Let's talk about linear to log, A-to-D in digital cameras

[Carl Looper]

If the difference between the darkest stop and next darkest stop is just one value/bit at capture, it doesn't matter if the ADC converts that difference to, let's say, 100 values, there's still not gonna be any usable values in the between because a linear sensor doesn't seem to be able to distinguish 100 shades between those two darkest stops.

 

And after converting those linear values to log in order to ~evenly~ distribute those stops into a 8/10/12 bits image, those two darkest stops will still be easily distinguishable by us, without any usable information in between.

 

The example above is a depiction of the 2 darkest stops after ADC log2 conversion, considering an image captured with a camera able to see 10 stops and 10 bit capture sensor into a 8 bit image. (I just put a black square next to a 10% bright square on a 8bit image)

 

It's clear the difference between those two shades, and without dithering there might exist clear banding on the darkest tones of the image.

 

But this doesn't seem to happen in reality, as it would be too noticeable, right? Maybe because of contrast curves or because the sensors don't use the lowest range they capture, maybe because of noise, or most likely because I'm misunderstanding something with the sensor's capturing process.

 

A 10 bit capture doesn't mean a capture of 10 values, if that is what is meant by using a figure of 10%. 10 bits means a capture of 2^10 values, ie. a capture of 1024 values. In other words the Sensor/ADC divides the incoming light up into 1024 shades. So try 0.09% instead. In the same way an 8 bit ADC divides a signal up into 2^8 values = 256 values (not 8 values).

 

Also sensor/ADCs will be capturing a distribution of target digital values as close as possible to a desired log/gamma/etc distribution during digitisation. Not afterwards. Some post processing will be cleaning up the top and tail and otherwise correcting for any deviation from the ideal target distribution. In other words the ADC itself will be programmable in terms of the distribution of values it will be extracting from a signal.

 

C

Edited September 15, 2015 by Carl Looper

[Carl Looper]

The term "stops" is not the same as the term "bits". The former is used to quantify a continuous signal. In other words you can have fractions of a stop (to whatever infinitely small fraction you like) whereas you can't have fractions of a bit.

 

Photons are likewise a continuous signal (strangely enough) despite the fact that photon detections are quantised. In quantum physics there is a function called the "wave function" which is a continuous signal. This signal is what we actually see when looking at the distribution of photon detections (rather than when we're looking at any single detection). We see the pattern of such detections, or what we otherwise call an image. The relationship between this image and any particular detection is quite peculiar (and the subject of endless debate in quantum physics). Basically photon detections (the marks made) are only statistically related to the wave function (the signal, the image) rather than strictly mathematically related (and causing Einstein sleepless nights). So the wave function squared is said to describe the probability of a photon detection occuring at a given point in space and time.

 

So a photon detection is always an approximation of what is otherwise occuring. Detections are noisy with respect to the signal they otherwise inscribe. For example, in quantum physics there is no such thing as zero energy. So if we detect zero photons, it is only because zero is an approximation of whatever the actual value (given by the wave function) would be.

 

C

Edited September 15, 2015 by Carl Looper

[Dinis Rodrigues]

 

A 10 bit capture doesn't mean a capture of 10 values, if that is what is meant by using a figure of 10%. 10 bits means a capture of 2^10 values, ie. a capture of 1024 values. In other words the Sensor/ADC divides the incoming light up into 1024 shades. So try 0.09% instead. In the same way an 8 bit ADC divides a signal up into 2^8 values = 256 values (not 8 values).

 

Also sensor/ADCs will be capturing a distribution of target digital values as close as possible to a desired log/gamma/etc distribution during digitisation. Not afterwards. Some post processing will be cleaning up the top and tail and otherwise correcting for any deviation from the ideal target distribution. In other words the ADC itself will be programmable in terms of the distribution of values it will be extracting from a signal.

 

C

You completely misunderstood me then. :P

 

Yes, in that case 10 bits mean 10 values, but at the limit of those two darkest stops, if light stops weren't exponencial. What I mean is, that even though 10 bits are indeed 1024 values, the number of values captured between the darkest stop and the next darkest is zero, while the number of values between the two lightest captured stops should be 510 values.

 

When that exponential behavior is converted into logarithmic, then you get a constant and even distribution (theoretically) of bits between those 11 stops, like 102,4 between each stop, but if you had no information in the first place between those two darkest stops, then there's no information to distribute between those two stops when it's converted into log.

 

But as David said, noise makes a lot of sense as a reason why we don't notice those harsh differences. In a way it's selective dithering to the darkest parts of the image.

[Carl Looper]

You completely misunderstood me then. :P

 

Yes, in that case 10 bits mean 10 values, but at the limit of those two darkest stops, if light stops weren't exponencial. What I mean is, that even though 10 bits are indeed 1024 values, the number of values captured between the darkest stop and the next darkest is zero, while the number of values between the two lightest captured stops should be 510 values.

 

When that exponential behavior is converted into logarithmic, then you get a constant and even distribution (theoretically) of bits between those 11 stops, like 102,4 between each stop, but if you had no information in the first place between those two darkest stops, then there's no information to distribute between those two stops when it's converted into log.

 

But as David said, noise makes a lot of sense as a reason why we don't notice those harsh differences. In a way it's selective dithering to the darkest parts of the image.

 

There is no case in which 10 bits means 10 values.

 

The term "stop" doesn't describe the difference between adjacent values. If there is an optimum capture of (say) 10 stops, across 1000 values, then each stop is represented by 100 values. Or to put it another way, each value would represent 1/100th of a stop.

 

But I think I see what you are suggesting - that you are roughly approximating what a linear sensor might be producing at the darker end (if the signal wasn't noisy). But not sure how you came up with 10%. In any case imaging sensors are not linear in the first place. They will already be sampling the sensor signal according to the already well understood idea that a non-linear log capture (or something similar to such) is far far better than a linear one.

 

C

Edited September 15, 2015 by Carl Looper

[Carl Looper]

I understand now where you got 10% from, and what you are otherwise saying: if it was a 10 bit linear sensor, then at the darkest end one could use a 10% difference from an otherwise log2 distribution to represent what a linear sensor would otherwise see at that end.

 

That we don't see such a large difference (10%) suggests that either noise is otherwise dithering the difference at that end, or that sensor signals are not being sampled in a linear fashion.

 

C

Edited September 15, 2015 by Carl Looper