We all know the importance of calibration and compensation for various sensor and signal-chain errors, whether they due to external factors or internal imperfections. Identifying error sources and deciding how to deal with them, if at all, is part of the engineer's job.
For errors due to repeatable, deterministic factors such as the nonlinearity of a thermocouple, engineers in the early days used sophisticated analog circuitry which implemented a complimentary transfer function. Now, of course, corrections are done either via a look-up table or even an executed polynomial algorithm, depending on the available processor resources and time.
But the real challenge for designers is to provide correction for imperfections which are either unknowable in advance or which vary. I see this especially in high-precision physics-related measurements which have both the benefit and drawback of being large and unique, and having many uncontrollable factors. In these cases, clever algorithms and software can't drive the error sources out of the picture, and other approaches must be used. Some are practical only for specialty applications while other techniques can be used in more mainstream products.
Among the methods used are to physically rotate a system 90 or 180 degrees (to cancel out factors such as gravity's effect or other “sideways” forces); to use bipolar differential signals throughout; or to run a signal along parallel paths, at two voltage levels or physical pathways, to extract the desired signal.
If you think that only today's real-time algorithms and complex software corrections can produce precise results, you are wrong. In the 1930s, physicist Isidor Isaac Rabi (1944 Nobel Prize winner) led a team which measured nuclear magnetic moments using an experimental setup and calibration equipment which was astonishingly crude and coarse by our standards (http://physicsworld.com/cws/article/print/906). By studying their error sources, and understanding which ones could be worked around or self-cancelled, they achieved results with accuracy to six and seven significant figures. That's very impressive, even today.
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