Dynamic range revisited.
The subject of an enlightening and enjoyable email conversation between myself and a blog visitor: dB and dynamic range in sensors. I was under the impression that the best way to measure the dynamic range of the D700 sensor was to consider 10 times the log10 of the ratio between the highest and lowest light intensities recorded. (Intensity here defined as the number of pixels per exposure length per pixel area) Perhaps I was wrong.
It's all about the electron hole pairs, baby.
Photons hit a sensor, interact with atoms and liberate an electron. Not every photon generates an electron. The pixel has a capacitance and integrates the charged electrons overtime. The noise floor determines the dynamic range. The sample we floated was as follows:
Our pixel has a capacitance (C) of 100 femtofarads (1x10-13 fF)
Our pixel can output 1 volt (V)
Our pixel needs about 38 electrons to read anything above noise and one e- has a charge (q) (absolute value) of 1.6Ã—10âˆ’19coulomb.
V = q/C
It follows then that in order to max out the pixel at 1 V, we need 1x10-13 C worth of charge, meaning we need about 625,000 electrons. Our noise floor is at 38 electrons, however, generating a voltage ratio between the highest and lowest values of 16,447. In order to read this number in binary we need a 14-bits for this pixel. But dB in electronic devices is measured as the log of the power ratio. The power ratio is (for voltages) (V1/V2)2 (this is because the resistance (R) between pixels that are recording different light levels is constant and power P = V2/R .
In a dB calculation we now have to scale the log10 of the ratio between voltages by 20 instead of 10. Therefore our theoretical pixel will have a dynamic range of 84.3 dB between the 38 electron noise floor and the 625,000 needed to generate a maximum 1 V output voltage.
So what visual dynamic range is captured by this 84.3 dB sensor?
This depends on how many photons on average generate an electron hole pair - this is not a one-to-one ratio. The best solution I can come up with (I am an experimentalist not a theoretician) is to build something that outputs a defined and calibrated photon flux and measure it with the sensor. This was done by dpreview.com and they found that NEF files produced under their best Adobe Camera Raw conditions produced about 11.6 EV worth of dynamic range. That is, the brightest value recorded before the sensor hit its maximum output voltage was 211.6 = 3,104 times brighter than the darkest recorded value which comes out to 34.9 dB using our old calculations. This was done in 14-bit mode. In the end I think this value and the sensor's dB RE: output voltage that matters.
I have seen the light.
"Materials and methods" updated.