Singular analysis of stereoscopic serif

The article is devoted to the development of a methodological apparatus for evaluating the influence of geometric survey conditions on the ratio of errors in the planned and altitude components of determining the terrain points’ spatial coordinates. For this purpose, an approach based on the singular analyzing the matrix of the system of equations for intersecting lines in the basis plane is used. It is shown that singular numbers characterize the ellipse of coordinate definition errors in plane and height. They are calculated for the most typical cases of stereo surveying. It is noted that the geometric conditions of stereo photography are mainly determined by the serif angle. By interpolating the results of calculating singular numbers, the formulas characterizing the direct and inverse dependence of the ratio of the stereo-cut in plan and height on the serif angle errors’ are obtained. The author considers the practical issues of using the developed methodological apparatus to justify the solutions related to the assessment of the ratio between the errors in determining the plane coordinates and the heights of terrain points from stereo images.

Antiferromagnetic Conic Refraction of Sound in Hematite

In a trigonal easy-plane -Fe2O3 antiferromagnet magnetic-field-dependent conic refraction due to the renormalization of the coefficients of elasticity effective magnetoelastic interaction is experimentally found in addition to the conventional internal conic refraction of the transverse elastic waves propagating along the trigonal C3 axis. It is shown that the deflection angle () of the energy flow from the C3 axis upon the internal conic refraction does not depend on the value of the magnetic field applied in the basis plane (HC3) and is a constant value determined by the correlation of the C14 and C44 coefficients of elasticity. The deflection angle of the energy flow upon the antiferromagnetic conic refraction () increases with increase in the field and tends to the  value at large H values. The obtained results agree well with the theory of this phenomenon in antiferromagnets and support its conclusions.