In practice, as a rule, measuring systems are developed on the basis of heuristic consideration. It is possible to show a simple example from area of length measurements. The length can be measured by a ruler or a range finder. Having many independent measurements of the same length, it is possible to process data (to average) for obtaining of higher accuracy. The question on an optimum way of averaging is generally rather vital(average arithmetic, average geometrical or any other algorithm). The theory of statistical decisions gives the powerful tool for synthesis of processing algorithms. In our example with measurement of length the theory considers the average arithmetic value to be the best in accuracy (in the specific case of Gaussian statistics of mistakes).
The given example is very simple. However frequently in practice there are such problems when it is heuristically difficult to determine the initial scheme of correct measurement. The similar situation was arisen, for example, in adaptive optics where many algorithms of measurement and correction of wave front (Hartman sensors, systems of aperture sounding and so forth) were offered, each being complicated in realization and having rather narrow scope. In particular, in case of coherent illumination of observable object the problem of adaptive optics is reduced to the "phase problem" which is well-known in optics.
The theory of statistical decisions is remarkable in the sense that it allows to synthesize the initial scheme of correct measurement, providing thus the best theoretically achievable accuracy. We are led to assume, that 21st century will become the century when parameters of various devices achieve their theoretical limits. Operation of practically all products created in ASC "Femto", is based on application of the original synthesized schemes. It causes their high performance while being rather simple in realization.