Difference between revisions of "Tophat bands for Data Challenge"

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(Added discussion of overlap between paired bands)
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The figure below shows calculated atmospheric brightness spectra (at zenith) for South Pole at 0.5 mm PWV and Atacama at 1.0 mm PWV (both are near median values). Atmospheric spectra are courtesy of Denis Barkats, generated using [https://www.cfa.harvard.edu/~spaine/am/ am]. I plotted the tophat bands on top of these spectra, with the height of each rectangle equal to the band-averaged brightness temperature using the South Pole spectrum. Also shown (in green) are the BICEP2 / Keck Array 150 GHz bandpass and the Keck Array 95 and 220 GHz bandpasses, for comparison.  
 
The figure below shows calculated atmospheric brightness spectra (at zenith) for South Pole at 0.5 mm PWV and Atacama at 1.0 mm PWV (both are near median values). Atmospheric spectra are courtesy of Denis Barkats, generated using [https://www.cfa.harvard.edu/~spaine/am/ am]. I plotted the tophat bands on top of these spectra, with the height of each rectangle equal to the band-averaged brightness temperature using the South Pole spectrum. Also shown (in green) are the BICEP2 / Keck Array 150 GHz bandpass and the Keck Array 95 and 220 GHz bandpasses, for comparison.  
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The table includes a column that gives the overlap fraction for pairs of bands that split each atmospheric window. This fraction is defined as the ratio between the width of the intersection and the width of the union. Note that it is quite small for the low and high frequency windows, but substantial for the 90 GHz and 150 GHz windows. There has only been a minimal amount of optimization put into the choice of how to split the windows. Furthermore, if we use multichroic detectors, we would end up with pairs of bands that have little to no overlap. See Adrian's [[Candidate_Frequency_Bands | discussion of split vs staggered bands here]].
  
 
[[File:Tophat_bandpass.png]]
 
[[File:Tophat_bandpass.png]]
  
 
{| border="1" style="border-collapse: collapse;" cellpadding="5"
 
{| border="1" style="border-collapse: collapse;" cellpadding="5"
! Name !! center [GHz] !! width [GHz] !! dust scale factor <br /> from 353 GHz !! sync scale factor <br /> from 23 GHz !! T<sub>sky</sub> (Pole) [K] !! T<sub>sky</sub> (Atacama) [K]
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! Name !! center [GHz] !! width [GHz] !! dust scale factor <br /> from 353 GHz !! sync scale factor <br /> from 23 GHz !! T<sub>sky</sub> (Pole) [K] !! T<sub>sky</sub> (Atacama) [K] !! overlap fraction
 
|-
 
|-
| 30 || 30.00 || 9.00 || 0.0059 || 0.3876 ||  6.3 ||  5.2
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| 30 || 30.00 || 9.00 || 0.0059 || 0.3876 ||  6.3 ||  5.2 || rowspan="2" | 2%
 
|-
 
|-
 
| 40 || 40.00 || 12.00 || 0.0076 || 0.1352 || 12.0 ||  8.8
 
| 40 || 40.00 || 12.00 || 0.0076 || 0.1352 || 12.0 ||  8.8
 
|-
 
|-
| 85 || 85.00 || 20.40 || 0.0179 || 0.0104 || 14.5 || 10.9
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| 85 || 85.00 || 20.40 || 0.0179 || 0.0104 || 14.5 || 10.9 || rowspan="2" | 37%
 
|-
 
|-
 
| 95 || 95.00 || 22.80 || 0.0210 || 0.0074 || 11.7 ||  9.2
 
| 95 || 95.00 || 22.80 || 0.0210 || 0.0074 || 11.7 ||  9.2
 
|-
 
|-
| 145 || 145.00 || 31.90 || 0.0454 || 0.0024 || 10.5 || 10.3
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| 145 || 145.00 || 31.90 || 0.0454 || 0.0024 || 10.5 || 10.3 || rowspan="2" | 53%
 
|-
 
|-
 
| 155 || 155.00 || 34.10 || 0.0526 || 0.0021 || 10.9 || 11.7
 
| 155 || 155.00 || 34.10 || 0.0526 || 0.0021 || 10.9 || 11.7
 
|-
 
|-
| 220 || 220.00 || 48.40 || 0.1368 || 0.0012 || 16.4 || 18.6
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| 220 || 220.00 || 48.40 || 0.1368 || 0.0012 || 16.4 || 18.6 || rowspan="2" | 4%
 
|-
 
|-
 
| 270 || 270.00 || 59.40 || 0.2848 || 0.0010 || 21.4 || 24.5
 
| 270 || 270.00 || 59.40 || 0.2848 || 0.0010 || 21.4 || 24.5
 
|-
 
|-
| Keck 95 || 95.46 || 25.77 || 0.0212 || 0.0074 || 11.9 ||  9.3
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| Keck 95 || 95.46 || 25.77 || 0.0212 || 0.0074 || 11.9 ||  9.3 ||
 
|-
 
|-
| B2/Keck 150 || 148.92 || 43.52 || 0.0481 || 0.0023 || 11.9 || 12.0
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| B2/Keck 150 || 148.92 || 43.52 || 0.0481 || 0.0023 || 11.9 || 12.0 ||
 
|-
 
|-
| Keck 220 || 228.27 || 48.02 || 0.1545 || 0.0012 || 16.9 || 19.1
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| Keck 220 || 228.27 || 48.02 || 0.1545 || 0.0012 || 16.9 || 19.1 ||
 
|}
 
|}
  
 
Code used for calculations and plots in this posting: [http://bicep.rc.fas.harvard.edu/cbischoff/tophat_bandpass.py tophat_bandpass.py]
 
Code used for calculations and plots in this posting: [http://bicep.rc.fas.harvard.edu/cbischoff/tophat_bandpass.py tophat_bandpass.py]
  
''Colin Bischoff, 2016-11-02''
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''Colin Bischoff, 2016-11-02; Updated 2016-11-04''

Revision as of 11:06, 4 November 2016

In the process of science book forecasting, we came up with eight bands chosen to split up the four atmospheric windows. These bandpasses are listed in Table 1 of Victor's 2016-05-31 posting. I used the center frequencies and fractional bandwidths (Δν / ν). I then shifted the 215 GHz band up slightly (to 220 GHz) and widened the 270 GHz band (to 22%) to close a small gap between those bands.

For each band, I calculated

  • relative brightness of a dust-type signal with βd = 1.59 and Td = 19.5 K; compared to 353 GHz reference frequency
  • relative brightness of a synchrotron-type signal with βsync = -3.0; compared to 23 GHz reference frequency

This calculation requires us to specify the convention that we use for our tophat bandpass. I define this tophat to be such that a single-moded antenna (AΩ scales as λ2) would have uniform response as a function of frequency to a beam-filling Rayleigh-Jeans source. Before we start generating signal simulations, it would be a good idea to check that people generating foreground models agree on this calculation.

The figure below shows calculated atmospheric brightness spectra (at zenith) for South Pole at 0.5 mm PWV and Atacama at 1.0 mm PWV (both are near median values). Atmospheric spectra are courtesy of Denis Barkats, generated using am. I plotted the tophat bands on top of these spectra, with the height of each rectangle equal to the band-averaged brightness temperature using the South Pole spectrum. Also shown (in green) are the BICEP2 / Keck Array 150 GHz bandpass and the Keck Array 95 and 220 GHz bandpasses, for comparison.

The table includes a column that gives the overlap fraction for pairs of bands that split each atmospheric window. This fraction is defined as the ratio between the width of the intersection and the width of the union. Note that it is quite small for the low and high frequency windows, but substantial for the 90 GHz and 150 GHz windows. There has only been a minimal amount of optimization put into the choice of how to split the windows. Furthermore, if we use multichroic detectors, we would end up with pairs of bands that have little to no overlap. See Adrian's discussion of split vs staggered bands here.

Tophat bandpass.png

Name center [GHz] width [GHz] dust scale factor
from 353 GHz
sync scale factor
from 23 GHz
Tsky (Pole) [K] Tsky (Atacama) [K] overlap fraction
30 30.00 9.00 0.0059 0.3876 6.3 5.2 2%
40 40.00 12.00 0.0076 0.1352 12.0 8.8
85 85.00 20.40 0.0179 0.0104 14.5 10.9 37%
95 95.00 22.80 0.0210 0.0074 11.7 9.2
145 145.00 31.90 0.0454 0.0024 10.5 10.3 53%
155 155.00 34.10 0.0526 0.0021 10.9 11.7
220 220.00 48.40 0.1368 0.0012 16.4 18.6 4%
270 270.00 59.40 0.2848 0.0010 21.4 24.5
Keck 95 95.46 25.77 0.0212 0.0074 11.9 9.3
B2/Keck 150 148.92 43.52 0.0481 0.0023 11.9 12.0
Keck 220 228.27 48.02 0.1545 0.0012 16.9 19.1

Code used for calculations and plots in this posting: tophat_bandpass.py

Colin Bischoff, 2016-11-02; Updated 2016-11-04