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It makes me think how the lens of the camera, is focusing the light/image at the center of the sensor, so it would make sense that data is also denser at the ce

by nico 2y ago

It makes me think how the lens of the camera, is focusing the light/image at the center of the sensor, so it would make sense that data is also denser at the center, where the lens concentrated more light

jameshart 2y ago
So… I think you’re a bit confused about how lenses work and what they do (they don’t focus all the light into the middle, they focus light from one plane onto another one. They only focus light from the center of the frame onto the center of the image - that’s why it’s an image) But… there is something interesting about what ‘focusing’ looks like in the frequency domain, and the difference between the frequency-space-transform of a sharply focused image and a blurred image - or of the same image focused at different focal planes - shows up as a predictable transformation in the frequency space; which means you can apply transformations in frequency space that cause focus changes in the image domain like a lens does.
- kragen 2y ago
  your first paragraph is completely wrong. the lens concentrates collimated light parallel to its axis at its focal point, regardless of where it falls on the lens. (and, strictly speaking, only at a single wavelength.) collimated light coming from near-axial directions gets focused more or less to a point on more or less the focal plane. but light at a single point doesn't have a direction, being a wave. there is in fact a very profound connection between the action of a lens and the 2d fft; see my sibling comment for more details your second paragraph is correct, and it is a special case of the convolution theorem; see https://en.wikipedia.org/wiki/Fourier_optics#The_2D_convolution_of_input_function_against_the_impulse_response_function https://en.wikipedia.org/wiki/Fourier_optics#The_2D_convolut...
  - jameshart 2y ago
    I don't think the idea that (idealized, camera) lenses focus light from distinct points in one plane (or at infinity) onto distinct points in another plane is 'completely wrong', but I'm open to being educated on my error. A lens focuses light parallel to its axis onto its focal point; it focuses parallel light coming in off-axis to other points on the focal plane. Alternatively, and equivalently, it focuses divergent light coming from common points on planes closer than infinity, onto matching points on other planes behind its focal plane.
    - smallnamespace 2y ago
      Lenses bring parallel rays of light (alternatively, light from infinitely far away) to the focal point. They don’t bring idealized points to points. One consequence is you can’t use lenses to bring anything to a temperature higher than the temperature of the source light. For example you can’t use lenses + moonlight to light things on fire. Here’s an HN thread going into the physics of it: https://news.ycombinator.com/item?id=18736700 https://news.ycombinator.com/item?id=18736700
meindnoch 2y ago
What are you talking about?
kragen 2y ago
yes, as it happens, the image on the focal plane of the camera resulting from light coming from a particular direction is in fact the 2d fourier transform of the spatial distribution of that light at the lens. this property has been used to build optical-computing military machine vision systems using spatial light modulators since the 01980s, because of some other useful properties of the fourier transform, that spatial shifts become phase shifts, so you can look for a target image everywhere in an image at once. as far as i know, these systems have never made it past the prototype stage see https://en.wikipedia.org/wiki/Fourier_optics#Fourier_transforming_property_of_lenses https://en.wikipedia.org/wiki/Fourier_optics#Fourier_transfo...
- nico 2y ago
  > is in fact the 2d fourier transform of the spatial distribution of that light at the lens. this property has been used to build optical-computing military machine vision systems Amazing. Do you have any links/references about those systems and how they should work in theory?
  - kragen 2y ago
    yes, see the link above

by nico 2y ago

jameshart 2y ago

So… I think you’re a bit confused about how lenses work and what they do (they don’t focus all the light into the middle, they focus light from one plane onto another one. They only focus light from the center of the frame onto the center of the image - that’s why it’s an image) But… there is something interesting about what ‘focusing’ looks like in the frequency domain, and the difference between the frequency-space-transform of a sharply focused image and a blurred image - or of the same image focused at different focal planes - shows up as a predictable transformation in the frequency space; which means you can apply transformations in frequency space that cause focus changes in the image domain like a lens does.

kragen 2y ago
your first paragraph is completely wrong. the lens concentrates collimated light parallel to its axis at its focal point, regardless of where it falls on the lens. (and, strictly speaking, only at a single wavelength.) collimated light coming from near-axial directions gets focused more or less to a point on more or less the focal plane. but light at a single point doesn't have a direction, being a wave. there is in fact a very profound connection between the action of a lens and the 2d fft; see my sibling comment for more details your second paragraph is correct, and it is a special case of the convolution theorem; see https://en.wikipedia.org/wiki/Fourier_optics#The_2D_convolution_of_input_function_against_the_impulse_response_function https://en.wikipedia.org/wiki/Fourier_optics#The_2D_convolut...
- jameshart 2y ago
  I don't think the idea that (idealized, camera) lenses focus light from distinct points in one plane (or at infinity) onto distinct points in another plane is 'completely wrong', but I'm open to being educated on my error. A lens focuses light parallel to its axis onto its focal point; it focuses parallel light coming in off-axis to other points on the focal plane. Alternatively, and equivalently, it focuses divergent light coming from common points on planes closer than infinity, onto matching points on other planes behind its focal plane.
  - smallnamespace 2y ago
    Lenses bring parallel rays of light (alternatively, light from infinitely far away) to the focal point. They don’t bring idealized points to points. One consequence is you can’t use lenses to bring anything to a temperature higher than the temperature of the source light. For example you can’t use lenses + moonlight to light things on fire. Here’s an HN thread going into the physics of it: https://news.ycombinator.com/item?id=18736700 https://news.ycombinator.com/item?id=18736700

meindnoch 2y ago

What are you talking about?

kragen 2y ago

yes, as it happens, the image on the focal plane of the camera resulting from light coming from a particular direction is in fact the 2d fourier transform of the spatial distribution of that light at the lens. this property has been used to build optical-computing military machine vision systems using spatial light modulators since the 01980s, because of some other useful properties of the fourier transform, that spatial shifts become phase shifts, so you can look for a target image everywhere in an image at once. as far as i know, these systems have never made it past the prototype stage see https://en.wikipedia.org/wiki/Fourier_optics#Fourier_transforming_property_of_lenses https://en.wikipedia.org/wiki/Fourier_optics#Fourier_transfo...

nico 2y ago
> is in fact the 2d fourier transform of the spatial distribution of that light at the lens. this property has been used to build optical-computing military machine vision systems Amazing. Do you have any links/references about those systems and how they should work in theory?
- kragen 2y ago
  yes, see the link above