When is a Numerical Aperture considered High?

[ecastro]

When will you consider that the numerical aperture is high?

I was told that the numerical Angular Spectrum Method is only valid low numerical aperture values, I want to know the boundary of this value.

Thank you in advance.

 

[blue_leaf77]

To the best of my knowledge, angular spectrum method is exact, hence one needs not restrict the applicability to low numerical aperture only.

 

[ecastro]

I found this paper, https://www.osapublishing.org/ao/abstract.cfm?uri=ao-51-29-7080.

Unfortunately, I can't access it...

 

[blue_leaf77]

The very first sentence of the abstract says, "The angular spectrum (AS) method is a popular solution to the Helmholtz Equation without the use of approximations.".
So, what do you actually want to tell us by referencing to this paper?

 

[ecastro]

Well, it says in the abstract of the paper "It is shown that for the case of high numerical aperture the conventional AS method requires a very large amount of zero-padding, making it impractical due to requirements on memory and computational effort."

 

[blue_leaf77]

That sentence addresses the numerical impracticality of the angular spectrum method, but it does not necessarily suggest that this method is bound to fail to give accurate calculation when the NA is high as your first post implied. Provided you have a super computer with which AS method for high NA works fine, it will give you accurate result.

 

[ecastro]

Maybe I have misused the word 'valid'. What I want to know is when does the numerical Angular Spectrum Method becomes impractical, i.e. what must be the value of the numerical aperture for me to add very large amounts of zero-padding.