A unified aberration theory for magnetic deflection systems with rectilinear or curvilinear axes

A unified deflection aberration theory has been further developed for magnetic deflection systems with curvilinear or rectilinear axes. By using variational method, primary-order deflection aberrations with respect to curvilinear or rectilinear axis can be universally calculated by means of gradient operations on eikonal (the function of optical length). Conventional pure-order rectilinear-axis theory can be derived from a curvilinear axis eikonal of mixed-order in the rectilinear limit. By introducing general aberration integration functions in terms of mathematical operators, all primary-order deflection aberrations have been explicitly expressed in compact formulae suitable for computer computations. It is to be expected that the unified deflection aberration theory may be useful in designing high-quality magnetic deflection systems for high-definition television color picture tubes.