respectively ( Kodak, 1982 ). This means that the films do not meet 
the requirements for signal to noise ratio for a good replication of 
the grey value distribution in the image. Precision will be lost in 
the replication of the grey levels and the system will no longer be 
balanced. In other words the digitizing system will be film limited. 
If formula ( 3.5 ) is applied to the 3414 film scanned with a 10 ym 
aperture there will be only about 40 distinguishable density levels. 
Still we have 256 digital level$ in the digitizer if we are working 
with an eight bit system. As a consequence the digitizing need to be 
correct only within + 5 digital levels. The analysis of the 
requirements for a balanced system should thus be supplemented by an 
analysis of the required precision in the assignment of the digital 
levels to the samples from the image. 
T. IMAGE QUALITY AND SYSTEM PERFORMANCE 
Image quality and system performance are closely related. In the 
preceding section system performance is evaluated in terms of the 
signal to noise ratio S/o and the parameter B. In Section 4 ( formula 
5.9 ) one quality measure is suggested. It has the disadvantage that 
we have to specify the original image function f(x,y) and this will be 
possible only for a very simple image and thus it is more of theo- 
retical interest. Image quality can also be approached in terms of 
signal to noise ratio or in terms of information content of the image. 
If signal to noise ratios are used we can compare the signal to noise 
ratio in the photographic image to that in the digital image. If the 
system 1s balanced these should be equal. If the system is not 
balanced the reason may be that the requirements on S/o to get a 
balanced system can not be met. This means that due to grain noise we 
cannot reach the accuracy we want in the quantization and hence a 
degradation of the image will result. 
The most attractive solution is to treat image quality in terms of 
information theory. The information I(x,y) in an optical image f(x,y) 
or in its spectrum F(u,v) is a measure of its quality (Frieden,1983) 
and related to the ability to retrieve object structure. Information 
is not a measure of pre-existing resolution. The higher the 
information content is, the better ultimate resolution can be made, 
but a restoration step is required. The information is the difference 
between noise and data entropy. When data entropy is maximized we will 
get the channel capacity that reflects the capability of the system to 
transmit information. For evaluation we can also use information 
density expressed as bits/unit area. Thus we can evaluate both image 
quality and system performance of digital and emulsion based systems 
in terms of information theory ( Frieden, 1983; Shaw, 1962 ). 
An analysis of an optical system along these lines shows that if the 
noise is low enough, even poor quality optics can pass high 
information into the image. To retrieve the information a restoration 
step is needed. Image restoration is outside the scope of this paper, 
but there exists an extensive litterature on this subject. 
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