Model of field electron emitter surface structure

In this article SEM-images of experimental monocrystal field emitter tips are studied. As a result of digital image processing the point chart of selected sample surface contour is received. It is defined which of three considered surfaces of revolution of the second order (an ellipsoid of rotation, a cavity of a two-sheeted hyperboloid, a rotation paraboloid) in the best way approximates this contour. The problem of curvilinear regression according to the least-squares method is solved and it is revealed that the best approximation of the shape of a researched tip is hyperboloidal. The problem of equidistance is solved by a bisektion method. The surface structure of the model tip with hyperboloidal shape is calculated in thin shell approach.