Data Reduction

In the analytical chemist's dream world, a measured quantity is directly proportional to the quantity of sought-for substance, independent of all other substances, and remains linear from single atom/specimen to 100%. In reality, this is impossible. Suppose a single atom in a sample gave rise to a burst of 100 photons against a zero background. Then proportionate response to 10²⁰ atoms would generate 10²² photons. If the measurement system was efficient enough to detect even 1 photon from the single atom, it would detect 10²⁰ photons in the high concentration sample. 10²⁰ electrons is about 16 Coulombs. Thus, a single electron response in the former case results in a huge signal in the latter. If the single electron gave rise to only 1 nV, a level very difficult to quantify, the latter would generate 10²⁰ × 10^-9 V = 10¹¹ V, 100 gigavolts. This is higher than the highest potential humanity has ever generated intentionally. One thus must choose a measurement strategy appropriate for the expected signal from the analyte, keeping in reserve more or less sensitive or selective techniques if the original estimate turns out to be erroneous.