Pixel size and dynamic range

[klitza]

I am confounded by the (often cited) discussion on Cambridge Colour of the relation between pixel size and dynamic range, and the suggestion that larger pixels mean less overflow. A large pixel, compared with its two halves, will receive exactly the same number of photons (on average) as the sum of the two smaller ones, and so should be subject to exactly the same danger of overflow, according to the bucket metaphor used by Cambridge. Is the answer instead in a second-order effect, namely Poisson fluctuations (either in the light flux or in the A/D conversion) playing a smaller role with larger buckets?

[Manfred M]

The comments are not pixel size and dynamic range, but pixel size and noise and high ISO performance

Your assumption is incorrect as larger sized photodiode captures MORE photons (it will have a larger surface area), which means there will be proportionately less noise captured versus good data.

Dynamic range is related to sensor capabilities and the dynamic range of any camera is always highest at the base ISO setting.

[xpatUSA]

I am confounded by the (often cited) discussion on Cambridge Colour of the relation between pixel size and dynamic range, and the suggestion that larger pixels mean less overflow.

Is there a link or links to where that suggestion was made?

"Dynamic Range" has several different definitions. Which one did you have in mind?

Doug Kerr discusses ISO's definition here:

http://dougkerr.net/Pumpkin/articles...amic_range.pdf

A large pixel, compared with its two halves, will receive exactly the same number of photons (on average) as the sum of the two smaller ones, and so should be subject to exactly the same danger of overflow, according to the bucket metaphor used by Cambridge.

Correct in the most simplistic of terms and in accordance with the bucket analogy. I'm a bit confused by the phrase "danger of overflow" as if somehow probability is involved.

Is the answer instead in a second-order effect, namely Poisson fluctuations (either in the light flux or in the A/D conversion) playing a smaller role with larger buckets?

On my Sigma cameras, there is a low-resolution mode where 4 pixels are binned together on the sensor. Noise is reduced by binning even though the number of photons collected per sensor unit area remains the same. If the noise is less (all other things being equal), then the dynamic range is more.

The ISO definition provides a headroom below saturation (well full), therefore concerns about overflow do not apply in their standard.

You might be less confounded if you consider Signal-to-Noise-Ratio rather than dynamic range.

[klitza]

I'll try again. I am NOT concerned with noise, but the opposite end of the photon range, namely overflow of the bin, i.e. too many photons leading to bleaching, and total white. Two pixels, each half of a larger one, will receive in total the same number of photons as the larger one. That's not rocket science. If their capacity, i.e. their limit before overflow, is half of the larger one, then the danger of overflow in any one of them is one-half of that for the larger one, but the total danger is the same. Thus pixel count, for the same size sensor, seems to play not role in overflow.

[xpatUSA]

I'll try again. I am NOT concerned with noise,

Then perhaps a Moderator should remove "dynamic range" from your title.

but the opposite end of the photon range, namely overflow of the bin, i.e. too many photons leading to bleaching, and total white.

I think we get it, in spite of the interesting phraseology.

Two pixels, each half [the area] of a larger one, will receive in total the same number of photons as the larger one.

Obviously.

That's not rocket science

Nobody said it was.

. If their capacity, i.e. their limit before overflow, is half of the larger one, then the danger of overflow in any one of them is one-half of that for the larger one, but the total danger is the same.

Obviously.

Thus pixel count, for the same size sensor, seems to play not role in overflow.

Seemingly so

For those of us less knowledgeable, could you please explain the exact mechanism of "overflow"?

[klitza]

Thank you - I think we are making progress. My use of the word "overflow" , well, flows from the bucket metaphor used by the Cambridge Colour site to explain buckets getting filled to the point of overflowing, and so any additional photons that come along are wasted; and accordingly one has a loss of subtlety in the colors of a bright area such as a sky That problem is just one-half of the dynamic range problem, noise being the other. To fight the noise problem, one uses as low an ISO as possible, and/or use a smaller number of pixels. To fight the other end, one might underexpose and then brighten dark areas up while editing. It looks from your comments that you agree - one can not fight that second problem by choosing a camera with fewer pixels.

[dem]

The dynamic range that a pixel can record is defined as the log of the ratio of the maximum signal (the overflow capacity) to the total noise (of which shot noise is the main component under the overflow conditions).

As you say, the signal (the number of photons, N) is proportional to the pixel area.

The shot noise is proportional to the square root of the signal (sqrt(N)), not the signal itself!

That is why the signal-to-noise ratio, and the dynamic range, changes with pixel size - the larger the pixels, the higher their dynamic range.

The same logic explains why dynamic range decreases with ISO by about 1/2 stop per 1 stop of ISO.

[Manfred M]

When you refer to "overflow", you are effectively writing about when the digital conversion process has assigned the maximum value to the pixel. This can have two causes:

1. Overexposure, which can be corrected by letting less light hit the sensor through the usual means of smaller aperture, higher shutter speed, reducing the ISO or using a neutral density filter.

2. Exceeding the dynamic range of what the sensor can handle. This, at base ISO, can be in excess of 14 stops on a modern camera.

[pnodrog]

There is of course another dimension to this discussion. Well capacity is not solely set by area of light collecting surface.

[Manfred M]

To fight the other end, one might underexpose and then brighten dark areas up while editing.

This is a great way of introducing noise into your image, so not a recommended approach.

If you are posting your images to the internet only, then any resolution sensor is going to be fine, as your final output is going to be in the range of 2MP for a standard screen and 8MP for a 4K resolution screen. If you are printing, then you will be sacrificing resolution for other image aspects.

I am really quite puzzled as to what issue you are trying to solve as for the type of shooting I do, my high resolution (36MP) camera seems to handle dynamic range quite nicely at base ISO and I rarely have to deal with issues where I blow out my highlights.

[dje]

If their capacity, i.e. their limit before overflow, is half of the larger one, then the danger of overflow in any one of them is one-half of that for the larger one, but the total danger is the same.

Hi klitza

I think where your reasoning is falling down is in your statement "but the total danger is the same". This doesn't really make sense to me.

The smaller pixels will have smaller full well capacity than the larger ones which means they will produce a lower maximum output voltage than the larger ones. This is the fundamental limit to the upper value used in a dynamic range calculation.

Roger Clarke's article here might help.

For a modern CMOS sensor, the saturation characteristic is more complex than a simple full well point. As signal is increased, non-linearity creeps in before complete saturation occurs. The ADC range is usually adjusted so that the non-linear part is not used. ie the ADC reaches it's limit before full well capacity. And of course as ISO is increased from the base value, the full well capacity of the sensels is never reached anyway.

Dave

[MrB]

Overexposure, which can be corrected by letting less light hit the sensor through the usual means of smaller aperture, higher shutter speed, reducing the ISO or using a neutral density filter.

?

Cheers.
Philip

[xpatUSA]

The smaller pixels will have smaller full well capacity than the larger ones which means they will produce a lower maximum output voltage than the larger ones.

Sorry, Dave, that's the wrong way round. Smaller pixels have a smaller capacitance which increases their output in terms uV/e- (microvolts per electron).

For example my SD10 with a pixel pitch of 9.12um gives 7.14uV/e- but my SD14 with a pixel pitch of 7.8um gives 9uV/e-.

[Manfred M]

?

Cheers.
Philip

Okay - it still works but there is still the same amount of light hitting the sensor. I should have been more clear.

[dje]

Sorry, Dave, that's the wrong way round. Smaller pixels have a smaller capacitance which increases their output in terms uV/e- (microvolts per electron).

For example my SD10 with a pixel pitch of 9.12um gives 7.14uV/e- but my SD14 with a pixel pitch of 7.8um gives 9uV/e-.

That may be so Ted, I don't know, but your figures are for conversion gain ie volts per electron. The larger pixels will have more electrons and it is the conversion gain and the number of electrons that will determine the output voltage.

Dave

[xpatUSA]

That may be so Ted, I don't know, but your figures are for conversion gain ie volts per electron. The larger pixels will have more electrons and it is the conversion gain and the number of electrons that will determine the output voltage.

Dave

Dave, you said "The smaller pixels will have smaller full well capacity than the larger ones which means they will produce a lower maximum output voltage than the larger ones"

That still doesn't sound right. Were you thinking of the same photon flux and of course QE, perhaps. In which case, taking the capacitance as inversely proportional to the pixel area, the maximum voltage output is the same, not lower.

[dje]

Dave, you said "The smaller pixels will have smaller full well capacity than the larger ones which means they will produce a lower maximum output voltage than the larger ones"

That still doesn't sound right. Were you thinking of the same photon flux and of course QE, perhaps. In which case, taking the capacitance as inversely proportional to the pixel area, the maximum voltage output is the same, not lower.

Ted I think you are on the right track with capacitance and voltage. It would have been better if I had spoken in terms of charge rather than voltage. viz

The smaller pixels will have smaller full well capacity than the larger ones which means they will have a lower maximum charge (smaller number of electrons) than the larger ones. The other end of the dynamic range scale is read noise (at least by one common definition) and read noise can also be measured in terms of charge (electrons). As read noise in electrons is dependant on technology rather than pixel size, if you take dynamic range as the ratio of max charge to read noise charge, you will get a larger dynamic range for the larger pixels (for a given technology).

Dave

[klitza]

Thanks to all from the person who started this thread. Yes, noise is important and has been discussed here beautifully. It is of course the opposite end of the photon flux spectrum that I was concerned with. The consensus is, and I recommend the Roger Clarke article cited above, that the ability to handle large numbers of photons is roughly proportional to size, and so two pixels can handle the same as one of double size. Pixel count thus does not affect the upper end of dynamic range, all other things being equal.
Klitza

[pnodrog]

Thanks to all from the person who started this thread. Yes, noise is important and has been discussed here beautifully. It is of course the opposite end of the photon flux spectrum that I was concerned with. The consensus is, and I recommend the Roger Clarke article cited above, that the ability to handle large numbers of photons is roughly proportional to size, and so two pixels can handle the same as one of double size. Pixel count thus does not affect the upper end of dynamic range, all other things being equal.
Klitza

You obviously knew the answer. I am curious as to what motivated you to ask the question.

[klitza]

I asked the question because I, while a chemical physicist, am a neophyte when it comes to cameras. A recent discussion, perhaps in dphoto review, remarked that Panasonic had cut back the number of pixels in its "travel" cameras, and opined that that would lead to better dynamic range. This sounded unlikely to me. Indeed, it's at the other, the noise end of the spectrum, where any such improvement might be found.