# Is “Light Field” a useful concept in mathematics or physics, or just in marketing?

The company lytro.com has an Illum and an Immerge [Light Field Camera] which presumably photograph Light Fields.

If I understand correctly the term light field refers to a 5D concept - at each point in 3D space there are rays of light from all directions. Those directions use 2 more dimensions (e.g. $(\theta, \phi)$) and $2+3=5$. This could be called the 5D plenoptic function. I think at each point in this 5D space you have some kind of spectral intensity information. It could be RGB values or a complete spectrum, and would have units of (for example) power per unit area, per unit solid angle, per unit wavelength.

Is this just a name for a thing, or are there real, substantial mathematical things you can do with a light field? For example, if I know the Electric and Magnetic fields in a volume, I suppose could calculate the resulting light field in a straightforward way. But what can I actually DO with a light field besides market it?

Related question and answer, and a random popular article that repeats the term light field over and over.

So, a phase space number density of photons can be written as $$\rho(\mathbf{x}, \mathbf{p})$$, a density over real space, which is 3D, and momentum space, which is also 3D. The magnitude of $$\mathbf{p}$$ is the "spectrum" direction, and the direction of $$\mathbf{p}$$ is the direction the light is traveling. This is related to the spectral radiance, $$I_\nu$$, by: \begin{align}I_\nu(\mathbf{x},\theta, \phi, \nu) &= hcp^3 \rho(\mathbf{x}, \mathbf{p}) \\ &= \frac{h^4 \nu^3}{c^2} \rho(\mathbf{x}, \mathbf{p}), \end{align} where $$\mathbf{p} = [ \sin \theta \cos \phi,\ \sin\theta \sin \phi,\ \cos\theta] \times h\nu /c.$$