spherical_deproject

sofia_redux.scan.coordinate_systems.projection.projection_numba_functions.spherical_deproject(phi, theta, celestial_pole_x, celestial_pole_y, celestial_cos_lat, celestial_sin_lat, native_pole_x)

Deproject single coordinates about a celestial pole to a native pole.

The following conversions are used depending on the value of the celestial pole native latitude (lat_cp) to convert the coordinates (x_cp, y_cp) about a celestial pole to coordinates about a native pole (x, y). Here _cp denotes “celestial pole”, _np denotes “native pole”, and any numbers are in degrees.

lat_cp = 90:

x = lon_cp + x_cp - lon_np - 180 y = y_cp

lat_cp = -90:

x = lon_cp + lon_np - x_cp y = -y_cp

Otherwise:

d_cp = x_cp - lon_np C = -cos(y_cp)sin(d_cp) D = sin(y_cp)cos(lat_cp) - cos(y_cp)sin(lat_cp)cos(d_cp) x = lon_cp + arctan2(C, D) y = arcsin(sin(y_cp)sin(lat_cp) + cos(y_cp)cos(lat_cp)cos(d_cp))

The reverse operation (native to celestial poles) can be performed using spherical_project().

Parameters:

phifloat

The coordinate longitude in radians about the celestial pole (x_cp).

thetafloat

The coordinate latitude in radians about the celestial pole (y_cp).

celestial_pole_xfloat

The celestial pole native longitude in radians (lon_cp).

celestial_pole_yfloat

The celestial pole native latitude in radians (lat_cp).

celestial_cos_latfloat

The cosine of celestial_pole_y.

celestial_sin_latfloat

The sine of celestial_pole_y.

native_pole_xfloat

The coordinate’s native pole longitude in radians.

Returns:

x, yfloat, float

The native longitude (x) and latitude (y) coordinates about the native pole in radians.