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Pixel field-of-view

Figure 5.5:
		    \epsfig {file=Figures/,width=3cm,height=3.5cm} }

In order to calculate the approximate intersection volume of the voxel in equation (5.3), the pixel field-of-view must be calculated.

Once the parameters of the optical transfer function are determined as outlined in chapter 4, the pixel field-of-view, $ d\Omega$, can be determined by standard calculus. With $ \theta$ as the angle relative to the optical axis of the camera, and $ \phi$ as the azimuthal angle, the field-of-view is calculated as:

$\displaystyle d\Omega(u,v) = \sin \theta d\phi d\theta = \sin\theta\vert\frac{\...
		    ...dudv = \sin\theta\vert\frac{\partial(u,v)}{\partial(\phi,\theta)}\vert^{-1}dudv$ (5.14)

for which $ (u,v)$ are the horizontal and vertical image coordinates and $ \vert\frac{\partial(u,v)}{\partial(\phi,\theta)}\vert$ is the absolute value of the determinant of the Jacobian of the optical transfer function, which, for the ALIS cameras, is given by equations (4.6 and 4.7).

copyright Björn Gustavsson 2000-10-24