# The instrument model

## Contents

## Overview[edit]

The RIMO, or *Reduced Instrument Model* is a FITS file containing selected instrument characteristics that are needed by users who work with the released data products. It is described in detail in *The HFI and LFI RIMO ICD* (ref). There will be two RIMOs, one for each instrument, which will follow the same overall structure, but will differ in the details. The type of data in the RIMO can be:

- Parameter
- namely scalars to give properties such as a noise level or a representative beam FWHM
- Table
- to give, e.g., filter transmission profiles or noise power spectra
- Image
- namely 2-D "flat" array, to give, e.g., the beam correlation matrices

The FITS file begins with primary header that contains some keywords that mainly for internal use and no data. The different types of data are written into different BINTABLE (for parameters and tables) or IMAGE (for 2-D arrays) extensions, as described below.

### File Names[edit]

## Map-level parameter data[edit]

The map-level data table contains the effective beam solid angle (total and out to different multiples of the beamFWHM) and noise information. It is written into a BINTABLE extension named *MAP_PARAMS* whose structure is different for HFI and LFI and is as follows. The noise description below is very simplified; a more accurate rendition can be obtained from the half-ring maps. Regarding the characterization of systematics, the user should use the survey differences.

### HFI[edit]

*FREQUENCY*(String)- a 3-digit string giving the reference frequency in GHz, i.e., of the form
*217* *OMEGA_F*,*OMEGA_F_ERR*(Real*4)- the full beam solid angle and its uncertainty, in armin
^{2} *OMEGA_1*,*OMEGA_1_DISP*(Real*4)- the beam solid angle out to 1FWHM, and its dispersion, in arcmin
^{2} *OMEGA_2*,*OMEGA_2_DISP*(Real*4)- the beam solid angle out to 2FWHM, and its dispersion, in arcmin
^{2} *FWHM*(Real*4)- FWHM of a Gaussian beam having the same (total) solid angle, in armin
^{2}. This is the best value for source flux determination *FWHMGAUS*(Real*4)- FWHM derived from best Gaussian fit to beam maps, in armin
^{2}. This is the best value for source identification *NOISE*(Real*4)- This is the typical noise/valid observation sample as derived from the high-
*l*spectra of the half-ring maps, in the units of the corresponding map

For the Omega columns, the 'DISP' (for *dispersion*) column gives an estimate of the spatial variation as a function of position on the sky. This is the variation induced by combining the scanning beam determined from the planet observations with the scanning strategy, as described in Beams.

### LFI[edit]

*FREQUENCY*(String)- a 3-digit string giving the reference frequency in GHz, i.e., of the form
*030, 044, 070* *FWHM*(Real*8)- FWHM of a Gaussian beam having the same (total) solid angle, in arcmin
*NOISE*(Real*8)- This is the average noise in T
^{1/2}
s *CENTRALFREQ*(Real*4)- This is the average central frequency in GHz
*FWHM_EFF*,*FWHM_EFF_SIGMA*(Real*4)- This is the average FWHM of the effective beam, in arcmin, and its dispersion
*ELLIPTICITY_EFF*,*ELLIPTICITY_EFF_SIGMA*(Real*4)- This is the average ellipticity and its dispersion
*SOLID_ANGLE_EFF*,*SOLID_ANGLE_EFF_SIGMA*(Real*4)- This is the average full beam solid angle, in arcmin
^{2}, and its dispersion

## Effective band transmission profiles[edit]

The effective filter bandpasses are given in different BINTABLE extensions. The extension is named *BANDPASS_{name}*, where *name* specified the frequency channel. In the case of the maps, the bandpasses are a weighted average of the bandpasses of the detectors that are used to build the map. For details see Planck-2013-IX^{[1]}. The bandpasses are given as 4-column tables containing:

### HFI[edit]

*WAVENUMBER*(Real*4)- the wavenumber in cm-1, conversion to GHz is accomplished by multiplying by [mks].
*TRANSMISSION*(Real*4)- the transmission (normalized to 1 at the max for HFI)
*ERROR*(Real*4)- the statistical uncertainty for the transmission profile.
*FLAG*(Integer)- a flag indicating if the data point is an independent frequency data point (nominally the case), or an FTS instrument line shape (ILS)-interpolated data point. The frequency data has been over-sampled by a factor of ~10 to assist in CO component separation efforts Planck-2013-XIII
^{[2]}Planck-2013-IX^{[1]}.

The number of rows will differ among the different extensions, but are the same, by construction, within each extension. Tables with the unit conversion coefficients and color correction factors for the HFI detectors (and LFI in some instances), including uncertainty estimates based on the uncertainty of the HFI detector spectral response are given in this appendix.

### LFI[edit]

*WAVENUMBER*(Real*8)- the wavenumber in GHz.
*TRANSMISSION*(Real*8)- the transmission (normalized to have an integral of 1 for LFI)
*UNCERTAINITY*(Real*4)- the statistical LFI) uncertainty for the transmission profile (not provided for
*FLAG*(Character)- a flag, not used by now by the LFI

The number of rows will differ among the different extensions, but are the same, by construction, within each extension.

## Beam Window Functions[edit]

Beam window functions and associated error descriptions are written into a BINTABLE for each *detection unit*, where *detection unit* consists of an auto or a cross product (for HFI only) of one (or two) frequency maps or detset maps used in the likelihood. Here they are:

*For the HFI*

- the 6 HFI frequency channels, producing 21 extensions
- 100, 143, 217, 353, 545, 857

- 26 detsets, producing 351 extensions; the detsets used are, by frequency channel:
- 100-DS1, 100-DS2,
- 143-DS1, 143-DS2, 143-5, 143-6, 143-7,
- 217-DS1, 217-DS2, 217-1, 217-2, 217-3, 217-4,
- 353-DS1, 353-DS2, 353-1, 353-2, 353-7, 353-8,
- 545-1, 545-2, 545-4,
- 857-1, 857-2, 857-3, 857-4

*For the LFI*

- the 3 LFI frequency channels, producing 3 extensions
- 30, 44, 70

and the extension names are of the form *BEAMWF_U1XU2* where U1 and U2 are one (possibly the same) detection unit from one of the main groups above (i.e. there are no cross products between detsets and frequency channels, or between HFI and LFI). Each extension contains the columns:

*NOMINAL*(Real*4)- the beam window function proper,
*EIGEN_n*(Real*4, n=1-5 for the HFI, n=1-4 for the LFI)- the five/four corresponding error modes.

and the following keywords give further information, only for the HFI:

*NMODES*(Integer)- the number of EIGEN_* modes,
*LMIN*and*LMAX*(Integer)- the starting and ending (both included) multipoles of the vectors NOMINAL and EIGEN_*
*LMIN_EM*and*LMAX_EM*(Integer)- that give the range of the valid samples of the EIGEN_* vectors. Here
*LMAX_EM*is always less than or equal to*LMAX*. On the range*LMAX_EM*+1 to*LMAX*the values of EIGEN_* are set to NaN, while the values of NOMINAL only are a Gaussian extrapolation of the lower multipole window function, only provided for convenience. *CORRMAT*(string)- the name of the extension containing the corresponding beam correlation matrix

## Beam Correlation Matrix[edit]

Two beam correlation matrices are given for the HFI, in two *IMAGE* extensions:

*CORRBEAM_FREQ*(Real*8)- for the frequency channels (21 units), 105x015 pixel matrix,
*CORRBEAM_DSET*(Real*8)- for the detsets (351 units), 1755x1755 pixel matrix

Each is a symmetric matrix with 1-valued diagonal, made of NBEAMS*NBEAMS blocks, each block being NMODES*NMODES in size. The n$^{th}$ row- (and column-) block entry relates to the B(l) model whose name is indicated in ROWn = BEAMWF_U1XU2 keywords, and the corresponding eigenmodes are stored in a HDU of the same name.

Each extension contains also the following keywords:

*NDETS*(Integer)- the number of detector units
*NBEAMS*(Integer)- the number of beams = NSETS * (NSETS+1) / 2
*NMODES*(Integer)- here 5
*L_PLUS*(Integer)- Eigenmode > 0 to break degeneracies
*BLOCKn*(string)- for n=1-NBEAMS, gives the name of the extension containing the beam WF and error eigenmodes for the nth block

and some other ones for internal data checking and traceability

No beam correlation matrices are produced by the LFI by now.

## Appendices[edit]

## References[edit]

- ↑
^{1.0}^{1.1}**Planck 2013 results: HFI spectral response**, Planck Collaboration 2013 IX, A&A, in press, (2014). - ↑
**Planck 2013 results: Galactic CO emission as seen by Planck**, Planck Collaboration XIII, A&A, in press, (2014).

reduced IMO

Flexible Image Transfer Specification

(Planck) High Frequency Instrument

(Planck) Low Frequency Instrument

Interface Control Document

Full-Width-at-Half-Maximum

Instrument Line Shape