Add reflected light component

[rodluger]

We may wish to generalize the code to include reflected light, particularly for phase curve modeling. Shouldn't be too hard to do.

[rodluger]

For the eyeball planet case, the reflect light map is coincident with the thermal emission map, so that's super easy. For the limb-darkened planet case, we can treat the map as a superposition of a radially symmetric emission map and the "elliptically" symmetric reflected light map, which basically involves running the code twice and summing the intensity at each wavelength.

[rodluger]

@ericagol When I look at the moon, the illuminated side is the same brightness everywhere, even close to the terminator. This is not the case for thermal emission, which approaches zero at the terminator. So can I model reflected light with a single irradiance for the dayside, and zero irradiance for the nightside? Is this what it means to be a Lambertian reflector?

[ericagol]

@rodluger I don't think the Moon is uniform. A Lambertian reflector scatters light uniformly in solid angle, but for the Moon at, say, half phase, the incident flux decreases towards the terminator as \cos{\phi}. I think what you are seeing by eye may be two things: the eye is a logarithmic detector, and the Moon is not Lambertian. For instance, self-shadowing of surface particles decreases the brightness of reflected light at larger angles of incidence; conversely, back-scattered light isn't subject to scattering, causing the Moon to be brighter at full phase (the "opposition" effect), in addition to coherent back-scatter. See discussion here: http://www.planetary.brown.edu/pdfs/4306.pdf