The Apodization Factor determines what the Gaussian beam’s intensity profile looks like across the aperture (or the entrance pupil of the system).  More specifically, it determines how fast a Gaussian beam’s intensity falls off within the aperture.  A simple way to think about it to ask the question:  Where do I want the 1/e^2 intensity point of my beam to be relative to the edge of the aperture? For example, do I want the wings of the Gaussian to be cut off, or do I prefer to have the wings contained well within the boundary of the pupil?  After some basic math (see below), the answer is rho_0 = 1/sqrt(G), where rho is the normalized radial pupil (aperture) coordinate, rho_0 is the specific value where the Gaussian intensity falls to 1/e^2, and G is the corresponding Apodization Factor. 

So, if you have G = 6.5, then this means the 1/e^2 intensity point of your source will reside at rho_0 = 1/sqrt(6.5) = 0.39.  This is a normalized radial coordinate value.  With an EPD = 25 mm, the aperture radius is 12.5 mm.  So, in absolute terms, the 1/e^2 intensity point of the beam within the pupil corresponds to (0.39)(12.5 mm) = 4.9 mm.  If you define the “beam size” to be the *diameter* of the Gaussian beam as measured between the 1/e^2 intensity points, then the beam size is 2(4.9mm) = 9.8 mm.  (However, I think it is best to use the terms “beam diameter” or “beam radius” when discussing Gaussian beams because “beam size” is somewhat ambiguous.)

Some more details can be found here: Gaussian Beam Apodization in Zemax

Jeff.Wilde, Pefect! Thank you,

talimu

@Jeff.Wilde Could you please also help me understand apodization with example in case the beam is defined as object space NA rather than EPD. 

@saurabh  There’s really no difference when the aperture type changes.  The pupil coordinate (rho) is a normalized dimensionless quantity, so the relation rho_0 = 1/sqrt(G), which defines the value of rho at which the normalized intensity falls to the 1/e^2 value, is independent of aperture type. 

Here are two examples using Object Space NA.

G = 1 (so the 1/e^2 value occurs at the pupil edge, rho_0 = 1)

G = 2.25 (so the 1/e^2 value occurs two-thirds of the way to the pupil edge, rho_0 = 0.667)

When G = 1, the wings of the Gaussian profile are clipped by the system aperture, which may be okay (or perhaps even desirable) in some applications.  However, I often use G = 2.25 so that essentially the entire Gaussian profile passes through the aperture.