THEORETICAL FUNDAMENTALS OF THE CALCULATING THREE-MIRROR DECENTER ANASTIGMATS METHODOLOGY

The article is devoted to the theory of calculating mirror systems with anastigmatic properties, namely, the area of research in terms of developing methods for parametric calculation of dimensions and aberration correction. The such systems can correct three third-order aberrations. Mirror anastigmats allow developing the angular field of view of devices while maintaining a high numerical aperture, which allows them to be used in optoelectronic equipment operating in a wide spectral range. Complete absence of chromatic aberrations, high resolution, permissible wave criteria for image quality provide excellent opportunities for using mirror anastigmatic systems. General methodological approaches have been developed that can be applied to the creation of detailed engineering and technical methods for calculating a group of mirror anastigmatic systems. A serious drawback of reflective optics is center without central screening, which degrades image quality. To eliminate it, rotations or displacements of the mirrors are intro-duced, but non-elementary aberrations of even orders appear, which must be corrected. The creation of compositions with decentered catoptric elements requires further development of the calculation and methodological base. Mathematical solutions to the problem of creating basic models of non-centered mirror systems are presented. Accurate formulas are obtained for the calculation of real rays from the conditions of astigmatism and coma correction for the given angles of incidence of the chief ray on the mirror surfaces and the «oblique» thickness , which determines their relative position. Based on the proposed formulas, a new method for parametric calculation of decentered mirror systems has been created, which allows one to compose algorithms and design both basic models and complex mirror systems from off-axis mirrors. The development of new algorithms for two- and three-mirror decenter lenses will increase the accumulated potential of computational optics. The scope of the proposed technique can be expanded in terms of the number of components.

Mathematical solutions to the problem of creating basic decenter optical mirror models from the coma and astigmatism correction conditions

A serious drawback of reflective optics is a center without central screening that degrades the image quality. To eliminate it, rotations or displacements of mirrors are introduced, but there appear even-order non-elementary aberrations that must be corrected. The creation of compositions with decentered catoptric elements requires further development of the calculation and methodological base. The exact formulas are obtained for calculation of real rays from the astigmatism and coma correction conditions for the given angles of incidence of the main ray on the mirror surfaces and the “oblique” thickness d, that determines their mutual position. Based on the proposed formulas, a new method for parametric calculation of decentered mirror systems has been created, which allows one to compose algorithms and to design both basic models and complex mirror systems from off-axis mirrors. The development of new algorithms for two- and three-mirror off-center lenses will increase the accumulated potential of computational optics. The scope of the proposed technique can be expanded in terms of the number of components.

Relation between serum and whole-blood ethanol concentrations

An algorithm is suggested for interpretation of serum ethanol concentrations under legal statutes that specify whole-blood alcohol concentrations. The algorithm uses the distribution of individual serum:whole-blood alcohol concentration ratios to allow calculations at various levels of confidence that can be related to legal standards of evidence. Serum:whole-blood alcohol concentration ratios were determined for 211 patients. The ratios ranged from 0.88 to 1.59 (median 1.15). The distribution of ratios was positively skewed, but the logarithms of the ratios were normally distributed. This allowed the parametric calculation of a range of ratios of 0.90-1.49 for the central 99% of the population and a range of 0.95-1.40 for the central 95%. The serum:whole-blood alcohol concentration ratio was independent of both the serum alcohol concentration (R2 = 0.005) and the hematocrit (R2 = 0.03).