How to understand the definition of dynamic range?

Question

I have the following formula:

DR=(1.4L_Sat G_i)/N_D

where DR is the dynamic range;
L_sat is the luminance at the “margin level”，70.1% of the maximum recordable （saturation）luminance（yes，L_sat is a peculiar symbol for that);
G_i is the incremental gain at the reference black luminance;
N_D is the measured digital noise at the reference black luminance

But L_sat is 100/140(1/1.4) of the actual saturation luminance (which we call here L_clip ).Thus we can recast equation 2 thus:

DR=(L_clip G_i)/N_D

I cannot understand this L_clip and L_Sat and the relationship between them.

Answer 1

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_D. The numerator is "the maximum luminance that receives a unique coded representation (the “saturation” luminance)", L_clip in your notation. But digital luminance is not equal to luminance (The famous "gamma correction"). This slope factor is the G_I (the incremental gain).

L_sat and L_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.