pcij_matrix#

overlappy.wcs.pcij_matrix(roll_angle: Unit('deg'), dispersion_angle: Unit('deg'), order=1)[source]#

Create a PC_ij matrix for an slitless spectrogram.

Calculate a PC_ij matrix for a slitless spectrogram with a grating angle of \(\gamma\), a satellite roll angle of \(\alpha\), and a spectral dispersion of \(\mu\). This has the form,

\[\begin{split}P(\alpha, \gamma, \mu) &= R(\alpha - \gamma)D(\mu)R(\gamma) \\ &= \begin{bmatrix} \cos{(\alpha)} & -\sin{(\alpha)} & -\mu\cos{(\alpha - \gamma)}\\ \sin{(\alpha)} & \cos{(\alpha)} & -\mu\sin{(\alpha - \gamma)}\\ 0 & 0 & 1 \end{bmatrix}\end{split}\]
Parameters:

  • roll_angle (~astropy.units.Quantity) – Angle between the second pixel axis and the y-like world axis. This is the roll angle of the satellite.

  • dispersion_angle (~astropy.units.Quantity) – Angle between the direction of spectral dispersion and the x-like pixel axis. This is the angle between the dispersive element and the detector.

  • order (int, optional) – Order of the spectral dispersion. Default is 1.