Limit of Focal Spot Size for Lensing EM Radiation Across Frequencies

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    Focal Limit
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Discussion Overview

The discussion revolves around the behavior of electromagnetic (EM) radiation when lensed, particularly focusing on how the minimum spot size that can be achieved is influenced by frequency or wavelength. Participants explore concepts related to diffraction limits, beam waist, and the effects of aperture size on beam spreading.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant seeks an equation to describe how EM radiation can be focused as a function of frequency, noting that RF waves cannot be focused to a point.
  • Another participant mentions that no EM waves can be focused down to a point, introducing the concept of "beam waist" and referencing the possibility of building converging lenses for radio waves.
  • A participant introduces the Abbe diffraction limit, suggesting it may relate to the minimum obtainable spot radius.
  • Another participant proposes the Airy Disk as relevant to the discussion and suggests reviewing associated mathematical concepts.
  • One participant expresses gratitude for the information and questions whether the spot size is solely a function of the hardware, linking the Airy pattern and diffraction effects to lensing and aperture size.
  • A later reply confirms that a lens can produce a smaller Airy disk than an aperture but emphasizes that fundamental limits still exist based on aperture size and wavelength.

Areas of Agreement / Disagreement

Participants generally agree on the existence of limits to how small the spot size can be, but there are multiple competing views regarding the specifics of how different factors like aperture size and wavelength influence this behavior. The discussion remains unresolved regarding the precise relationships and equations involved.

Contextual Notes

Participants reference various concepts such as diffraction limits, beam waist, and the Airy Disk without fully resolving the mathematical relationships or assumptions underlying these concepts.

houlahound
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Did not know how to word this properly.

Looking for an equation to show the behaviour of how EM can be "lensed" as a function of wavelength/frequency.

ie RF waves can not be lensed/focussed to a spot.

what equation determines the minimum spot size a lens can focus EM radiation as a function of frequency?
 
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houlahound said:
what equation determines the minimum spot size a lens can focus EM radiation as a function of frequency?

I believe you're asking about the Airy Disk. Try the math in this article: https://en.wikipedia.org/wiki/Airy_disk
 
thanks guys. this is precisely the physics I was looking for.

haven't read through it all in detail but am I right in thinking the spot size is purely a function of the hardware transforming the light?

in the airy pattern, which is what is caused by diffraction from a circular aperture, would that increase the beam diameter after the aperture ie in general the smaller the aperture will cause greater spreading ie more diffraction. so therefore, if I am thinking right, a smaller beam will be achieved by a transparent lens than an aperture via diffraction.

I am going to try link the beam waist formula to the airy disc radius, but not sure if I am messing up the wrong two concepts.
 
houlahound said:
in the airy pattern, which is what is caused by diffraction from a circular aperture, would that increase the beam diameter after the aperture ie in general the smaller the aperture will cause greater spreading ie more diffraction. so therefore, if I am thinking right, a smaller beam will be achieved by a transparent lens than an aperture via diffraction.

You're right in that a lens will make a smaller airy disk than an open aperture, but there's still a fundamental limit to how small the airy disk can be which is based on the size of the aperture and the wavelength of the incoming light/radiation. A larger aperture and/or smaller wavelength gives a smaller airy disk.
 

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