Next: Analysis of Defocus Blur
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Two factors combine to cause defocus blur in catadioptric sensors, that
is in addition to the normal causes present in conventional dioptric
systems, such as diffraction and lens aberrations. They are (1) the
finite size of the lens aperture, and (2) the curvature of the mirror.
To analyze how these two factors cause defocus blur, we first consider
a fixed point in the world and a fixed point in the lens. We then find
the point on the mirror which reflects a ray of light from the world
point through the lens point. Next, we compute where on the image
plane this mirror point is imaged. By considering the locus of imaged
mirror points as the lens point varies, we can compute the area of the
image plane onto which a fixed world point is imaged. In
Section 4.1, we derive the constraints on the mirror point
at which the light is reflected, and show how it can be projected onto
the image plane. Afterwards, in Section 4.2, we present
numerical results for the hyperboloid mirror. Generalization to the
other mirrors described in Section 2 is straightforward.
Figure 9:
The geometry used to analyze the defocus
blur. We work in the 3D cartesian frame
where and are orthogonal unit
vectors in the plane z=0. In addition to the assumptions of
Section 3, we also assume that the effective pinhole is
located at the center of the lens and that the lens has a circular
aperture. If a ray of light from the world point is reflected at the mirror point
and then passes through the
lens point ,there are three constraints on : (1) it
must lie on the mirror, (2) the angle of incidence must equal the
angle of reflection, and (3) the normal to the mirror at
, and the two vectors and
must be coplanar.

Next: Analysis of Defocus Blur
Up: No Title
Previous: Resolution of a Catadioptric
Simon Baker
1/22/1998