by alter-ego » Fri Apr 22, 2016 6:59 am
Chris Peterson wrote:alter-ego wrote:Chris Peterson wrote:In the image, they're 0.26 arcsec/pixel, which is exactly half the native resolution of the camera. That strongly suggests that the image is binned 2x2, either in the original data or in subsequent processing.
The paper mentions that binning was necessary to make the analyses tractable. Once a good fit was obtained for binned (pixelated) data, the same visibility binning and noise estimations were applied to mock (simulated) data. Then a best-fit smooth model could be found. This probably explains the smoothness of the APOD's Einstein Ring, but I don't understand why the paper used a binned (pixelated) HST image. Maybe it's simply meant to show the binned FoV used in the analyses?
I saw those references. The paper is pretty dense, and I'm not a radio astronomer, so there's some terminology I don't understand. I have the impression that the radio data binning under discussion isn't spatial, however, but in the frequency or phase domains, and that the radio data in spatial form (as we see it in the image) is quite a bit higher resolution than the optical data, even unbinned.
Yeah, I'm not a radio astronomer either, and dense is an understatement!
From what I've read, a "visibility" is the product of frequency data sets between various antennas. 2D spatial images are obtained by Fourier transforming the visibility (frequency) files. (For the SDP.81 analysis, two bands 6 & 7, treated as spectral channels, were used; after binning each channel containing ~10
6 visibilities). Binned frequency data will result in binned transformed data (pixelated images).
I don't follow your comment about comparing radio data in spatial form to optical data, but I believe I understand ALMA spatial resolution limits:
The maximum reduced spatial resolution for SDP.81 image is 23mas (listed elsewhere). For a maximum 16km baseline, the theoretical spatial resolution limits for Band 6 (λ
center=243GHz) and Band 7 (λ
center=342GHz) are ≈18mas and ≈12mas respectively (
ALMA Basics and
ALMA Front End). ALMA's Long Baseline Campaign achieved 15km, so these resolutions are compatible with the claimed 23mas SDP.81 resolution. However, the paper mentioned maximum 2km baseline data, and also mentioned that the best-fit parameters were found with ≤2km baselines:
"We first use only the
subset of baselines shorter than 2 km in our initial MCMC
analysis to localize the neighborhood of the best fit. This
Figure 4. The SDP.81 system. Grayscale shows HST/WFC3 F160W data,
while red contours show ALMA continuum emission in band 6.
approach greatly expedites our MCMC optimization, since
many evaluations of the likelihood are required to fully search
the highly multidimensional parameter space of our smooth
model. Once this initial localization has been achieved, we
can use the full dataset.
Does the full data set mean a 15km baseline? It must because a 2km baseline yields a maximum resolution ~8x larger, or 144mas and 96mas respectively for Bands 6 and 7 - poorer resolution by 4x to 6x.
Interestingly, in the HST overlap image, I'm thinking the red Band 6 continuum contours may correspond to the 15km baseline data sets. Contour features are 10% or less of the 0.26" HST pixel size.
[quote="Chris Peterson"][quote="alter-ego"][quote="Chris Peterson"]In the image, they're 0.26 arcsec/pixel, which is exactly half the native resolution of the camera. That strongly suggests that the image is binned 2x2, either in the original data or in subsequent processing.[/quote]
The paper mentions that binning was necessary to make the analyses tractable. Once a good fit was obtained for binned (pixelated) data, the same visibility binning and noise estimations were applied to mock (simulated) data. Then a best-fit smooth model could be found. This probably explains the smoothness of the APOD's Einstein Ring, but I don't understand why the paper used a binned (pixelated) HST image. Maybe it's simply meant to show the binned FoV used in the analyses?[/quote]
I saw those references. The paper is pretty dense, and I'm not a radio astronomer, so there's some terminology I don't understand. I have the impression that the radio data binning under discussion isn't spatial, however, but in the frequency or phase domains, and that the radio data in spatial form (as we see it in the image) is quite a bit higher resolution than the optical data, even unbinned.[/quote]
Yeah, I'm not a radio astronomer either, and dense is an understatement!
From what I've read, a "visibility" is the product of frequency data sets between various antennas. 2D spatial images are obtained by Fourier transforming the visibility (frequency) files. (For the SDP.81 analysis, two bands 6 & 7, treated as spectral channels, were used; after binning each channel containing ~10[sup]6[/sup] visibilities). Binned frequency data will result in binned transformed data (pixelated images).
I don't follow your comment about comparing radio data in spatial form to optical data, but I believe I understand ALMA spatial resolution limits:
The maximum reduced spatial resolution for SDP.81 image is 23mas (listed elsewhere). For a maximum 16km baseline, the theoretical spatial resolution limits for Band 6 (λ[sub]center[/sub]=243GHz) and Band 7 (λ[sub]center[/sub]=342GHz) are ≈18mas and ≈12mas respectively ([url=https://almascience.nrao.edu/about-alma/alma-basics]ALMA Basics[/url] and [url=http://www.almaobservatory.org/en/about-alma/how-does-alma-work/technology/front-end]ALMA Front End[/url]). ALMA's Long Baseline Campaign achieved 15km, so these resolutions are compatible with the claimed 23mas SDP.81 resolution. However, the paper mentioned maximum 2km baseline data, and also mentioned that the best-fit parameters were found with ≤2km baselines:
[quote]"We first use only the
subset of baselines shorter than 2 km in our initial MCMC
analysis to localize the neighborhood of the best fit. This
Figure 4. The SDP.81 system. Grayscale shows HST/WFC3 F160W data,
while red contours show ALMA continuum emission in band 6.
approach greatly expedites our MCMC optimization, since
many evaluations of the likelihood are required to fully search
the highly multidimensional parameter space of our smooth
model. [color=#0000FF]Once this initial localization has been achieved, we
can use the full dataset.[/color][/quote]
Does the full data set mean a 15km baseline? It must because a 2km baseline yields a maximum resolution ~8x larger, or 144mas and 96mas respectively for Bands 6 and 7 - poorer resolution by 4x to 6x.
Interestingly, in the HST overlap image, I'm thinking the red Band 6 continuum contours may correspond to the 15km baseline data sets. Contour features are 10% or less of the 0.26" HST pixel size.