irfpy.cena.fov

fov module is for Chap 3. in the CENA FM calibration report.

The CENA calibration report issue 1 rev 1 is implemented here. The module treats Chapter 3: Sensor properties.

A simple use of the module can be found as a script of cena_visualize_fov.

Conversion between $\theta$ $\varphi$ system to a vector is implemented in irfpy.cena.frame module. See also How to convert between frames.

Definition of $\theta$ and $\varphi$ is as follows. Primary axis is -z axis. $\theta$ is measured from xy plane and positive in -z axis. In other word, this is a co-latitude measured from -z axis. $\varphi$ is measured from y axis (strictly speaking yz plane) and positive toward x axis. See Figure 1.1 in CENA calibration report.

irfpy.cena.fov.shape_of_response(n, theta, phi)

Return the shape of response.

$\theta$ is elevation angle and $\varphi$ is the azimuthal angle in degrees. $\theta$ should be -90 to 90, and $\varphi$ should be -180 to 180. n is the channel ID from 0 to 6.

irfpy.cena.fov.pixel_shape(n, elevresolution=0, azimresolution=0, resolution=None, fill=False)

Return an array of the pixel edge angle of its FWHM.

Parameters

• n – Channel number. 0 to 6.

• azimresolution – Azimuthal resolution. Number of division in azimuthal direction.

• elevresolution – Elevation resolution. Number of division in elevation direction.

• resolution – Resolution. Overwrite azimresolution and elevresolution.

• fill – If true, the first point is added to the end.

Returns

A tuple of 2 numpy array. Array of $\theta$ and array of $\varphi$.

The number of elements is 4+2*azimresolution+2*elevresolution. If fill is True, one more element is added. However, it is recommend to check the number after you get the array.

>>> pix0 = pixel_shape(0, azimresolution=50, elevresolution=3)
>>> print(len(pix0[0]), len(pix0[1]))
110 110

irfpy.cena.fov.azim_pix_center(n)

Returns the azimuth ($\varphi$) center in degrees for the pixel n.

Implements equation (3.2), -19.06*n + 57.19

irfpy.cena.fov.azim_pix_fwhm(n)

Returns the FWHM of the azimuthal directions ($\varphi$) in degrees.

Implements equation (3.3). Indeed it does not depend on n, 45.0 degrees.

irfpy.cena.fov.elev_pix_center(n)

Returns the elevation center ($\theta$) in degrees for the pixel n.

Implements equation (3.4). It does not indeed depend on n: -6.05 degrees.

irfpy.cena.fov.elev_pix_fwhm(n)

Returns the FWHM of the elevation ($\theta$) directions in degrees.

Implements equation (3.5). Independent of n, 6.44 is returned.

irfpy.cena.fov.solid_angle(n)

Returns the approximate soliad angle.

Equation (3.8) gives the definition.

$$\mathrm{\Delta }{\mathrm{\Omega }}_n\approx FWH{M}_{\varphi ,n}\cdot FWH{M}_{\theta ,n}$$

>>> print('%.3f' % solid_angle(0))
0.088

irfpy.cena.fov.infov(theta, phi)

A simple FOV envelope checker.

Parameters

• theta – The $\theta$ angle(s), from -90 to 90 in degrees. Looking direction.

• phi – The $\varphi$ angle(s), from -180 to 180 in degrees. Looking direction.

>>> infov(0, 0)
True
>>> infov(5, 0)    # Theta=5, False
False
>>> infov(-5, 0)
True
>>> infov([-6, -6, -6, -6, -6], [-180, -90, 0, 90, 180])
array([False, False,  True, False, False])