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Understanding Bill Claff's PDR-Shadow-Improvement-vs-ISO chart - as indication of ISO-Invariance

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JohnTheKeenAmateur

JohnTheKeenAmateur

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In this thread: ISO Invariance and Exposure Strategy the OP asked "Can you explain this chart?" ... with reference to Bill Claff's PDR-Shadow-Improvement-vs-ISO chart as published on his www.photonstophotos.net site

I'm repeating my original reply here/below (along with a few embellishments) - as this chart is often referred to, in the context of ISO-Invariance, but I've never seen an explanation of it (that a layperson, like me! might readily understand). So, here's my attempt at doing so.

As per the original thread, I am using the Sony a6000 as an example;

The original OP was wondering about the following chart:

From: http://www.photonstophotos.net/Charts/PDR_Shadow.htm
From: http://www.photonstophotos.net/Charts/PDR_Shadow.htm

------------------------------------------------- My answer to the original OP's question:

I was puzzled/bewildered by this chart too, for quite some time, even after reading the accompanying primer ! ... then, one day, "the penny dropped".

What Bill Claff has done here is both simple and clever.

The starting point for the Photographic Dynamic Range (PDR) Shadow Improvement vs ISO chart (above) is the standard PDR vs ISO chart from his site (as follows);

From: http://www.photonstophotos.net/Charts/PDR.htm
From: http://www.photonstophotos.net/Charts/PDR.htm

To get the numbers for the PDR Shadow Improvement vs ISO chart, Bill imagines/assumes a perfectly ISO-invariant camera - for which there would be an exact decrease of 1-stop of dynamic range corresponding to each 1-stop increase in ISO (eg. as ISO is increased from 100 to 200, 200 to 400, 400 to 800, etc).

He draws a line, starting at the base-ISO point for the camera in question (which is PDR 10.24 at ISO-100 for the Sony a6000) and passing thru PDR 9.24 at ISO-200, PDR 8.24 at ISO-400, etc) ... equating to a 1-stop decrease in PDR for each 1-stop increase in ISO.

Then he measures the difference, at each ISO point, between the theoretical PDR vs ISO line (that a perfectly ISO-invariant camera would display) and the actual PDR vs ISO line (for the camera in question).

For example, at ISO-200, PDR=9.42 - which is exactly what is expected for a truly ISO-Invariant camera. But at ISO-400, PDR=8.73 ... which is 0.49 (1/2 stop) better than the expected 8.24 at ISO-400.

This difference, at each ISO point (eg. 0.49, rounded to 0.5 at ISO-400), is what is being graphed on the PDR Shadow Improvement vs ISO chart.

The basic idea being: If the difference is significant (and especially if it's also non-linear) then it demonstrates that the camera in question cannot be ISO-Invariant - - 'cos that's precisely what it is different from.

------------------

Bill's use of the label "Shadow Improvement" makes sense in the context of this dpreview article ... {A camera with a very low noise floor is able to capture a large amount of dynamic range, since it will add very little noise to the detail captured in the shadow regions of the image. This means you can push those shadow regions and make them visible, allowing you to expose your scene for the highlights, and 'rescue' shadows later.}

Bill's rule-of-thumb for determining the point at which a camera becomes ISO-Invariant is to look for where the curve (on the PDR Shadow Improvement vs ISO chart) stops going up significantly as the ISO setting is increased ... (as well as looking for a flat curve - - signifying consistency with the theoretical ISO-Invariant version of this camera).

eg. Check out the Sony RX10 m2, which exhibits ISO-Invariance tendencies in the range ISO-100 to ISO-5091. On the other hand, I would interpret the Sony a6000 as NOT being ISO-Invariant.



Sony a6000 (Blue curve) c/w Sony RX10 ii (Black curve).
Sony a6000 (Blue curve) c/w Sony RX10 ii (Black curve).

--
Regards, John (the keen amateur)
 
As a follow-up question to my own thread (!)

Why is it that there is a 1-stop decrease in dynamic range for each 1-stop increase in ISO setting ?

Is it, perhaps, that the amplification involved in the implementation of ISO has the exact cause and effect of boosting the signal "over the top" of the pixel's storage capacity ?
 
JohnTheKeenAmateur said:
As a follow-up question to my own thread (!)

Why is it that there is a 1-stop decrease in dynamic range for each 1-stop increase in ISO setting ?

Is it, perhaps, that the amplification involved in the implementation of ISO has the exact cause and effect of boosting the signal "over the top" of the pixel's storage capacity ?
Click to expand...
Yes, independently of whether amplification is implemented in hardware or software if you double the ISO you should get twice the raw value all else equal. But, say, a 14-bit camera has a maximum value of 16000, so if you had some highlights around there and doubled the ISO aotbe, they would be clipped. In fact you would lose a full stop because all values between 8001 and above would be clipped once doubled.

Jack
 
Jack Hogan said:
JohnTheKeenAmateur said:
As a follow-up question to my own thread (!)

Why is it that there is a 1-stop decrease in dynamic range for each 1-stop increase in ISO setting ?

Is it, perhaps, that the amplification involved in the implementation of ISO has the exact cause and effect of boosting the signal "over the top" of the pixel's storage capacity ?
Click to expand...
Yes, independently of whether amplification is implemented in hardware or software if you double the ISO you should get twice the raw value all else equal. But, say, a 14-bit camera has a maximum value of 16000, so if you had some highlights around there and doubled the ISO aotbe, they would be clipped. In fact you would lose a full stop because all values between 8001 and above would be clipped once doubled.

Jack
Click to expand...
Excellent - Thank you, Jack ... I was hoping my intuition was on the right track.
 
JohnTheKeenAmateur said:
As a follow-up question to my own thread (!)

Why is it that there is a 1-stop decrease in dynamic range for each 1-stop increase in ISO setting ?
Click to expand...
That's common, but not necessary. There's no reason why a camera couldn't have the same DR at all ISO settings, and some, like the Sigma DSLRs, do just that.
JohnTheKeenAmateur said:
Is it, perhaps, that the amplification involved in the implementation of ISO has the exact cause and effect of boosting the signal "over the top" of the pixel's storage capacity ?
Click to expand...
No; it's because gain (analog or mathematical) has pushed the upper range of sensor charge to clip in the ADC, or in the firmware math that puts the data in the RAW file.
 
John Sheehy said:
JohnTheKeenAmateur said:
As a follow-up question to my own thread (!)

Why is it that there is a 1-stop decrease in dynamic range for each 1-stop increase in ISO setting ?
Click to expand...
That's common, but not necessary. There's no reason why a camera couldn't have the same DR at all ISO settings, and some, like the Sigma DSLRs, do just that.
Click to expand...
Yes because most of the Sigma cameras only have one analog gain and the ISO setting is simply metadata that is acted on later.

This isn't really an advantage, unless you're entire ISO Invariant you lose any shadow improvement increasing gain would provide.
 
bclaff said:
John Sheehy said:
That's common, but not necessary. There's no reason why a camera couldn't have the same DR at all ISO settings, and some, like the Sigma DSLRs, do just that.
Click to expand...
Yes because most of the Sigma cameras only have one analog gain and the ISO setting is simply metadata that is acted on later.

This isn't really an advantage, unless you're entire ISO Invariant you lose any shadow improvement increasing gain would provide.
Click to expand...
It's a decision-making advantage if you are already using that camera. There is no point in under-exposing at a lower ISO to protect highlights, when that would only mean a darker review/JPEG image.
 
John Sheehy said:
JohnTheKeenAmateur said:
As a follow-up question to my own thread (!)

Why is it that there is a 1-stop decrease in dynamic range for each 1-stop increase in ISO setting ?
Click to expand...
Click to expand...
<snip>

John Sheehy said:
John Sheehy said:
Is it, perhaps, that the amplification involved in the implementation of ISO has the exact cause and effect of boosting the signal "over the top" of the pixel's storage capacity ?
Click to expand...
No; it's because gain (analog or mathematical) has pushed the upper range of sensor charge to clip in the ADC, or in the firmware math that puts the data in the RAW file.

Click to expand...
Thanks for the clarification, John - - This is a good example of my technical limitations in this field! ... I sorta meant what you said, but I lack the terminology to express it clearly :-(
 
bclaff said:
John Sheehy said:
JohnTheKeenAmateur said:
As a follow-up question to my own thread (!)

Why is it that there is a 1-stop decrease in dynamic range for each 1-stop increase in ISO setting ?
Click to expand...
That's common, but not necessary. There's no reason why a camera couldn't have the same DR at all ISO settings, and some, like the Sigma DSLRs, do just that.
Click to expand...
Yes because most of the Sigma cameras only have one analog gain and the ISO setting is simply metadata that is acted on later.

This isn't really an advantage, unless you're entire ISO Invariant you lose any shadow improvement increasing gain would provide.
Click to expand...
 
JohnTheKeenAmateur said:
bclaff said:
John Sheehy said:
JohnTheKeenAmateur said:
As a follow-up question to my own thread (!)

Why is it that there is a 1-stop decrease in dynamic range for each 1-stop increase in ISO setting ?
Click to expand...
That's common, but not necessary. There's no reason why a camera couldn't have the same DR at all ISO settings, and some, like the Sigma DSLRs, do just that.
Click to expand...
Yes because most of the Sigma cameras only have one analog gain and the ISO setting is simply metadata that is acted on later.

This isn't really an advantage, unless you're entire ISO Invariant you lose any shadow improvement increasing gain would provide.
Click to expand...
Excellent to see you here, Bill ... Since you haven't corrected my understanding of your work, I'm assuming (with bated breath !) that I got it reasonably right (?)
Click to expand...
If there were any issue I would have chimed in :-)
 
JohnTheKeenAmateur said:
As a follow-up question to my own thread (!)

Why is it that there is a 1-stop decrease in dynamic range for each 1-stop increase in ISO setting ?

Is it, perhaps, that the amplification involved in the implementation of ISO has the exact cause and effect of boosting the signal "over the top" of the pixel's storage capacity ?

--
Regards, John (the keen amateur)
Click to expand...
When it comes to analogue gain (which isn’t the same as ISO), to put it in simple terms (because I like simple!), each sensor pixel can produce a certain maximum voltage, V_m say, which is set by the design of the chip. So it would make sense if, at base ISO, the analogue gain between sensor and analogue-to-digital converter (ADC) was set so that voltage V_m at the output of your sensor gave the maximum digital output from your ADC, e.g. 11111111111111 or 16k say, for a 14 bit ADC.

Now, if the exposure for a particular photograph is less than the maximum (e.g. because you needed a faster shutter speed), so that the highest voltage from your sensor is, say V_m/2 for example, then you might choose to add 2x analogue voltage gain between the sensor and the ADC so that the range of voltages from your sensor still maps to the full range of digital outputs 0-16k from your ADC; but now any brighter areas that produce voltages greater than V_m/2 from the sensor will be “clipped”, because the ADC output can’t exceed 11111111111111. So you lost a whole stop of headroom.

The benefits of adding the gain are 2x finer discrete levels in your digital output and, depending on the electronics, the gain can reduce the effect of noise that gets added further down the chain, but that’s getting into technical stuff.

As someone said, the gain isn’t ISO. It’s just hardware stuff in the camera. Some cameras do it different, but they still have an ISO setting. Mapping a certain value in the raw image to maximum brightness in the output image still clips all the values higher than that, so the effect is similar in terms of losing headroom.

For real systems it is of course more complicated. One system I worked on (not a camera) had two programmable attenuators and three variable analogue gain stages, with subsystems having their own noise contributions and non-linearities in between, and setting it up to meet various noise and DR requirements was surprisingly complicated.

J.
 
Last edited:
Joe Pineapples II said:
JohnTheKeenAmateur said:
As a follow-up question to my own thread (!)

Why is it that there is a 1-stop decrease in dynamic range for each 1-stop increase in ISO setting ?

Is it, perhaps, that the amplification involved in the implementation of ISO has the exact cause and effect of boosting the signal "over the top" of the pixel's storage capacity ?
Click to expand...
Click to expand...
 
JohnTheKeenAmateur said:
Then he measures the difference, at each ISO point, between the theoretical PDR vs ISO line (that a perfectly ISO-invariant camera would display) and the actual PDR vs ISO line (for the camera in question).
Click to expand...
Problem is, PDR is not a useful source of data for determining ISO-invariance.

ISO invariance has NOTHING directly to do with DR. Neither "DR" nor "PDR" break the calculated range into clipping headroom and noise footroom, relative to an accurate, externally metered ISO exposure index, or calculated SNR differences between different cameras with the same exposure. ISO-invariance as the term has been adopted is ONLY about footroom, period (although headroom is the other factor relevant to making ISO setting decisions).

You might look with awe upon the information and charts available as someone new to this topic, but what exists is incomplete and very easy to misinterpret. P2P data includes ISOs which DxO doesn't, which is good, but not as good as it could be, because P2P does not measure the actual RAW clipping points, so any RAW file that can't go all the way up to using 4095, 16383, or 65,535 despite "overexposure" has less PDR than is charted. This is always true of ISOs that are mathematically pulled (RAW values are scaled downward). Manufacturers often clip RAW values much lower than the bitdepth limits for other reasons. DxO does something better, though; they they actually measure RAW clipping levels and the absolute exposures that that they occur at, so when they shift their DR datapoints horizontally, they are positioning them to reflect actual footroom at that shifted ISO. Alas, DxO sees only full-stop ISOs as relevant, and uses the settings of 50, 100, 200 etc, even if they are not the original digitizations, but are pushes and pulls, instead. Everything out there is broken, in one way or another. Still, if we narrow our interest to the full-stop standard ISOs, DxO's DR is a better starting point for doing something like what PDR shadow improvement is trying to do, because PDR has nothing directly to do with shadows, as it doesn't isolate footroom, and the PDR isn't even necessarily as high as it is charted. DxO's DR chart shows both DR and footroom at the same time, and you can calculate headroom by the difference. It is not complete in ISO settings, but it is more complete than PDR for the ISO settings actually charted.

More accurate to the heart of ISO invariance is the P2P chart for input-referred read noise in electrons. The relationship between different cameras has no absolute relevance there, as the read noise in electrons means nothing at the pixel level without knowing the size and QE of the pixels, and the number of those pixels for image-level noise. There is no attempt to normalize the cameras on this chart, but it is truer to the idea of ISO variance, and does not rely on accurate headroom measurements.

One possible interpretation I see for those erratic PDRs for the camera you showed the chart for here is that the manufacturer is allowing an erratic pattern in the blackpoint offset at various ISOs (or even at different times, due to temperature variations in the camera. Since P2P doesn't measure actual RAW clipping points, PDR might be varying regardless of whether the actual headroom is varying a lot, or it is not, because it is not measured.
 
Last edited:
John Sheehy said:
JohnTheKeenAmateur said:
Then he measures the difference, at each ISO point, between the theoretical PDR vs ISO line (that a perfectly ISO-invariant camera would display) and the actual PDR vs ISO line (for the camera in question).
Click to expand...
Problem is, PDR is not a useful source of data for determining ISO-invariance.
Click to expand...
I strongly disagree.
Photographic Dynamic Range Shadow Improvement is a very good indicator.
For example:

The Nikon D7000 is ISO Invariant whereas the Canon EOS 6D is not.
The Nikon D7000 is ISO Invariant whereas the Canon EOS 6D is not.

Shadow Improvement is essentially a normalized measure of Input-referred Read Noise .

It doesn't matter if the "stair steps" on the 6D are entirely "accurate"; the trend is very clear.

It doesn't matter if the x-axis is shifted slightly left/right.

--
Bill ( Your trusted source for independent sensor data at PhotonsToPhotos )
 
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