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An optical lense is essentially transforming the image into fourier space and back again. The radius of the lense (approx) is a limit to the spacial-frequencies

An optical lense is essentially transforming the image into fourier space and back again. The radius of the lense (approx) is a limit to the spacial-frequencies, i.e. some frequencies are clipped off. In the image plane, the signal has been backtransformed - however, some frequencies were lost due to the aperture. I.e. the fourier transform explains, why apertures limit the resolution of optical devices. It is not only absolute brightness, but fundamentally an information-bottleneck.

wirrbel 9y ago
quite happy my thesis supervisor does not read this really really simplified portrayal.
ttul 9y ago
Good lord.
dpwm 9y ago
You can actually use a laser, run it through a beam expander, pass it through a projector slide, run it through a lens, apply the filtering operations at the focal plane just like you would with a fourier transformed image, and get the expected result out. I thought this was just something cool you could do with lasers, but it seems that there is maybe some use for this: https://en.wikipedia.org/wiki/Optical_computing#Optical_Fourier_Co-processors https://en.wikipedia.org/wiki/Optical_computing#Optical_Four...
deleted 9y ago
[deleted]
CarVac 9y ago
When you have straight-edged aperture blades, the diffraction pattern creates spikes on the point spread function of the lens, and this can be predicted by just taking the Fourier transform of the aperture shape.
gone35 9y ago
I know some (rudimentary) harmonic analysis and am familiar with the Shannon-Nyquist theorem but I'm not sure I follow. Care to explain? Edit: nevermind, I got it [1]. I see, however, the result only holds 'modulo' paraxial waves well-behaved in the linear regime... So it's not that every lens automagically computes a FFT at the speed of light as it seemed at first! [1] https://en.wikipedia.org/wiki/Fourier_optics#Fourier_transforming_property_of_lenses https://en.wikipedia.org/wiki/Fourier_optics#Fourier_transfo...
calebm 9y ago
Wow, that's awesome, I've never thought of that! I guess it's similar to how a prism deconvolutes light eh?
- wirrbel 9y ago
  not sure what you mean by a prism deconvoluting light.

wirrbel 9y ago

quite happy my thesis supervisor does not read this really really simplified portrayal.

ttul 9y ago

Good lord.

dpwm 9y ago

You can actually use a laser, run it through a beam expander, pass it through a projector slide, run it through a lens, apply the filtering operations at the focal plane just like you would with a fourier transformed image, and get the expected result out. I thought this was just something cool you could do with lasers, but it seems that there is maybe some use for this: https://en.wikipedia.org/wiki/Optical_computing#Optical_Fourier_Co-processors https://en.wikipedia.org/wiki/Optical_computing#Optical_Four...

deleted 9y ago

[deleted]

CarVac 9y ago

When you have straight-edged aperture blades, the diffraction pattern creates spikes on the point spread function of the lens, and this can be predicted by just taking the Fourier transform of the aperture shape.

gone35 9y ago

I know some (rudimentary) harmonic analysis and am familiar with the Shannon-Nyquist theorem but I'm not sure I follow. Care to explain? Edit: nevermind, I got it [1]. I see, however, the result only holds 'modulo' paraxial waves well-behaved in the linear regime... So it's not that every lens automagically computes a FFT at the speed of light as it seemed at first! [1] https://en.wikipedia.org/wiki/Fourier_optics#Fourier_transforming_property_of_lenses https://en.wikipedia.org/wiki/Fourier_optics#Fourier_transfo...

calebm 9y ago

Wow, that's awesome, I've never thought of that! I guess it's similar to how a prism deconvolutes light eh?

wirrbel 9y ago
not sure what you mean by a prism deconvoluting light.