# Usage of primaryBeamArcsec

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Computes the expected FWHM of a single dish beam by implementing the Baars formula (b*lambda / D), where b is taken either from Equation 18 in

ALMA Memo 456:

- where b = 1.243 - 0.343*10**(-0.05*taper) + 0.12*(10**(-0.05*taper))**2

or by Equation 4.13 in Baars (2007) book:

- where b = 1.269 - 0.566*tau + 0.534*(tau)**2 - 0.208*(tau)**3

The effect of the central obstruction on the pattern is also accounted for by using a spline fit to Table 10.1 of Schroeder's Astronomical Optics.

### Usage:

au.primaryBeamArcsec(vis='', spw='', frequency='',wavelength='', diameter=12.0,
taper=10.0, obscuration=0.75, verbose=False, showEquation=True,
use2007formula=True, fwhmfactor=None)

Inputs:

- diameter: dish diameter given in meters
- taper: edge taper specified in dB. Note that the current best representation of the ALMA 12m antennas (based on celestial holography) is a taper=10dB. It a negative value of taper is entered, it is converted to positive because the formula above expects this.
- obscuration: diameter of central hole given in meters.
- fwhmfactor: if specified, then ignore the taper value and compute it instead

For the rest of the arguments, specify one of the following combinations:

- vis and spw (uses median dish diameter from the ANTENNA table)
- vis (uses median freq of OBSERVE_TARGET spws, and median dish diameter)
- frequency in GHz (assumes 12m)
- wavelength in mm (assumes 12m)
- frequency in GHz and diameter (m)
- wavelength in mm and diameter (m)

### Examples:

CASA <2>: au.primaryBeamArcsec('X279.ms',17,taper=12)
Coefficient from ALMA memo 456 Eq. 18 for a -12.0dB edge taper and obscuration ratio=0.75/12 = 1.151 * lambda/D
Out[2]: 17.635362496326586
CASA <4>: au.primaryBeamArcsec(frequency=345, taper=-9)
Coefficient from ALMA memo 456 Eq. 18 for a -9.0dB edge taper and obscuration ratio=0.75/12: 1.120 * lambda/D
Out[8]: 16.734581857952524