Effective Beams

The second part of this section is mostly unreadable. Please use proper style in terms of sectioning (i.e. pseudo headings that are underlined), lists (bullet or numbered) - see other pages for examples. Info regarding M3 (and NERCS) is probably irrelevant to external users)

Product description

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The effective beam is the average of all scanning beams pointing at a certain direction within a given pixel of the sky map for a given scan strategy. It takes into account the coupling between azimuthal asymmetry of the beam and the uneven distribution of scanning angles across the sky. The effective beam captures the complete information about the difference between the true and observed image of the sky. They are, by definition, the objects whose convolution with the true CMB sky produce the observed sky map.

The effective beam is computed by stacking within a small field around each pixel of the HEALPix sky map. Due to the particular features of Planck scanning strategy coupled to the beam asymmetries in the focal plane, and data processing of the bolometer and radiometer TOIs, the resulting Planck effective beams vary over the sky.

We show here a comparison of the FEBeCoP derived effective beams, and associated point spread functions (see here), to the actual images of a few compact sources observed by Planck, for 30GHz and 100GHz frequency channels. We show below a few panels of source images organized as follows:

• Row #1- DX9 images of four ERCSC objects with their galactic (l,b) coordinates shown under the color bar
• Row #2- linear scale FEBeCoP PSFs computed using input scanning beams BS Mars12 apodized for the CMB channels and the BS Mars12 for the sub-mm channels
• Row #3- log scale of #2; PSF iso-contours shown in solid line, elliptical Gaussian fit iso-contours shown in broken line

• 30 GHz and 100 GHz

||border=1, width=1200, align=center || 100 GHz || || 143 GHz || || %width=600px,%Attach:30.png || || %width=600px,%Attach:100.png ||

Production process

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The methodology for computing effective beams for a scanning CMB experiment like Planck was presented in our [| paper].

FEBeCoP, or Fast Effective Beam Convolution in Pixel space, is an approach to representing and computing effective beams (including both intrinsic beam shapes and the effects of scanning) that comprises the following steps:

• identify the individual detectors' instantaneous optical response function (presently we use elliptical Gaussian fits of Planck beams from observations of planets; eventually, an arbitrary mathematical representation of the beam can be used on input)
• follow exactly the Planck scanning, and project the intrinsic beam on the sky at each actual sampling position
• project instantaneous beams onto the pixelized map over a small region (typically <2.5 FWHM diameter)
• add up all beams that cross the same pixel and its vicinity over the observing period of interest
• create a data object of all beams pointed at all N'_pix_' directions of pixels in the map at a resolution at which this precomputation was executed (dimension N'_pix_' x a few hundred)
• use the resulting beam object for very fast convolution of all sky signals with the effective optical response of the observing mission

In order to optimize the generation of such effective beams for HFI and LFI detectors, and to deploy the data and associated application software at the DPC, the requisite pre-computation is executed at NERSC in Berkeley, and deliver the beam data over the network, on tape, and disk to the DPC, and assist in ingesting the data into the DMC, developing pertinent I/O routines, and instaing the applications that use effective beams, e.g. fast Monte Carlo full sky convolution.

Inputs

In order to fix the convention of presentation of the scanning and effective beams, we show the classic view of the Planck focal plane as seen by the incoming CMB photon. The scan direction is marked, and the toward the center of the focal plane is at the 85 deg angle w.r.t spin axis pointing upward in the picture.

"'Planck Focal Plane

A list (and brief description to the extent possible) of the input data used to generate this product (down to file names), as well as any external ancillary data sets which were used.

1. Detector pointings:
2. Intrinsic beam description:
3. Beam cutoff radius: 2.25 times geometric mean of FWHM of all detectors in a channel
4. map resolution for the derived beam data object:

• N'_side_' = 1024 for 100GHz
• N'_side_' = 2048 for all other frequencies

Related products

A description of other products that are related and share some commonalities with the product being described here. E.g. if the description is of a generic product (e.g. frequency maps), all the products falling into that type should be listed and referenced.

Effective beams are located at nersc: ??

and in both the HFI and LFI DPCs at:

• On disk: /space/SimuData/effBeam_HFI_v41
• DMC group: /data/dmc/MISS01/DATA/FEBeCoP_v41

Interface modules were developed to easily access the beams and the PSFs from the disk and the database. For HFI: The codes for reading the beams/PSFs and demonstration programs (http://cvs.planck.fr/cvs/Level2/Task_pkg/HL2_FEBeCoP/) FOr LFI:

The interface contains Fortran 90 routines to read the beams either from disk or from database. There are IDL routines also to read the beams from disk with detailed inbuilt help and fast examples.

There are two sets of (serial) demonstration programs:

• to extract beams/PSF at any given set of pixels from disk/database and make .fits skymaps
  • beam_extract_f : extract beams from disk
  • beam_extract_f_PIO: extract beams from database
  • psf_extract_f  : extract PSF from disk
  • psf_extract_f_PIO : extract PSF from database

• to make a full sky convolution of input maps with effective beams
  • effConv : convolve map reading beam from disk
  • effConv_PIO : convolve map reading beam from database

Example parameter files (with explanation) for these demonstration programs are available here: http://cvs.planck.fr/cvs/Level2/Task_pkg/HL2_FEBeCoP/params/

A detailed README on the usage of the routines and the programs are available as: http://cvs.planck.fr/cvs/Level2/Task_pkg/HL2_FEBeCoP/README.txt included here:

• HFI

How to use FEBeCoP effective beams and PSFs on magiqueIII

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Is this of any relevance? external users don't use M3

The methodology for computing effective beams for a scanning CMB experiment like Planck was presented in our paper: http://arxiv.org/pdf/1005.1929

For easy access to the FEBeCoP  beams and PSFs computed on NERSC, they have been transferred to magiqueIII. They are currently stored at two locations:

1. Hard disk: /space/SimuData/effBeam_HFI_v41 2. DMC group: /data/dmc/MISS01/DATA/FEBeCoP_v41

The gory details of how binary data is organized in the files / DMC objects are not essential to the user and may also change in the future. Here we present how the FEBeCoP I/O interface (installed and tested on magiqueIII) can be used to read effective beams and PSFs for any given set of pixels.

I/O routines to read effective beams are in: http://cvs.planck.fr/cvs/Level2/Task_pkg/HL2_FEBeCoP/src/util/

At present, the Fortran routines are available as .f90 sources, they will be available as a compiled library in future. getBeam.f90 can be used read beams from the disk and getBeam_PIO.f90 to read from the database.

Example Fortran programs and Makefiles to load beams/PSFs either from disk or from database and make their .fits skymaps are in:

http://cvs.planck.fr/cvs/Level2/Task_pkg/HL2_FEBeCoP/src/beam_extract_f/ and http://cvs.planck.fr/cvs/Level2/Task_pkg/HL2_FEBeCoP/src/psf_extract_f/

There are two test programs to make full sky effective beam convolved maps, reading beams either from disk or from database, in: http://cvs.planck.fr/cvs/Level2/Task_pkg/HL2_FEBeCoP/src/convolve/

List of programs

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beam_extract_f  : extract beams from disk beam_extract_f_PIO : extract beams from database psf_extract_f  : extract PSF from disk psf_extract_f_PIO  : extract PSF from database effConv  : convolve map reading beam from disk effConv_PIO  : convolve map reading beam from database

Example parameter files with brief explanations are provided in: http://cvs.planck.fr/cvs/Level2/Task_pkg/HL2_FEBeCoP/params/

The IDL routines (beaminit.pro and getbeam.pro/getpsf.pro) can be used to read the beams/PSFs from disk. These routines have detailed inbuilt help with easy to use examples.

Details on the subroutines

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(Please look at the appropriate routines to get the exact syntax)

The basic scheme to load the beams/PSFs (in Fortran or IDL) has two steps:

1. Init

function: "beaminit"

arguments:

"beaminfo" (output of this routine, users need not worry about this)

"prefix" is the prefix to the beam files or DMC objects, e.g., for 100GHz beams

from disk: prefix=/data/smitra/effBeam_HFI_v41/100/beams_

from DMC: prefix=/data/dmc/MISS01/DATA/FEBeCoP_v41/100_

2. Read beams/PSFs

function: "readbeam"/"readpsf"

arguments:

"beam"/"psf" structure describes beams/PSFs using the following elements:

pix  : (int_32) pixel index of the beam centre

nlist  : (int_32) number of pixels used to describe the beam (typically ~200)

listpix : (nlist int_32) list of pixel indices describing the beam

map  : (nlist or 6 x nlist float_32) values at the pixels listed in listpix

nobs  : (1 or 6 float_64) effective number of observation matrix

"beaminfo" (output of beaminit, no need to worry about this)

"pixlist" is the list of pixels for which beam should be loaded

"npixel" number of pixels for which beam should be loaded

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Meta data

A detailed description of the data format of each file, including header keywords for fits files, extension names, column names, formats….