When is a Numerical Aperture considered High?

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    Numerical Optics
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Discussion Overview

The discussion revolves around the concept of numerical aperture (NA) in the context of the angular spectrum method (AS method) used in optics. Participants explore the conditions under which the AS method is considered valid or practical, particularly focusing on high numerical aperture values and the implications for computational requirements.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant inquires about the threshold at which numerical aperture is considered high and its implications for the angular spectrum method.
  • Another participant asserts that the angular spectrum method is exact and does not require restriction to low numerical aperture values.
  • A reference to a paper is made, which discusses the AS method's performance without approximations, but access to the paper is limited for some participants.
  • It is noted that the referenced paper mentions that high numerical aperture requires significant zero-padding, which raises concerns about practicality due to memory and computational demands.
  • A participant clarifies that the numerical impracticality does not imply that the AS method fails to provide accurate results at high NA, provided sufficient computational resources are available.
  • One participant seeks to clarify their use of the term 'valid' and asks specifically about the numerical aperture value at which the AS method becomes impractical due to zero-padding requirements.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of the angular spectrum method at high numerical aperture values. There is no consensus on a specific threshold for numerical aperture that defines when the method becomes impractical.

Contextual Notes

Participants highlight limitations related to computational resources and the need for zero-padding in the context of high numerical aperture, but specific numerical thresholds or conditions remain unresolved.

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

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