Signal critical points

A note concerning terminology Lp (Ref. 2) and Sp have been used interchangeably to denote the detection limit for the net signal (y-B) xp is used here to denote the analyte detection limit (concentration or amount). Lq (or Sc or xq) denotes the decision level it is also called the critical point or level, test level, or threshold by various authors. The directly observed gross signal (y) is here referred to as the response.]... 

Fig. 2 Typical heterodyne diffraction signals measured for a critical PDMS/PEMS mixture for different distances T — Tc to the critical point. All curves have been normalized according to (15). The dashed line indicates the nearly constant initial slope of the concentration signal (an exponential function in the logarithmic plot) caused by the almost constant value of Dj- The inset shows, for comparison, a considerably smaller signal for an off critical PDMS/PEMS mixture (860 and 980g mol-1)...

As predicted by the expressions for the critical divergence of the Soret coefficient in (12) and (13), the heterodyne diffraction efficiency of the induced concentration grating dramatically increases on approach of the critical point. Figure 2 shows normalized heterodyne diffraction efficiencies that have been recorded for different distances T — Tc. A few hundred milli-Kelvin away from Tc, the modulation depth, which is proportional to the heterodyne signal, exceeds the values typically found for small molecules and off-critical mixtures by nearly four orders of magnitude. 

Signal processing is a critical point in the accurate determination of NMR parameters. 

As is well-known, the critical point can be found from locating the divergence of the response function ( susceptibility ) S = dm/dH, which signals the onset of symmetry breaking and spontaneous order. The simplest case occurs for Hj=0, and then... 

Practical understanding and appreciation of detector saturation limits are critical when using any of the aforementioned detectors. The saturation limit can be defined as the point at which a nonlinear detector response is observed with an increase in ion concentration. The saturation characteristics of a detector can be proportional to concentration up to a critical point, at which no additional signal can be obtained, or can be nonlinear, where detector response changes with concentration but in a nonlinear way. 

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