Doug Kerr
Well-known member
Of interest as we probe such things as sensor dynamic range, the effect of various noise sources, and the like, is the matter of the incremental relationship between:
• The number of electron charges ("electrons", for short) "captured" by a sensel, and
• The digital number (DN) delivered by the ADC for that sensel.
We note that this is, for any given camera, affected by the "ISO sensitivity" setting. (I won't elaborate on that yet, for reasons that will become obvious.)
Sadly, this parameter is very commonly spoken of as the "gain" of the sensor-ADC chain, a wildly inappropriate term. This usage helps to confuse what should be a very straightforward notion.
In this practice, the so-called "gain" is usually stated as the number of additional electrons that need to be captured to produce an increase of one in the DN (sometimes called "one count", although that is not useful either - nothing is "counting").
There are two serious flaws in this use of the term.
Firstly, almost everywhere else in technology, "gain" is the ratio between two quantities of the same dimensionality, such as between the output and input voltages of an amplifier, or attenuator, or the ratio between the output and input pressures of a fluidic amplifier.
We can reasonably extend it to a ratio between abstract numbers that represent physical quantities, such as the ratio of the output number to the input number with respect to a digital multiplication (although we need to be very cautious in extending the term to that).
Gains are dimensionless (pure numbers, not length, voltage, mass, etc.) and unitless (not meters, volts, kilograms, or any ratios of such).
Now suppose we have a temperature sensor with its own amplifier, delivering a voltage proportional to temperature. Suppose than for a 1° C change in temperature, the voltage changes by 0.1V. Does this part of the system have a gain? Is it 0.1? is it 10? Is it 0.1 V/°C? Is it 10 °C/V?
It does not have a gain, since temperature and voltage are not the same quantity.
It does have a transfer constant, which is 0.1 V/°C.
In our situation of interest, we are speaking about a transfer constant, not a gain.
The second problem is that the usual definition of this so-called "gain" is in terms of the number of "electrons" needed to make a change of one unit in the DN. This is in the wrong direction for a gain, which should be larger if the output is larger for any given input.
So it's not a gain, and if it were, it would be upside down.
The parameter is the inverse of the transfer constant of the sensor-ADC chain. Its unit is the electron charge.
Now, inside the "box" we are considering (the sensor-ADC chain) there is a bona fide gain, the ratio of the output voltage of the analog amplifier (to be presented to the ADC) to its input voltage (indicative of the charge in the sensel, which is indicative of the number of "electrons" captured). It is that gain that typically is changed when we vary the "ISO sensitivity" setting (perhaps with other things).
I would not expect our community to forswear the use of the name "gain" for the "inverse transfer constant" of a sensor-ADC chain (I consider myself ahead in that almost nobody here but Asher still speaks of rotating the camera around "the nodal point" for multi-shot panoramic photography). But I did want to make sure that those who can't quite grasp why this is a "gain" understand the realities.
Best regards,
Doug
• The number of electron charges ("electrons", for short) "captured" by a sensel, and
• The digital number (DN) delivered by the ADC for that sensel.
We note that this is, for any given camera, affected by the "ISO sensitivity" setting. (I won't elaborate on that yet, for reasons that will become obvious.)
Sadly, this parameter is very commonly spoken of as the "gain" of the sensor-ADC chain, a wildly inappropriate term. This usage helps to confuse what should be a very straightforward notion.
In this practice, the so-called "gain" is usually stated as the number of additional electrons that need to be captured to produce an increase of one in the DN (sometimes called "one count", although that is not useful either - nothing is "counting").
There are two serious flaws in this use of the term.
Firstly, almost everywhere else in technology, "gain" is the ratio between two quantities of the same dimensionality, such as between the output and input voltages of an amplifier, or attenuator, or the ratio between the output and input pressures of a fluidic amplifier.
We can reasonably extend it to a ratio between abstract numbers that represent physical quantities, such as the ratio of the output number to the input number with respect to a digital multiplication (although we need to be very cautious in extending the term to that).
Gains are dimensionless (pure numbers, not length, voltage, mass, etc.) and unitless (not meters, volts, kilograms, or any ratios of such).
Now suppose we have a temperature sensor with its own amplifier, delivering a voltage proportional to temperature. Suppose than for a 1° C change in temperature, the voltage changes by 0.1V. Does this part of the system have a gain? Is it 0.1? is it 10? Is it 0.1 V/°C? Is it 10 °C/V?
It does not have a gain, since temperature and voltage are not the same quantity.
It does have a transfer constant, which is 0.1 V/°C.
In our situation of interest, we are speaking about a transfer constant, not a gain.
The second problem is that the usual definition of this so-called "gain" is in terms of the number of "electrons" needed to make a change of one unit in the DN. This is in the wrong direction for a gain, which should be larger if the output is larger for any given input.
So it's not a gain, and if it were, it would be upside down.
The parameter is the inverse of the transfer constant of the sensor-ADC chain. Its unit is the electron charge.
Now, inside the "box" we are considering (the sensor-ADC chain) there is a bona fide gain, the ratio of the output voltage of the analog amplifier (to be presented to the ADC) to its input voltage (indicative of the charge in the sensel, which is indicative of the number of "electrons" captured). It is that gain that typically is changed when we vary the "ISO sensitivity" setting (perhaps with other things).
Note that in a CMOS sensor, the charge decreases for each "electron" captured. Often the voltage at the input of the amplifier is the difference between the voltage on the sensel after the exposure and a reference voltage that mimics the initial voltage to which the sensel was charged before the exposure.
I would not expect our community to forswear the use of the name "gain" for the "inverse transfer constant" of a sensor-ADC chain (I consider myself ahead in that almost nobody here but Asher still speaks of rotating the camera around "the nodal point" for multi-shot panoramic photography). But I did want to make sure that those who can't quite grasp why this is a "gain" understand the realities.
Best regards,
Doug