Quantitative Relations Between Operating Variables

From the discussion above we may deduce useful quantitative relationships between variables which may be at the disposal of the operator. The emphasis here will be on the interdependence of pairs of variables. Any attempt to combine these in a single, all-encompassing expression leads at best to a quasimathematical relation, which would tend to becloud the decision making process. 

Resolution may be expressed in terms of the smallest frequency difference Av between neighboring bands which can be distinguished from each other. Except near the inherent limits of resolution Av is proportional to the physical slit width W. A change in slit width for 

However, there are other effects of changing the slit width, as indicated in equation (2-1). Specifically, the signal reaching the detector is proportional to the square of the slit width. To maintain the same dynamic response the gain of the amplifier must be changed inversely proportional to the signal—i.e., inversely proportional to W. As previously described, the recorded noise N is directly proportional to this gain. From this we conclude  

In the above discussion, N is a dependent variable. Within limits the noise is subject to operator control through the response time t of the pen or amplifier. The longer the response time the lower the noise level, because of the smoothing effect on noise peaks of the slower response. Quantitatively this relationship, which involves a square root dependence, is expressed as follows  

When the response time is changed this interacts with the dynamic response of the system and must be compensated by a proportional change in scan time, thus  

---