Modulation transfer function of image tube lenses.

The modulation transfer function (MTF) of the proximity focusing biplanar lens and the sharp focusing electrostatic and electromagnetic lenses is derived and presented. It is shown that for a Maxwellian emission energy distribution, the MTF of the biplanar lens is MTF = exp(-4pi(2)epsilon/V(s)L(2)F(2)), where L is the screen to cathode separation in mm, f is the spatial frequency in lp/mm, V(s), is the screen voltage, and epsilon is the voltage equivalent of the most probable emission energy. For a cosine distribution, the MTF of the biplanar lens is MTF = exp(-7 piepsilon/V(s)L(2)f(2)). The MTF of sharp focusing image tube lenses is MTF = exp(-0.06pi(2)epsilon(2)M(2)f(2)/E(c)(2)), where E(c), is the cathode field strength in volts per mm and M is the magnification. In general, the MTF of image tube lenses is MTF = exp[-(pirhof)(2)], where rho is the focusing error coefficient of a particular lens.