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Wigner Distributions and How They Relate to the Light Field

Abstract In wave optics, the Wigner distribution and its Fourier dual, the ambiguity function, are important tools in optical system simulation and analysis. The light field fulfills a similar role in the computer graphics community. In this paper, we establish that the light field as it is used in computer graphics is equivalent to a smoothed Wigner distribution and that these are equivalent to the raw Wigner distribution under a geometric optics approximation. Using this insight, we then explore two recent contributions: Fourier slice photography in computer graphics and wavefront coding in optics, and we examine the similarity between explanations of them using Wigner distributions and explanations of them using light fields. Understanding this long-suspected equivalence may lead to additional insights and the productive exchange of ideas between the two fields.

Magnetic pressure

Magnetic pressure is an energy density associated with the magnetic field.

Interplay between magnetic pressure and ordinary gas pressure is important to both the fields of magnetohydrodynamics and plasma physics. Any magnetic field has an associated pressure that is contained by the boundary conditions on the field, and a gradient in field strength causes a force due to the magnetic pressure gradient; this force is called the magnetic pressure force.

Gravitational waves are generated by accelerating masses. So, our planet, which is constantly accelerating towards the sun, is sending out a constant stream of gravitational waves. Just really small ones. Likewise, colliding neutron stars will emit a strong burst of gravitational waves. How strong? Well, if the stars were on the other side of our galaxy, a one meter bar on Earth would elongate by about 0.1am (attometer = 10-18m). 

orbit of an electron around a hydrogen atom (about 0.05nm),

In a light field, the amplitude (a measure of the brightness of the light) and the phase (which controls how to combine light fields) can't both be measured with absolute accuracy—even if you had the perfect measuring device. You can picture the problem as bunches of photons popping into and out of existence, causing the phase and amplitude of the of the light to jitter around. This doesn't add or subtract energy, but it does continuously redistributes the energy along the light beam.

Throughout the universe more than 99 percent of matter looks nothing like what's on Earth.

This material that pervades the universe, making up the stars and our sun, and also – far less densely, of course – the vast interstellar spaces in between, is called plasma. Plasmas are similar to gases, and indeed are made of familiar stuff such as hydrogen, helium, and even heavier elements like iron, but each particle carries electrical charge and the particles tend to move together as they do in a fluid.

"Which particles are moving, what is the source of energy for the motion, how does a moving wave interact with the particles themselves, do the wave fields rotate to the right or to the left – all of these get classified," says Lynn Wilson who is a space plasma physicist at NASA's Goddard Space Flight Center in Greenbelt, Md.

Wendy M. Edelberg Economist Macroeconomic Analysis Section Division of Research and Statistics

Fields of Interest Consumption Consumer Finance Real Estate Education Ph.D., Economics, University of Chicago, 2003 M.B.A., Econometrics & Finance, University of Chicago, Graduate School of Business, 1997 B.A., Economics, Columbia University, 1993

wendy.m.edelberg@frb.gov