2 a — O0 
d 
1d 
- y 
6.2 2 orman a 
Let “digitizing to M useful bits” be defined as digitizing the (M+1)th 
bit correctly with a probability of 0.5 with the effect of the -noise 
taken into account. From fig. 6.2 we can see that this requires B=1.4 
for the (M+1) bit. As a result we will have B=2.8 for the Mth bit. For 
an eight bit system this will lead to a demand that S/0=717. With 
this S/0 the eighth bit will have a probablility of 0.72 of being 
correct. Of course the choice of définition above is arbitrary and can 
be adjusted if P=0.72 is not satisfactory for the eighth bit. 
what is illustrated above is the significance of the parameter 8g. The 
demands on the accuracy of the quantization can be formulated in terms 
of the probability of the Mth bit being correct and this results in 
requirements on B and S/o. 
System performance can also be approached in terms of the noise 
introduced by the digitizer. The noisg power introduced by the ct.» of 
digitizing is given by o(digitizing) = (quantizing step size) / 12. 
A balanced system can be defined as a system where the quantizing 
noise is equal to the rms sum of the contributions of all prior noise 
sources in the system. Thus o(prior) = quantizing step size 4 :LA2. 
Since B is the step size divided by o, we get ß = /12 3.3.46: and 
S/o = 886. 
Both approaches give a value of B = 3. Consequently the noise into the 
digitzer should not exceed 1/3 of the step size. 
6.3 Application to Film Digitizing 
For digitizing a film the requirements in terms of the black to white 
signal to noise ratio S/o can be derived in the following way 
0 = 1/3 x ( the size of one digital step ) = (1/3)AT 
AT = 1/N ( For 8 bit system N = 256, 0<T<1) 
S$ ioe Ril OTHE) 
This gives S/o = 1 / ( 1/3 x 1/N ) = 3N = 768. From formula 4.2 we can 
determine the worst case transmittance noise. This occurs at T=0.5 and 
for eight bit digitizing we get o - 1/168/4T(1-T) = 0.0026/T(1-T). 
Granularity is quoted at 0D=1.0 or T=0.1 . If T=0.1 is inserted in the 
expression above we get 0:0.00078 and this is the worst case noise 
permissible at that level. Using formula 4.1 and the relation between 
granularity measured with different apertures we get 0-0.00007xA. This 
is the required granularity at 0=1.0 measured with a 48ym aperture to 
achieve $-3 for eight bit digitizing. The actual aperture used in the 
digitizer should be substituted for A. 
A system that resolves 35 lp/mm would give a pixel size of 10 ym if 
the formula in section 3.1 is used. This gives a permissible o of 
0.0007. If we compare with granularity for some films manufactured by 
Kodak this should be multiplied by 1000 ( section 4.1 ) and we get o = 
0.7. If we consider the granularity given by Kodak for Panatomic-X 
2412 and High definition aerial film 3414 the values are 9 and 7 
151