## § The Plenoptic Function

- What can we see because of light?
- Key idea: at each point $(x, y, z)$, we should be able to know, for all wavelenghts $\lambda$, the intensity of the wavelength in all directions $(\theta, \phi)$. Even more generally, this can vary with time $t$.
- Intuition: we should be able to reproduce at all points in spacetime, what happens if one builds a camera!
- This function $P(\theta, \phi, \lambda, t, x, y, z)$ is called as the
*plenoptic function *. - Notice that when one builds a pinhole camera, what one is doing is to, in fact, use the pencil of rays at that point to capture an image! Thus, the plenoptic function contains
*all possible *pinhole images at all positions. - The key conjecture of the paper "The plenoptic function and the elements of early vision" is that the visual cortex is extracting local changes / derivatives of the plenoptic function.

### § Crash Course Radiometry

- Irradiance at a point: density of radiant flux (power) per unit surface area.
- Radiance at a point in a direction: density of radiant flux (power) per unit surface area per unit solid angle.

### § Light field rendering

- See that if we restrict to only radiance of light at a fixed time $t_0$, then we have $(x, y, z, \theta, \phi)$, a 5 dimensional function.
- Also note that if there is no obstruction, then the radiance does not change along lines. So we can quotient $(x, y, z)$ to get a lower dimensional 4D field, given by $(\texttt{pos}_\theta, \texttt{pos}_\phi, \texttt{look}_\theta, \texttt{look}_phi)$.
- This 4D field is called as a light field.
- Alternatively, we can parametrize these by $(x_1, y_1)$ and $(x_2, y_2)$, and the paper canonically calls these as $(u, v, s, t)$. This coordinate system they call a
*light slab *, and represents light starting from the point $(u, v)$ at the first plane and ending at $(s, t)$ at the second plane.