# How to understand the definition of dynamic range?

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.

• Hi, I've attempted to reformat your question as it's very hard to understand at the moment. Please check I haven't changed the meaning. Jul 31, 2012 at 11:20
• This question has strayed off-topic for this site. It's no longer about photography as such; it has become a question belonging in the physics, math or electronics SE sites, so I have voted to close.
– user2719
Jul 31, 2012 at 12:21
• Where did you found these formulas? What exactly you don't undestand? Is this related to photography? Jul 31, 2012 at 18:08
• sorry for the obvious typo: did you found -> have you found :-) Jul 31, 2012 at 18:32
• Hi，Chrisf. the definition i mentioned from this article "The ISO Definition of the Dynamic Range of a Digital Still Camera",i cannot understand the numerator "the maximum luminance that receives a unique coded representation (the “saturation” luminance)", L_clip in your notation. can you help me? thank you very much? Aug 1, 2012 at 9:19

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.

• Thank you Francesco. These formulas from the article you mentioned above.Now i am learning the Dynamic Range of DSC. about its definition i feel confused. thanks for your explain,but i still can't understand completely. I again understand it. Aug 1, 2012 at 2:15
• Hi，Francesco. the input (L_clip) through the gamma correction(camera sensor in-built) get to the output( L_sat) ,can i understand it? if so, how to calculate the L_sat ? Aug 1, 2012 at 3:16
• @petalse I tried to expand on that a bit Aug 1, 2012 at 9:48
• perhaps i can question like this::" Now if i give you a mobile phone, how do you measure the dynamic range of his camera depend on the ISO definition ?" Aug 2, 2012 at 2:51
• the sensor of a mobile phone camera is a sensor all the same. So: find out (or measure, if you have the adequate capabilities) the values for L_sat, G_i, N_d, and compute the ratio. Just to be sure, have you read the numerous other questions and answers on the topic of Dynamic Range on this same site? Aug 2, 2012 at 6:44