A closed-form expression for the bandwidth of the plenoptic function under finite field of view constraints

The plenoptic function enables Image-based rendering (IBR) to be viewed in terms of sampling and reconstruction. Thus the spatial sampling rate can be determined through spectral analysis of the plenoptic function. In this paper we examine the bandwidth of the plenoptic function when both the field of view and the scene width are finite. This analysis is carried out on two planar Lambertian scenes, a fronto-parallel plane and a slanted plane, and in both cases the texture is bandlimited. We derive an exact closed-form expression for the plenoptic spectrum of a slanted plane with sinusoidal texture. We show that in both cases the finite constraints lead to band-unlimited spectra. By determining the essential bandwidth, we derive a sampling curve that gives an adequate camera spacing for a given distance between the scene and the camera line.