# Opacity/transparency of conductive meshes to charged particles (electrons/ions)

When using a conductive (metal) mesh, effectively a metallic woven fabric, in vacuum applications as a "grid" for charged particle optics, how does one calculate (or at least estimate) the opacity or transparency of this grid?

$$\begin{array} { l } { \mathrm { d } = \text { Wire diameter } } \\ { w = \text { Aperture width } } \\ { \mathrm { p } = \text { Pitch } } \\ { \mathrm { A } _ { 0 } = \text { Open area } } \\ { \mathrm { A } _ { 0 } = \frac { \mathrm { w } ^ { 2 } } { ( \mathrm { w } + \mathrm { d } ) ^ { 2 } } \times 100 } \\ { \mathrm { Nr } = \frac { 25,4 } { \mathrm { w } + \mathrm { d } } } \end{array}$$

If given the wire diameter $$d$$, the aperture width (from edge to edge) $$w$$ or the pitch (from center to center) $$p$$, one can determine mathematically the smallest (macroscopic) particle that could go through the aperture, as if using the mesh as a sieve. Only particles with a cross-sectional area smaller than the open area $$A_0$$ will make it through.

Electromagnetically, the question is more complex, because it then entails the wavelength of the photons passing through it, and the effects of diffraction and interference.

What about for charged particles? How would someone go about calculating this? If the grid/mesh is biased, it will attract particles of one charge, accelerating them on approach, decelerating them as the depart, and vice-versa for the opposite charge. What then, prevents 100% of the charged particles from being absorbed by the grid itself?

Examples:

1. The amount of current generated by a cathode, passing through a given grid (either biased or grounded), and making it to the anode.

2. The amount of detected current by a Faraday cup with a grid (biased or grounded) in front of it.