# The instrument model

## Contents

## Overview[edit]

The RIMO, or *Reduced Instrument Model* is a FITS file or a set of FITS files 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 (the HFI RIMO will consists of several parts), 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
- Vector or Table
- to give, e.g., filter transmission profiles or noise power spectra, beam window functions. When possible, namely when they are of equal length, such as the noise power spectra, an effort is made to put them together into a table, otherwise they are given as separate vectors.
- 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.

The HFI-RIMO separates the beam window functions and associated data from the main set of parameters, and this because the beam window functions are delivered for two cases covering 100% and 75% of the sky, as described in detail below.

### File Names[edit]

## Detector-level parameter data[edit]

The detector parameter data are given in the form of a table giving the parameter values for each detector. The table columns (whose names are in *BOLD ITALICS*) are:

- Bolometer name -
*DETECTOR* - These are the detector names. For HFI these will be of the form
*217-3*for SWBs or*100-3b*for PSBs, and for LFI they will have the form 27M or 18S. There are 52 HFI detectors and 22 LFI detectors.

- Focal plane geometry parameters -
*PHI_UV*,*THETA_UV*, and*PSI_UV* - These parameters give the geometry of the focal plane, or the positions of the detectors in the focal plane in the Dxx reference frame. The angles that give the rotation of the beam pattern from a fiducial orientation (forward beam direction (z-axis) pointing along the telescope line of sight, with y-axis aligned with the nominal scan direction) to their positions in the focal plane. The fiducial position is that given by the Star Tracker. All angles are in radians. These parameters are derived from observations of bright planets; see Detector pointing for details.

- Polarization parameters -
*PSI_POL*,*EPSILON* - These are the direction of maximum polarization, defined with the beam in the fiducial orientation described above, that is, before rotation onto the detector position, and the cross-polarization contamination (or leakage). These values are determined from ground-based measurements.

- Beam parameters -
*FWHM*,*ELLIPTICITY*,*POSANG* - These are the mean FWHM of the scanning beam (in arcmin, the beam ellipticity (no units), and the position angle of the beam major axis. The scanning beam is that recovered from the observation of bright planets; details in Beams section.

- Noise parameters -
*NET_TOT*,*NET_WHT*,*NET_OOF*,*F_KNEE*,*ALPHA* - Three NETs are given: one determined from the total noise (rms of the noise timeline, excluding glitched data and other non-valid data), one determined from the white noise level of the noise amplitude spectrum, and one determined from fitting a
*1/f*noise spectrum, described by the function to the noise**Power**spectrum. In the latter, the*F_KNEE*and*ALPHA*parameters are the frequency where the*1/f*component meets the white noise level, and the slope of the former. so that the slope is is about twice the slope of the amplitude spectrum. The NETs are in units of Kcmb or MJy/sr * sqrt(s). Not sure what of this applies also to LFI

- Detector sampling frequency -
*F_SAMP*, which is self-explanatory.

In the HFI RIMO, this table includes entries for the RTS bolometers (143-8 and 545-3), which are approximate or 0.00 when not evaluated.

## 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* specifies the detector or the maps. For the latter, the bandpasses are a weighted average of the bandpasses of the detectors that are used to build the map, using the same weights that are used in the mapmaking. These merged bandpasses are given for the full channel maps (all detectors of the frequency channel) and for the PSBs only in each frequency channel for HFI. For details on the measurements and compilation of the bandpasses 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-IX
^{[1]}Planck-2013-XIII^{[2]}.

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]

there was some talk of changing wn to freq ... TBD

*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.

## Detector noise spectra[edit]

- HFI
- these are the ring noise amplitude spectra averaged over about 5000 rings in order to give a representative spectrum. The spectra of all 50 valid bolometers are given in a single table. The spectra have a maximum frequency (Nyquist) of 90.18685Hz, also given the the
*F_NYQ*keyword, and are built over 32768 points, giving a lower frequency of 2.75 mHz. - LFI
- TBW

The keyword *F_NYQ* gives the Nyquist frequency, and can be used together with the number of points in the spectrum to reconstruct the frequency scale. The BINTABLE has Ndetector columns by Npoints rows.

## 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 + 3 psb-only subsets, producing 45 extensions
- 100, 143, 217, 353, 545, 857, 143p, 217p, 353p

- 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

Note for HFI these (and also the associated covariance matrices) are given in separate files named *HFI_RIMO-Beams-nnnpc_Rm.nn.fits*, where nnn is 100 or 075 and indicates the percentage (pc) of the sky included (see Masks section).

*For the LFI*

- the 3 LFI frequency channels (auto- products only), producing 3 extensions
- 30, 44, 70

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

And finally see also the *COMMENTs* of each header for more specific details.

## 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. And for HFI these, together with the beam window functions, are given in a file separate from the main RIMO (see subsection above).

## Appendices[edit]

## References[edit]

- ↑
^{1.0}^{1.1}**Planck 2013 results. IX. HFI spectral response**, Planck Collaboration, 2014, A&A, 571, A9 - ↑
*Planck 2013 results. XIII. Galactic CO emission*, Planck Collaboration, 2014, A&A, 571, A13

reduced IMO

Flexible Image Transfer Specification

(Planck) High Frequency Instrument

(Planck) Low Frequency Instrument

Interface Control Document

Full-Width-at-Half-Maximum

Noise Equivalent Temperature

random telegraphic signal

Instrument Line Shape

To be defined / determined