NP, June 1st, 2012
Thanks to Robert's and Samuel's verifications, I found a bug in my simulation (the disk diameter was actually taken as the radius, hence doubling the effective size of the disk and enlarging the broadening). I remove the old plot of May 29 to avoid confusion and provide updated plots here below.
The following plot shows the result of the convolution of a Gaussian (FWHM=10 arcsec) by a Gaussian (FWHM=8arcsec) or a disk (D=8arcsec). The gaussian indeed leads to a large broadening compared to the disk. Fitting an effective gaussian on the result of disk convolution leads to a slight overestimation of the input 10 arcsec.
If we proceed with the same exercise but with a 20arcsec gaussian or disk, this time the difference between the convolution by a disk or a gaussian becomes significant. An effective gaussian can still be fit, but only around the peak (crosses highlight the points on which the fit is performed).
Finally, we propose a chart of this effect for various beam FWHM and planet disk diameters:
RZ, May 30 2012
The figure fwhm_planet.png gives effective FWHM ~16 and 20arcsec for an 8arcsec disk convolved with 10 and 17arcsec Gaussians (input FWHM) correspondingly. This cannot be correct ! The upper limits for the resulting FWHM can be calculated for a convolution of a Gaussian with FWHM=8arcsec instead a disk: sqrt(82+102)=12.8 and sqrt(82+172)=18.8arcsec. To get the correct numbers I calculated the 2 cases, i.e. convolved an 8arcsec disc with FWHM=10 and 17arcsec Gaussians. The resulting sources are very well represented by Gaussians with FWHM of 11.1 and 17.7arcsec (no restrictions for the fitting). The difference of the resulting sources and the Gaussian fits are presented below. The discrepancy is -0.4 to +0.14% for the convolution with a FWHM=10arcsec and much below 1% for the convolution with a FWHM=17arcsec Gaussian. The effective FWHM in figure fwhm_planet.png therefore do not represent the correct values - or do I have a problem in reading this figure ?
NP, May 29 2012
In preparation for beam studies on Mars, we wanted to estimate the impact of Mars diameter (8 arcsec these days) on the determination of NIKA's FWHM.
First estimations of this effect were wrong and have been removed to avoid confusion, please see update at June 1st.