Optimal energy resolution of a hemispherical analyzer with virtual entry

Abstract

For an ideal hemispherical deflector analyzer (HDA) utilizing a virtual entry aperture whose size is controlled by an injection lens, the “slit” and angular contributions to the overall base resolution RB are not independent, but constrained by the Helmholtz–Lagrange law. Thus, RB becomes a function of the linear lens magnification ∣ML∣ and has a minimum, RBo¯≡RB(∣ML∣o), at the optimal magnification ∣ML∣=∣ML∣o. RBo¯ and ∣ML∣o are shown to be analytic expressions of basic experimental parameters. RBo¯ is thus the ultimate resolution that can be attained in this case. The generality and simplicity of this result should be very helpful in the efficient design and performance evaluation of any modern HDA.