Mike Stark

Homework #4

An implementation of the Thin-Lens Camera Model

Overview

For this assignment we were asked to implement a simple, but fairly realistic, thin-lens camera model, and demonstrate that it works by displaying some images here. So, without further ado...

Images

The following images were created using a reasonably realistic camera parameters, modeled after a 35mm camera (with a "square" film plane rather than the typical 2:3 aspect ratio) having a 50 mm focal length. The camera was arranged in space so that the center of projection is on the main axis, 50 mm (the focal length) in front of the film plane. The film plane is fixed in space and the lens is allowed to move for focusing, analogous to a real camera mounted on a tripod. Specifically, for all the images below, except otherwise noted, the parameters are: The orientation thus has the camera mounted one meter above the origin of the xy-plane, looking along the positive x-axis, declined slightly from the horizon. The xy-plane is painted with an infinite unit checkerboard, with red checks decreasing in brightness with increasing x coordinate. (This was done to avoid the pathological aliasing problems of the checkerboard near the horizon.)

There are four "signs" indicating distance from the center of projection. Each is raised about 0.9m above the plane for aesthetic reasons; however, this may cause some perceptual confusion as they tend to make the plane look closer than it is. The first checker corner visible at the bottom of the screen is actually the point (1, 0). There is an image of the full moon visible about 400,000 km away along the x-axis, which is sufficiently far away to be considered at "infinity". The only lighting in the scenes is the ambient lighting.

The scene looks like this, using a "pinhole" camera.

This, along with most of the other images on this page, were done using a simple box filter and 64 samples per pixel, jittered on both the image plane and the lens. The aperture is circular, and the sampling is accomplished using Pete's concentric square-to-disk map.

Variation of the Focus

The following images were rendered at f5.6, which amounts to an aperture diameter of about 8.9mm.

One thing worth noting here is that the effective field of view is somewhat narrower when the focus is close than when it is far. The reason for this is that a closer focus causes the lens to be further from the film plane, so it subtends a smaller angle and hence a smaller field of view. The effect is perhaps easier to visualize with the pinhole camera model; one can certainly see more through a tiny hole by putting an eye nearly against it!

Even more obvious than the change of field of view with the focus is the change in the apparent size of the ".25 m" object in the scene, which is greater than the change in the field of view itself. This is a result of the fact that the lens is moving (closer to the object) as the focus is drawn in. Another orientation option would be to leave the lens fixed in space, and move the film plane to focus. In this case the field of view would change, but the apparent size of the near objects would only change as much as the field of view.
Focus at 0.25m
Focus at 0.5m
Focus at 1m
Focus at 2m
Focus at "infinity"

Variation of the Aperture

The following images have focus plane fixed at 0.5m but have significant variation the aperture. Note that differences the image rendered at f22 is
f22
f11
f5.6
f3.3

Some Movies

Here are a couple of not particularly good animations showing the variation in the focus and the aperture. Both are in SGI format, despite the ".qt" extension. I'd rather have made them into QuickTime movies, but the software on the SGI's I was using didn't seem to want to let me do it. I don't know why, I didn't have any trouble creating the movies in homework 4. The focus animation goes from focusing at 0.20 meters to about 5 meters, in steps proportional to the inverse of the focus distance. The aperture animation starts with an aperture of 25 mm and goes to zero, in increments of 1 mm. Neither one turned out very good, I'm afraid.