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A Frequency Analysis of Light Transport
We present a signal-processing framework for light transport. We study the frequency content of radiance and how it is affected by phenomena such as shading, occlusion, and travel in free space. This extends previous work that considered either spatial or angular dimensions, and offers a comprehensive treatment of both space and angle. We characterize how the radiance signal is modified as light propagates and interacts with objects. In particular, we show that occlusion (a multiplication in the primal space) amounts in the Fourier domain to a convolution by the frequency content of the blocker. Propagation in free space corresponds to a shear in the space-angle frequency domain, while reflection on curved objects performs a different shear along the angular frequency axis. As described by previous work, reflection is a convolution in the primal space, and therefore amounts to a multiplication in the Fourier domain. Our extension shows how the spatial components of lighting are affected by this angular convolution. We show that our signal-processing framework predicts the characteristics of interactions such as caustics, and the disappearance of the shadows of small features. Predictions on the frequency spectrum of the radiance function can then be used to control sampling rates or the choice of reconstruction kernels for rendering. Other potential applications include pre-computed radiance transfer and inverse rendering.