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## Fourier Slice Photography

Ren NgStanford University

*In ACM Transactions on Graphics, July 2005 *

*(Proceedings of SIGGRAPH) *

**Abstract**

This paper contributes to the theory of photograph formation from light fields. The main result is a theorem that, in the Fourier
domain, a photograph formed by a full lens aperture is a 2D slice in the 4D light field. Photographs focused at different depths
correspond to slices at different trajectories in the 4D space. The paper demonstrates the utility of this theorem in two
different ways. First, the theorem is used to analyze the performance of digital refocusing, where one computes photographs
focused at different depths from a single light field. The analysis shows in closed form that the sharpness of refocused

photographs increases linearly with directional resolution. Second, the theorem yields a Fourier-domain algorithm for digital
refocusing, where we extract the appropriate 2D slice of the light field's Fourier transform, and perform an inverse 2D
Fourier transform. This method is faster than previous approaches.

**Paper **

600 dpi (2.5 MB)

© Ren Ng 2004-2005