When is a Numerical Aperture considered High?

In summary, the conversation discusses the applicability of the angular spectrum method for high numerical aperture values. The referenced paper suggests that for high NA values, the conventional AS method requires a large amount of zero-padding, making it impractical due to memory and computational constraints. However, this does not necessarily mean that the method cannot provide accurate results with a powerful enough computer. The exact boundary for when the AS method becomes impractical for high NA values is still unclear.
  • #1
ecastro
254
8
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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  • #2
To the best of my knowledge, angular spectrum method is exact, hence one needs not restrict the applicability to low numerical aperture only.
 
  • #4
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?
 
  • #5
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."
 
  • #6
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.
 
  • #7
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.
 

FAQ: When is a Numerical Aperture considered High?

What is Numerical Aperture (NA) in optics?

Numerical Aperture is a measure of the acceptance angle of an optical system, which is the maximum angle at which light can enter or exit the system. It is calculated as the product of the refractive index of the medium and the sine of the half-angle of the cone of light entering or exiting the system.

How is Numerical Aperture related to light collection efficiency?

A higher Numerical Aperture means a larger cone of light can be collected, resulting in a higher light collection efficiency. This is because a larger acceptance angle allows for more light to enter the system, increasing the amount of light that can be used for imaging or detection.

What is considered a high Numerical Aperture?

A Numerical Aperture of 0.95 or higher is generally considered high. However, the value of a high Numerical Aperture varies depending on the specific application and type of optical system being used. For example, a high NA for a microscope objective may be different from a high NA for a fiber optic cable.

What are the advantages of using a high Numerical Aperture?

Using a high Numerical Aperture can improve the resolution and sensitivity of an optical system. This is because a larger cone of light allows for finer details to be captured and more light to be collected, resulting in a clearer and brighter image. High NA also allows for better control of the depth of field and the ability to image deeper into a sample.

What are the limitations of using a high Numerical Aperture?

One limitation of using a high Numerical Aperture is that it requires careful alignment and maintenance of the optical system. The angle of the cone of light must be precisely controlled, which can be challenging and may lead to reduced stability and increased complexity of the system. Additionally, high NA may result in a smaller field of view and decreased working distance, making it more difficult to image larger or thicker samples.

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