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IMAGE SENSORS, PIXEL SIZE, AND POISSON NOISE (continued)

6. OTHER KINDS OF NOISE FIGURES
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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Lots of manufacturers do not publish the linear SNR, but a logarithmic noise figure  NF  in the units of   "deziBel" = dB .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 8-bit 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 real-world example, poisson noise is calculated from image sensor data.

Continued: 7. CALCULATING NOISE FIGURES FROM PHOTONS FROM WATTS

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