Problem with yesterday's work:
A*B = IFT(FT(A)*FT(B))A*B - A*C != IFT(FT(A)*(FT(B)-FT(C)))
If instead of yesterday's "bandpass filter" you use the convolution - convolution 'filter', the agreement in real space and most of fourier space is much better:
though map20 clearly reproduces some structures better (higher) but is overall less powerful than the filtered map.
I've attempted to model the spatial filter function as a gaussian (or PSF) plus an inverse gaussian. i.e., the high-spatial-frequency components are smoothed with the PSF, and the low spatial frequency components are convolved with a (1-gaussian) high-pass filter. First, the mildly good news: With a 300" FWHM large-scale cutoff, the filter PSD reasonably resembles the iterative map PSD:
Luckily, the double-filter goes a very long way in explaining the scale-free flux loss. In the following diagram, I show the effect of the filter compared to the input map.
The filter only recovers about 75% of the flux at ANY wavenumber. The map does slightly worse at high frequencies, which I can't explain yet. These show the recovery fraction of the iterative maps, a gaussian smoothing function with FWHM=33", and the mid-pass-filter. Map20 (no smooth) has a lot of additional "noise power" at high spatial frequencies; if it wasn't for the telescope filter function, we would apparently have pretty good high-frequency recovery. Hmph. Note that map20 is higher than the filter at some intermediate frequencies, but quite a bit lower at higher frequencies. Also note the moderately poor agreement between the 'smoothed' and 'smoothed (theory)' lines.
Finally, look at the comparison between map20 and fiiltered. The agreement is not bad for positive points; filtered is apparently slightly higher but that can be adjusted. The problem: the filter forces some structures that are negative or zero to be positive. For example, look at the feature at 210,300 that is negative in Map20 but positive in Filtered. In the real (input) map, this feature is lower than its surroundings - it is legitimately negative.
I raised the possibility that the ratty edges of a scan could affect the power spectrum measurements, leading to a scale-free power loss. This doesn't appear to happen... instead, the masking adds some small-scale power and apparently a small amount of large-scale power.
The majority of the past week has been dedicated to debugging; it looks like cross-scanned simulations finally work. The plot below is a derivation of the spatial transfer function for a number of different intrinsic sky power-law power spectra.
Justifying the above plot is essential. First, the very steep power-laws [-3 in the example below] show a recovery fraction >1. This is simply because their S/N was inadequate - the output power spectrum is nearly flat, but at a level higher than the sky.
Second, the most plausible power-laws [-1.5 in the example below] show pretty good recovery (90-95% over the relevant range):
There are some "white" power losses, particularly in the flatter power-spectra. My best guess is that this has something to do with the relative scales being offset from a mean of 1, but so far all tests to show that that is the cause have in fact shown no problems at all. What else could cause a scale-independent power loss? Also, the flat power spectrum (and inverted) aren't quite flat because I impose a "galactic scale height" on them. Should I stop doing that?
There are a few cases in the L=30 field that look awful. 050706_o31 probably observed the inside of the dish. 070727_ob6 shows some streaking that I can't easily explain... though it appears that there are some bad bolos that need to get flagged out. I wonder if that's systematic over 070727 observations....
First Author [ ADS ] [ arXiv ]
A mm and near-IR study of the IRAS 05358+3543 system. Recently (2011), it has become clear that "protocluster" is unlikely to be the right label for IRAS 05358+3543. "proto-association" might be more accurate. Perhaps the most interesting result of this paper is the discovery that the central source is likely to be a 400-AU binary with two massive (>8 msun) stars at different evolutionary stages. It is just barely in ALMA's range...
ADS arXiv As with the other Bolocam papers, I reduced the data. All of the analysis work was done by Miranda. Because of Gem OB1's known distance (~2 kpc), it was possible to derive the physical properties of all of the 34 BGPS sources. NH3 temperatures and line widths were combined to measure total dust mass, density, and virial parameter. This paper is the best characterization of "typical" BGPS sources, at least for the outer galaxy.
ADS arXiv My primary contribution to this work was reducing the data from which catalogs were derived. As part of this process, I also made the noise maps that were part of the Bolocat process and did some of the by-eye verification work. Bolocat extracted >8000 sources from the BGPS using a watershed decomposition method. Most of these sources have now been observed with the HHT in HCO+ and N2H+ to determine their velocity and kinematic distance.