3 ms·

So - score my understanding of this. A lens performs a fourier transform, right? So the idea here is that instead of doing the transform with a lens, we grab

So - score my understanding of this. A lens performs a fourier transform, right? So the idea here is that instead of doing the transform with a lens, we grab the raw information and do an fft in software?

davnicwil 11y ago
I'm not sure on the implementation details of this particular method, and not really qualified to score anyone's understanding of anything in this field :-) but the shape of what you say is correct - you're modelling the physics of what happens in a lens system X (X can be a range of systems of course, not necessarily one particular system, but you get the idea), and in an alternate system Y (in this case Y is no lens, but a coded aperture used to add extra contextual information to the captured light) so you can use software to do a virtualised mapping of what your light captured from the scene via system Y would have looked like if had instead passed through system X - in other words, estimating virtually what a photo of the scene would have looked like if you'd used a lens, even though you've actually got no lens. Very clever application indeed!
Ono-Sendai 11y ago
A lens doesn't compute the fourier transform of the image, it inverts it (geometrically speaking). On a wave level (far-field diffraction) it does something like the fourier transform.
- tortle 11y ago
  A lens is a convolution. Imagine if a photograph was a 1D signal, then a lens would be a convolution of a signal with a square wave (Lens sliced along one plane). Now, typically when a square wave is convolved with a signal, if you look at the magnitude of the fourier transform, you'll notice that you are multiplying the frequencies of the signal with a sinc function. Sinc functions hit zero amplitudes at various points, thereby destroying information when multiplied. Therefore, if you could create a lens (known as a mask), which didn't destroy signal, but instead was more like a band-pass filter, then you could effectively recover the signal and adjust for amplitude changes digitally. Now take this model to the 3D and you've just created a lightfield.
  - Ono-Sendai 11y ago
    Calling a lens a convolution is an idealisation. It only convolves the signal on the focal plane/sensor, for perfectly focused light.

davnicwil 11y ago

I'm not sure on the implementation details of this particular method, and not really qualified to score anyone's understanding of anything in this field :-) but the shape of what you say is correct - you're modelling the physics of what happens in a lens system X (X can be a range of systems of course, not necessarily one particular system, but you get the idea), and in an alternate system Y (in this case Y is no lens, but a coded aperture used to add extra contextual information to the captured light) so you can use software to do a virtualised mapping of what your light captured from the scene via system Y would have looked like if had instead passed through system X - in other words, estimating virtually what a photo of the scene would have looked like if you'd used a lens, even though you've actually got no lens. Very clever application indeed!

Ono-Sendai 11y ago

A lens doesn't compute the fourier transform of the image, it inverts it (geometrically speaking). On a wave level (far-field diffraction) it does something like the fourier transform.

tortle 11y ago
A lens is a convolution. Imagine if a photograph was a 1D signal, then a lens would be a convolution of a signal with a square wave (Lens sliced along one plane). Now, typically when a square wave is convolved with a signal, if you look at the magnitude of the fourier transform, you'll notice that you are multiplying the frequencies of the signal with a sinc function. Sinc functions hit zero amplitudes at various points, thereby destroying information when multiplied. Therefore, if you could create a lens (known as a mask), which didn't destroy signal, but instead was more like a band-pass filter, then you could effectively recover the signal and adjust for amplitude changes digitally. Now take this model to the 3D and you've just created a lightfield.
- Ono-Sendai 11y ago
  Calling a lens a convolution is an idealisation. It only convolves the signal on the focal plane/sensor, for perfectly focused light.