Determination of the error of measurements obtained by the optical micrometry

We present the results of measuring the volume of polyvinyl alcohol polymer granules crosslinked with epichlorohydrin in water and in aqueous solutions of KCl, MgCl₂ and their mixtures, obtained by optical micrometry, and consider the main sources of errors in the measurement errors. The purpose of this study is to analyze and evaluate the effect of the main sources of errors on the accuracy of determining the relative volumes of granules, as well as to search for techniques that can minimize the resulting measurement errors. The diameters of the granules were determined using specialized software implementing machine vision algorithms from the images obtained by optical microscopy. Their volumes were calculated using the formula for the volume of the ellipsoid of revolution. The maximum accuracy of volume determination is known to be achieved when the measured granule has a sphere shape. It is shown that deviation from this shape, for example, in case of an ellipsoid, gives errors in determining the third axis of the ellipsoid, invisible in the image, which creates an error in determining the relative volume of the granule. The instrument error is determined and a statistical estimate of the error attributed to the non-sphericity of the granules is given. It is shown that a typical instrument error in determining the relative volumes of granules is 0.4%. The non-sphericity of the measured granules increases the measurement error up to 3.5%. The error for a single granule can be reduced to 2.3% by combination of methodological techniques and statistical processing of the results, whereas and for an ensemble of at least 5 granules — up to 1.5%. The reproducibility of the properties of polymer granules in cyclic measurements was studied. It is shown that the degree of swelling the granules is reproduced with an error of 1%, which allows the sensor to be used repeatedly. The results obtained can be used in experiments and data processing for analytical applications.

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