What do L_sat and L_clip mean in the ISO dynamic range formula?
Asked 7/31/2012
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I'm trying to understand the ISO definition of dynamic range for a digital still camera:
DR = (1.4 × L_sat × G_i) / N_D
where:
- DR is dynamic range
- L_sat is the luminance at the “margin level” (70.1% of the maximum recordable luminance)
- G_i is the incremental gain at the reference black luminance
- N_D is the measured digital noise at the reference black luminance
Since L_sat is 1/1.4 of the actual saturation luminance, it seems this can be rewritten as:
DR = (L_clip × G_i) / N_D
What is the difference between L_sat and L_clip in practical terms, and why does the ISO formula use L_sat with a factor of 1.4 instead of using the clipping/saturation luminance directly?
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
14y ago
2 Answers
2
I have found the following interesting reference "The ISO Definition of the Dynamic Range of a Digital Still Camera" which, at pages 6, clarifies your formula.
It is based on the assumption that a useful signal is one for which the Signal-to-Noise ratio is >= 1.
This luminance level is your denominator \$N_\mathrm{D}\$. The numerator is "the maximum luminance that receives a unique coded representation (the “saturation” luminance)", \$L_\mathrm{clip}\$ in your notation. But digital luminance is not equal to luminance (The famous "gamma correction"). This slope factor is the \$G_\mathrm{i}\$ (the incremental gain).
\$L_\mathrm{sat}\$ and \$L_\mathrm{clip}\$ are directly related: if one is known, the other follows by simply multiplying (or dividing) by a factor. It is a matter of definition.
The 1.4 factor (roughly the inverse of 70%, as you note) provides a sort of a buffer (the paper calls it "the well-known so-called 'half stop margin' against overexposure").
The ratio of:
- (numerator) Gamma corrected maximum luminance
- (denominator) lowest luminance level where the SNR is >= 1
gives the output, the dynamic range of the sensor. It is (as it must be) based on a series of convention: but if you apply them consistently to various sensor you can numerically describe them according to this metric.
Originally by user5032. Source · Licensed CC BY-SA 4.0
user5032
14y ago
0
Generated from our catalog & community — verify before relying on it.
L_clip is the maximum scene luminance that still gets a unique recorded code value before clipping. L_sat is a related ISO “margin level” defined as about 70.1% of that maximum luminance, so the two differ only by a fixed factor: L_clip = 1.4 × L_sat.
That is why the ISO formula
DR = (1.4 × L_sat × G_i) / N_D
is effectively the same as
DR = (L_clip × G_i) / N_D.
The other important term is G_i, the incremental gain near black. Digital output is not necessarily linearly proportional to scene luminance, so G_i accounts for the local slope of the camera’s tone encoding at the reference black level.
N_D is the measured digital noise at black, and the definition assumes the lowest useful signal is where signal-to-noise ratio is about 1. So dynamic range is basically the ratio between the highest uniquely recordable luminance and the noise floor, adjusted by the encoding slope.
In short: L_sat is an ISO-defined reference point below clipping; L_clip is the actual clipping limit; they are interchangeable via the 1.4 factor.
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