Doug Kerr
Well-known member
Simplistically, the dynamic range of an imaging system refers to the ability of the system to "capture" the range of luminance occurring over all the points in the image of a scene.
It is often expressed in terms of the ratio of maximum to minimum luminance that can be "captured". Often we give the base 2 logarithm of that ratio, and thus give the result in "stops".
But as we try and get more specific in our definition of maximum and minimum luminance, various conundrums appear. For example, even a very incapable imaging system can "capture" the range of luminance in a scene where some points have zero luminance, and thus would seem to have an infinite dynamic range.
The next step on our journey toward a meaningful definition of this matter is to consider as the "maximum" the maximum luminance that receives a unique digital representation, and to consider as the "minimum" the minimum luminance that receives a unique non-zero digital representation.
Before we proceed further down this road to enlightenment, let's step back and look at what we are really interested in. It is not really useful to us in photography to be able to capture a wide range of scene luminance values if, for the "minimum" value, the signal-to-noise ratio is "poor".
Thus, under the ISO definition of the dynamic range of a digital imaging system (widely used as the premise for reporting dynamic range performance), we consider the dynamic range to be the ratio of:
• The greatest luminance that receives a unique digital representation (that is, is just short of the "clipping" level of the imaging system)
to
• The lowest luminance at which the result of the imaging system has a signal-to-noise ratio (SNR) of 1.0.
Now why 1.0? Is that a magic value of SNR that represents the boundary between "bothersome" and "not bothersome" noise. No. It is essentially chosen arbitrarily.
Now, as we look into measuring the dynamic range under this definition, we run into a fundamental problem. The "noise" value is defined as the standard deviation of the output value of the sensor system for a constant actual luminance over many instances. The "signal" value is defined as the mean (average) of the output value of the sensor system for a constant actual luminance over many instances.
But (assuming any likely statistical distribution of output values), at an SNR of 1.0, a substantial fraction of the output values would be negative! Of course our sensor system does not deliver negative output values. Thus we cannot actually determine by observation at what luminance will the SNR be 1.0. Oh, great!
So we finesse the matter. We determine what is the SNR at a luminance 18% of what has been determined to be the "maximum" luminance. Typically, the SNR we will have there would be such that only an inconsequential fraction of all the output values would have to be negative. Thus we can essentially ignore that matter.
We then take that noise value and say, "well, at our minimum luminance (which we have not yet determined), the noise value will doubtless be the same". But since our definition of the minimum luminance is the luminance at which, conceptually, the SNR would be 1.0, then the "signal" at that luminance would be numerically the same as the noise we just measured (at a luminance of 18% of our maximum luminance).
So we take the luminance corresponding to that hypothetical "signal" value (that is, corresponding to the measured noise value at 18% luminance) to be our "minimum" luminance. And thus we take the ratio of our maximum luminance to this minimum luminance as the dynamic range of the imaging system.
Best regards,
Doug
It is often expressed in terms of the ratio of maximum to minimum luminance that can be "captured". Often we give the base 2 logarithm of that ratio, and thus give the result in "stops".
But as we try and get more specific in our definition of maximum and minimum luminance, various conundrums appear. For example, even a very incapable imaging system can "capture" the range of luminance in a scene where some points have zero luminance, and thus would seem to have an infinite dynamic range.
The next step on our journey toward a meaningful definition of this matter is to consider as the "maximum" the maximum luminance that receives a unique digital representation, and to consider as the "minimum" the minimum luminance that receives a unique non-zero digital representation.
Before we proceed further down this road to enlightenment, let's step back and look at what we are really interested in. It is not really useful to us in photography to be able to capture a wide range of scene luminance values if, for the "minimum" value, the signal-to-noise ratio is "poor".
Thus, under the ISO definition of the dynamic range of a digital imaging system (widely used as the premise for reporting dynamic range performance), we consider the dynamic range to be the ratio of:
• The greatest luminance that receives a unique digital representation (that is, is just short of the "clipping" level of the imaging system)
to
• The lowest luminance at which the result of the imaging system has a signal-to-noise ratio (SNR) of 1.0.
Now why 1.0? Is that a magic value of SNR that represents the boundary between "bothersome" and "not bothersome" noise. No. It is essentially chosen arbitrarily.
Now, as we look into measuring the dynamic range under this definition, we run into a fundamental problem. The "noise" value is defined as the standard deviation of the output value of the sensor system for a constant actual luminance over many instances. The "signal" value is defined as the mean (average) of the output value of the sensor system for a constant actual luminance over many instances.
But (assuming any likely statistical distribution of output values), at an SNR of 1.0, a substantial fraction of the output values would be negative! Of course our sensor system does not deliver negative output values. Thus we cannot actually determine by observation at what luminance will the SNR be 1.0. Oh, great!
So we finesse the matter. We determine what is the SNR at a luminance 18% of what has been determined to be the "maximum" luminance. Typically, the SNR we will have there would be such that only an inconsequential fraction of all the output values would have to be negative. Thus we can essentially ignore that matter.
We then take that noise value and say, "well, at our minimum luminance (which we have not yet determined), the noise value will doubtless be the same". But since our definition of the minimum luminance is the luminance at which, conceptually, the SNR would be 1.0, then the "signal" at that luminance would be numerically the same as the noise we just measured (at a luminance of 18% of our maximum luminance).
So we take the luminance corresponding to that hypothetical "signal" value (that is, corresponding to the measured noise value at 18% luminance) to be our "minimum" luminance. And thus we take the ratio of our maximum luminance to this minimum luminance as the dynamic range of the imaging system.
Best regards,
Doug