light travels in rays (0D at a point in time, 1D over time), while by the Huygens–Fresnel principle, a sound wave front can be modeled as spherical waves (2D at a point in time, 3D over time): light moves in a single direction (2D of information), while sound expands in every direction. However, light travelling in non-vacuous media may scatter in a similar fashion, and the irreversibility or information lost in the scattering is discernible in the apparent loss of a system dimension. Image refocusing Because light field provides spatial and angular information, we can alter the position of focal planes after exposure, which is often termed refocusing. The principle of refocusing is to obtain conventional 2-D photographs from a light field through the integral transform. The transform takes a lightfield as its input and generates a photograph focused on a specific plane. Assuming represents a 4-D light field that records light rays traveling from position on the first plane to position on the second plane, where is the distance between two planes, a 2-D photograph at any depth can be obtained from the following integral transform: , or more concisely, , where , , and is the photography operator. In practice, this formula cannot be directly used because a plenoptic camera usually captures discrete samples of the lightfield , and hence resampling (or interpolation) is needed to compute . Another problem is high computation complexity. To compute an 2-D photograph from an 4-D light field, the complexity of the formula is . Fourier slice photography One way to reduce the complexity of computation is to adopt the concept of Fourier slice theorem: The photography operator can be viewed as a shear followed by projection. The result should be proportional to a dilated 2-D slice of the 4-D Fourier transform of a light field. More precisely, a refocused image can be generated from the 4-D Fourier spectrum of a light field by extracting a 2-D slice, applying an inverse 2-D transform, and scaling. The asymptotic complexity of the algorithm is . Discrete focal stack transform Another way to efficiently compute 2-D photographs is to adopt discrete focal stack transform (DFST). DFST is designed to generate a collection of refocused 2-D photographs, or so-called Focal Stack. This method can be implemeted by fast fractional fourier transform (FrFT). The discrete photography operator is defined as follows for a lightfield sampled in a