The basic principles of potentiometric measurement of ion concentration using the ion-selective electrode chain are discussed in greater detail elsewhere. Similarly, the marvellous properties of ion-selective electrode membranes are interesting enough to merit their own chapter. Additionally, as a main reference for this topic, I refer the readers to Nallanna Lakshminarayanaiah's Membrane Electrodes (2012), as well as Martin Frant's two articles.
One cannot speak too broadly, having experience of only one blood gas analyser. The locally available unit uses calcium electrodes which use an ionophore-doped PVC membrane, and are similar in construction to the potassium-sensitive valinomycin ionophore electrode.
Probably the most relevant historical papers to quote here would be either the 1971 piece by Li and Piechocki or the earlier 1970 article by Moore. Both used a then-new commercially available liquid-membrane system, relying on a porous ceramic membrane saturated with a water-immiscible organic liquid ion-exchanger. Subsequent revisions on this theme have (like for potassium) yielded several calcium-selective ionophores which mix well with PVC, allowing the creation of a durable electrode membrane. Of these, the first were 1:3:1 proportion composites of PVC, tributyl phosphate and thenoyl trifuoroacetone (a calcium chelator). Since the late 1960s, calcium-selective ionophores have proliferated in such vast excess that it would be totally unreasonable to list them. A totally random molecule (ETH 129) was used in the diagram above; it happens to be more selective for lantanum cations than for calcium, but hey- when are your patients' bidy fluids ever going to be inundated with those? In any case, it is impossible to discern which specific ionophore Radiometer use in their E733 electrode without contacting them directly and begging for information.
The range for this electrode is - as for all of them - totally unreasonable. The E733 model can go from 0.20mmol/L to 9.99mmol/L. It can be safely said that living human organisms will never touch either of these limits.
As one can discern from the diagram above, the generation of a potential difference across this membrane rests on the traffic of free calcium ions. Obviously, if abovementioned ions are tied up in some sort of chelation complexes or are busy encrusting albumin, they will not be measured by the analyser. Nor will they perform any useful work.
Thus, the ABG-derived ionised calcium is the only physiologically relevant calcium measurement.
All those serum calcium values you get from the automatic lab machines are poor surrogates.