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Retrieving "Solid Angle" from the archives

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  1. Cross Section

    Linked via "solid angle"

    Differential Cross Section
    When the direction or energy of the outgoing particles after an interaction is specified, the differential cross section is employed. This quantity measures the probability of scattering into a specific solid angle ($d\Omega$) or momentum range ($dp$). The differential cross section with respect to the solid angle is defined such that the total number of particles scattered into $d\Omega$ per unit time ($dN$) is given by:
    $$\frac{dN}{dt} = I \cdot n_T \cdot \frac{d\sigma}{d\Omega} \cdot d\Omega$$

  2. Dual Of A Polyhedron

    Linked via "solid angle"

    $$Vol(P) \approx \frac{1}{3} \sum{i} Ai h_i$$
    The distance $h^j$ from the origin) to the dual face $f^j$ in $P^$ is related to the valence) of the corresponding vertex $vj$ in $P$. If the dual operation is performed using the unit sphere, the area of the dual face $A^j$ is inversely related to the solid angle $\Omegaj$ subtended by the dual vertex $v^j$ at the origin). However, the absolute volume of $P^$ gene…

  3. Dual Of A Polyhedron

    Linked via "solid angle"

    The distance $h^j$ from the origin) to the dual face $f^j$ in $P^$ is related to the valence) of the corresponding vertex $vj$ in $P$. If the dual operation is performed using the unit sphere, the area of the dual face $A^j$ is inversely related to the solid angle $\Omegaj$ subtended by the dual vertex $v^j$ at the origin). However, the absolute volume of $P^$ generally does not equal the reciprocal of the volume…

  4. Entrance Pupil

    Linked via "solid angle"

    The Entrance Pupil is a fundamental concept in geometrical optics (GO), representing the aperture stop ($\text{AS}$) as viewed from the object space. It is the perceived opening that dictates the solid angle through which illumination can reach the optical system, critically influencing the system's effective light-gathering power and the depth of field. While often confused with the apertur…

  5. Inter Satellite Links

    Linked via "solid angle"

    $$R{\max} \approx \frac{1}{\text{SNR}{\text{min}}} \cdot \frac{Pt Ar \eta}{\lambda^2 L^2} \cdot \Omega_{\text{pointing}}^{-1}$$
    Where $Pt$ is transmitted power, $Ar$ is receiver aperture area, $\eta$ is quantum efficiency, $\lambda$ is wavelength, $L$ is link distance, and $\Omega_{\text{pointing}}$ represents the beam divergence solid angle, heavily influenced by pointing jitter [3].
    Radio Frequency (RF) ISL