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IMAGE SENSORS, PIXEL SIZE, AND POISSON NOISE (continued)
6. OTHER KINDS OF NOISE FIGURES

Key words:
SNR  deziBel  dB  ENOB  EFFECTIVE NUMBER OF BITS  ENOGL  EFFECTIVE NUMBER OF GRAY LEVELS
Knowing SNR from para. 5, you might ask for the meaning of other noise figures.
Noise Figure in dB:
Lots of manufacturers do not publish the linear SNR, but a logarithmic noise figure NF in the units of "deziBel" = dB .
Let Vs = Signal Voltage and Vn = noise voltage, then NF is simply:
NF / dB = 20 * log(Vs/Vn) and hence:
NF / dB = 20 * log (SNR)
ENOB:
Happily knowing two different noise figures, I admit that I prefer a third one.
For me, the ENOB is extremly handy.
Funny acronym, that. It means "EFFECTIVE NUMBER OF BITS".
You see, transmitting 12 Bits is useless, if the lower 5 Bits carry just noise.
This would be so, if ENOB was 7.
But how do we calculate the ENOB figure from SNR? The transformation is easy:
In the usual binary coded digital signal, every bit position carries the value of one integer power of two.
For those not used to using digital signals, table 1 shows the bit positions and their values in a common 8bit word
that is, in a byte. And table 2 shows two example bytes.
Table 1: The bits in a byte.
position 
7 (MSB) 
6 
5 
4 
3 
2 
1 
0 (LSB) 
value (dec.)

2^7 = 128 
2^6 = 64 
2^5 = 32 
2^4 = 16 
2^3 = 8 
2^2 = 4 
2^1 = 2 
2^0 = 1 
Table 2: Code examples
description 
binary value 
decimal transcribing 
decimal value 
biggest codeable value 
1111 1111 
128+64+32+16 + 8+4+2+1 
255 
smallest codeable step 
0000 0001 
000+00+00+00 + 0+0+0+1 
001 
Well, I won't bore you with more details. Perhaps you can simply believe (or prove on your own) that
ENOB = ld(SNR) = [log(SNR)] / [log(2)]
This fine and simple equation shows how many useful bits you get.
Admitted: it's a logarithmic noise figure like dB. But it is wonderfully close to all our digital applications.
ENOGL:
Do you like these funny acronyms like ENOB? 
Try the following: The SNR in fact is an EFFECTIVE NUMBER OF GRAY LEVELS. Just call it ENOGL.
ENOGL = SNR
In the next paragraph, we'll use what we learnt:
In a realworld example, poisson noise is calculated from image sensor data.
Continued: 7. CALCULATING NOISE FIGURES FROM PHOTONS FROM WATTS
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Last modified March 16th 2006