According to the theory of the cathode lens

the formulas of monochromatic electron-optical transfer function（ETF） and of multichromatic ETF under Beta and Maxwell distributions are derived from the formula of first order lateral aberration. Considering the effects of spectral distributions of incident light and photocathode response

the ETF’s formula for multicolour light is also given

if the system’s object surface is a photocathode. These formulas including off-focus parameters can be used to study the ETF’s off-focus properties in the image space of the cathode lens. For sharp-focusing system

the expressions for the position of optimum image plane and its corresponding ETF are also given. It has been proved that by substituting the corresponding off-focus parameter the above formulas can be-used to describe the ETF of proximity system. And still simpler approximate formulas of ETF are obtained. Furthermore

the expressions for rms values of first order lateral aberration and the relationship-between the low frequency ETF and the current density distribution function of a point image are derived s o as to make the ETF organically related with other parameters of image quality.