Pixel field-of-view Figure 5.5: 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: $$d\Omega(u,v) = \sin \theta d\phi d\theta = \sin\theta\vert\frac{\... ...dudv = \sin\theta\vert\frac{\partial(u,v)}{\partial(\phi,\theta)}\vert^{-1}dudv$$ (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).