# Usage of primaryBeamArcsec

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:
1. vis and spw (uses median dish diameter from the ANTENNA table)
2. vis (uses median freq of OBSERVE_TARGET spws, and median dish diameter)
3. frequency in GHz (assumes 12m)
4. wavelength in mm (assumes 12m)
5. frequency in GHz and diameter (m)
6. 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: 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: 16.734581857952524

```
Topic revision: r12 - 2014-07-30, ToddHunter
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