Mosaic sensitivity

As of 2011-February (it has since been fixed using the formulae on this page), the ALMA sensitivity calculator reports rms values for the central position of a single pointing. For well-sampled mosaics, it is thus an underestimate. Here we estimate the true sensitivity at a point inside the region of regular sampling, assuming a Gaussian primary beam of FWHM=1.13*lambda/D, and equal time sampling at all points.

Hexagonal patterns

Logic: Consider a point source at the center of the mosaic. Taking the example of case (3) below, there are six surrounding points each 0.5109*FWHM away, where the S/N is 0.4850*(S/N)_center. Thus, if the central pointing is worth Time = 1 second, then each of the surrounding 6 pointings is worth Time = 0.4850**2 = 0.2352 second. Six of the 12 points in the surrounding ring will be 1.022 beam diameter away which contributes at the 5.53% level, worth 0.003058 seconds each. The other six are at 0.885 beams away, which is the 11.4% level and each worth 0.01300 seconds. The total effective time on source is then = 1 + 6*0.2352 + 6*0.003058 + 6*.01300 = 2.5075. The effective sensitivity is then sqrt(2.5075) = 1.583 better than the ALMA calculator predicts.

(0) Spacing equal to the FWHM = the largest separation allowed by the Observing Tool

Anything coarser than NVSS is not recommended. It is too wide for the automatic selection of the imsize parameter in the Cycle 6 pipeline: CAS-12249. My python script (au.mosaicSensitivity) yields:
• 7-pt: 1.012
• 19-pt: 1.012
• 37-pt: 1.012

(1) Spacing equal to the 25% level of the beam = FWHM / sqrt(2) = 0.7071 * FWHM = 0.7989 * lambda/D

This spacing is derived in the NVSS paper by Condon et al. as the coarsest pattern that provides uniform sensitivity across the mosaic. (But note that they actually used a somewhat coarser pattern in the end for their survey). My python script yields:
• 7-pt: 1.173
• 19-pt: 1.173
• 37-pt: 1.173

• 7-pt: 1.502
• 19-pt: 1.524
• 37-pt: 1.524

• 7-pt: 1.553
• 19-pt: 1.583
• 37-pt: 1.583

• 7-pt: 1.740
• 19-pt: 1.826
• 37-pt: 1.828

(5) Spacing equal to 0.447 * lambda/D = 0.3752 * FWHM = oversampled (for better sensitivity over less area)

• 7-pt: 1.876
• 19-pt: 2.037
• 37-pt: 2.045

-- ToddHunter - 2011-08-08

Topic attachments
I Attachment Action Size Date Who Comment
txt mosaic.py.txt manage 1 K 2011-08-10 - 16:46 ToddHunter
This topic: Main > TWikiUsers > ToddHunter > MosaicSensitivity
Topic revision: 2019-07-09, ToddHunter
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