ISOs

4. Exposure blending - this is basically results in increasing normalized SNR (by reducing STD) - this works across whole ISO range.

All that is not very exiting , may be DXO measurements are not correct somewhere ?

Maybe I am missing something ?