Rami Arieli: "The Laser Adventure" Chapter 7 Section 2, page 14
Spot Size after Passing through Small Hole

There is a difference between a plan parallel beam and a Gaussian beam.

A Gaussian beam remains Gaussian along its path.

A Plane beam have a different intensity distribution in the near field (right after the hole) and stable distribution in the far field.

When a Gaussian beam pass through a small hole, part of its energy is blocked by the edges of the hole (see figure 7.11).

Figure 7.11: A Gaussian Beam with Diameter 2W pass through a Hole with Diameter 2a.

Part of the power transmitted through the hole:

T = Transmitted part of the power.

r = The radius of the hole.

2W = Beam spot size (Beam diameter at e-2 of its power).
When the Transmitted part of the power is given (or the Input power and transmitted power), the beam radius can be calculated by: