4-D grid , : Because is usually not on the 4-D grid, DFST adopts trigonometric interpolation to compute the non-grid values. The algorithm consists of these steps: Sample the light field with the sampling period and and get the discretized light field . Pad with zeros such that the signal length is enough for FrFT without aliasing. For every , compute the Discrete Fourier transform of , and get the result . For every focal length , compute the fractional fourier transform of , where the order of the transform depends on , and get the result . Compute the inverse Discrete Fourier transform of . Remove the marginal pixels of so that each 2-D photograph has the size Methods to create light fields Light fields are a fundamental representation for light with many methods for defining them. In computer graphics, light fields are typically produced either by rendering a 3D model or by photographing a real scene. In either case, to produce a light field, views must be obtained for a large collection of viewpoints. Depending on the parameterization, this collection typically spans some portion of a line, circle, plane, sphere, or other shape, although unstructured collections are possible. Devices for capturing light fields photographically may include a moving handheld camera or a robotically controlled camera, an arc of cameras (as in the bullet time effect used in The Matrix), a dense array of cameras, handheld cameras, microscopes, or other optical system. How many images should be in a light field? The largest known light field (of Michelangelo's statue of Night) contains 24,000 1.3-megapixel images. At a deeper level, the answer depends on the application. For light field rendering to completely capture an opaque object, images must be taken of at least the front and back. Less obviously, for an object that lies astride the st plane, finely spaced images must be taken on the uv plane (in the two-plane parameterization shown above). The number and arrangement of images in a light field, and the resolution of each image, are together called the "sampling" of the 4D light field. Also of interest are the effects of occlusion, lighting and reflection. Applications Selected applications: Illumination engineering–Gershun's reason for studying the light field was to derive (in closed form) illumination patterns that would be observed on surfaces due to light sources of various shapes positioned above these surface. The branch of