Light in Saturns Rings: The Interaction of Diffraction, Refraction, and Reflection
The Cassini spacecraft is currently exploring Saturn and gathering vast amounts of data about the giant planets ring system. The rings are extemely thin when compared to their radial extent. The main rings are less than 100 meters thick, yet stretch out over 38,000 miles from the inside to the outside. Because of the distance at which Cassini orbits Saturn, individual particles in the rings cannot be seen by the imaging system, however, the size distribution of the rings can be determined in other ways.
In the second half of 2005, Cassini performed numerous Ring Occultation experiments, in which the spacecraft passed behind the rings as seen from Earth, and send radio waves tunned to three specific wavelengths through the rings, and were captured on Earth by the Deep Space Network. Even though a constant amplitude, single frequency signal is sent by Cassini, what is received on the ground is an intricate broadband signal. By observing how the frequency, phase, and amplitude of the sine waves change as they go through the rings, much can be learned. Information can also be gathered from stellar occultations, although they do not have a coherent phase signal.
Complex spectral analysis shows which wavelengths are able to penetrate different regions of the rings, and an initial guess at the particle size distribution can be realized.
I generated the two images seen above [not for this class, sperate work] using only the direct signal intensity of the radio occultation data, mapped onto a disk of correct radius, iteritively applied to make the planera ring system seen. The technique I propose to incorporate diffraction would be quite different, and would not be based off of the occultation data, but conversely, would try to simulate Cassini procuding the wavefront, and the result would be (in addition to pretty pictures!) the broadband spectrum seen in the experiment. The closer I can simulate the true signal, the closer my model is to reality.
The most significant challenge is to implement a diffraction system in pbrt. Because of the disances and size of the particles involved, we would be implementing a Fraunhofer Diffraction system instead of the more general Fresnel diffraction. However, even this problem is not analytically practical. In order to simulate the diffraction of the radio waves by using only rays of light in pbrt, we shall rely on Huygen's Principle, whom part of the Cassini-Huygens mission is named after. Huygen, in an attempt to explain diffraction, conjectured that a planar wavefront can be approximated by numerous point sources. These point sources then interfere with each other such that their crests will recreate the planar wavefront!
To recreate this in pbrt, I will chain together multiple series of point light sources, and observe their interference incrementally along the path.
In oder to simulate the Saturn ring system, I will be using a model describing particle sizes and locations, which is the same model being used by scientists in the process of interpreting the results of the occultations.
In the limit, as the wavelength decreases, the problem becomes geometrically observable. That is, the effects of diffraction become small enough that geometric calculation (ie: ray-particle intersections) dominate. This is mostly the case with visible light.
Secondary effects include interparticle refraction, and reflection of the radio wave off the particles, although both of these are likely to be much smaller factors in the overall signal path reconstruction.