Due: February 15
The goal of this written assignment is to first do some exercises in radiometry, and then to work on camera models. The mathematics that you derive for camera models will be used in your next programming assignment.
1. Assume the sky has constant radiance L over the entire upper hemisphere (it is a perfectly cloudy day). In class, we showed that a constant radiance hemispherical source would contribute irradiance E = π L to a point on the ground.
Suppose at some point on the terrain the ground plane is tilted by an angle θ with the respect to the horizon. These means a angular wedge of the hemispherical sky will not be visible at that point because parts of the sky are below the local horizon of the surface.
What is the irradiance E at this point?
2. Consider a square light source with constant radiance L and vertices (-1,-1,1), (-1,1,1), (1,1,1), and (1,-1,1). What is the irradiance E at the point (0,0,0), assuming that the surface at (0,0,0) has a normal vector of (0,0,1) [i.e., it points straight towards the center of the square]?
3. A real optical system exhibits vignetting. Vignetting causes the exposure to vary from a maximum at the center of the image to a lesser value at the edges.
Assume you have a camera with a infinitesimal disk aperture da (e.g., not a pinhole camera). Behind the aperture at distance equal to the focal length f is the film plane. Show that the irradiance on the film plane falls off as cos^4 θ.
Write your answers to the three questions above as a web page. Then, just mail the URL to the TA.
When submitting assignments, NEVER mail the TA anything other than a URL.