Light Field Spectral Analysis

Abstract

As illustrated in Chapter 1, light field is a four-dimensional signal recording the light rays in the space. The goal of light field spectral analysis is to compute the Fourier transform of the light field signal, so that it can be used to determine the sampling rate of the scene (sampling is discussed in Chapter 3). Denote l(x) as the light field signal, where x = [x_s x_t x_u x_v]^T. The Fourier transform of the light field signal is formally defined as

$$L(\Omega)=\int_{-\infty}^{\infty} l({\rm{x}}){\rm{e}}^{{-{{{\rm{j}}\Omega}^{T}}_{\rm{x}}}}{\rm{dx}},$$

((2.1))

where Ω= [Ω_s Ω_t Ω_u Ω_v]^T. To convert the Fourier transform back to the light field, we have the inverse transform as

$$l(\rm{x}) =\frac{1}{{(2\pi)}^D}\int_{-\infty}^{\infty} L(\Omega){\rm{e}}^{{{{{\rm{j}}\Omega}^{T}}_{\rm{x}}}}{d\Omega},$$

((2.2))

where D is the dimension of the signal, which is 4 in the case of a 4D light field.