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SPIRE Photometer Beam ProfilesSummary of beam profile analysis and solid angle revision ( Bernhard Schulz, September 2012)  
Added:  
> >  Note: this analysis is outdated, please use the one from October 2014, available here.  
SPIRE Photometer Solid Angles

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SPIRE Photometer Beam ProfilesSummary of beam profile analysis and solid angle revision ( Bernhard Schulz, September 2012)  
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Added:  
> >  Note that the position angle keyword posAngle is not set in the FITS headers. This is the position angle of the Zaxis of the spacecraft coordinate system projected onto the sky at the time of the observation. The Zaxis runs parallel to the short side of the SPIRE photometer FOV. For these observations the position angle is 250.6 degrees.  
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SPIRE Photometer Beam ProfilesSummary of beam profile analysis and solid angle revision ( Bernhard Schulz, September 2012)  
Line: 32 to 32  
Radial Beam Profile ModelDatasets to construct the radial beam profile model are available below. These allow to take into account the color dependent FWHM of the true beam profiles.  
Added:  
> >  An implementation of the beam profile model in IDL is available for download.  
The radial beam profile model for SPIRE was developed and described by Griffin et al. 2013. The peak normalized monochromatic flux, depending on the distance from the peak (Theta) can be described as:
 
Changed:  
< <  A value of 0.85 should be adopted for gamma, which controls the dependence of the FWHM of the variable part of the beam on wavelength. The reference frequency nu_eff is the isophotal frequency for the product of the spectrum of Neptune and the respective SPIRE spectral filter profile.  
> >  A value of 0.85 should be adopted for gamma, which controls the dependence of the FWHM of the variable part of the beam on wavelength. The reference frequency nu_eff is the isophotal frequency for the product of the spectrum of Neptune and the respective SPIRE spectral filter profile. The frequencies 1217.27, 867.75, 610.87 GHz for PSW, PMW, PLW respectively make the model beam profile consistent with the measured Neptune beam using the spectral indices 1.29, 1.42, 1.47 respectively to describe the Neptune SED in the three filter bands.  

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SPIRE Photometer Beam ProfilesSummary of beam profile analysis and solid angle revision ( Bernhard Schulz, September 2012)  
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Changed:  
< <  The values in the first line were measured from a very finely sampled observation of Neptune as outlined below. Note that these are only accurate for a source of the same spectral shape. Since SPIRE flux densities for point sources are conventionally quoted for the reference wavelengths 250, 350, and 500 microns, assuming a source spectrum rising proportionally to wavelength (nu*F_nu=const.), we can adopt the same convention for (infinitely) extended sources. In this case the values in the second line apply. For sources of other colors a correction will have to be applied. The radial model beam profile described in a technical document by North, Griffin, AmaralRogers 2011 (v2.6) with the data files given below can be used to calculate such.  
> >  The values in the first line were measured from a very finely sampled observation of Neptune as outlined below. Note that these are only accurate for a source of the same spectral shape. Since SPIRE flux densities for point sources are conventionally quoted for the reference wavelengths 250, 350, and 500 microns, assuming a source spectrum rising proportionally to wavelength (nu*F_nu=const.), we can adopt the same convention for (infinitely) extended sources. In this case the values in the second line apply. For sources of other colors a correction will have to be applied. The radial model beam profile is described in Griffin et al. 2013 and the data files given below can be used to calculate such beam profiles.  
Normalized Beam Profile Products to Download  
Line: 33 to 33  
Datasets to construct the radial beam profile model are available below. These allow to take into account the color dependent FWHM of the true beam profiles.  
Changed:  
< <  The radial beam profile model for SPIRE was developed and described by North, Griffin, AmaralRogers 2011 (v2.6). The peak normalized monochromatic flux, depending on the distance from the peak (Theta) can be described as:  
> >  The radial beam profile model for SPIRE was developed and described by Griffin et al. 2013. The peak normalized monochromatic flux, depending on the distance from the peak (Theta) can be described as:  
Line: 1 to 1  

SPIRE Photometer Beam ProfilesSummary of beam profile analysis and solid angle revision ( Bernhard Schulz, September 2012)  
Line: 23 to 23  
 
Changed:  
< < 
 
> > 
 
Deleted:  
< <  Radialized Beam Profile Model  
Changed:  
< <  Datasets to construct a radial beam profile model are available too. These allow to take into account the color dependent FWHM of the true beam profiles.  
> > 
Radial Beam Profile ModelDatasets to construct the radial beam profile model are available below. These allow to take into account the color dependent FWHM of the true beam profiles. The radial beam profile model for SPIRE was developed and described by North, Griffin, AmaralRogers 2011 (v2.6). The peak normalized monochromatic flux, depending on the distance from the peak (Theta) can be described as:
A value of 0.85 should be adopted for gamma, which controls the dependence of the FWHM of the variable part of the beam on wavelength. The reference frequency nu_eff is the isophotal frequency for the product of the spectrum of Neptune and the respective SPIRE spectral filter profile.  
Changed:  
< < 
 
> > 
 
 
Changed:  
< <  Solid angles derived from integrating the radial beam profile model over area and frequency were consistent with the numbers above within 1.5%.  
> >  Solid angles derived from integrating this radial beam profile model over area and frequency were consistent with the numbers above within 1.5%.  
Analysis Details 
Line: 1 to 1  

 
Changed:  
< <  THIS PAGE IS UNDER CONSTRUCTION  
> >  SPIRE Photometer Beam ProfilesSummary of beam profile analysis and solid angle revision ( Bernhard Schulz, September 2012)  
Added:  
> >  SPIRE Photometer Solid Angles  
Changed:  
< <  Photometer Beam Profie Data and AnalysisSummary of beam profile analysis and solid angle revision ( B. Schulz, September 2012)
Beam profile Data
SPIRE Photometer Solid Angles  
> >  
The values in the first line were measured from a very finely sampled observation of Neptune as outlined below. Note that these are only accurate for a source of the same spectral shape. Since SPIRE flux densities for point sources are conventionally quoted for the reference wavelengths 250, 350, and 500 microns, assuming a source spectrum rising proportionally to wavelength (nu*F_nu=const.), we can adopt the same convention for (infinitely) extended sources. In this case the values in the second line apply. For sources of other colors a correction will have to be applied. The radial model beam profile described in a technical document by North, Griffin, AmaralRogers 2011 (v2.6) with the data files given below can be used to calculate such.  
Deleted:  
< <  Normalized Beam Profile ProductsThe beam profile maps are available with all backgrounds subtracted and in a normalized form to the peak.
Datasets to construct a radial beam profile model are available too. These allow to take into account the color dependent FWHM of the true beam profiles.
Solid angles derived from integrating the radial beam profile model over area and frequency were consistent with the numbers above within 1.5%.
Analysis Details!!Initial Beam Profile The beam profile was reconstructed from four fine scan maps with obsids: 1342186522, 1342186523, 1342186524, 1342186525 Pointing for Neptune proper motion was corrected. HIPE 9.0.1782 and SPIA 1.8 were used. The map reconstruction was performed after median subtraction excluding a radius of 4 arcmin around the source. The maps have 1 arcsec sky bin size. The resulting original files are:
Complications that arise when using these maps directly for derivation of beam profiles and solid angles were discussed in a https://nhscsci.ipac.caltech.edu/spire/docs/beam_profiles/omegaCheck.pptx.pdfpresentation and led to a few corrections as follows.
Background fit and removalThe background was not flat at the level 0.1e5 from the peak, most likely due to Zodiacal Light background variation, however galactic Cirrus could also be the reason. A two dimensional polynomial was fitted and removed. The removed background can be examined in the following files: 0x5000241aL_PSW_pmcorr_1arcsec_bgfit.fits, 0x5000241aL_PMW_pmcorr_1arcsec_bgfit.fits, 0x5000241aL_PLW_pmcorr_1arcsec_bgfit.fits%width=500% Ovarlaying the ecliptic coordinate system over the background fit (contours) shows that a an interpretation by a Zodiacal light gradient is at least qualitatively consistent. Using IRSKY to obtain a rough estimate through extrapolation of its Zodiacal model to SPIRE wavelengths at the position of the observation and one degree towards the ecliptic pole, the following gradients were obtained.  
Changed:  
< < 
 
> >  Normalized Beam Profile Products to Download  
Added:  
> >  The beam profile maps are available with all backgrounds subtracted and in a normalized form to the peak.  
Deleted:  
< <  Background source removalA large number of extragalactic sources contaminated the maps. These were removed in HIPE using Sussextractor.
Solid AnglesAfter background tilt subtraction and background source removal the signal was averaged over concentric annuli around the source and this radialized beam profile was plotted against radius (Plot 1). To ensure symmetry, e.g. flatness of the background, the same was also plotted for three sectors (Plot 2 and 3). From the radialized beam profile a new background was determined and subtracted based on the necessity to have only positive flux within the errors (Plot 4). The average background outside a given radius was plotted for all radii (Plot 5). The integrated solid angle within a given radius was plotted for all radii (Plot 6). All the aforementioned diagrams are seen for the three detector arrays in files: neptune_omega_PSW4.pdf, neptune_omega_PMW4.pdf, neptune_omega_PLW4.pdf
%width=500px% This map shows green rings at 600, 650, and 1000 arcsec radius. The maps become less reliable outside of about 700 arcsec due to decreasing coverage and S/N. The background seems to rise again in the plots of average annular signal vs. radius, which is likely to be due to the lower coverage.
ResultsThe diagrams showing solid angle vs. radius show a plateau around 600 arcsec which may signal the end of significant contribution from the beam profile. At different integration radii, the following values in arcsec^2 result:
These data are between 3.6 and 6.7% different from the North&Griffin numbers for 1000 arcsec integration radius and between 2.0 and 3.9% for 600 arcsec integration radius. SPIRE plans to conduct shadow observations of the same region on the sky without Neptune in it in the fall of 2012. These will be used to determine whether the apparent rise outside 700 arcsec is real and they will improve the accuracy of the background level determination substantially, especially for the longer wavelength observations. A presentation of this data was given to the HCalSG, the Hfi/Spire Cross Calibration Group and the SDAG.
ErrorsAnother presentation was given at the SDAG, which discussed various sources of uncertainties and concluded that an error of +/ 4% is a conservative estimate at this time.  
Added:  
> >  
Deleted:  
< <  Correction between Isophotal and Reference Wavelength  
Deleted:  
< <  It is important to point out that solid angles are color dependent. The FWHM of the beam varies with frequency proportional to nu^gamma. The most recent estimate from Griffin (priv. comm) for gamma is 0.78, 0.85, 0.85, respectively for PSW, PMW and PLW.  
Changed:  
< <  As the beam profiles and the solid angles were derived from a map of Neptune, there is a discrepancy to the n*Fnu = const. spectrum that all photometry is color corrected for.  
> > 
 
Deleted:  
< <  To determine the magnitude of this variation, a radial beam profile model was derived from the final background subtracted 2D beam profiles, following the idea in North, Griffin, AmaralRogers 2011 (v2.6). The radial beam profiles are split up into a constant and a variable core part whose radial scale varies with nu^gamma as mentioned above. The solid angle can be found by integrating the product of beam profile, relative spectral response function (RSRF) and source spectrum over radius and wavelength and dividing by the integral over RSRF and source spectrum. The source spectrum for Neptune was approximated by a power law with exponent 1.39. The ratio of the solid angles found for the Neptune power law and a power law with exponent 1 was used to correct the Neptune solid angles to the standard SPIRE reference spectrum.  
Added:  
> >  Radialized Beam Profile Model  
Changed:  
< < 
%width=600px%  
> >  Datasets to construct a radial beam profile model are available too. These allow to take into account the color dependent FWHM of the true beam profiles.
 
Changed:  
< <  This diagram shows the frequency dependency of the solid angles of PSW, PMW, and PLW in comparison to conveniently scaled power law curves with different exponents.  
> >  Solid angles derived from integrating the radial beam profile model over area and frequency were consistent with the numbers above within 1.5%.  
Added:  
> >  Analysis DetailsThe interested reader can find a detailed description of the data analysis that led to the data products on this page.  
 BernhardSchulz  11 Oct 2012 
Line: 1 to 1  

 
Added:  
> >  THIS PAGE IS UNDER CONSTRUCTION
Photometer Beam Profie Data and AnalysisSummary of beam profile analysis and solid angle revision ( B. Schulz, September 2012)
Beam profile Data
SPIRE Photometer Solid Angles
The values in the first line were measured from a very finely sampled observation of Neptune as outlined below. Note that these are only accurate for a source of the same spectral shape. Since SPIRE flux densities for point sources are conventionally quoted for the reference wavelengths 250, 350, and 500 microns, assuming a source spectrum rising proportionally to wavelength (nu*F_nu=const.), we can adopt the same convention for (infinitely) extended sources. In this case the values in the second line apply. For sources of other colors a correction will have to be applied. The radial model beam profile described in a technical document by North, Griffin, AmaralRogers 2011 (v2.6) with the data files given below can be used to calculate such.
Normalized Beam Profile ProductsThe beam profile maps are available with all backgrounds subtracted and in a normalized form to the peak.
Datasets to construct a radial beam profile model are available too. These allow to take into account the color dependent FWHM of the true beam profiles.
Solid angles derived from integrating the radial beam profile model over area and frequency were consistent with the numbers above within 1.5%.
Analysis Details!!Initial Beam Profile The beam profile was reconstructed from four fine scan maps with obsids: 1342186522, 1342186523, 1342186524, 1342186525 Pointing for Neptune proper motion was corrected. HIPE 9.0.1782 and SPIA 1.8 were used. The map reconstruction was performed after median subtraction excluding a radius of 4 arcmin around the source. The maps have 1 arcsec sky bin size. The resulting original files are:
Complications that arise when using these maps directly for derivation of beam profiles and solid angles were discussed in a https://nhscsci.ipac.caltech.edu/spire/docs/beam_profiles/omegaCheck.pptx.pdfpresentation and led to a few corrections as follows.
Background fit and removalThe background was not flat at the level 0.1e5 from the peak, most likely due to Zodiacal Light background variation, however galactic Cirrus could also be the reason. A two dimensional polynomial was fitted and removed. The removed background can be examined in the following files: 0x5000241aL_PSW_pmcorr_1arcsec_bgfit.fits, 0x5000241aL_PMW_pmcorr_1arcsec_bgfit.fits, 0x5000241aL_PLW_pmcorr_1arcsec_bgfit.fits%width=500% Ovarlaying the ecliptic coordinate system over the background fit (contours) shows that a an interpretation by a Zodiacal light gradient is at least qualitatively consistent. Using IRSKY to obtain a rough estimate through extrapolation of its Zodiacal model to SPIRE wavelengths at the position of the observation and one degree towards the ecliptic pole, the following gradients were obtained.
Background source removalA large number of extragalactic sources contaminated the maps. These were removed in HIPE using Sussextractor.
Solid AnglesAfter background tilt subtraction and background source removal the signal was averaged over concentric annuli around the source and this radialized beam profile was plotted against radius (Plot 1). To ensure symmetry, e.g. flatness of the background, the same was also plotted for three sectors (Plot 2 and 3). From the radialized beam profile a new background was determined and subtracted based on the necessity to have only positive flux within the errors (Plot 4). The average background outside a given radius was plotted for all radii (Plot 5). The integrated solid angle within a given radius was plotted for all radii (Plot 6). All the aforementioned diagrams are seen for the three detector arrays in files: neptune_omega_PSW4.pdf, neptune_omega_PMW4.pdf, neptune_omega_PLW4.pdf
%width=500px% This map shows green rings at 600, 650, and 1000 arcsec radius. The maps become less reliable outside of about 700 arcsec due to decreasing coverage and S/N. The background seems to rise again in the plots of average annular signal vs. radius, which is likely to be due to the lower coverage.
ResultsThe diagrams showing solid angle vs. radius show a plateau around 600 arcsec which may signal the end of significant contribution from the beam profile. At different integration radii, the following values in arcsec^2 result:
These data are between 3.6 and 6.7% different from the North&Griffin numbers for 1000 arcsec integration radius and between 2.0 and 3.9% for 600 arcsec integration radius. SPIRE plans to conduct shadow observations of the same region on the sky without Neptune in it in the fall of 2012. These will be used to determine whether the apparent rise outside 700 arcsec is real and they will improve the accuracy of the background level determination substantially, especially for the longer wavelength observations. A presentation of this data was given to the HCalSG, the Hfi/Spire Cross Calibration Group and the SDAG.
ErrorsAnother presentation was given at the SDAG, which discussed various sources of uncertainties and concluded that an error of +/ 4% is a conservative estimate at this time.
Correction between Isophotal and Reference WavelengthIt is important to point out that solid angles are color dependent. The FWHM of the beam varies with frequency proportional to nu^gamma. The most recent estimate from Griffin (priv. comm) for gamma is 0.78, 0.85, 0.85, respectively for PSW, PMW and PLW. As the beam profiles and the solid angles were derived from a map of Neptune, there is a discrepancy to the n*Fnu = const. spectrum that all photometry is color corrected for. To determine the magnitude of this variation, a radial beam profile model was derived from the final background subtracted 2D beam profiles, following the idea in North, Griffin, AmaralRogers 2011 (v2.6). The radial beam profiles are split up into a constant and a variable core part whose radial scale varies with nu^gamma as mentioned above. The solid angle can be found by integrating the product of beam profile, relative spectral response function (RSRF) and source spectrum over radius and wavelength and dividing by the integral over RSRF and source spectrum. The source spectrum for Neptune was approximated by a power law with exponent 1.39. The ratio of the solid angles found for the Neptune power law and a power law with exponent 1 was used to correct the Neptune solid angles to the standard SPIRE reference spectrum.
%width=600px% This diagram shows the frequency dependency of the solid angles of PSW, PMW, and PLW in comparison to conveniently scaled power law curves with different exponents.  
Line: 1 to 1  

Added:  
> > 
 BernhardSchulz  11 Oct 2012
