I'm wondering if it's possible to test the mash during mash for an all grain batch to determine concentrations of calcium, magnesium, etc. Or if that is better determined by pre-mash calculations.
Commercial brewries in the UK, as Grain Mother points out will start with the water quality report provided by the local water company. Smaller breweries here in the UK will reguallay send of samples to companies such as BrewLab, Murphy & Son and Campden BRI to have water analysis done on a 500ml sample.
Murphy do one or two free tests a year for their customers, and do more for a small fee.
Larger breweies will have in house labs and daily or weekly check the water entering their facilities, using titration, indicator chenicals and a photospectrometer. Also they will often pass the water through RO and then add back the ions to the correct levels for the brand being produced that day.
There are off the shelf tests, previously not availabale via home brew suppliers, but lab supply shops do carry these tests.
Simple test strips you can get via amazon etc..
These tests are not hugely accuarate but do at least give you banding tha you can pair up with a municipal water report to have a good idea of the incoming water hardness.
In the UK the local water company can provide a report on the water quality and content. One would presume that any local water company providing drinking water would perform similar and regular analysis - just to check the water is safe to consume. That would be the easiest and best way to get the information on the amount of ions in the water used. In general one is most interested in the levels of Calcium and Magnesium cations and chloride, suplphate, carbonate and bi-carbonate anions.
Usual practice is to test the source water, then determine what needs to be added. There are two calculators for additions in the form of Excel file, one from John Palmer (howtobrew.com), another from Braukaiser. I prefer the latter one.
Testing-wise, I'd say that for homebrewing just water report from your local water provider is enough. Some pet shops and swimming pool shops (if you have them around) do water tests for cheap/free. If you want to go full geek on this and have extra money, then BrewLab from LaMotte should suffice -- Jamil Z. mentions it a lot in his podcasts.
During mash the only reasonable measurement to do is probably pH (best range is 5.2-5.4).
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