Impact of rebin resolution and convolution kernel

The 450um results all derive from analyses using a resolution in the final, rebin-ned, map of 3". This choice is fairly standard for SCUBA data but is not mandatory and the impact of this choice needs exploring, especially with these smaller 450um beamsizes.

A 450um map of Mars (#0016 on UT 20000124 - the point at lowest airmass in the plot ) - was reduced with a final resolution of each of 1", 2", 3", 4" and 5". The resulting statistics were determined by repeated application of the stats and psf routines :

rebin output pixel size
image statistics
peak_stats
peak_psf
gamma
FWHM(*)
1"
3.290
2.989
2.248
8.15
2"
3.290
3.117
2.219
7.92
3"
3.290
3.034
2.045
7.30
4"
3.290
3.021
2.163
7.62
5"
3.290
3.016
2.002
7.45
(*) - Note that FWHM here is the minor axis dimension
uncorrected (deconvolved) for the size of the planetary disk

As far as the issue of calibration is concerned, the use of psf seems to underestimate the peak flux by between 5% and 9%.

It is curious that the FWHM (and thereby the HPBW) is at its largest for the smallest rebin size chosen, and then reaches a minimum at our standard choice of 3". The behaviour of the other parameters in this table are less clearly related to the choice of resolution.

The above analyses all use a linear rebin method; the impact of using the other two options is illustrated with regards to the same map of Mars used above with a 3" pixel :

rebin convolution kernel
image statistics
type
default
SCALE
output
pixel size
peak_stats
peak_psf
gamma
FWHM
linear
3.05"
3"
3.290
3.034
2.045
7.30
gaussian
1.22"
3"
3.353
3.143
2.193
8.17
bessel
3.05"
3"
3.462
3.396
2.126
7.18

Not surprisingly, the broader kernel (the gaussian) propogates a broader image, and the use of the narrower option (the besselian) shows that the default choice (linear) might overestimate the intrinsic beam size by 1-2%.

The breadth of the kernel is the rebin SCALE parameter. SCALE means different things for each kernel. For LINEAR it is the zero of the cone, for bessel the first zero of the function and for Gaussian the HWHM. It is taken as the (June 2000) default throughout the previous set of reductions, but this variable too may be contributing to a broadening in the measured beam size :

rebin convolution kernel
image statistics
type
scale
output
pixel size
peak_stats
peak_psf
gamma
FWHM
linear
3"
3"
3.308
3.058
2.059
7.40
linear
4"
3"
2.847
2.677
2.239
8.20
linear
5"
3"
2.685
2.394
2.038
8.87

Using values of SCALE smaller than the pixel size in the output array will suppress the contribution of the kernel to the image width. In this light a default value of SCALE for the LINEAR method that matches the output pixel size seems totally appropriate.

Similar experiments performed using the gaussian kernel (June 2000 default SCALE = HWHM = 1.22"), and a fixed output pixel size of 3", suggest that adopting a value of 1.5"+0.1" would give a slightly smaller FWHM for this map (8.05" cf 8.17"). This is still notably larger than the 7.2" or so achievable with the other kernels.

Keeping the SCALE of the linear and gaussian convolution kernels equal to the output pixel size suggests optimal values in both cases of 1.0" or 1.4" or 2.3" - see the minima in the plot. The images are not filled in the linear case for pixel sizes smaller than 1.5", leaving 2.3" as a possible single optimal choise for SCALE for both the linear and gaussian methods. The FWHM, axis ratio and gamma at this minimum, for this particular observation, are 6.7", 1.158 and 2.118, respectively.

Iain M. Coulson
28 June 2000