# What does the term "saturation luminance" mean in the definition of dynamic range?

The concept behind the dynamic range definition given by ISO 15739 is based on the ratio of the maximum luminance that receives a unique coded representation （the "saturation" luminance) to the lowest luminance for which the signal to noise ratio (SNR）is at least 1.0.

Can someone help me understand the meaning of the part in bold?

## 2 Answers

The maximum saturation point of a pixel's photodiode in a digital sensor is the point at which it can no longer generate new electrons for additional photon strikes. At an electronic level, the saturation point varies with each type of sensor, as the maximum electron capacity of a given photodiode is dependent upon the physical area of the diode, its efficiency, its tendency to leak electrons, etc. Dynamic range can be described in a variety of ways, however a common way to describe it (often used by camera review sites like DXOMark) is as the ratio between maximum saturation, and the standard deviation of the sensors electronic noise floor.

The ISO 15739 specification you are referring to is describing a specific, standardized approach to describing dynamic range. From what I can find, this standard is a little convoluted, and used terms that don't seem to have an adequate explanation of why they are derived the way they are derived. The saturation point they are referring to, if I understand correctly, is actually 100/140th (71%) of the sensors actual maximum saturation level (as described above in my answer.) The full ISO 15739 specification is not freely available as far as I can tell, so the information I have to go off of is simply derivative works based on the ISO 15739 standard.

If my understanding is correct, however, dynamic range in this standard is described as the ratio between the point where shadow SNR is 1.0 and 71% of the sensors maximum saturation point (where no more electrons can be held in the photodiodes of each pixel.) The saturation luminance is that 71% of maximum saturation. In more detailed terms, ISO 15739 DR is the ratio between a luminance level that matches the noise ratio (say 8 electrons worth) and the 71% of the maximum saturation point, which for say Canon's 18mp sensors would be about 22000 electrons * .71, or 15620 electrons. That is a ratio of 1952.5:1 in terms of electrons, or in terms of stops, a little less than 11 (2^11 = 2048).

• That 71% (1/√2) isn't quite arbitrary; it's the point where there is a 0.5 probability that an additional photon will be absorbed and change the energy state (below that value, the probability is greater than 0.5; above it is less). It's the equivalent of the "shoulder" of a film density curve, just as the SNR value limit at the other end is equivalent to "film base plus fog". Exposure values above the shoulder become increasingly non-linear, compressing the tonal scale. (Ansel Adams would have called it the difference between Zone VIII and IX.)
– user2719
Jul 27, 2012 at 22:44
• Ah, thanks Stan! As I said, I didn't have an official document to work with, and none of the resources I found could explain the 100/140 ratio. Makes total sense though, that the 71% mark is where the shoulder would begin in film. I would like to point out, however, that in the absence of a digital tone curve applied at processing time in a RAW processor...a digital sensor is a linear device. If you are computing DR with software, then I can see how the 71% might apply...however at a hardware level, I'm curious if it still does... Jul 28, 2012 at 4:02
• When using open-source RAW processing software, it is possible to load a RAW image without applying any kind of processing outside of your basic demosaicing. The nature of RAW truly becomes apparent at that point, and while a photograph tends to look eye-scratchingly dull, flat, and lifeless, there does not appear to be much in the way of a natural curve to the raw data strait off the hardware. There is probably some, but I wouldn't say anywhere close to what film naturally has. Jul 28, 2012 at 4:05
• It's linear as long as there are sufficient low-state bound electrons in the well. When they begin to become scarce (as the cell approaches electrical saturation), photons have fewer targets to hit. The curve isn't exactly a hockey stick at that point, though, it's just not as linear as it is below the shoulder; you don't get really flat until you get very near electrical saturation.
– user2719
Jul 28, 2012 at 4:41
• thank you jrista,i understand your meaning " 100/140*the maxmum saturation point equation to the saturation luminance " is this? if so, i donnot know why take 71%.could you explain it again? thank you very much. Jul 30, 2012 at 3:02

A digital sensor has a range of values it can store - for example with 8 bits, it can store values between 0 and 255. The value 255 represents the highest (brightest) luminance value. That is what they are referring to by "receives a unique coded representation".

Anything brighter than that maximum value will also be registered at that same digital value of 255, so the luminance is "saturated" and the camera can't record any higher. The camera will report any brighter areas at the same digital value and you won't be able to distinguish them - they'll all look the same.

• Thank you Mikew, i understand you mean.But i want to know how to get this value that the "saturated luminance" when you calculate DR. In a real-life situation,for example with 8 bits, you get the value-"127" as the saturated luminance or others? how do you decide? thank you Jul 30, 2012 at 2:33
• Downvoted you by accident, can't seem to undo this until the question is edited, sorry! Oct 17, 2012 at 11:01