opd_effelsberg¶
- pyoof.telgeometry.opd_effelsberg(x, y, d_z)[source]¶
Optical path difference (OPD) function, \(\delta(x,y;d_z)\). Given by the geometry of the telescope and radial offset parameter, \(d_z\). This function is specific for the Effelsberg telescope.
- Parameters
- x
Quantity Grid value for the \(x\) variable in length units.
- y
Quantity Grid value for the \(y\) variable in length units.
- d_z
Quantity Radial offset, \(d_z\), added to the sub-reflector in meters. This characteristic measurement adds the classical interference pattern to the beam maps, normalized squared (field) radiation pattern, which is an out-of-focus property. It is usually of the order of centimeters.
- x
- Returns
- opd
Quantity Optical path difference function, \(\delta(x,y;d_z)\).
- opd
Notes
For a Gregorian configuration, and with the dish diameter of Effelsberg, the OPD function becomes,
\[\delta(x,;d_z) = d_z\left( \frac{1-a^2}{1+a^2} + \frac{1-b^2}{1+b^2} \right),\]\[a = \frac{\sqrt{x^2+y^2}}{2F_\mathrm{p}}, \qquad b = \frac{\sqrt{x^2+y^2}}{2F_\mathrm{eff}},\]where \(F_\mathrm{p}=30\) m corresponds to the parabola focal length and \(F_\mathrm{eff}=387.4\) m, the effective or total focal length.
