Multivariate optical computing (MOC) is an instrumentation design concept for optically demultiplexing the spectroscopic signals in radiometric measurements. The advantages of optically demultiplexing are improved precision, optical throughput, improved reliability, and reduced cost of instrumentation. Conceptually, the instrument implements a multivariate regression vector whose dot product with the spectrum yields a single value related to a spectroscopically active physical property of interest. Instrumentation designs for implementing MOC are diverse, and there has been no systematic comparison of the performance of these designs. This report develops a general expression for comparing the precision of the different instrumentation designs of MOC. Additionally, an expression is given for the transition from low- to high-signal-limited performance of MOC instrumentation. These two general expressions are applied to the traditional multivariate analysis and five examples of MOC.
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